## _wp1198

## Source details

**Canonical URL:** [_wp1198](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp1198.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp1198.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp1198.pdf.json)

---

### I. INTRODUCTION — purpose and key takeaways
- Purpose: Evaluate nowcasts and one-step ahead forecasts of annualized quarterly real GDP growth for ten Latin American countries: Argentina, Brazil, Chile, Colombia, Ecuador, Dominican Republic, Mexico, Peru, Uruguay, and Venezuela.
- Coverage: The ten selected Latin American countries account for 94 percent of the regional GDP for Latin America.
- Main empirical findings:
  - Models that use monthly data generally outperform an AR model that uses only quarterly data.
  - Forecasts become more accurate as more information arrives within each quarter, despite higher noise in monthly data.
  - The dynamic factor model (DFM) consistently produces more accurate nowcasts and forecasts relative to other model specifications across most countries studied.
  - External indicators, such as commodity prices and U.S. variables, improve forecast accuracy for most Latin American countries.
- Motivation: Publication lags are significant and longer in emerging markets; timely short-term forecasts are crucial for macroeconomic policy decisions and central bank projections.

### II. MODELS SPECIFICATION AND ESTIMATION — models evaluated and estimation approach
- Five model specifications evaluated:
  - Baseline quarterly autoregressive model (AR(p)):
    - y^Q_t = c + sum_{i=1}^p β_i y^Q_{t−i} + ε^Q_t, with ε^Q_t ~ N(0, σ^2_ε). Lag length p selected by SIC.
    - Based only on quarterly GDP growth; AR(p) forecasts remain fixed for three consecutive months until new quarterly GDP data arrives.
  - Pooled bridge equations:
    - Step 1: Forecast each monthly indicator x_{i,t} with univariate AR(p_i).
    - Step 2: Aggregate to quarterly x^Q_{i,t} = x_{i,t} + x_{i,t−1} + x_{i,t−2}; estimate y^Q_{i,t} on lagged quarterly aggregates.
    - Step 3: Combine k indicator-based forecasts using weights proportional to inverse RMSE.
    - For BRIDGE: Uses a set of 10 monthly indicators with the highest contemporaneous correlation with quarterly GDP growth. Including more than 10 variables generally led to deterioration in forecast accuracy.
  - Pooled bivariate VARs (BIVAR):
    - Interpolate quarterly GDP to monthly frequency y^I_t; estimate bivariate VARs Z_{i,t} = [y^I_t x_{i,t}]' for each indicator; combine forecasts as in bridge equations.
    - Uses the same set of monthly indicators as BRIDGE.
  - Bayesian VAR (BVAR):
    - Z_t = c + sum_{s=1}^p β_s Z_{t−s} + ε_t, ε_t ~ (0, Ψ). Prior follows Litterman (Minnesota) formulation.
    - Small BVAR (BVAR) contains: real GDP growth, inflation, terms of trade, short-term interest rates, and stock prices.
    - Large BVAR (LBVAR) includes the entire set of monthly indicators.
    - Overall prior tightness μ1 set such that the average R2 across all equations is fixed at 0.6 to avoid “over-fitting”.
    - The BVARs contain 6 lags with autoregressive prior std. deviations selected using AR(6) error std. devs.
  - Dynamic factor model (DFM):
    - Measurement: X_t = Λ F_t + ε_t, ε_t ~ N(0, Ψ).
    - Dynamics: F_t = sum_{s=1}^p A_s F_{t−s} + B u_t, u_t ~ N(0, Σ).
    - Estimation: two-step Doz et al. (2007) procedure (principal components on balanced panel; Kalman Smoother on full panel).
    - Number of static factors r chosen so marginal improvement in R2 of regression of real GDP growth on the common component (quarterly) is less than 0.025.
    - Number of dynamic factors determined using Bai and Ng (2007) information criteria.

- Estimation practice across all models:
  - Re-estimate all model parameters, re-select lag lengths and hyperparameters, and re-run variable-selection algorithms in each month of the forecast evaluation period using the available quasi-real-time dataset.

### III. DATA — sample construction, indicators, and preprocessing
- Countries: Argentina, Brazil, Chile, Colombia, Dominican Republic, Ecuador, Mexico, Peru, Uruguay, Venezuela — represent 94 percent of regional GDP for Latin America.
- Coverage and heterogeneity:
  - Total number of selected indicators ranges from 81 (Dominican Republic) to 149 (Chile).
  - Activity surveys available only for Argentina, Brazil, Chile, and Mexico.
  - Good coverage for trade and financial condition indicators across most countries.
  - Examples of heterogeneity: some countries show double digit average inflation over the past decade; annual declines in real GDP exceeding five percent are not uncommon.
- Commodities and external indicators:
  - 11 commodity price series: Petroleum, Copper, Soy, Gold, Metals, Industrials, Food, Fats and oils, Coffee, Sugar, and Livestock.
  - 8 U.S. indicators: industrial production, 3 retail sales series, ISM survey for manufacturing, unemployment rate, employment, and consumer confidence (Conference Board).
- Sample periods and effective series (effective number of series used for forecast evaluation):
  - Brazil: 1995Q1 — 2010Q1; Forecast evaluation 2000Q1; n.o series 48
  - Mexico: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 129
  - Argentina: 2003Q1 — 2010Q1; Forecast evaluation 2008Q1; n.o series 102
  - Chile: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 150
  - Colombia: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 141
  - Peru: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 124
  - Ecuador: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 108
  - Uruguay: 2001Q1 — 2010Q1; Forecast evaluation 2006Q1; n.o series 134
  - Venezuela: 2004Q2 — 2010Q1; Forecast evaluation 2008Q1; n.o series 117
  - Dom. Rep.: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 147
- Pre-filtering and transformations:
  - Seasonal adjustment using X11; missing values linearly interpolated; beginning-of-sample missing observations backdated using a DFM set to explain 60 percent of variation.
  - Quarterly series interpolated into monthly by repeating quarterly observation for each month; daily series averaged into monthly.
  - Log quarterly differences ln(x_t) − ln(x_{t−3}) for non-stationary series except those measured in percentages or that can take negative values; those are differenced x_{i,t} − x_{i,t−3}.
  - Series changing less than 10 percent of the time discarded.
  - Series with less than 3 years of data discarded.
  - Series not released in the past year discarded.
  - Outliers (>6 times interquartile range) replaced with next admissible value.
  - Data source: Haver database (data downloaded on June 13, 2010).
  - Appendix I contains further detail on data transformation.

### IV. REAL-TIME FORECAST EXPERIMENT — design and evaluation
- Real-time stylization:
  - At arbitrary point ν within quarter (end of month 1, 2, or 3), information set Ω^n_ν contains most recent data for n monthly time series; some variables available up to month ν, others only up to month ν−1.
  - Forecaster projects y_{ν+h} for h = 0, ..., H based on Ω^n_ν: ŷ_{ν+h} = Proj[ GDP | Ω^n_ν ].
  - Typical timing: GDP data usually released in month t+3 after quarter end.
- Quasi-real-time data construction:
  - Use Haver Analytics release dates to compile quasi-real-time datasets by manipulating most recent vintages; these mimic data available to forecasters at beginning of each month but do not account for data revisions.
- Forecasting schedule and comparison:
  - Compute three nowcasts and three one-step-ahead forecasts each quarter using information available on the first day of each month of the quarter.
  - Compare each month’s nowcast/forecast of annualized quarterly real GDP growth with the latest final published GDP outturn and compute RMSE for each of the five models.
- Variable selection and parameter choice:
  - In each month of the forecast evaluation period: re-estimate model parameters, re-select lag lengths and hyperparameters, and re-run variable-selection algorithms given the available quasi-real-time dataset.

### Model specifications and data choices (additional details)
- AR(p) baseline:
  - Based only on quarterly GDP growth; AR(p) forecasts remain fixed for three consecutive months until new quarterly GDP data arrives.
- BRIDGE and BIVAR:
  - Monthly indicator selection: 10 highest contemporaneous correlations with quarterly GDP growth.
  - Missing values linearly interpolated.
- BVARs:
  - Overall prior tightness μ1 set so average R2 across equations = 0.6.
- DFM:
  - Number of static factors r: marginal improvement threshold 0.025 for R2 of GDP regression on common component.
  - Number of dynamic factors q: chosen by Bai and Ng (2007) information criteria.
  - Table 5 (in source) summarizes DFM parameters and percentage variation explained by common component.

### NOWCAST ACCURACY — key findings and exact figures (selected)
- General findings:
  - Models using monthly data generally outperform the quarterly AR model.
  - Nowcasts improve as more information arrives within the quarter (RMSE month 3 < month 1).
  - DFM consistently produces more accurate nowcasts relative to other specifications, except for Argentina and Peru (Argentina: BIVAR preferred; Peru: BRIDGE slightly better).
  - Large BVAR (LBVAR) is generally worst performer despite using same dataset as DFM.
  - Weighted-average nowcasts generally perform well but sometimes have larger errors than best single model.

- Absolute AR RMSE (month 1) and DFM relative RMSE (month 1) for annualized quarterly real GDP growth (Table 6, month 1):
  - Brazil: AR 4.97 ; DFM 0.74
  - Mexico: AR 8.24 ; DFM 0.68
  - Argentina: AR 4.81 ; DFM 1.15
  - Chile: AR 5.18 ; DFM 0.74
  - Colombia: AR 5.29 ; DFM 0.77
  - Peru: AR 4.26 ; DFM 0.93
  - Ecuador: AR 4.67 ; DFM 0.90
  - Uruguay: AR 5.60 ; DFM 0.77
  - Venezuela: AR 10.91 ; DFM 0.75
  - Dominican Republic: AR 7.93 ; DFM 0.86

- Selected relative RMSE patterns (Table 6, month 3 examples):
  - Brazil month 3: DFM 0.67 ; BRIDGE 0.62 ; BIVAR 0.68 ; BVAR 0.73 ; LBVAR 2.40 ; INVMSE 0.67 ; MEAN 0.82
  - Mexico month 3: DFM 0.69 ; BRIDGE 0.72 ; BIVAR 0.71 ; BVAR 0.73 ; LBVAR 0.93 ; INVMSE 0.74 ; MEAN 0.74
  - Argentina month 3: DFM 1.18 ; BRIDGE 1.20 ; BIVAR 0.93 ; BVAR 1.18 ; LBVAR 1.29 ; INVMSE 1.09 ; MEAN 1.00

### ONE-STEP-AHEAD FORECAST ACCURACY — key findings and exact figures (selected)
- Main findings:
  - One-step ahead forecast errors are larger than nowcast errors across all model specifications.
  - Additional monthly information generally helps one-step ahead forecasts for most countries, with exceptions: Argentina and Ecuador.
  - DFM again produces more accurate one-step ahead forecasts for most countries; BVARs tend to be more accurate for Mexico; BIVARs tend to be more accurate for Argentina.

- Absolute AR RMSE (one-step ahead, month 1) and DFM relative RMSE (Table 7, month 1):
  - Brazil: AR 4.91 ; DFM 0.91
  - Mexico: AR 9.38 ; DFM 0.77
  - Argentina: AR 6.30 ; DFM 1.09
  - Chile: AR 5.81 ; DFM 0.76
  - Colombia: AR 4.36 ; DFM 1.05
  - Peru: AR 5.05 ; DFM 0.86
  - Ecuador: AR 5.06 ; DFM 1.10
  - Uruguay: AR 5.83 ; DFM 0.97
  - Venezuela: AR 10.15 ; DFM 1.10
  - Dominican Republic: AR 7.77 ; DFM 1.00

- Notable one-step relative results:
  - Mexico one-step month 1: BVAR 0.63 (relative RMSE) — BVARs tend to be more accurate for Mexico.
  - Dominican Republic month 1: LBVAR 20.83 (relative RMSE) indicating extreme deterioration from LBVAR in that case.

### DYNAMIC FACTOR MODEL (DFM) — performance, interpretation, and external indicators
- DFM advantages:
  - Extracts timely information from a large set of indicators using a small handful of common factors.
  - Avoids “over-fitting” by using few factors.
  - Kalman Filter signal extraction helps separate signal from noisy monthly series.
- Empirical behavior:
  - Estimated common component from DFM generally tracks quarterly GDP growth closely and captures the sharp contraction over the crisis period.
  - Monthly growth indicator (seven-month moving average of estimated common component) at end of August 2010 shows slowdown in pace of expansion recently among Latin American countries, particularly Brazil, Mexico, Colombia; contraction synchronized around Q3 2008; recovery more synchronized with North America except for Venezuela.
- Usefulness of external indicators for DFM nowcasts:
  - Experiment: re-run real-time forecasting excluding external indicators (commodity prices and U.S. variables); report RMSE ratio = RMSE without external indicators / RMSE with external indicators. Ratio > 1 indicates external indicators improve nowcast accuracy.
  - RMSE ratios for DFM (Nowcast, month 1 / month 2 / month 3):
    - Brazil: 1.09 / 1.06 / 1.04
    - Mexico: 1.00 / 1.00 / 1.01
    - Argentina: 0.91 / 1.06 / 0.90
    - Chile: 1.09 / 1.04 / 1.08
    - Colombia: 1.07 / 1.08 / 1.04
    - Peru: 0.94 / 0.94 / 0.81
    - Ecuador: 1.15 / 1.14 / 1.15
    - Uruguay: 1.01 / 1.03 / 1.05
    - Venezuela: 0.89 / 1.23 / 0.94
    - Dominican Republic: 1.05 / 1.03 / 1.04
  - Interpretation:
    - For six of ten countries — Brazil, Chile, Colombia, Ecuador, Uruguay, Dominican Republic — removing external indicators leads to deterioration in nowcast accuracy (ratios > 1).
    - Mexico: RMSE largely unchanged (ratios ≈ 1).
    - Argentina, Peru, Venezuela: nowcasting performance improves by removing U.S. and commodity indicators (ratios < 1 in some months), suggesting weaker links to U.S. and commodity price developments for these countries in the sample.
    - Caution: relatively short evaluation period for some countries (Argentina, Venezuela) may affect interpretation.

### CONCLUSIONS AND IMPLICATIONS
- Main conclusions:
  - Models that incorporate monthly data outperform a quarterly AR model; nowcasts improve as more monthly information arrives within the quarter.
  - DFM produces more accurate nowcasts and short-term forecasts relative to other model specifications in most cases.
  - The DFM’s strength comes from extracting common signals via few factors and the Kalman Filter’s signal/noise separation.
  - External indicators (commodity prices, U.S. variables) improve forecast accuracy for most Latin American countries but not all.
- Caveats and avenues for future work:
  - Analysis assumes individual countries are independent except via external conditions; inter-regional dependence could be explored in future studies.
  - Short evaluation periods for some countries imply caution in interpreting results for those cases.

*Source: IMF Working Paper — content unit: _wp1198 - 1. The baseline AR(p) model is only based on quarterly GDP growth. This implies that (PDF chapter/section).*

### References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   24

### References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   24

### I. INTRODUCTION — purpose and key takeaways
- Purpose: Evaluate nowcasts and one-step ahead forecasts of annualized quarterly real GDP growth for ten Latin American countries: Argentina, Brazil, Chile, Colombia, Ecuador, Dominican Republic, Mexico, Peru, Uruguay, and Venezuela.
- Coverage: The ten selected Latin American countries account for 94 percent of the regional GDP for Latin America.
- Main empirical findings:
  - Models that use monthly data generally outperform an AR model that uses only quarterly data.
  - Forecasts become more accurate as more information arrives within each quarter, despite higher noise in monthly data.
  - The dynamic factor model (DFM) consistently produces more accurate nowcasts and forecasts relative to other model specifications across most countries studied.
  - External indicators, such as commodity prices and U.S. variables, improve forecast accuracy for most Latin American countries.
- Motivations:
  - Publication lags are significant and longer in emerging markets (example: first flash estimate of GDP in the U.S. is available four weeks after the quarter ends, while GDP for Brazil is not released until 10 weeks after the end of the quarter).
  - Timely short-term forecasts are crucial for macroeconomic policy decisions and central bank projections.

### II. MODELS SPECIFICATION AND ESTIMATION — models evaluated and estimation approach
- Models evaluated (five specifications):
  - Baseline quarterly autoregressive model (AR(p)):
    - y^Q_t = c + sum_{i=1}^p β_i y^Q_{t−i} + ε^Q_t, with ε^Q_t ~ N(0, σ^2_ε). Lag length p selected by SIC.
  - Pooled bridge equations:
    - Step 1: Forecast each monthly indicator x_{i,t} with univariate AR(p_i): x_{i,t} = μ_i + sum_{s=1}^{p_i} β_s x_{i,t−s} + ε_{i,t}.
    - Step 2: Aggregate to quarterly x^Q_{i,t} = x_{i,t} + x_{i,t−1} + x_{i,t−2}; estimate y^Q_{i,t} = c_i + sum_{s=1}^{q_i} β_s x^Q_{i,t−s} + ε^Q_{i,t}. Lag lengths p_i and q_i chosen by SIC.
    - Step 3: Combine k indicator-based forecasts y^Q_{i,t+h|t} into y^Q_{t+h|t} using weights proportional to inverse RMSE: y^Q_{t+h|t} = sum_{i=1}^k (RMSE_{i,h} / sum_{j=1}^k RMSE_{j,h}) y^Q_{i,t+h|t}.
  - Pooled bivariate VARs:
    - Interpolate quarterly GDP to monthly frequency y^I_t, set Z_{i,t} = [y^I_t x_{i,t}]', and estimate Z_{i,t} = c_i + sum_{s=1}^{p_i} β_s Z_{i,t−s} + ε_{i,t}. Lag length p_i by SIC. Forecast monthly GDP growth y^I_{t+h|t} using Kalman filter; combine forecasts as in bridge equations.
  - Bayesian VAR (BVAR):
    - Z_t = c + sum_{s=1}^p β_s Z_{t−s} + ε_t, ε_t ~ (0, Ψ). Prior follows Litterman (Minnesota) formulation:
      - E[(β_k)_{ij}] = δ_{i,j=i, k=1}; V[(β_k)_{ij}] = (1/(μ_1) * 1/k^λ * σ_i σ_j)^2.
      - In application, data are stationary so δ_i = 0 for all i. Hyper-parameter μ_1 controls tightness; μ_1 = 1 imposes prior exactly, μ_1 = 0 removes prior influence.
    - Implemented via dummy observations; posterior computed by OLS on augmented VAR. Interpolated GDP included; conditional forecasts via Kalman filter.
  - Dynamic factor model (DFM):
    - Measurement: X_t = Λ F_t + ε_t, ε_t ~ N(0, Ψ).
    - Dynamics: F_t = sum_{s=1}^p A_s F_{t−s} + B u_t, u_t ~ N(0, Σ).
    - Estimation (two-step Doz et al. (2007) procedure):
      1. Estimate common factors by principal components on latest complete balanced panel; estimate Λ̂ and Ψ̂ by OLS; estimate Â_1, ..., Â_p and Σ̂ by OLS with p chosen by SIC.
      2. Apply Kalman Smoother to entire (possibly unbalanced) panel using parameters from step 1 and re-estimate factors; h-step ahead forecasts of GDP growth via Kalman filter.
    - Number of static and dynamic factors r and q chosen to balance fit to quarterly GDP and over-parameterization.
- Estimation practice across all models:
  - Re-estimate all model parameters, re-select lag lengths and hyperparameters, and re-run variable-selection algorithms in each month of the forecast evaluation period using the available quasi-real-time dataset.

### III. DATA — sample construction, indicators, and preprocessing
- Countries: Argentina, Brazil, Chile, Colombia, Dominican Republic, Ecuador, Mexico, Peru, Uruguay, Venezuela — represent 94 percent of regional GDP for Latin America.
- Data coverage and heterogeneity:
  - Total number of selected indicators ranges from 81 (Dominican Republic) to 149 (Chile).
  - Activity surveys available only for Argentina, Brazil, Chile, and Mexico.
  - Good coverage for trade and financial condition indicators across most countries.
  - Regional heterogeneity examples: some countries show double digit average inflation over the past decade, others have inflation comparable to the U.S.; annual declines in real GDP exceeding five percent are not uncommon.
- Commodities and external indicators:
  - Include 11 commodity price series: Petroleum, Copper, Soy, Gold, Metals, Industrials, Food, Fats and oils, Coffee, Sugar, and Livestock.
  - Include 8 U.S. indicators (industrial production, 3 retail sales series, ISM survey for manufacturing, unemployment rate, employment, and consumer confidence (Conference Board)).
- Sample periods and effective series (Table 3 extract — sample starts, sample ends, forecast evaluation, n.o series):
  - Brazil: 1995Q1 — 2010Q1; Forecast evaluation 2000Q1; n.o series 48
  - Mexico: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 129
  - Argentina: 2003Q1 — 2010Q1; Forecast evaluation 2008Q1; n.o series 102
  - Chile: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 150
  - Colombia: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 141
  - Peru: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 124
  - Ecuador: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 108
  - Uruguay: 2001Q1 — 2010Q1; Forecast evaluation 2006Q1; n.o series 134
  - Venezuela: 2004Q2 — 2010Q1; Forecast evaluation 2008Q1; n.o series 117
  - Dom. Rep.: 2000Q1 — 2010Q1; Forecast evaluation 2005Q1; n.o series 147
  - (Note: table entry heading indicates "(1) This represents the effective number of series used for the forecast evaluation.")
- Pre-filtering and transformations:
  - Extensive pre-filtering: seasonal adjustment, removal of very short samples, backdating of series with missing values at the beginning, outlier correction.
  - After pre-filtering, all data measured monthly.
  - Stationarity transformations: log quarterly differences ln(x_t) − ln(x_{t−3}) for non-stationary series except those measured in percentages or that can take negative values; those are differenced x_{i,t} − x_{i,t−3}.
  - Appendix I contains further detail on data transformation.

### IV. REAL-TIME FORECAST EXPERIMENT — design and evaluation
- Real-time problem stylization:
  - At arbitrary point ν within quarter (end of month 1, 2, or 3), information set Ω^n_ν contains most recent data for n monthly time series.
  - Some variables (Ω^n1_ν) are available up to month ν (e.g., asset prices), while others (Ω^n2_ν) are available only up to month ν−1 (e.g., industrial production).
  - Forecaster projects y_{ν+h} for h = 0, ..., H based on Ω^n_ν: ŷ_{ν+h} = Proj[ GDP | Ω^n_ν ].
  - Stylized data panel example (X = available, O = missing):
    - Month ν−2: Activity X, Surveys X, Asset prices X, Foreign O, GDP O
    - Month ν−1: Activity O, Surveys X, Asset prices X, Foreign X, GDP O
    - Month ν: Activity O, Surveys O, Asset prices X, Foreign O, GDP O
  - Typical timing: GDP data usually released in month t+3 after quarter end.
- Quasi-real-time data construction:
  - Use Haver Analytics release dates to compile quasi-real-time datasets by manipulating most recent vintages; these mimic data available to forecasters at beginning of each month but do not account for data revisions.
- Forecasting schedule and comparison:
  - Compute three nowcasts and three one-step-ahead forecasts each quarter using information available on the first day of each month of the quarter.
  - Compare each month’s nowcast/forecast of annualized quarterly real GDP growth with the latest final published GDP outturn and compute RMSE for each of the five models.
- Variable selection and parameter choice:
  - In each month of the forecast evaluation period: re-estimate model parameters, re-select lag lengths and hyperparameters, and re-run variable-selection algorithms given the available quasi-real-time dataset.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp1198.pdf*

### 1. The baseline AR(p) model is only based on quarterly GDP growth. This implies that

### 1. The baseline AR(p) model is only based on quarterly GDP growth. This implies that

### Model specifications and data choices
- AR(p) baseline:
  - Based only on quarterly GDP growth; AR(p) forecasts remain fixed for three consecutive months until new quarterly GDP data arrives.

- Pooled bridge equation (BRIDGE):
  - Uses a set of 10 monthly indicators with the highest contemporaneous correlation with quarterly GDP growth and available prior to GDP release.
  - Including more than 10 variables generally led to deterioration in forecast accuracy for pooled bridge equations and pooled bivariate VAR forecasts.

- Pooled bivariate VAR (BIVAR):
  - Uses the same set of monthly indicators as BRIDGE.

- Bayesian VARs:
  - Small BVAR (BVAR) contains: real GDP growth, inflation, terms of trade, short-term interest rates, and stock prices.
  - Large BVAR (LBVAR) includes the entire set of monthly indicators.
  - Overall prior tightness μ1 set such that the average R2 across all equations is fixed at 0.6 to avoid “over-fitting”.
  - The BVARs contain 6 lags with a specified prior setup (autoregressive prior std. deviations selected using AR(6) error std. devs).

- Dynamic factor model (DFM):
  - Number of static factors (r) selected so marginal improvement in R2 of regression of real GDP growth on the common component (quarterly) is less than 0.025.
  - Number of dynamic factors determined using Bai and Ng (2007) information criteria.
  - Table 5 (in source) summarizes DFM parameters and percentage variation explained by the common component for GDP growth and entire data set across countries.

### Data and preprocessing highlights
- Monthly indicator selection for BRIDGE/BIVAR: 10 highest contemporaneous correlations with quarterly GDP growth.
- Missing values linearly interpolated.
- Seasonal adjustment using X11.
- Quarterly series interpolated into monthly by repeating quarterly observation for each month; daily series averaged into monthly.
- Log differences taken for non-stationary series (four quarter or twelve month) except series measured in percentages or that can take negative values (differences taken).
- Series changing less than 10 percent of the time discarded.
- Series with less than 3 years of data discarded.
- Series not released in the past year discarded.
- Outliers (>6 times interquartile range) replaced with next admissible value.
- Beginning-of-sample missing observations backdated using a DFM with number of factors set to explain 60 percent of variation.
- Data source: Haver database (data downloaded on June 13, 2010).

### Nowcast evaluation design
- Five model specifications evaluated per country: AR model; pooled bridge equation; pooled bivariate VAR; small and large BVARs; DFM.
- Two weighted-average forecasts computed:
  - INVMSE: recursively computed inverse RMSE weights.
  - MEAN: simple average across the six models.
- Nowcasts evaluated for annualized quarterly real GDP growth; month index indicates timing within quarter (month 1 = nowcast of previous quarter on first day of month).

### Key nowcast accuracy findings (summary)
- General findings:
  - Models using monthly data generally outperform the quarterly AR model.
  - Nowcasts improve as more information arrives within the quarter (RMSE month 3 < month 1).
  - DFM consistently produces more accurate nowcasts relative to other specifications, except for Argentina and Peru (Argentina: BIVAR preferred; Peru: BRIDGE slightly better).
  - Large BVAR (LBVAR) is generally worst performer despite using same dataset as DFM.
  - Weighted-average nowcasts generally perform well but sometimes have larger errors than best single model.

- Absolute AR RMSE (month 1) and DFM relative RMSE (month 1) for annualized quarterly real GDP growth (Table 6, month 1):
  - Brazil: AR 4.97 ; DFM 0.74
  - Mexico: AR 8.24 ; DFM 0.68
  - Argentina: AR 4.81 ; DFM 1.15
  - Chile: AR 5.18 ; DFM 0.74
  - Colombia: AR 5.29 ; DFM 0.77
  - Peru: AR 4.26 ; DFM 0.93
  - Ecuador: AR 4.67 ; DFM 0.90
  - Uruguay: AR 5.60 ; DFM 0.77
  - Venezuela: AR 10.91 ; DFM 0.75
  - Dominican Republic: AR 7.93 ; DFM 0.86

- Selected relative RMSE patterns (Table 6, month 3 examples):
  - Brazil month 3: DFM 0.67 ; BRIDGE 0.62 ; BIVAR 0.68 ; BVAR 0.73 ; LBVAR 2.40 ; INVMSE 0.67 ; MEAN 0.82
  - Mexico month 3: DFM 0.69 ; BRIDGE 0.72 ; BIVAR 0.71 ; BVAR 0.73 ; LBVAR 0.93 ; INVMSE 0.74 ; MEAN 0.74
  - Argentina month 3: DFM 1.18 ; BRIDGE 1.20 ; BIVAR 0.93 ; BVAR 1.18 ; LBVAR 1.29 ; INVMSE 1.09 ; MEAN 1.00

### One-step-ahead forecast accuracy (summary)
- Main findings:
  - One-step ahead forecast errors are larger than nowcast errors across all model specifications.
  - Additional monthly information generally helps one-step ahead forecasts for most countries, with exceptions: Argentina and Ecuador.
  - DFM again produces more accurate one-step ahead forecasts for most countries; BVARs tend to be more accurate for Mexico; BIVARs tend to be more accurate for Argentina.

- Absolute AR RMSE (one-step ahead, month 1) and DFM relative RMSE (Table 7, month 1):
  - Brazil: AR 4.91 ; DFM 0.91
  - Mexico: AR 9.38 ; DFM 0.77
  - Argentina: AR 6.30 ; DFM 1.09
  - Chile: AR 5.81 ; DFM 0.76
  - Colombia: AR 4.36 ; DFM 1.05
  - Peru: AR 5.05 ; DFM 0.86
  - Ecuador: AR 5.06 ; DFM 1.10
  - Uruguay: AR 5.83 ; DFM 0.97
  - Venezuela: AR 10.15 ; DFM 1.10
  - Dominican Republic: AR 7.77 ; DFM 1.00

- Notable one-step relative results:
  - Mexico one-step month 1: BVAR 0.63 (relative RMSE) — BVARs tend to be more accurate for Mexico.
  - Dominican Republic month 1: LBVAR 20.83 (relative RMSE) indicating extreme deterioration from LBVAR in that case (Table 7).

### Dynamic Factor Model (DFM) performance and interpretation
- DFM advantage:
  - Extracts timely information from a large set of indicators using a small handful of common factors.
  - Avoids “over-fitting” by using few factors.
  - Kalman Filter signal extraction helps separate signal from noisy monthly series.
- Figure 3 (in source): estimated common component from DFM generally tracks quarterly GDP growth closely and captures the sharp contraction over the crisis period.
- Figure 4 (in source): monthly growth indicator (seven-month moving average of estimated common component) for ten Latin American countries at end of August 2010 shows:
  - Slowdown in pace of economic expansion recently among Latin American countries, particularly Brazil, Mexico, Colombia.
  - Contraction in economic activity synchronized across region around Q3 2008; U.S. contraction started two quarters earlier.
  - Recovery more synchronized between Latin America and North America except for Venezuela.

### Usefulness of external indicators for DFM nowcasts
- Experiment: re-run real-time forecasting excluding external indicators (commodity prices and a set of U.S. variables); report RMSE ratio = RMSE without external indicators / RMSE with external indicators.
- Interpretation: ratio > 1 → external indicators improve nowcast accuracy.

- RMSE ratios for DFM (Nowcast, Table 8) — month 1 / month 2 / month 3:
  - Brazil: 1.09 / 1.06 / 1.04
  - Mexico: 1.00 / 1.00 / 1.01
  - Argentina: 0.91 / 1.06 / 0.90
  - Chile: 1.09 / 1.04 / 1.08
  - Colombia: 1.07 / 1.08 / 1.04
  - Peru: 0.94 / 0.94 / 0.81
  - Ecuador: 1.15 / 1.14 / 1.15
  - Uruguay: 1.01 / 1.03 / 1.05
  - Venezuela: 0.89 / 1.23 / 0.94
  - Dominican Republic: 1.05 / 1.03 / 1.04

- Interpretation of RMSE ratios:
  - For six of ten countries — Brazil, Chile, Colombia, Ecuador, Uruguay, Dominican Republic — removing external indicators leads to deterioration in nowcast accuracy (ratios > 1), highlighting importance of links to U.S. economy and commodity prices.
  - Mexico: size of RMSE largely unchanged (ratios ≈ 1).
  - Argentina, Peru, Venezuela: nowcasting performance improves by removing U.S. and commodity indicators (ratios < 1 in some months), suggesting weaker links to U.S. and commodity price developments for these countries in the sample.
  - Caution: relatively short evaluation period for some countries (Argentina, Venezuela) may affect interpretation.

### Conclusions and implications
- Main conclusions:
  - Models that incorporate monthly data outperform a quarterly AR model; nowcasts improve as more monthly information arrives within the quarter.
  - DFM produces more accurate nowcasts and short-term forecasts relative to other model specifications in most cases.
  - The DFM’s strength comes from extracting common signals via few factors and the Kalman Filter’s signal/noise separation.
  - External indicators (commodity prices, U.S. variables) improve forecast accuracy for most Latin American countries but not all.

- Caveats and avenues for future work:
  - Analysis assumes individual countries are independent of each other except via external conditions; inter-regional dependence could be explored in future studies.
  - Short evaluation periods for some countries imply caution in interpreting results for those cases.

*Italic source: IMF Working Paper — content unit: _wp1198 - 1. The baseline AR(p) model is only based on quarterly GDP growth. This implies that (PDF chapter/section).*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp1198.pdf_