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### Key findings and conclusions
- Policy context:
  - Financial vulnerabilities built up since before the pandemic include stretched asset valuations; the tradeoff is between supporting fragile growth and staving off financial crises.
  - Extraordinary pandemic-era policy support increased financial leverage already at historically high levels following the GFC.
- Main research questions:
  - Do financial cycles indeed last between 8 and 30 years?
  - Which indicator best forecasts banking crises—particularly, is the medium- to long-term cycle in the credit-to-GDP ratio the best measure?
  - What practical approach can policymakers use to assess financial overheating in real time?
- Core results:
  - Financial cycles are of medium-term frequency, lasting on average 6 years.
  - Equity cycles are the shortest and have the largest amplitude; credit and GDP have longer cycles, in line with business cycles.
  - Emerging market (EM) cycles tend to be shorter and have greater amplitude than advanced market (AM) cycles.
  - A single rule extracting a cycle of the same length across countries may not be appropriate.
  - Credit growth and credit-to-GDP gap are not always the most timely or accurate predictors of banking crises.
    - In advanced economies (AM), equity price and output gap are the best predictors of banking crises.
    - In emerging markets (EM), equity, property, and credit gap indicators offer useful early warnings.
  - Aggregating signals from the best leading indicators improves forecasting power; warnings of a banking crisis can be seen up to five years in advance.
- Policy implication:
  - Track multiple indicators (beyond credit) and aggregate signals to assess overheating and provide policymakers time to adjust macroprudential measures.

### Data, sample, and indicators
- Frequency and sample:
  - Quarterly data covering 1960 – 2014 (seasonally adjusted), dependent on availability.
- Country groups:
  - Advanced market countries (AM): 34 countries (listed in source).
  - Emerging market countries (EM): 25 countries (listed in source).
- Key series and sources:
  - Private credit: IFS (aggregate claims on private sector by banks).
  - Total credit to private non-financial sector: BIS.
  - Real equity prices: Haver.
  - Real property prices: IMF Research dataset (OECD and Global Property Guide inputs).
  - Loan-to-deposit ratio (LTDR): constructed from IFS loan and deposit data.
  - GDP, consumption, investment: WEO database.
  - Inflation deviation from target: IFS and IMF Research.
  - Banking crises: Laeven and Valencia (2018) 0-1 indicator of systemic banking crisis.

### Methodology — cycle dating and gap extraction
- Two-step cycle extraction:
  1. Date peaks and troughs using Harding and Pagan (2002a) turning point algorithm (peak and trough definitions preserved from source).
  2. Use empirically determined frequencies as inputs to the Christiano and Fitzgerald band pass filter to calculate cyclical deviations (financial cycle gaps).
- Cycle length calculation:
  - L_{i j} = L̄^{up} + L̄^{down} = (1/a) Σ_{d=1}^{a} D^{up}_{j d} + (1/m) Σ_{m=1}^{m} D^{down}_{j m} (equation (3) in source).
- Filters and robustness:
  - Two-sided filters (hindsight) estimated over complete sample.
  - One-sided filters (real-time) estimated recursively using only information available up until that point.
  - Robustness checks: ranges mean +/- 0.5 and +/- 1 standard deviation, HP filter gaps, deviation from quadratic time trend.
- Early Warning Systems (EWS) methods:
  - Primary approaches: non-parametric signal extraction (Kaminsky et al., 1998 style) and logit regressions with lag polynomials.
  - Loss function for threshold choice: L_min(x*) = CDC_C(x*) + (1 − CDC_¬C (x*)) (as presented).
  - Signal-to-noise (STN) ratio: STN = (1 − T1 − T2) / (T1 + T2) (equation (5) in source).
  - AUROC used for robustness and comparison.

### Stylized facts and cycle properties (counts and summary statistics)
- Identified complete cycles:
  - 251 complete credit cycles.
  - 356 equity price cycles.
  - 208 property price cycles.
  - 383 LTDR cycles.
- Average cycle lengths (selected exact figures from Table 1):
  - Advanced Markets (years):
    - Equity: Average 3.2; Median 3.1; Standard deviation 0.6
    - Property: Average 4.1; Median 3.6; Standard deviation 1.6
    - LTDR: Average 3.6; Median 3.6; Standard deviation 1.0
    - Credit: Average 6.0; Median 5.2; Standard deviation 2.4
    - Total credit: Average 6.3; Median 6.0; Standard deviation 2.3
    - GDP: Average 6.3; Median 5.5; Standard deviation 2.4
    - CI: Average 5.6; Median 5.5; Standard deviation 4.8
  - Emerging Markets (years):
    - Equity: Average 3.8; Median 3.5; Standard deviation 0.9
    - Property: Average 5.2; Median 4.7; Standard deviation 2.0
    - LTDR: Average 4.2; Median 3.9; Standard deviation 1.3
    - Credit: Average 7.1; Median 6.6; Standard deviation 2.7
    - Total credit: Average 3.7; Median 6.4; Standard deviation 3.4
    - GDP: Average 6.7; Median 5.9; Standard deviation 3.0
    - CI: Average 6.7; Median 5.7; Standard deviation 3.5
    - Other: Average 4.7; Median 4.5; Standard deviation 1.3
- Additional stylized magnitudes:
  - Equity cycles: average duration 3 to 4 years; swing from trough to peak of over 60 percent on average.
  - Bank credit expansion amplitudes: 50-90 percent during expansions; contraction amplitudes: 10-30 percent.
  - GDP expansion amplitude: 25-30 percent; contraction amplitude: 4-7 percent.
- Synchronization:
  - Financial and business cycles are not perfectly synchronized; the fraction of time the two cycles are in the same phase is 60 percent on average.
  - Example concordance matrix entries preserved: Credit–GDP: 0.66; Credit–Consumption: 0.70; Credit–Investment: 0.63; Property–GDP: 0.60; Equity–GDP: 0.65; LTDR–GDP: 0.61.

### Early Warning System (EWS) results — two-sided (hindsight) and one-sided (real-time)
- Two-sided filters (hindsight):
  - Advanced markets (AM):
    - Best indicators: stock prices and output gap, followed by property prices and inflation.
    - LTDR and bank credit have weaker signaling power.
    - Predictive power peaks in the year before the crisis; equity prices show a secondary STN peak four years before the crisis.
  - Emerging markets (EM):
    - Best indicators in year before crisis: property, equity prices and credit.
    - Credit-to-GDP and property prices show signals five years before crisis.
    - Output gap and inflation show signals three years before crisis.
  - BIS credit gap and Schularick measures mostly in lower range of STN estimates.
- One-sided filters (real-time):
  - STN estimates generally lower than two-sided.
  - Advanced markets:
    - Equity price is the best real-time predictor; predictive power shifts from one year to four years before crisis.
    - LTDR: notable at two years before crisis.
    - Credit: not a very strong indicator.
  - Emerging markets:
    - Property price: best at one year before crisis and even stronger four to five years before crisis.
    - Credit-to-GDP: second-best predictor at two and five years before crisis.
    - BIS credit gap: higher STN three years before crisis in EM.
- Growth-rate measures:
  - Generally weaker predictors than gap-based measures, but in AM equity price growth performs well across multiple years; in EM GDP growth and equity growth provide early signals at multi-year horizons.
- AUROC robustness:
  - Two-sided filters (AM): equity price and output gap have AUROCs above 0.8 in the year before the crisis.
  - Two-sided filters (EM): equity and property prices, credit and BIS credit gap have AUROC above 0.7 in the year before the crisis.
  - AUROC interpretation thresholds preserved: AUROC < 0.7 sub-optimal; 0.7–0.8 good; > 0.8 excellent.

### Logit regression results (panel logit, AM-focused)
- Specification highlights:
  - Dependent variable: probability of banking crisis (Laeven and Valencia).
  - Regressors: cyclical deviations with lag polynomial 훽1(L) containing lag orders 1 to 16, staggered across regressions to reduce autocorrelation.
  - Controls: credit spread, VIX, cyclically-adjusted primary balance, Chinn-Ito Index, REER.
  - Random effects used; country fixed effects not significant.
- Select numeric summaries (Table 3, AM; 2-sided filters — sum of lag coefficients):
  - Bank Credit: 26.40***
  - Property Prices: 101.92***
  - Equity Prices: 129.99**
  - LTDR: 17.71**
  - Pseudo R2 examples preserved: 0.0138; 0.0481; 0.1760; 0.0232.
  - Number of observations examples: 4,833; 3,630; 3,510; 5,014.
- Table 4 (AM; mixed filters with controls) — selected coefficient patterns (one-sided gap / two-sided gap as in source):
  - Bank credit: 0.05 / 0.00 / 0.17*** / -0.04*
  - Property price: 0.17*** / 0.13*** / 0.28*** / 0.07*
  - Equity prices: 0.16*** / 0.16*** / 0.19*** / 0.12***
  - LTDR: 0.20*** / 0.21*** / -0.03 / 0.20***
  - Lead time to crises (quarters) column entries include: 4, 3, 9, 9, 16, 3, 8, 8, “varies”, “varies”.
  - Number of observations examples: 3,123; 3,157; 2,761; 2,790; 2,825; 3,021; 2,303; 2,385.
  - Pseudo R2 examples: 0.10; 0.25; 0.13; 0.30; 0.24; 0.45; 0.09; 0.30; 0.40; 0.47.
- Nonlinear marginal effects (Figure 11 reported conclusions):
  - Excess home prices: a modest increase of 0.3 percentage points beyond the 1% level raises crisis probability by 18 percentage points (from about 12% to 30% when excess house price rises from 0.9% to 1.2%).
  - Equity valuation: at 4% overvaluation, probability of banking crisis reaches near certainty.
  - Bank credit and LTDR: despite non-linearity, cumulative crisis probability remains modest:
    - Bank credit: crisis probability no more than 12% with a 1.5% deviation.
    - LTDR: crisis probability no more than 2% with a 1.8% deviation.

### Why credit is not the best early warning indicator in AM (summary)
- Conceptual and empirical points:
  - Asset price corrections (valuation of collateral) often precede and trigger turns in credit cycles and balance-sheet stress.
  - Historical crises often preceded by asset price booms (examples noted qualitatively in source).
  - In EM, credit is more bank-intermediated: credit comprised on average 52 percent of bank asset portfolio in the last decade versus 41 percent in advanced economies ("41 percent" and "52 percent" explicitly reported), making credit gaps more predictive in EM.

### Overheating Index (OI): construction, thresholds, and performance
- Purpose and indicator choices:
  - Illustrate application of EWS results by constructing OI using best leading indicators per income group.
  - AM indicators: equity prices and output gap.
  - EM indicators: equity, property prices and credit. (GDP growth excluded for EM despite signaling power.)
- Construction steps:
  - Use one-sided filter to mimic real-time policy challenges.
  - Vulnerability thresholds: average levels for financial cycles estimated with two-sided filters in the year before the crisis ("Average of the four quarters before the crisis year").
  - Country crisis flag: I_i,t^x = 1 if gap for variable x breaches threshold; 0 otherwise.
  - Aggregation weights: w = 1 − Type I error − Type II error; normalized weights reported in Table 5.
- Table 5 thresholds and weights (values reproduced exactly):
  - Emerging Markets:
    - Credit threshold: 2.9 ; Weight: 0.32 ; Norm. weight: 4.2
    - Equity threshold: 10.3 ; Weight: 0.53 ; Norm. weight: 7.3
    - Property threshold: 7.5 ; Weight: 0.53 ; Norm. weight: 8.5
  - Advanced Markets:
    - Equity threshold: 6.7 ; Weight: 0.64 ; Norm. weight: 9.7
    - GDP threshold: 1.3 ; Weight: 0.65 ; Norm. weight: 0.3
- Index performance:
  - Indices tend to signal overheating in years preceding banking crises.
  - Indices correctly flag between 60 to 65 percent of banking crises on average, rising from about 50 percent five years before the crisis to 80 percent one year before the crisis.
  - Country examples where OI signaled overheating up to five years before crises include Sweden, Norway, Finland (Nordic crisis); Mexico and Colombia (Latin American debt crisis); Malaysia, Philippines, Thailand (Asian Financial Crisis); United States, United Kingdom, Iceland, Ireland, Greece, Latvia, Kazakhstan, Ukraine (Global Financial Crisis).
- Out-of-sample note:
  - Applied estimations to 2018 Laeven and Valencia update adding Cyprus in 2011 and Ukraine in [text ends in source]; the index picks up overheating in these contexts.

### Conclusions and policy recommendations
- Financial cycle features and policy implications:
  - Financial cycles vary by variable and country; one-size-fits-all cycle-extraction rules (e.g., fixed HP smoothing for CCyB calibration) may be inappropriate.
  - On average, financial cycles are on par with, or shorter than, business cycles.
- Predictive hierarchy for banking crises:
  - Equity prices: best signal.
  - Property prices: next best.
  - Credit: widely viewed as important but not the clearest early warning in AM.
- Operational guidance:
  - Use early warning models as one of many inputs when assessing financial vulnerabilities.
  - Track multiple indicators and aggregate signals (e.g., an Overheating Index) to improve real-time assessment and obtain lead time for policy action.
  - The lead time afforded by the OI can provide room for policymakers to adjust regulatory/supervisory responses and prepare for potential fallout, such as upgrading resolution frameworks.
- Prudential approach under uncertainty:
  - Consider a range of indicators.
  - Be alert to early signs of pickup in trends and widening gaps in financial variables.

*Source: wpiea2021116-print-pdf — References, Appendix 1, Appendix 2, Appendix 3, Appendix 4, Appendix 5, Appendix 6, and VII. CONCLUSIONS (excerpted content provided).*

### References .............................................................................................................

### wpiea2021116-print-pdf - References

### Key findings and conclusions (from Introduction and summary)
- Policy context:
  - Financial vulnerabilities built up since before the pandemic include stretched asset valuations; the tradeoff is between supporting fragile growth and staving off financial crises.
  - Extraordinary pandemic-era policy support increased financial leverage already at historically high levels following the GFC.
- Main research questions:
  - Do financial cycles indeed last between 8 and 30 years?
  - Which indicator best forecasts banking crises—particularly, is the medium- to long-term cycle in the credit-to-GDP ratio the best measure?
  - What practical approach can policymakers use to assess financial overheating in real time?
- Core results:
  - Financial cycles are of medium-term frequency, lasting on average 6 years.
  - Equity cycles are the shortest and have the largest amplitude; credit and GDP have longer cycles, in line with business cycles.
  - Emerging market (EM) cycles tend to be shorter and have greater amplitude than advanced market (AM) cycles.
  - A single rule extracting a cycle of the same length across countries may not be appropriate.
  - Credit growth and credit-to-GDP gap are not always the most timely or accurate predictors of banking crises.
    - In advanced economies (AM), equity price and output gap are the best predictors of banking crises.
    - In emerging markets (EM), equity, property, and credit gap indicators offer useful early warnings.
  - Aggregating signals from the best leading indicators improves forecasting power; warnings of a banking crisis can be seen up to five years in advance.
- Policy implication:
  - Track multiple indicators (beyond credit) and aggregate signals to assess overheating and provide policymakers time to adjust macroprudential measures.

### Literature and methodological positioning
- Contribution to literature:
  - Two strands: (i) measuring financial cycles and their statistical properties; (ii) early warning indicators (EWS) of banking crises.
- Approaches to measure cycles, summarized as described in source:
  - Turning point analysis (dating peaks and troughs) — agnostic; preferred in this paper.
  - Frequency-based filters (HP, bandpass) — require specifying cyclical frequencies; BCBS uses HP with smoothing parameter of 400,000 (cycle length of 8-30 years) for CCyB calibration.
  - Spectral density estimation — identifies dominant frequency; requires stationarity.
  - Unobserved component time series models (Kalman filter) — requires assumptions on trend smoothness and stochastic process.
  - Aggregation methods — averaging individual cycles, principal components, or multivariate models; aggregation can mask idiosyncratic behavior.
- Early warning approaches discussed:
  - Probit/Logit limited dependent variable regressions.
  - Signal extraction (Kaminsky et al., 1998) — non-parametric thresholds.
  - Decision trees and machine learning — recursive thresholds, neural networks, Markov switching models.
- Methods chosen:
  - Work with signal extraction and logit for EWS; avoid machine learning due to potential biases and out-of-sample weaknesses noted in literature.

### Data, methodology, and stylized facts (III)
- Overall extraction strategy:
  - Two-step approach:
    1. Date peaks and troughs using Harding and Pagan (2002a) turning point algorithm.
    2. Use empirically determined frequencies as inputs to the Christiano and Fitzgerald band pass filter to calculate cyclical deviations.
- Data series and definitions:
  - Quantity indicators:
    - Private credit from IFS (aggregate claims on private sector by banks).
    - Total credit to private non-financial sector from BIS (measures credit extended by banks and other financial institutions), available for a smaller subset of countries.
  - Price indicators:
    - Real equity prices and real property prices (IMF Research dataset using OECD and Global Property Guide; equity indices from Haver).
  - Leverage/noncore funding:
    - Loan-to-deposit ratio (LTDR) constructed from IFS loan and deposit data; proxy for bank dependence on non-core funding.
  - Real activity indicators:
    - GDP, consumption, investment from WEO database; output gap extracted using same approach as financial cycles; inflation deviation from target drawn from IFS and IMF Research.
- Sample and frequency:
  - All variables are quarterly, covering 1960 – 2014, depending on availability, and are seasonally adjusted.
  - Credit, total credit, equity and property prices are deflated by CPI.
- Stylized empirical facts (summarized):
  - Average cycle length across financial and real indicators is medium-term (~6 years on average).
  - Equity cycles: shortest and largest amplitude.
  - Credit and GDP cycles: longer, similar to business cycles.
  - EM versus AM: EM cycles shorter and larger amplitude.
  - Single, uniform cycle-extraction rules (e.g., HP with fixed smoothing) may be inappropriate across heterogeneous country samples.

### Early Warning Systems (EWS) results and implications (from summary and figures/tables list)
- Forecasting and indicator performance:
  - Equity price and output gap are top predictors of banking crises in AM.
  - In EM, equity, property, and credit gap indicators provide useful early warnings.
- Timing and lead:
  - Warnings about banking crises can be observed up to five years in advance when assessing financial overheating in real time.
- Aggregation:
  - Aggregating signals from multiple leading indicators improves crisis-forecasting power.
- Tools and robustness:
  - The paper employs both two-sided and one-sided filters in EWS robustness checks (referenced Figures: EWS Results (2-sided filter), EWS Results (1-sided filter), EWS Results (Growth)).
  - AUROC estimations and threshold selection are analyzed (referenced Figures: EWS Threshold Selection; EWS Versus AUROC; Appendix 6 robustness checks).

### Appendices, figures, and tables (content inventory relevant to methods/results)
- Figures enumerated include cycle examples, stylized cycles (AM and EM), behavior around crisis dates, EWS threshold and performance, overheating index behavior and country examples, and logit summaries.
- Tables enumerated include average cycle length, maximum and minimum cycle periods, probability of banking crisis estimations (AM; various filters and controls), thresholds and weights for overheating index, and numerous appendix tables covering cycle properties by country, BIS-definition cycles, LTDR cycles, equity and property price cycles, GDP cycles, synchronization across financial and real cycles, and robustness checks.
- Appendices include:
  - Appendix 1. Data Sources
  - Appendix 2. Cycle Properties by Country (multiple detailed tables)
  - Appendix 3. Country-Specific Results on Cycle Length
  - Appendix 4. Synchronization across Financial and Real Cycles
  - Appendix 5. Comparison of Cycle Length to Claessens et al. (2011a and 2011b)
  - Appendix 6. Robustness Checks for EWS: AUROC Estimations

*Source: wpiea2021116-print-pdf - References (excerpted content provided).*

### Appendix 1 for the summary of data sources.

### Appendix 1 — Summary of data sources and methods

### Country sample
- Advanced market countries (AM) sample includes 34 countries: Australia, Austria, Belgium, Canada, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hong Kong SAR, Iceland, Ireland, Israel, Italy, Japan, Korea, Luxembourg, Malta, Netherlands, New Zealand, Norway, Portugal, Singapore, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, Taiwan Province of China, United Kingdom, and United States.
- Emerging market countries (EM) sample includes 25 countries: Argentina, Brazil, Bulgaria, China, Colombia, Croatia, Hungary, India, Indonesia, Lithuania, Malaysia, Mexico, Philippines, Poland, Russia, Serbia, South Africa, Thailand, Turkey, Ukraine, Uruguay, Latvia, Kazakhstan, Romania, Vietnam.
- Low-income developing countries are excluded due to data constraints.

### Dating financial cycles (methodology)
- Turning points (peaks and troughs) are dated using the Harding and Pagan (2002a) turning point algorithm, following Claessens et al. (2011a and 2011b).
- Peak definition (for a quarterly log-level series f_t):
  - A peak at time t occurs if {[ (f_t − f_{t−2}) > 0, (f_t − f_{t−1}) > 0 ] and [ (f_{t+2} − f_t) < 0, (f_{t+1} − f_t) < 0 ]}  (equation (1) in source).
- Trough definition:
  - A trough at time t occurs if {[ (f_t − f_{t−2}) < 0, (f_t − f_{t−1}) < 0 ] and [ (f_{t+2} − f_t) > 0, (f_{t+1} − f_t) > 0 ]}  (equation (2) in source).
- Endpoint of analysis is set at 2014 (date of the latest banking crisis per Laeven and Valencia, 2018).
- Cycle length L_{i j} for series i in country j is the sum of average durations of upswing and downswing phases:
  - L_{i j} = L̄^{up} + L̄^{down} = (1/a) Σ_{d=1}^{a} D^{up}_{j d} + (1/m) Σ_{m=1}^{m} D^{down}_{j m}  (equation (3) in source).
- Duration definitions:
  - D^{up}_j = number of quarters from trough to next peak.
  - D^{down}_j = number of quarters from peak to next trough.
- Other cyclical characteristics:
  - Amplitude = change from peak to next trough.
  - Slope = amplitude / duration.

### Cycle properties (counts and stylized findings)
- Identified complete cycles:
  - 251 complete credit cycles.
  - 356 equity price cycles.
  - 208 property price cycles.
  - 383 LTDR cycles.
- Stylized findings:
  - Equity cycles tend to be the shortest, lasting on average 3 to 4 years, and have one of the largest amplitudes, with a swing from trough to peak of over 60 percent on average.
  - Bank credit and GDP tend to have the longest cycles, with long build-ups (around 5-6 years) and faster downturns (about 1-1.5 years).
  - Expansion amplitudes: 50-90 percent for credit, 25-30 percent for GDP.
  - Contraction amplitudes: 10-30 percent for credit, 4-7 percent for GDP.
  - Loan-to-deposit ratio (LTDR), real estate and equity prices tend to have peaks and slumps of relatively equal length and last on average 3 to 5 years.
- Emerging vs. advanced markets:
  - Emerging market cycles tend to be shorter and with greater amplitude.
  - Credit cycles in EMs are more volatile, with larger amplitude and much larger contraction.
- Dynamics interpretation:
  - Long build-ups and relatively swift downturns, particularly in AMs, reflect the procyclical and endogenous nature of leverage (easy credit → higher asset prices → more leverage; deleveraging → lower asset prices → defaults, rising NPLs, banking crises).

### Table 1 (average cycle length — as reported in source)
- Total number of cycles: 356 (equity), 208 (property), 383 (LTDR), 251 (credit), 171 (total credit), 163 (GDP), 146 (CI), 268 (other) — as presented in the source table.
- Cycle length (years) — Advanced Markets (as reported):
  - Equity: Average 3.2; Median 3.1; Standard deviation 0.6
  - Property: Average 4.1; Median 3.6; Standard deviation 1.6
  - LTDR: Average 3.6; Median 3.6; Standard deviation 1.0
  - Credit: Average 6.0; Median 5.2; Standard deviation 2.4
  - Total credit: Average 6.3; Median 6.0; Standard deviation 2.3
  - GDP: Average 6.3; Median 5.5; Standard deviation 2.4
  - CI: Average 5.6; Median 5.5; Standard deviation 4.8
- Cycle length (years) — Emerging Markets (as reported):
  - Equity: Average 3.8; Median 3.5; Standard deviation 0.9
  - Property: Average 5.2; Median 4.7; Standard deviation 2.0
  - LTDR: Average 4.2; Median 3.9; Standard deviation 1.3
  - Credit: Average 7.1; Median 6.6; Standard deviation 2.7
  - Total credit: Average 3.7; Median 6.4; Standard deviation 3.4
  - GDP: Average 6.7; Median 5.9; Standard deviation 3.0
  - CI: Average 6.7; Median 5.7; Standard deviation 3.5
  - Other: Average 4.7; Median 4.5; Standard deviation 1.3
- Note: The table in the source presents counts and multiple series-specific statistics; figures above are reproduced exactly as shown in the source table rows.

### Financial cycle gaps (construction and robustness)
- Financial cycle gaps computed using Christiano and Fitzgerald band pass filter to obtain cyclical deviations from trend.
- Filter time ranges set according to the sample average cycle length in EM or AM groups minus/plus two standard deviations (Table 1); Table 2 reports the range of frequencies to be extracted.
- Robustness checks include cycles in ranges of mean +/- 0.5 and +/- 1 standard deviation, HP filter gaps, and deviation from quadratic time trend.
- Two-sided vs. one-sided filters:
  - Two-sided filter estimated over the complete time sample — structural, hindsight view, clearer indicator identification.
  - One-sided filter estimated recursively using only information available up until that point — reflects real-time forecasting challenges and tends to produce lower signal extraction.
- Inflation treated differently: inflation gap measured as deviation from policy target.

### Table 2 (maximum and minimum periods of the cycle — as reported in source)
Minimum length of the cycle (p_l)  Maximum length of the cycle (p_h)
- Credit550
- Total credit256
- Property prices536
- Equity prices822
- LTDR727
- GDP351
- Credit543
- Total credit744
- Property prices429
- Equity prices818
- LTDR623
- GDP743
- Advanced Markets
- Emerging Markets

### Financial cycles and banking crises — Stylized facts
- Crisis definition: Systemic banking crisis per Laeven and Valencia (2008, 2012, 2018) — episode with a large number of defaults and sharp increases in NPLs, with financial institutions and corporations facing difficulties repaying contracts on time.
- Average two-sided gap behavior around crises (AMs):
  - Equity and property prices tend to peak before the crisis — good leading indicators.
  - Equity prices tend to bottom out in about one year after crisis; property price booms take about two years to unwind.
  - Private credit (BIS measure) peaks after the crisis, suggesting other financial institutions pick up lending while banks deleverage — more pronounced in AMs.
  - Credit-to-GDP ratio shows limited early warning power; rises during and after crisis, partly due to output contractions reducing affordability.
  - LTDR (loan-to-deposit ratio) peaks provide longer lead time: peaks two years before crisis in AMs and four years before crisis in EMs.
  - Output and inflation are weak early warning indicators: in AMs they peak during the crisis; in EMs they tend to lag the crisis with output falling and inflation spiking the year after crisis.
- One-sided filter (real-time perspective):
  - Signals of overheating appear three to four years prior to crisis, though weaker than two-sided results.
  - For AMs: equity prices can give guidance four years before, property prices two years before, and credit one year before crisis.
  - For EMs: performance less clear-cut but tendency for positive gaps prior to crisis and negative thereafter persists.
- Growth-rate measures (year-on-year growth of underlying series) generally weaker predictors than financial gap analysis:
  - In AMs, peaks in growth of credit, property and LTDR occur two-three years before crisis; equity prices show broad boom with multiple peaks.
  - In EMs, growth-based signals are less clear.

### Early Warning System (EWS) model — signal extraction approach
- Non-parametric signal extraction similar to Kaminsky et al. (1998):
  - Sample split into crisis and non-crisis observations.
  - Cumulative distribution functions (CDFs) of financial cycle gaps are computed for each subsample.
  - Critical threshold values chosen to minimize sum of missed crises (Type I error) and false alarms (Type II error).
- Loss function minimized for each variable:
  - L_min(x*) = CD C_C(x*) + (1 − C D C_¬C (x*))  — represented in source as equation (4) with indicator-sum formulation; calculations are done variable by variable.
- Signal-to-noise (STN) ratio used to assess performance:
  - STN = (1 − T1 − T2) / (T1 + T2)  — as presented in source (equation (5)).
  - Higher STN indicates better early warning indicator (signal = share of properly identified crisis and non-crisis episodes; noise = missed crises + false alarms).
- Comparison to AUROC:
  - AUROC (area under ROC curve) is described as another non-parametric discriminator between crisis and non-crisis cases; AUROC of 0.5 = random classifier, AUROC of 1 = perfect classifier.
- Threshold selection visualized in Figure 6: threshold chosen to maximize distance between crisis and non-crisis CDFs, balancing Type I and Type II errors.

*Source: Appendix 1 for the summary of data sources (wpiea2021116-print-pdf).*

### 0.8 means that in 80 percent of the cases, the model is correctly assigning the variable’s

### wpiea2021116-print-pdf - 0.8 means that in 80 percent of the cases, the model is correctly assigning the variable’s

### Methodological approach: loss-function thresholding versus AUROC
- The paper chooses a particular loss function and compares signaling performance of variables at the best threshold chosen by that loss function (equation 2).  
- The threshold minimizing the loss function is equivalent to choosing the point under the ROC curve furthest away from the 45-degree line (max distance between ROC and random choice model).  
- Rationale for preference over AUROC:
  - AUROC compares combined signaling power across all thresholds (area under ROC curve).
  - The loss-function approach yields a single, policy-relevant threshold and clear rules for action, useful when ROC curves cross (indicator with larger AUROC may perform worse at the policy threshold).

### Early Warning System (EWS) results — two-sided filters (hindsight)
- Each data point is a separate estimation; example: value of 1.6 for two-sided equity price gap in year 1 quarter 2 before the crisis is the STN at the optimal threshold.  
- Two-sided filters (with hindsight) have better forecasting power (Figure 8).  
- Advanced markets (AM):
  - Best indicators of overheating: stock prices and output gap, followed by property prices and inflation.
  - LTDR and bank credit tend to have weaker signaling power.
  - Predictive power is best in the year before the crisis and drops as lag increases, except equity prices which show a second smaller STN peak four years before the crisis.
- Emerging markets (EM):
  - Output gap weaker than in AM.
  - Best early warning indicators:
    - Property and equity prices and credit in the year before the crisis.
    - Credit-to-GDP and property prices five years before the crisis.
    - Output gap and inflation three years before the crisis.
- BIS credit gap and Schularick measures: mostly in the lower range of STN estimates.

### EWS results — one-sided filters (real-time application)
- One-sided filters acknowledge difficulty of real-time inference due to dependence on forecasts; STN estimates are generally lower (Figure 9).  
- Advanced markets:
  - Equity price is the best predictor; predictive power shifts forward from one year to four years before the crisis (allows earlier warning but complicates timing).
  - Next best indicator: LTDR two years before the crisis.
  - Credit is not a very strong indicator.
- Emerging markets:
  - Property price: best indicator one year before crisis and even more so four to five years before crisis.
  - Credit-to-GDP: second-best predictor two and five years before crisis.
  - BIS credit gap: notable exception with higher STN three years before crisis in EM.
- Growth-rate indicators (Figure 10):
  - Generally on par with one-sided filters.
  - Advanced markets: growth rate of equity prices has best predictive power, offering multiple signals during the four-to-five years period and two years before the crisis.
  - GDP growth less useful in AM; property price growth useful three years before crisis.
  - Emerging markets: GDP growth best indicator four-five years before banking crisis; equity price growth three years before crisis; credit-to-GDP two years before crisis; property price growth useful throughout sample.

### AUROC comparisons
- AUROC estimations are broadly comparable with STN estimations (Appendix 6).
- Two-sided filters:
  - Advanced markets: AUROC shows equity price and output gap excellent indicators, with AUROCs above 0.8 in the year before the crisis; other indicators AUROC below 0.7.
  - Emerging markets: only equity and property prices, credit and BIS credit gap show AUROC above 0.7 in the year before the crisis.

### Logit regressions — specification and findings
- Panel logit specification (equation 6):
  - Dependent variable: probability of banking crisis (Laeven and Valencia).
  - Regressors: cyclical deviations of financial variables with lag polynomial 훽1(L) containing lag orders 1 to 16; additional controls: credit spread, VIX, cyclically-adjusted primary balance, Chinn-Ito Index, and REER.
  - Lags are staggered across separate regressions to minimize autocorrelation (e.g., L(1,5,9,13) separate from L(2,6,10,14), etc.). Specification uses random effects; country fixed effects not significant. Exercise considers advanced economies only due to limited data.
- Two-sided filter logit results (summary):
  - Credit booms over 1 year prior, property booms over previous 2 years, sharp equity price changes within previous 2 years useful in predicting banking crises (Table 3).
  - LTDR offers longer lead: significant loan expansion in previous 2½ years useful.
  - Introducing real economy controls (output gap, inflation gap) reduces significance of credit measures; property price, equity price and LTDR remain significant (Table 4).
- Nonlinearities and marginal effects (Figure 11):
  - Excess home prices: a modest increase of 0.3 percentage points beyond the 1% level raises crisis probability by 18 percentage points (from about 12% to 30% when excess house price rises from 0.9% to 1.2%).
  - Equity valuation: at 4% overvaluation (based on metrics), probability of banking crisis reaches near certainty.
  - Bank credit and LTDR: despite non-linearity, cumulative crisis probability remains modest:
    - Bank credit: crisis probability no more than 12% with a 1.5% deviation.
    - LTDR: crisis probability no more than 2% with a 1.8% deviation.
- One-sided vs two-sided filters:
  - Predictive power of one-sided filters shifts forward (notably equity prices from within one year to four years before crisis).
  - Property and equity prices remain most useful indicators for real-time analysis with one-sided filters.
- Robustness: detrended financial variables (bank credit, property prices, equity prices) yield qualitatively similar results for two-sided filters.

### Logit regression tables — selected numeric highlights
- Table 3 (AM; 2-sided filters) — sum of lag coefficients:
  - Bank Credit: 26.40***
  - Property Prices: 101.92***
  - Equity Prices: 129.99**
  - LTDR: 17.71**
  - Pseudo R2: Note 3 values vary; examples listed: 0.0138, 0.0481, 0.1760, 0.0232 (preserved as in table).
  - Number of observations for regressions: 4,833; 3,630; 3,510; 5,014 (as reported).
- Table 4 (AM; 1- and 2-sided filters with controls) — selected coefficients and metrics:
  - Lead time to crises (quarters): reported as 4, 3, 9, 9, 16, 3, 8, 8, “varies”, “varies” across columns (preserved as in table header).
  - Example coefficients (One-sided gap / Two-sided gap):
    - Bank credit: 0.05 / 0.00 / 0.17*** / -0.04* (with standard errors shown in table).
    - Property price: 0.17*** / 0.13*** / 0.28*** / 0.07*.
    - Equity prices: 0.16*** / 0.16*** / 0.19*** / 0.12***.
    - LTDR: 0.20*** / 0.21*** / -0.03 / 0.20***.
  - Output gap and Inflation-from-target coefficients vary by regression; see table for full values and significance.
  - Number of observations across regressions: examples include 3,123; 3,157; 2,761; 2,790; 2,825; 3,021; 2,303; 2,385 (as reported).
  - Pseudo R2 examples: 0.10, 0.25, 0.13, 0.30, 0.24, 0.45, 0.09, 0.30, 0.40, 0.47.

### Why credit is not the best early warning indicator in AM
- Key conceptual points:
  - While aggregate credit level plays a crucial role in financial stability and sharp credit increases have been linked to crises, the linkage often operates through collateral valuation channels.
  - Correction in asset prices (valuation of collateral) can trigger the turn in credit cycles and ensuing balance sheet stress.
  - Asset prices historically precede banking crises (examples enumerated qualitatively in text: 1929 U.S. crash, Tulipmania, South Sea bubble, Japan 1990, Nordic 1991, Asian 1997, Global Financial Crisis 2007-08).
- Empirical explanation for AM vs EM differences:
  - In EM, credit is more heavily intermediated by banks: credit made up on average 52 percent of bank asset portfolio in the last decade versus 41 percent in advanced economies (Figure 12: "41 percent" and "52 percent" explicitly reported).
  - Banking systems in EM are more vulnerable to swings in capital inflows, making domestic credit bubble-like in behavior (examples: Eastern Europe late 1990s and early 2000s).

### Overheating Index (OI): construction and performance
- Purpose: illustrate application of EWS results by constructing an overheating index based on best leading indicators per income group.
- Indicator choices:
  - Advanced economies (AM): equity prices and output gap.
  - Emerging economies (EM): equity and property prices and credit.
  - GDP growth excluded for EM despite signaling power.
- Construction steps:
  - Estimate financial cycles and cyclical gaps with a one-sided filter to mimic real-time policy challenges.
  - Vulnerability thresholds: set at average levels for financial cycles estimated with two-sided filters in the year before the crisis (Table 5: "Average of the four quarters before the crisis year").
  - Country assigned crisis warning flag I_i,t^x = 1 if financial cycle gap for variable x breaches threshold; 0 otherwise.
  - Crisis flags aggregated into OI with weights equal to 1 - Type I error - Type II error (weights normalized so Type I and Type II errors sum to one); higher weight indicates better signal extraction power.
- Formulas (as reported):
  - OI_{i,t}^{EM} = w1 * I_{i,t}^{credit} + w2 * I_{i,t}^{equity} + w2 * I_{i,t}^{property}
  - OI_{i,t}^{AE} = w1 * I_{i,t}^{equity} + w2 * I_{i,t}^{GDP}
- Table 5 thresholds and weights (Average of the four quarters before the crisis year; Threshold measured as percent deviation from the trend):
  - Emerging Markets:
    - Credit threshold: 2.9 ; Weight: 0.32 ; Norm. weight: 4.2
    - Equity threshold: 10.3 ; Weight: 0.53 ; Norm. weight: 7.3
    - Property threshold: 7.5 ; Weight: 0.53 ; Norm. weight: 8.5
  - Advanced Markets:
    - Equity threshold: 6.7 ; Weight: 0.64 ; Norm. weight: 9.7
    - GDP threshold: 1.3 ; Weight: 0.65 ; Norm. weight: 0.3
  - (Table text preserved as presented; "Norm. weight" entries shown as reported.)
- Index performance:
  - Indices tend to signal overheating in years preceding banking crises.
  - Indices correctly flag between 60 to 65 percent of banking crises on average, rising from about 50 percent five years before the crisis to 80 percent one year before the crisis (Figures 13 and 14).
  - Country examples where OI signaled overheating up to five years before crises: Sweden, Norway, Finland (Nordic banking crisis); Mexico and Colombia (Latin American debt crisis); Malaysia, Philippines, Thailand (Asian Financial Crisis); United States, United Kingdom, Iceland, Ireland, Greece, Latvia, Kazakhstan, Ukraine (Global Financial Crisis).
- Out-of-sample test:
  - Applied estimations to 2018 update of Laeven and Valencia database; update adds two crises to estimation: Cyprus in 2011 and Ukraine in [text ends here].

*Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021116-print-pdf.pdf*

### 2014. While we do not use these data to estimate the critical thresholds, the index picks up

### VII. CONCLUSIONS

### Overheating index: timing and early warning
- The Overheating Index (OI) picks up overheating in countries years before their crises (Figure 16).
- The OI can signal a looming banking crisis even in real time – often a few years in advance.
- The lead time provided by the OI:
  - Gives policy makers time to take policy actions to contain overheating.
  - Allows policy makers time to prepare for potential fallouts, such as upgrading resolution frameworks.

### Financial cycle characteristics and implications
- Financial cycles behave differently than economic cycles, but there is limited agreement on their characteristics.
- Using an agnostic approach, the study finds:
  - On average, the length of financial cycles is on par with, or shorter, than that of business cycles.
  - There are variations in cycle duration for different financial variables and across different countries.
  - Implication: A one-size-fits-all metric for cycle extraction used in the calculations for CCyBs across countries may need to be reconsidered.

### Predictive power of indicators
- As leading indicators of banking crisis:
  - Financial variables offer strong predictive power, often on par with and in many instances better than that of real sector variables.
  - Equity prices offer the best signal.
  - Property prices offer the next-best signal.
  - Credit, while widely seen as a strong crisis predictor, does not offer the clearest signals.
- Methodological notes:
  - Financial cycles extracted with two-sided filters offer stronger predictive power than those with one-sided filters but are not applicable in real time.
  - Aggregating financial cycle indicators in an overheating index improves prediction in real time, emphasizing the need to look at a wide range of indicators.

### Policy recommendations and practical guidance
- Early warning models should be used as one of many inputs in the assessment and identification of financial vulnerabilities.
- Given the lagged impact of policy, the lead time afforded by the OI can provide room for policy makers to:
  - Adjust regulatory and supervisory response.
  - Prepare for potential fallouts.
- A prudent policy approach under research uncertainty:
  - Consider a range of indicators.
  - Be alert to early signs of a pickup in trends of and widening gaps in financial variables.

### Selected figure annotations (as in source)
- Axis ticks shown: 0.0 0.2 0.4 0.6 0.8 1.0 1.2
- Years depicted: 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
- Labels appearing in figure areas: Advanced Markets, Cyprus, Emerging Markets, Ukraine

### Appendix 1 — Data sources (selected)
- Stock indicators:
  - Private credit: International Financial Statistics (IFS)
  - Total credit to the private non-financial sector: Bank of International Settlements (BIS)
- Price indicators:
  - Property price: IMF Research department
  - Equity price: Haver
- Leverage or noncore funding indicators:
  - Loan-to-deposit ratio: International Financial Statistics (IFS)
- Real series:
  - Gross Domestic Product: World Economic Outlook
  - Consumption: World Economic Outlook
  - Investment: World Economic Outlook
  - CPI: International Financial Statistics (IFS)
  - Inflation deviation from target: IMF Research department
- Banking Crises:
  - 0-1 indicator of systemic banking crisis: Laeven and Valencia (2018)
- Logit regression controls:
  - Credit spread: Haver
  - VIX: Haver
  - Cyclically-adjusted primary balance: World Economic Outlook
  - Capital controls: Chinn-Ito Index
  - REER: World Economic Outlook

*Source: Excerpt from VII. CONCLUSIONS and Appendix 1, wpiea2021116-print-pdf.*

### Appendix 2. Cycle Properties by Country

### Appendix 2. Cycle Properties by Country

### Table 1A. Credit Cycles (AM)
- Number of cycles: 144 total (peak / trough)
- Average cycle length (years): 7.1 (total), 5.6 (peak), 1.5 (trough)
- Median cycle length (years): 6.6 (total), 5.4 (peak), 1.2 (trough)
- St. dev.: 2.7 (total), 2.6 (peak), 0.8 (trough)
- Aggregate summary statistics:
  - mean 5.9; 60.8; 22.5; 50.4; 2.5
  - median 5.5; 61.5; 21.5; 47.4; 2.2
  - st. dev. 2.5; 16.6; 10.5; 28.3; 1.5
  - sum 178 peaks
- Representative country-level entries (selected, values preserved from table):
  - Australia: Number 5; Time 51.9; Duration 24.0; Amplitude 57.9; Slope 2.4
  - Canada: Number 5; Time 79.1; Duration 36.4; Amplitude 71.7; Slope 2.0
  - United States: Number 5; Time 52.8; Duration 30.5; Amplitude 38.2; Slope 1.3

### Table 1A. Credit Cycles (AM) — Troughs (selected)
- Aggregate trough summary:
  - mean 5.8; 18.6; 5.9; -9.0; -1.5
  - median 6.0; 18.9; 4.9; -6.5; -1.3
  - st. dev. 2.6; 9.1; 3.2; 7.6; 1.0
  - sum 174 troughs
- Representative trough entries (selected):
  - Australia: 6; 73; -6; -2
  - Canada: 6; 94; -5; -1
  - United States: 5; 199; -12; -1

### Table 1B. Credit Cycles (EM)
- Number of cycles: 107 total (peak / trough)
- Average cycle length (years): 6.0 (total), 4.5 (peak), 1.5 (trough)
- Median cycle length (years): 5.2 (total), 3.8 (peak), 1.5 (trough)
- St. dev.: 2.4 (total), 2.3 (peak), 0.5 (trough)
- Aggregate summary statistics:
  - mean 5.3; 53.3; 18.0; 89.0; 4.8
  - median 4.0; 56.8; 15.0; 60.8; 4.2
  - st. dev. 3.1; 14.4; 9.4; 71.1; 2.1
  - sum 127 peaks
- Representative country-level entries (selected):
  - Argentina: Number 5; Time 50.4; Duration 11.6; Amplitude 49.9; Slope 4.3
  - India: Number 8; Time 56.7; Duration 18.7; Amplitude 48.0; Slope 2.6
  - Turkey: Number 9; Time 56.8; Duration 13.0; Amplitude 58.8; Slope 4.5

### Table 1B. Credit Cycles (EM) — Troughs (selected)
- Aggregate trough summary:
  - mean 5.5; 21.4; 5.9; -29.6; -5.1
  - median 4.5; 20.7; 5.9; -27.1; -4.3
  - st. dev. 3.3; 11.5; 2.0; 21.3; 3.7
  - sum 131 troughs
- Representative trough entries (selected):
  - Argentina: 6; 32.2; -7.4; -6.3
  - Brazil: 6; 20.9; -5.8; -6.0
  - Ukraine: 4; 20.5; -49.6; -8.3

### Table 2A. BIS-Definition Credit Cycles (AM)
- Number of cycles: 117 total (peak / trough)
- Average cycle length (years): 7.3 (total), 6.0 (peak), 1.4 (trough)
- Median cycle length (years): 6.4 (total), 5.2 (peak), 1.2 (trough)
- St. dev.: 3.4 (total), 3.3 (peak), 0.6 (trough)
- Aggregate summary statistics:
  - mean 5.7; 55.6; 23.8; 42.7; 1.8
  - median 5.0; 58.3; 20.8; 33.2; 1.6
  - st. dev. 2.3; 16.7; 13.2; 32.7; 0.8
  - sum 142 peaks
- Representative country-level entries (selected):
  - Australia: Number 6; Time 85.7; Duration 32.8; Amplitude 55.2; Slope 1.7
  - Korea: Number 3; Time 59.0; Duration 52.5; Amplitude 175.2; Slope 3.3
  - United States: Number 3; Time 44.3; Duration 51.0; Amplitude 63.6; Slope 1.2

### Table 2A. BIS-Definition Credit Cycles (AM) — Troughs (selected)
- Aggregate trough summary:
  - mean 5.5; 17.1; 5.5; -4.8; -0.9
  - median 5.0; 17.4; 4.9; -4.9; -0.8
  - st. dev. 2.2; 8.4; 2.3; 2.3; 0.4
  - sum 137 troughs
- Representative trough entries (selected):
  - Australia: 7; 83; -3; -2
  - Canada: 5; 74; -4; -1
  - United States: 3; 129; -6; -1

### Table 2B. BIS-Definition Credit Cycles (EM)
- Number of cycles: 54 total (peak / trough)
- Average cycle length (years): 6.3 (total), 4.9 (peak), 1.4 (trough)
- Median cycle length (years): 6.0 (total), 4.7 (peak), 1.3 (trough)
- St. dev.: 2.3 (total), 2.2 (peak), 0.7 (trough)
- Aggregate summary statistics (peaks):
  - mean 4.6; 49.0; 19.7; 73.3; 3.7
  - median 4.0; 58.3; 18.9; 64.3; 3.8
  - st. dev. 2.6; 19.5; 8.7; 39.8; 1.1
  - sum 60 peaks
- Aggregate summary statistics (troughs):
  - mean 4.9; 18.2; 5.5; -18.0; -3.2
  - median 4.0; 16.5; 5.3; -12.7; -2.4
  - st. dev. 2.4; 10.3; 2.7; 14.5; 2.2
  - sum 64 troughs
- Representative entries (selected):
  - Argentina (peaks): Number 4; Time 58.3; Duration 17.5; Amplitude 49.0; Slope 2.8
  - India (peaks): Number 10; Time 73.5; Duration 18.8; Amplitude 48.0; Slope 2.6
  - Mexico (peaks): Number 4; Time 42.2; Duration 19.0; Amplitude 93.8; Slope 4.9

### Table 3A. LTDR Cycles (AM)
- Number of cycles: 291 total (peak / trough)
- Average cycle length (years): 4.2 (total), 2.3 (peak), 1.9 (trough)
- Median cycle length (years): 3.9 (total), 2.1 (peak), 1.7 (trough)
- St. dev.: 1.3 (total), 0.9 (peak), 0.9 (trough)
- Aggregate summary statistics:
  - mean 9.8; 48.2; 9.4; 17.0; 1.8
  - median 9.0; 50.0; 8.5; 14.2; 1.5
  - st. dev. 5.0; 10.5; 3.6; 13.1; 0.8
  - sum 324 peaks
- Representative country-level entries (selected):
  - United States (peaks): Number 13; Time 48.9; Duration 9.4; Amplitude 8.6; Slope 0.9
  - United Kingdom (peaks): Number 11; Time 43.0; Duration 8.9; Amplitude 20.4; Slope 2.3
  - Korea (peaks): Number 14; Time 53.0; Duration 8.3; Amplitude 16.2; Slope 1.9

### Table 3A. LTDR Cycles (AM) — Troughs (selected)
- Aggregate trough summary:
  - mean 9.8; 36.3; 7.4; -13.0; -1.8
  - median 9.0; 37.9; 6.9; -11.6; -1.6
  - st. dev. 5.1; 12.8; 3.6; 6.2; 0.8
  - sum 324 troughs
- Representative trough entries (selected):
  - United States: 13; 47; -9
  - United Kingdom: 11; 51; -10 to -15 (table shows ranges per country)
  - Iceland: 18; 47; -6 to -20 (table shows ranges)

### Table 3B. LTDR Cycles (EM)
- Number of cycles: 92 total (peak / trough)
- Average cycle length (years): 3.6 (total), 2.1 (peak), 1.4 (trough)
- Median cycle length (years): 3.6 (total), 2.2 (peak), 1.4 (trough)
- St. dev.: 1.0 (total), 0.9 (peak), 0.5 (trough)
- Aggregate summary statistics:
  - mean 4.8; 43.0; 8.6; 25.2; 2.9
  - median 4.0; 42.4; 8.8; 21.8; 2.7
  - st. dev. 3.2; 12.1; 3.5; 15.8; 1.7
  - sum 120 peaks
- Representative country-level entries (selected):
  - Argentina: Number 12; Time 39.8; Duration 7.8; Amplitude 42.8; Slope 5.5
  - India: Number 16; Time 33.9; Duration 5.2; Amplitude 32.0; Slope 6.2
  - Vietnam: Number 5; Time 57.7; Duration 6.0; Amplitude 41.6; Slope 6.9

### Table 3B. LTDR Cycles (EM) — Troughs (selected)
- Aggregate trough summary:
  - mean 4.7; 31.9; 5.8; -17.2; -3.1
  - median 4.0; 36.5; 5.8; -12.7; -2.5
  - st. dev. 3.1; 14.7; 2.1; 11.9; 1.9
  - sum 117 troughs
- Representative trough entries (selected):
  - Argentina: 11; 53.7; -10.5; -4.5
  - India: 15; 44.8; -6.9; -5.1
  - Ukraine: 3; 40.4; -22.7; -3.2

### Table 4A. Equity Price Cycles (AM)
- Number of cycles: 231 total (peak / trough)
- Average cycle length (years): 3.8 (total), 2.3 (peak), 1.4 (trough)
- Median cycle length (years): 3.5 (total), 2.2 (peak), 1.3 (trough)
- St. dev.: 0.9 (total), 0.8 (peak), 0.4 (trough)
- Aggregate summary statistics:
  - mean 7.4; 50.0; 9.4; 67.0; 7.6
  - median 7.0; 50.3; 8.9; 61.2; 7.1
  - st. dev. 3.7; 11.9; 3.1; 21.5; 2.9
  - sum 251 peaks
- Representative country-level entries (selected):
  - United States: Number 10; Time 58.3; Duration 10.5; Amplitude 44.2; Slope 4.2
  - Japan: Number 12; Time 59.4; Duration 8.9; Amplitude 63.6; Slope 7.1
  - Germany: Number 7; Time 50.5; Duration 8.0; Amplitude 53.3; Slope 6.7

### Table 4A. Equity Price Cycles (AM) — Troughs (selected)
- Aggregate trough summary:
  - mean 7.8; 32.6; 5.7; -59.1; -10.1
  - median 7.5; 30.8; 5.3; -45.3; -8.4
  - st. dev. 3.9; 8.6; 1.6; 40.6; 4.1
  - sum 265 troughs
- Representative trough entries (selected):
  - United States: 11; 285; -30; -6
  - Japan: 12; 366; -43; -7
  - Italy: 12; 325; -45; -9

### Table 4B. Equity Price Cycles (EM)
- Number of cycles: 125 total (peak / trough)
- Average cycle length (years): 3.2 (total), 1.8 (peak), 1.4 (trough)
- Median cycle length (years): 3.1 (total), 1.8 (peak), 1.3 (trough)
- St. dev.: 0.6 (total), 0.6 (peak), 0.3 (trough)
- Aggregate summary statistics:
  - mean 5.9; 45.0; 7.3; 77.8; 11.2
  - median 5.0; 47.6; 7.0; 63.3; 9.9
  - st. dev. 2.4; 10.8; 2.3; 32.4; 4.6
  - sum 141 peaks
- Representative country-level entries (selected):
  - China: Number 8; Time 39.6; Duration 5.4; Amplitude 63.5; Slope 11.7
  - Russia: Number 4; Time 53.6; Duration 9.3; Amplitude 99.0; Slope 10.7
  - Turkey: Number 9; Time 51.4; Duration 6.1; Amplitude 88.0; Slope 14.4

### Table 4B. Equity Price Cycles (EM) — Troughs (selected)
- Aggregate trough summary:
  - mean 6.2; 37.9; 5.5; -62.6; -11.3
  - median 5.5; 36.4; 5.2; -58.6; -10.6
  - st. dev. 2.3; 7.8; 1.2; 25.8; 3.6
  - sum 149 troughs
- Representative trough entries (selected):
  - Ukraine: 4; 31.3; -125.5; -17.9
  - Kazakhstan: 4; 45.6; -94.7; -10.9
  - Latvia: 5; 9.2; -43.2; -7.4

### Table 5A. Property Price Cycles (AM)
- Number of cycles: 166 total (peak / trough)
- Average cycle length (years): 5.2 (total), 3.0 (peak), 2.2 (trough)
- Median cycle length (years): 4.7 (total), 2.7 (peak), 2.0 (trough)
- St. dev.: 2.0 (total), 1.3 (peak), 1.5 (trough)
- Aggregate summary statistics:
  - mean 6.5; 47.9; 12.0; 22.0; 2.0
  - median 7.0; 51.8; 11.0; 23.7; 1.7
  - st. dev. 2.4; 14.4; 5.1; 10.7; 1.0
  - sum 195 peaks
- Representative country-level entries (selected):
  - United Kingdom: Number 7; Time 57.5; Duration 7.1; Amplitude 34.7; Slope 2.5
  - United States: Number 6; Time 53.6; Duration 19.2; Amplitude 16.5; Slope 0.9
  - Singapore: Number 5; Time 53.5; Duration 10.6; Amplitude 43.7; Slope 4.1

### Table 5A. Property Price Cycles (AM) — Troughs (selected)
- Aggregate trough summary:
  - mean 6.5; 34.6; 8.7; -14.0; -1.7
  - median 7.0; 34.4; 7.8; -11.7; -1.5
  - st. dev. 2.6; 8.7; 6.0; -8.7; 1.0
  - sum 196 troughs
- Representative trough entries (selected):
  - United Kingdom: 8; 34; -49; -16 (table shows ranges per country)
  - Japan: 2; 4339; -44 (table shows ranges)

### Table 5B. Property Price Cycles (EM)
- Number of cycles: 42 total (peak / trough)
- Average cycle length (years): 4.1 (total), 1.9 (peak), 2.2 (trough)
- Median cycle length (years): 3.6 (total), 1.8 (peak), 1.9 (trough)
- St. dev.: 1.6 (total), 1.1 (peak), 1.2 (trough)
- Aggregate summary statistics (peaks):
  - mean 3.5; 36.7; 7.8; 22.3; 2.2
  - median 4.0; 37.6; 7.1; 15.3; 1.8
  - st. dev. 1.2; 19.9; 4.2; 28.6; 1.5
  - sum 56 peaks
- Aggregate summary statistics (troughs):
  - mean 3.5; 35.8; 8.7; -22.4; -2.8
  - median 4.0; 36.3; 7.5; -21.3; -1.8
  - st. dev. 1.5; 14.3; 4.8; 17.6; 2.1
  - sum 59 troughs
- Representative country-level entries (selected):
  - Argentina (peaks): Number 5; Time 56.2; Duration 10.0; Amplitude 20.4; Slope 2.0
  - Ukraine (peaks): Number 2; Time 67.2; Duration 19.5; Amplitude 118.0; Slope 6.0
  - Russia (peaks): Number 3; Time 69.5; Duration 13.7; Amplitude 47.5; Slope 3.5

### Table 6A. GDP Cycles (AM)
- Number of cycles: 126 total (peak / trough)
- Average cycle length (years): 6.7 (total), 5.7 (peak), 1.1 (trough)
- Median cycle length (years): 5.9 (total), 4.9 (peak), 1.1 (trough)
- St. dev.: 3.0 (total), 2.9 (peak), 0.3 (trough)
- Aggregate summary statistics:
  - mean 4.7; 58.0; 22.6; 24.6; 1.0
  - median 4.0; 65.0; 19.5; 19.0; 0.9
  - st. dev. 2.3; 18.7; 11.8; 21.5; 0.5
  - sum 156 peaks
- Representative country-level entries (selected):
  - United States: Number 6; Time 79.2; Duration 29.2; Amplitude 28.0; Slope 1.0
  - Germany: Number 11; Time 70.9; Duration 15.6; Amplitude 12.1; Slope 0.8
  - Japan: Number 7; Time 45.7; Duration 10.7; Amplitude 6.2; Slope 0.6

### Table 6A. GDP Cycles (AM) — Troughs (selected)
- Aggregate trough summary:
  - mean 4.8; 13.7; 4.3; -4.4; -1.0
  - median 5.0; 13.3; 4.2; -3.8; -0.8
  - st. dev. 2.3; 5.8; 1.2; 2.6; 0.5
  - sum 159 troughs
- Representative trough entries (selected):
  - United States: 7; 93; -2
  - Germany: 10; 16; -4
  - Greece: 11; 305; -7

### Table 6B. GDP Cycles (EM)
- Number of cycles: 37 total (peak / trough)
- Average cycle length (years): 6.3 (total), 5.3 (peak), 1.0 (trough)
- Median cycle length (years): 5.5 (total), 4.6 (peak), 0.9 (trough)
- St. dev.: 2.3 (total), 2.3 (peak), 0.2 (trough)
- Aggregate summary statistics:
  - mean 4.4; 56.2; 21.3; 29.3; 1.4
  - median 4.0; 60.7; 18.3; 28.9; 1.4
  - st. dev. 1.9; 19.1; 9.0; 14.5; 0.4
  - sum 48 peaks
- Representative country-level entries (selected):
  - Argentina: Number 4; Time 62.5; Duration 18.3; Amplitude 29.6; Slope 1.6
  - India: Number 6; Time 76.4; Duration 33.6; Amplitude 50.7; Slope 1.5
  - South Africa: Number 7; Time 46.8; Duration 17.2; Amplitude 16.4; Slope 1.0

### Table 6B. GDP Cycles (EM) — Troughs (selected)
- Aggregate trough summary:
  - mean 4.4; 14.3; 3.9; -6.7; -1.8
  - median 4.0; 15.9; 3.7; -7.9; -1.4
  - st. dev. 1.7; 5.8; 0.9; 3.0; 1.0
  - sum 48 troughs
- Representative trough entries (selected):
  - Argentina: 4; 25.0; -5.5; -7.9; -1.4
  - Brazil: 6; 16.0; -2.7; -2.9; -1.1
  - India: 6; 9.5; -3.5; -3.5; -1.0

*Appendix 2. Cycle Properties by Country — data tables and country-level statistics extracted from the source PDF.*

### Appendix 3. Country-Specific Results on Cycle Length

### Appendix 3. Country-Specific Results on Cycle Length

### Average cycle length by country (Figure 1)
- Panels present average cycle length (Years) by country for: AM GDP, AM Credit, AM Property, AM Equity, EM GDP, EM Credit, EM Property, EM Equity.
- Example top values shown in figures:
  - AM GDP: Korea 6.7
  - AM Credit: Finland 7.1
  - AM Property: Japan 5.2
  - AM Equity: Netherlands 3.8
  - EM GDP: Malaysia 6.3
  - EM Credit: Latvia 6.0
  - EM Property: Ukraine 4.1
  - EM Equity: Ukraine 3.2

### Distribution of cycle length (AM) (Figure 2)
- Distribution charts for AM (number of observations vs. length in years) for:
  - AM GDP: Expansion Distribution; AM GDP: Contraction Distribution
  - AM Credit: Expansion Distribution; AM Credit: Contraction Distribution
  - AM Property: Expansion Distribution; AM Property: Contraction Distribution
  - AM Equity: Expansion Distribution; AM Equity: Contraction Distribution
- Visuals indicate counts across lengths up to 25+ years for expansions and contractions.

### Distribution of cycle length (EM) (Figure 3)
- Distribution charts for EM (number of observations vs. length in years) for:
  - EM GDP: Expansion Distribution; EM GDP: Contraction Distribution
  - EM Credit: Expansion Distribution; EM Credit: Contraction Distribution
  - EM Property: Expansion Distribution; EM Property: Contraction Distribution
  - EM Equity: Expansion Distribution; EM Equity: Contraction Distribution
- Visuals show frequency of short cycles (1–9 years) and longer tails up to 25 years in some series.

### Synchronization across cycles (Appendix 4)
- Concordance index (Harding and Pagan (2002b)) defined as:
  - CCI_xe = 1/T Σ_t [ C_t^x C_t^e + (1−C_t^x)(1−C_t^e) ] (equation (1))
  - C_t^x = {0, if x is downturn at time t | 1, if x is in upturn at time t}
  - C_t^e = {0, if e is downturn at time t | 1, if e is in upturn at time t}
- Key findings:
  - Financial cycles tend to be more synchronized in AMs rather than EMs, especially for property price, credit and equity cycles and between leverage cycle and equity price (Table 1).
  - Output and consumption tend to be more synchronized with credit.
  - Investment tends to be more synchronized with equity markets.
  - Financial and business cycles are not perfectly synchronized; the fraction of time the two cycles are in the same phase is 60 percent on average.
  - Policy implication: scope for macroprudential policy to supplement monetary policy in achieving financial stability goals.

### Synchronization across cycles within a country (Table 1)
- Presentation: Fraction of time the two series are in the same phase of their respective cycles.
- Select matrix entries (as presented in the table):
  - Credit–GDP: 0.66
  - Credit–Consumption: 0.70
  - Credit–Investment: 0.63
  - Property–GDP: 0.60
  - Equity–GDP: 0.65
  - LTDR–GDP: 0.61
- Two-block summary rows: Advanced markets / Emerging markets (matrix structure preserved in source).

### Synchronization of financial cycles within a country (AM) (Table 2A)
- Table header: "Equity with: propertyequityLTDRequityLTDRLTDR"
- Per-country entries (selected lines preserved exactly as in source):
  - 1 Australia 0.500.490.620.600.680.53
  - 2 Austria 0.220.490.650.540.400.47
  - 3 Belgium 0.740.690.580.660.530.36
  - 4 Canada 0.720.640.640.660.460.58
  - 5 Cyprus 0.880.880.630.970.530.54
  - 6 Czech Republic 0.740.250.250.210.230.97
  - 7 Denmark 0.730.630.500.650.520.42
  - 8 Estonia 0.740.350.400.260.220.82
  - 9 Finland 0.680.670.700.730.630.45
  - 10 France 0.770.580.650.560.590.39
  - 11 Germany 0.610.800.700.470.630.56
  - 12 Greece 0.640.610.630.880.510.46
  - 13 Hong Kong SAR 0.820.790.260.790.300.25
  - 14 Iceland 0.510.660.580.310.590.51
  - 15 Ireland 0.770.150.540.370.690.56
  - 16 Israel 0.380.820.250.400.740.23
  - 17 Italy 0.640.550.600.570.640.63
  - 18 Japan 0.700.640.520.560.720.49
  - 19 Korea 0.330.840.650.300.540.60
  - 20 Luxembourg 0.800.220.220.190.160.87
  - 21 Malta 0.890.220.160.230.120.75
  - 22 Netherlands 0.750.770.930.680.680.70
  - 23 New Zealand 0.710.540.860.750.680.59
  - 24 Norway 0.610.660.800.620.490.56
  - 25 Portugal 0.570.510.660.270.440.61
  - 26 Singapore 0.300.670.660.430.460.47
  - 27 Slovak Republic 0.750.790.950.870.770.82
  - 28 Slovenia 0.280.220.360.890.880.83
  - 29 Spain 0.670.500.700.610.740.53
  - 30 Sweden 0.570.510.630.630.600.52
  - 31 Switzerland 0.720.750.610.600.630.60
  - 32 United Kingdom 0.700.400.550.490.610.44
  - 33 United States 0.890.670.670.720.660.47
- Summary statistics (AM):
  - mean0.650.570.580.560.550.56
  - median0.700.630.630.600.590.54
  - st. dev.0.180.200.190.210.180.17

### Synchronization of financial cycles within a country (EM) (Table 2B)
- Per-country (selected lines preserved exactly as in source):
  - 1 Argentina 0.64 0.39 0.500.290.550.45
  - 2 Brazil 0.660.530.42 0.69 0.080.25
  - 3 Bulgaria 0.820.260.880.220.870.28
  - 4 China 0.51 0.700.45 0.70 0.200.31
  - 5 Colombia 0.53 0.58 0.440.21 0.820.09
  - 6 Croatia 0.100.850.930.13 0.11 0.88
  - 7 Hungary 0.740.350.94 0.30 0.750.32
  - 8 India 0.41 0.580.41 0.28 0.650.42
  - 9 Indonesia 0.260.290.82 0.630.19 0.35
  - 10 Lithuania 0.880.84 0.930.920.87 0.83
  - 11 Malaysia 0.29 0.550.320.37 0.830.31
  - 12 Mexico 0.620.58 0.560.840.880.78
  - 13 Philippines 0.820.220.220.220.31 0.80
  - 14 Poland 0.650.500.570.32 0.350.76
  - 15 Russia 0.320.240.880.840.250.17
  - 16 Serbia 0.220.790.870.180.240.86
  - 17 South Africa 0.380.750.320.270.880.23
  - 18 Thailand 0.83 0.710.770.780.710.70
  - 19 Turkey 0.400.510.530.690.870.73
  - 20 Ukraine 0.820.750.290.870.15 0.22
  - 21 Latvia 0.170.800.410.120.720.25
  - 22 Kazakhstan 0.310.80 0.320.260.940.20
  - 23 Romania 0.770.88 0.270.820.120.22
  - 24 Vietnam 0.090.870.200.22 0.830.17
- Summary statistics (EM):
  - mean0.510.600.55 0.470.550.44
  - median0.520.580.480.310.680.32
  - st. dev.0.250.220.260.280.320.27

### Synchronization of financial and real cycles within a country (AM) (Table 3A)
- Per-country entries (selected lines preserved exactly as in source; table groups GDP with: creditpropertyequityLTDR, Consumption with: creditpropertyequityLTDR, Investment with: creditpropertyequityLTDR):
  - 1 Australia 0.880.540.480.550.560.720.670.780.400.700.630.60
  - 2 Austria 0.820.210.570.590.880.200.510.580.870.200.570.69
  - 3 Belgium 0.530.610.600.430.530.650.550.460.610.680.630.47
  - 4 Canada 0.920.730.690.580.920.740.700.580.750.660.740.64
  - 5 Czech Republic 0.640.850.330.330.170.400.760.780.760.820.350.32
  - 6 Denmark 0.530.690.550.560.640.670.630.420.630.580.630.49
  - 7 Estonia 0.460.250.850.920.930.770.360.390.350.260.910.83
  - 8 Finland 0.690.680.680.750.450.620.430.660.400.610.420.64
  - 9 France 0.780.720.630.560.790.720.670.520.680.790.650.45
  - 10 Germany 0.690.440.740.540.780.510.750.550.630.510.590.61
  - 11 Greece 0.700.780.730.550.600.630.600.560.600.650.630.52
  - 12 Hong Kong SAR 0.770.760.780.180.770.780.680.310.780.800.710.25
  - 13 Ireland 0.140.370.780.590.960.740.180.510.310.540.800.72
  - 14 Israel 0.180.720.180.910.830.350.790.230.740.310.850.23
  - 15 Italy 0.740.610.520.650.740.630.580.650.640.610.700.79
  - 16 Japan 0.730.530.650.330.700.530.690.330.560.580.600.65
  - 17 Korea 0.870.340.830.630.870.270.880.630.790.490.770.55
  - 18 Luxembourg 0.200.070.870.830.240.110.860.850.260.220.800.74
  - 19 Netherlands 0.700.680.660.630.870.800.760.790.800.670.740.76
  - 20 New Zealand 0.640.750.850.640.800.650.430.690.540.710.910.58
  - 21 Norway 0.820.590.620.850.770.600.590.830.530.550.510.42
  - 22 Portugal 0.700.730.310.580.740.740.300.600.470.330.820.57
  - 23 Singapore 0.780.370.810.580.790.370.780.630.580.600.590.47
  - 24 Slovak Republic 0.780.780.890.780.270.150.260.270.820.810.840.82
  - 25 Slovenia 0.430.780.710.810.910.250.200.300.880.320.270.34
  - 26 Spain 0.790.660.590.650.640.740.690.670.820.710.590.66
  - 27 Sweden 0.630.670.680.540.590.650.700.540.440.600.600.59
  - 28 Switzerland 0.680.580.610.560.710.610.720.550.840.680.770.60
  - 29 United Kingdom 0.850.730.500.570.850.750.500.570.610.680.520.50
  - 30 United States 0.840.840.740.560.820.820.750.540.800.830.770.64
- Summary statistics (AM):
  - mean0.660.600.650.610.700.570.600.560.630.580.660.57
  - median0.700.670.670.580.770.640.670.560.630.610.640.59

### Synchronization of financial and real cycles within a country (EM) (Table 3B)
- Per-country entries (selected lines preserved exactly as in source):
  - 1 Argentina 0.420.230.780.520.400.250.770.510.420.230.800.52
  - 2 Brazil 0.370.100.330.880.360.120.290.860.420.180.280.81
  - 3 China 0.590.100.280.850.990.510.690.450.680.190.370.77
  - 4 Hungary 0.49 0.300.790.460.510.310.790.470.500.360.840.45
  - 5 India 0.550.120.710.410.850.260.690.320.640.160.750.45
  - 6 Indonesia 0.930.290.360.770.890.330.350.730.500.680.680.50
  - 7 Malaysia 0.750.260.640.170.220.850.380.760.190.810.430.79
  - 8 Mexico 0.730.830.720.750.680.850.740.770.640.800.780.78
  - 9 Poland 0.34 0.120.690.710.340.120.690.710.640.840.380.36
  - 10 Russia 0.920.300.260.870.940.310.240.880.350.920.880.26
  - 11 South Africa 0.70 0.400.650.320.820.390.720.310.690.480.500.46
  - 12 Thailand 0.740.740.830.830.780.760.820.860.780.780.860.81
  - 13 Turkey 0.780.240.370.350.660.120.350.190.440.800.730.86
- Summary statistics (EM):
  - mean0.640.310.570.610.650.400.580.600.530.560.640.60
  - median 0.700.260.650.710.680.310.690.710.500.680.730.52

### Comparison of cycle length to Claessens et al. (2011a and 2011b) (Appendix 5)
- Commonalities with Claessens et al.:
  - Median length for the equity price cycle in the range of 3 years.
  - Median length for the property price cycle in the range of 4 years.
- Methodological adjustments made for comparability in Figure 1:
  - (i) estimate median length across all turning points, rather than within each country first and then across countries;
  - (ii) allow incomplete cycles in the turning point procedure;
  - (iii) stop sample estimation in 2007Q4 as in Claessens;
  - (iv) match Claessens’ country sample (exact match for AM; for EM, Claessens has more data on Latin America, this sample has more on Eastern Europe).
- Key differences from Claessens et al.:
  - Claessens finds median business cycle length under two years; this analysis finds business cycle closer to six years, with none of the countries having average GDP cycle length below three years.
  - Only twenty percent of the entire sample of turning points has upswing length of 1 year (Appendix 3, Figure 2).
  - Claessens conclude financial cycles are longer than business cycles; this analysis finds cycles in credit and real activity are of similar length, while cycles in asset prices are shorter.
  - The difference likely stems from Claessens underestimating the length of the business cycle and from averaging methodology.
- Averaging methodology effect:
  - Preferred approach: find typical length in a country then average across countries (equal weight per country).
  - Alternative (pooling turning points) leads to downward bias because countries with more frequent (shorter) cycles dominate.
  - Figure 1 shows the green line (average across turning points) shifting below the red line (preferred results) when averaging method changes.

### Robustness checks for EWS: AUROC estimations (Appendix 6)
- How to read charts:
  - AUROC < 0.7 indicates sub-optimal performance.
  - AUROC between 0.7 and 0.8 indicates good performance.
  - AUROC > 0.8 indicates excellent performance.
  - AUROC < 0.5 implies model may be predicting crises in the opposite direction (i.e., more negative indicator values may signal higher crisis probability).
  - Both very large positive and very large negative financial cycle gaps can signal higher crisis risk.
- Figures and panels:
  - Figure 1: Two-Sided Filters (Overheating)
    - AUROC panels for Advanced Economies and Emerging Economies, showing indicators (Equity, Output gap, Credit: Total credit, Credit in percent of GDP, LTDR, Property, Inflation - target) across horizons: 6 years before crisis, 5 years, 4 years, 3 years, 2 years, 1 year.
    - Separate AUROC panels for Schularick and BIS credit gap for AM and EM.
  - Figure 2: One-Sided Filters (Overheating)
    - AUROC panels analogous to Figure 1 for one-sided filters.
    - Includes BIS credit gap and Schularick benchmarks.
  - Figure 3: Two-Sided Filters (Full Sample)
    - Signal-to-Noise Ratio panels ( (1−T1−T2)/(T1+T2) ) for Schularick and BIS credit gap for AM and EM.
    - AUROC panels for full sample across indicators and horizons.
  - Figure 4: One-Sided Filters (Full Sample)
    - AUROC and Signal-to-Noise Ratio panels for one-sided filters across AM and EM.
- Interpretation guidance preserved from source: use AUROC and STN to assess indicator predictive performance over varying horizons; thresholds for interpretation as stated above.

*Source: Appendix 3, Appendix 4, Appendix 5, Appendix 6 (figures and tables) of the supplied IMF content unit.*

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