## Annex I. Data Description

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### Introduction and role of nowcasting
- Nowcasting: estimating current or very recent state of an economic, financial, or other dynamic variable using partially available, real time, high-frequency data (see Giannone et al. 2008).
- Purpose:
  - Fill information gap between latest official statistics and real-time developments to help policymakers monitor the economy with minimal delays.
  - Provide current-quarter numbers as initial condition inputs for longer-term forecasting models (e.g., QPM and DSGE).
- Empirical motivation and risks:
  - Nowcasts are crucial during crises (example: COVID-19) when official GDP releases are delayed or insufficiently timely.
  - Risk of parameter proliferation and the "curse of dimensionality" when many high-frequency predictors are used relative to observations, leading to overfitting and reduced forecasting accuracy (Giannone et al., 2008).
- Paper objective:
  - Present a systematic approach combining expert knowledge, variable selection methods, statistical techniques, ML algorithms, and monitoring to address parameter proliferation.

### Standard nowcasting techniques (overview)
- Bridge equation: convert higher-frequency indicators to target frequency; missing HF months forecasted by AR/ARMA; aggregation by summation or average. OLS estimation of lag polynomials 훽푖(L) and intercept 훼̂ and slopes 훽̂.
- MIDAS: time-series regression allowing mixed sampling frequencies using distributed lag polynomials (DLPs), typically estimated by NLS.
- U-MIDAS: unrestricted linear lag polynomials estimated by OLS.
- Factor Models (FMs and DFMs): dimensionality reduction via static/dynamic factor models; DFM in state-space form estimated with Kalman filter and maximum likelihood (X_t = λ(L) f_t + e_t; f_t = Ψ(L) f_{t−1} + η_t).
- Machine Learning regularization:
  - Ridge penalty = 휆∑훽_j^2
  - LASSO penalty = 휆∑|훽_j|
  - Elastic Net penalty = 휆 (∑[(1−훼)훽_j^2 + 훼|훽_j|])
  - Hyperparameters λ and α chosen via cross-validation to minimize expected out-of-sample performance.
- Empirical note: simpler models often deliver better nowcasting performance than more complex models; traditional econometric models can outperform ML models (references to Akepanidtaworn and Akepanidtaworn 2025; Richardson et al. 2021).

### Approaches to parameter proliferation
- Three systematic approaches described:
  A. Variable selection
    - Automated model selection algorithms: Information Criteria (AIC, SIC), portfolio of best subsets, General-to-specific (AUTO/Autometrics), Forward-stepwise (FW), Bayesian Model Averaging, inclusion of all variables.
    - AUTO (Autometrics) noted to outperform others in over 90% of experiments under restricted conditions but has shortcomings (forecast ability, sign constraints).
    - AS-ARIMAX (Xie, 2023): Adjusted Stepwise–ARIMAX procedure that selects variables that are economically meaningful, statistically significant, and improve nowcast accuracy; prior applications showed at least a 30% reduction in out-of-sample RMSE compared to benchmark models.
  B. Regularization in ML models
    - Ridge, LASSO, Elastic Net formalized (penalty terms above); cross-validation for hyperparameter selection.
  C. Dimensionality reduction using PCA
    - PCA reduces predictors to principal components summarizing covariability.
    - Stock and Watson two-step PCA forecasting: (1) estimate Principal Component Factors; (2) regress target on factors.
- Conclusion: no single approach dominates universally; trade-offs between interpretability, robustness, and forecasting accuracy.

### Application: Nowcasting China’s Real GDP during COVID-19 — Data preparation and sample
- Data inventory and filtering:
  - Collected 166 monthly indicators covering November 1952 to April 2023; preliminary filtration yields 132 variables.
- Five preparation steps applied to filtered indicators:
  1. Year-to-Date to flow conversion:
    - Working-day weights: w_{t,Jan} = NWD_{t,Jan} / (NWD_{t,Jan} + NWD_{t,Feb}); w_{t,Feb} = NWD_{t,Feb} / (NWD_{t,Jan} + NWD_{t,Feb}).
    - X_{Jan}^{Flow} = w_{t,Jan} * X_{Feb}^{YTD}; X_{Feb}^{Flow} = w_{t,Feb} * X_{Feb}^{YTD}; other months X_m^{Flow} = X_m^{YTD} − X_{m−1}^{YTD}.
  2. Nominal variables deflation:
    - Five deflator groups: Export Value Index; Import Value Index; Purchasing Price Index; Consumer Price Index- Consumer Goods; Consumer Price Index.
    - Deflation formula: X_{real} = 100 * X_{nominal} / Deflator.
  3. Seasonal adjustment:
    - X-13ARIMA-SEATS used with holiday regressors via Win Genhol to account for Lunar New Year and shifting holidays.
  4. Stationarity:
    - First-difference or log-difference transformations applied; interest rates and PMI left untransformed if stationary.
  5. Frequency conversion:
    - Flow variables: quarterly = sum of monthly values; stock/index variables: quarterly = average of monthly values; end-of-period variables use last month in quarter.

### Methodology: three variable-selection/regularization approaches applied
- AS-ARIMAX (Xie, 2023)
  - Modified stepwise adds variables only if all three criteria met: (i) decreases AIC, (ii) coefficient sign matches economic prior, (iii) statistically significant at 5% level.
  - Three-step AS-ARIMAX procedure includes manual checking of ARIMA orders and ensuring ARIMA terms statistically significant at 15% and regressors at 5%.
- Machine Learning
  - Use LASSO for initial selection, then implement LASSO, Ridge, and Elastic Net for nowcasts.
  - Three sign-restriction procedures:
    - Restriction #1: Sign Consistency with Aggressive Dropping.
    - Restriction #2: Stepwise Sign-Based Dropping.
    - Restriction #3: Relaxed Sequential Sign-Based Restriction (retains more variables than Restriction #2).
- PCA
  - Generate principal components from pre-filtered indicators and include components in nowcasting models.

### Pseudo out-of-sample experimental design
- Rolling fixed window estimation method (following Zhang et al. 2023).
- Sample for experiment: 2007Q2-2023Q1.
- First in-sample period: 2007Q2 to 2019Q4; first out-of-sample period: 2020Q1.
- First out-of-sample nowcast produced for 2020Q1; re-estimation rolls forward until final nowcast for 2023Q1.
- Fixed window chosen to address model instability and avoid biases from "old" data (Elliott and Timmermann, 2016).

### Model performance and key quantitative results
- RMSE comparison over out-of-sample period 2020Q1 to 2023Q1:
  - Best model: ML method using LASSO regularization with sign restrictions (Lasso + Sign Restriction 3) achieved RMSE = 0.01472.
  - Comparable simple model: AS-ARIMAX selection combined with Bridge nowcast recorded RMSE = 0.01655.
- Performance ordering and observations:
  - ML + Sign Restriction 3: best-performing ML variant; even outperformed the ARIMA Bridge Model.
  - ML regularization overall helps selection, but without economic sign restrictions regularization alone did not capture turning points during the COVID peak and subsequent periods.
  - ML Selected + Sign Restriction 1 (aggressive dropping) improved performance relative to unrestricted ML Selected model.
  - ML + Sign Restriction 2 yielded slightly poorer performance compared to Restriction 1.
  - PCA-based variable selection models performed worse than AS-ARIMAX and ML approaches.
- Data and model scope:
  - Number of variables utilized: 166 variables.
  - Nowcasting models evaluated: Bridge, MIDAS, U-MIDAS, DFMs (DFM-1 uses one factor and DFM-2 uses two factors), and ML techniques such as Ridge Regression, LASSO, and Elastic Net.

### Selected variables and method-specific patterns
- AS-ARIMAX selection:
  - Identifies variables related to macroeconomics, firms production, and government indicators; largely overlooks many financial and prices indicators, except for deposit rates and sector loans.
- PCA selection:
  - Treats all variables as a weighted average, potentially diluting impact of more relevant predictors; weakest forecasting performance among tested approaches.
- ML LASSO regularization:
  - Includes a wide range of variables from almost all categories, except for real estate indicators; performs best when combined with economic judgment and sign restrictions.
- Representative selected variables (examples preserved from source):
  - Target and lags: China: Gross Domestic Product (SA, Bil.2020.Yuan) DLOG_RGDP(-1), DLOG_RGDP(-2)
  - Consumption: China: Retail Sales (SA, 100 Mil.Yuan) DLOG(RETAIL)
  - Firm and production indicators: DLOG(II); DLOG(FI_MAN); DLOG(OUT_MV); DLOG(OUT_CMT); DLOG(IP_NAT_GAS)
  - Survey/forward-looking and external indicators: PMI_SERV_CAIXIN; PMI_AE; GPMI_SERV
  - Financial variables and principal components: DLOG(UF_SL); DEP_R_PC1; SP_PC1; SHIBOR_PC1; NLR_PC1
  - Prices and external: DLOG(PPI_CG); DLOG(PP_ALL); VVIX_USA

### Evaluation takeaways and policy-relevant guidance
- Variable-selection matters: a simple but economically intuitive selection procedure (AS-ARIMAX) can produce performance close to more complex ML methods.
- Regularization benefits from economic guidance: LASSO and related ML methods achieve best RMSE only when combined with sign-restriction filters consistent with economic priors.
- PCA dimension-reduction alone was less effective in this China COVID-19 nowcasting exercise compared to targeted variable selection and regularized selection combined with economic sign constraints.
- Practical guidance:
  - Variable selection guided by economic judgment and sign restrictions materially improves ML regularization outcomes (notably LASSO).
  - Simple models (e.g., Bridge) with careful variable selection (AS-ARIMAX plus economic judgment and sign restrictions) can yield forecasting results comparable to, and sometimes superior to, more complex regularization methods.
  - PCA is less desirable for nowcasting here because it may dilute the impact of more relevant predictors by treating all variables as weighted averages.

### Annex I — Data description highlights
- Metadata fields provided: Description, Deflation Method, Seasonal adjustment, Aggregation, Start Date, End Date, Source.
- Deflation methods used: CPI; PPI; Export price index; CPI of goods; CPI of goods (appears for retail/consumer series); many series report "No" under Deflation Method.
- Seasonal adjustment statuses: Yes--regular X13; Yes--CHN SA; No; Not Allowed.
- Aggregation conventions: Average; Sum; End of Period; End of Period (EOP); Not Allowed.
- Time coverage patterns:
  - Start dates range from Nov-1952 (data collection coverage) with individual series starting as early as Dec-1969 and Jan-1970; end dates mostly end in Feb-2023 or Mar-2023; some extend to Apr-2023 and Dec-2022/Dec-2023 where noted.
  - Date precision is monthly unless otherwise indicated.
- Representative first 20 entries (exactly as reported):
  - 1 — CBOE Market Volatility Index: VIX (Index) | Deflation Method: No | Seasonal adjustment: Yes--regular X13 | Aggregation: Average | Start Date: Jan-1990 | End Date: Mar-2023 | Source: Wall Street Journal
  - 2 — CBOE VIX Volatility Index [VVIX] (AVG, Index) | Deflation Method: No | Seasonal adjustment: Yes--regular X13 | Aggregation: Average | Start Date: Jan-2007 | End Date: Mar-2023 | Source: Chicago Board Options Exchange
  - 3 — China PMI: Manufacturing (SA, 50+=Expansion) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Apr-2004 | End Date: Mar-2023 | Source: Caixin/S&P Global
  - 4 — China: Acquisition of Land by Real Estate Developers (SA, Mil.Sq.Meters) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Sum | Start Date: Jan-2001 | End Date: Dec-2022 | Source: China National Bureau of Statistics/Haver Analytics
  - 5 — China: Aggregate Social Financing to the Real Economy (EOP, SA, Tril.Yuan) | Deflation Method: CPI | Seasonal adjustment: No | Aggregation: End of Period | Start Date: Dec-2002 | End Date: Mar-2023 | Source: People's Bank of China/Haver Analytics
  - 6 — China: Composite PMI Output Index (SA, 50+=Expansion) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Jan-2017 | End Date: Mar-2023 | Source: China Federation of Logistics & Purchasing/CNBS
  - 7 — China: Consumer Confidence (SA, 100+=Optimistic) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Jan-1990 | End Date: Feb-2023 | Source: China National Bureau of Statistics/Haver Analytics
  - 8 — China: Consumer Price Index (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Jan-1984 | End Date: Mar-2023 | Source: China National Bureau of Statistics
  - 9 — China: CPI Excluding Food and Energy (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Jan-2005 | End Date: Mar-2023 | Source: China National Bureau of Statistics
  - 10 — China: CPI: Clothing (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
  - 11 — China: CPI: Food (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
  - 12 — China: CPI: Housing (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
  - 13 — China: CPI: Medicine (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
  - 14 — China: CPI: Recreation, Education & Cultural Services (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
  - 15 — China: CPI: Transportation and Communications (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
  - 16 — China: Deposit Rates: 3-Month Certificates of Deposit (% per annum) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: May-1990 | End Date: Mar-2023 | Source: People's Bank of China
  - 17 — China: Deposit Rates: 6-Month Certificates of Deposit (% per annum) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: May-1990 | End Date: Mar-2023 | Source: People's Bank of China
  - 18 — China: Electricity Consumption (SA, Bil.KWH) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Sum | Start Date: Jul-2008 | End Date: Mar-2023 | Source: China Electricity Council
  - 19 — China: Export Volume Index (NSA, 2010=100) | Deflation Method: No | Seasonal adjustment: Yes--CHN SA | Aggregation: Average | Start Date: Jan-2005 | End Date: Feb-2023 | Source: General Administration of Customs, China
  - 20 — China: Exports: Mechanical & Electrical Products (NSA, Bil.USD) | Deflation Method: Export price index | Seasonal adjustment: Yes--CHN SA | Aggregation: Sum | Start Date: Jan-2001 | End Date: Mar-2023 | Source: General Administration of Customs, China

*Source: wpiea2025217-source-pdf - Annex I. Data Description (page 24).*

### Annex I. Data Description ..............................................................................................

### Annex I. Data Description

### Location
- Page 24

*Source: wpiea2025217-source-pdf - Annex I. Data Description (page 24).*

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

### References

### Figures and Tables
- Figures listed:
  - Figure 1. Model Performance: Approach #1 AS-ARIMAX
  - Figure 2. Model Performance: Approach #2 ML Regularization
  - Figure 3. Model Performance: Approach #3 PCA
- Tables listed:
  - Table 1. Forecast Evaluation Statistics
  - Table 2. Selected Variables by Different Approaches

### Introduction and role of nowcasting
- Nowcasting: estimating current or very recent state of an economic, financial, or other dynamic variable using partially available, real time, high-frequency data (see Giannone et al. 2008).
- Purpose:
  - Fill information gap between latest official statistics and real-time developments to help policymakers monitor the economy with minimal delays.
  - Provide current-quarter numbers as initial condition inputs for longer-term forecasting models (e.g., QPM and DSGE).
- Empirical context and motivation:
  - Nowcasts are crucial during crises (example: COVID-19) when official GDP releases are delayed or insufficiently timely.
  - China example: first-quarter 2020 GDP contraction; first official estimates published in mid-April; policymakers relied on high-frequency indicators and eased policy during February and March 2020.
- Risks:
  - Parameter proliferation and the "curse of dimensionality" when many high-frequency predictors are used relative to observations, leading to overfitting and reduced forecasting accuracy (Giannone et al., 2008).
- Paper objective:
  - Present a systematic approach combining expert knowledge, variable selection methods, statistical techniques, ML algorithms, and monitoring to address parameter proliferation.
- Structure overview:
  - Section II: nowcasting process and techniques.
  - Section III: three approaches to parameter proliferation.
  - Section IV: application to nowcast China’s real GDP during COVID-19, with pseudo out-of-sample forecast evaluation.
  - Section V: conclusion.

### Standard nowcasting techniques (overview)
- Bridge equation:
  - Convert higher-frequency indicators to target frequency and estimate relationship with OLS; missing HF months forecasted by AR/ARMA; aggregation by summation or average.
  - Mathematical form presented with lag polynomials 훽푖(L) and OLS estimators 훼̂ and 훽̂.
- MIDAS:
  - Time-series regression allowing mixed sampling frequencies using distributed lag polynomials (DLPs); typically estimated by NLS.
- U-MIDAS:
  - Unrestricted linear lag polynomials estimated by OLS; useful when sampling frequency discrepancies are small.
- Factor Models (FMs and DFMs):
  - Reduce dimensionality via static/dynamic factor models; DFM in state-space form estimated with Kalman filter and maximum likelihood; equations X_t = λ(L) f_t + e_t and f_t = Ψ(L) f_{t−1} + η_t shown.
  - DFMs require significant parametrization and are more prone to misspecification.
- Machine Learning regularization (Ridge, LASSO, Elastic Net):
  - Ridge: penalizes sum of squared coefficients; does not set coefficients to zero.
  - LASSO: penalizes sum of absolute coefficients; can set coefficients exactly to zero (feature selection).
  - Elastic Net: combines Ridge and LASSO penalties; hyperparameters λ and α chosen via cross-validation.
- Standard nowcasting procedure components:
  - Preparation, Estimation, Evaluation and Combination.
  - Empirical finding noted: simpler models often deliver better nowcasting performance than more complex models; traditional econometric models can outperform ML models (references to Akepanidtaworn and Akepanidtaworn 2025; Richardson et al. 2021).

### Approaches to parameter proliferation
- Three systematic approaches described:
  A. Variable selection
    - Automated model selection algorithms overview (Castle et al. 2009): categories include Information Criteria (AIC, SIC), portfolio of best subsets, General-to-specific (AUTO/Autometrics), Forward-stepwise (FW), Bayesian Model Averaging, and inclusion of all variables.
    - AUTO (Autometrics) noted to outperform others in over 90% of experiments under restricted conditions but has shortcomings: does not consider overall forecast ability or ensure coefficient signs aligned with economic priors.
    - AS-ARIMAX (Xie, 2023) introduced as an Adjusted Stepwise–ARIMAX procedure that:
      - Selects variables that are economically meaningful, statistically significant, and improve nowcast accuracy.
      - Achieved at least a 30% reduction in out-of-sample RMSE compared to benchmark models in previous applications.
  B. Regularization in ML models
    - Ridge, LASSO, and Elastic Net described formally with penalty terms preserved:
      - Ridge Penalty = 휆∑훽_j^2
      - LASSO Penalty = 휆∑|훽_j|
      - Elastic Net Penalty = 휆 (∑[(1−훼)훽_j^2 + 훼|훽_j|])
    - Hyperparameter selection via cross-validation to minimize expected out-of-sample performance.
  C. Dimensionality reduction using PCA
    - PCA reduces predictors to principal components (latent factors) that summarize covariability.
    - Stock and Watson two-step PCA forecasting: (1) estimate Principal Component Factors; (2) regress target on factors.
    - Factor representation: X_t = Λ F_t + e_t and y_{t+h} = β_F' F_t + β_w' w_t + e_{t+h}.
    - PCA combined with MIDAS/U-MIDAS and other frameworks in literature (examples: Ahir et al. 2019; Mählmann and Gebauer 2016; Hallin et al. 2020).
- Conclusion: no single approach dominates universally; trade-offs exist between interpretability, robustness, and forecasting accuracy.

### Application: Nowcasting China’s Real GDP during COVID-19
- Motivation:
  - Nowcasting China’s quarterly real GDP important for domestic and global policy given China’s role in supply chains and commodity markets.
  - Challenges: short macro time series history, missing observations, data quality variability, structural changes (e.g., rebalancing toward consumption).
- Data Preparation (key steps and sample)
  - Collected 166 monthly indicators covering November 1952 to April 2023; preliminary filtration yields 132 variables.
  - Five preparation steps applied to filtered indicators:
    1. Year-to-Date to flow conversion:
      - Example: “China: Online Retail Sales of Goods and Services (YTD, NSA, 100 Mil. CNY)” disaggregated between January and February using working-day weights w_{t,Jan} and w_{t,Feb}, with formulas:
        - w_{t,Jan} = NWD_{t,Jan} / (NWD_{t,Jan} + NWD_{t,Feb})
        - w_{t,Feb} = NWD_{t,Feb} / (NWD_{t,Jan} + NWD_{t,Feb})
        - X_{Jan}^{Flow} = w_{t,Jan} * X_{Feb}^{YTD}
        - X_{Feb}^{Flow} = w_{t,Feb} * X_{Feb}^{YTD}
      - For other months: X_m^{Flow} = X_m^{YTD} − X_{m−1}^{YTD}.
    2. Nominal variables deflation:
      - Five deflator groups: Export Value Index; Import Value Index; Purchasing Price Index; Consumer Price Index- Consumer Goods; Consumer Price Index.
      - Deflation formula: X_{real} = 100 * X_{nominal} / Deflator.
    3. Seasonal adjustment:
      - X-13ARIMA-SEATS used with holiday regressors via Win Genhol to account for Lunar New Year and other shifting holidays.
    4. Stationarity:
      - Apply first-difference or log-difference transformations; interest rates and PMI left untransformed if stationary.
    5. Frequency conversion:
      - For flow variables, quarterly = sum of monthly values; for stock/index variables, quarterly = average of monthly values; end-of-period variables use last month in quarter.
- Methodology: three variable-selection/regularization approaches applied to nowcasting
  1. AS-ARIMAX (Xie, 2023)
    - Modified stepwise adding variables only if all three criteria met:
      (i) decreases AIC, (ii) coefficient sign matches economic prior, (iii) statistically significant at 5% level.
    - Three-step AS-ARIMAX procedure described, including manual checking of ARIMA orders and ensuring ARIMA terms statistically significant at 15% and regressors at 5%.
  2. Machine Learning
    - Use LASSO for initial variable selection, then implement LASSO, Ridge, and Elastic Net for nowcasts.
    - Three sign-restriction procedures applied:
      - Restriction #1: Sign Consistency with Aggressive Dropping.
      - Restriction #2: Stepwise Sign-Based Dropping.
      - Restriction #3: Relaxed Sequential Sign-Based Restriction (retains more variables than Restriction #2).
  3. PCA
    - Use PCA to generate principal components from the pre-filtered indicators and include components in nowcasting models.
- Pseudo out-of-sample experimental design
  - Rolling fixed window estimation method used (following Zhang et al. 2023); first M observations used to estimate parameters; first out-of-sample nowcast at M + 1.
  - Sample: entire sample noted as 2007Q2-2023Q1 for the experiment.
  - First in-sample period: 2007Q2 to 2019Q4; first out-of-sample period: 2020Q1.
  - First out-of-sample nowcast produced for 2020Q1; re-estimation progresses by rolling the fixed window forward until final nowcast for 2023Q1.
  - Fixed window chosen to address model instability and avoid biases from "old" data (Elliott and Timmermann, 2016).
- Model performance and key quantitative results
  - RMSE comparison over out-of-sample period 2020Q1 to 2023Q1 (Table 1 referenced).
  - Best model: ML method using LASSO regularization with sign restrictions (Lasso + Sign Restriction 3) achieved RMSE = 0.01472.
  - Comparable simple model: AS-ARIMAX selection combined with Bridge nowcast recorded RMSE = 0.01655.
  - PCA-based variable selection models performed worse than AS-ARIMAX and ML approaches.
  - Important qualitative finding: ML regularization (LASSO) required sign restriction filters to perform well; without sign restrictions, regularization alone did not capture turning points during the COVID peak and subsequent periods.
  - Specific ML sign-restriction observations:
    - ML Selected + Sign Restriction 1 (aggressive dropping by perceived incorrect signs) improved performance relative to unrestricted ML Selected model.
    - ML + Sign Restriction 2 (sequential removal by incorrect signs) yielded slightly poorer performance compared to Restriction 1 (details in Figure 2 references).

### Evaluation takeaways
- Variable-selection matters: a simple but economically intuitive selection procedure (AS-ARIMAX) can produce performance close to more complex ML methods.
- Regularization benefits from economic guidance: LASSO and related ML methods achieve best RMSE only when combined with sign-restriction filters consistent with economic priors.
- PCA dimension-reduction alone was less effective in this China COVID-19 nowcasting exercise compared to targeted variable selection and regularized selection combined with economic sign constraints.
- Experimental design: fixed-rolling-window pseudo out-of-sample evaluation focused on post-COVID nowcasting (2020Q1–2023Q1) to assess real-time performance under structural shifts.

*IMF WORKING PAPERS Parameter Proliferation in Nowcasting: Issues and Approaches*

### 1. Meanwhile, the ML + Sign Restriction 3 model also applies the sequential dropping of variables with

### Parameter Proliferation in Nowcasting: Issues and Approaches

### Model performance and comparisons
- ML + Sign Restriction 3:
  - Applies the sequential dropping of variables with incorrect signs but retains more variables compared to ML + Sign Restriction 2.
  - Achieved the best performance among the three ML models.
  - Even outperformed the ARIMA Bridge Model.
- ML regularization overall:
  - Regularization through Machine Learning is helpful in the selection of variables, but not applying additional filters does not guarantee good forecasting performance.
- AS-ARIMAX (Xie, 2023) selection method:
  - Despite simplicity, performed well when combined with the Bridge Model and the Bridge model with an autoregressive form of some selected variables.
  - Also performs well when combined with the DFM nowcasting model.
  - Did not yield strong results when integrated with the MIDAS and U-MIDAS.
  - Based on results, AS-ARIMAX demonstrates best forecasting performance for China’s Real GDP when combined with the Bridge Model.
- PCA selection method:
  - Performed the worst among the three variable selection methods tested when combined with Bridge, MIDAS, U-MIDAS, and DFM nowcasting models.

### Definitions of ML sign restrictions (as presented)
- Restriction #1: Sign Consistency with Aggressive Dropping: Incorporate variables with reasonable signs based on economic intuition and drop variables with perceived incorrect signs at once.
- Restriction #2: Stepwise Sign-Based Dropping: Removing variables with incorrect signs sequentially.
- Restriction #3: Relaxed Sequential Sign-Based Restriction: Applies the sequential dropping of variables with incorrect signs but retain more variables compared to Restriction #2.

### Data, estimation strategy, and evaluation periods
- Number of variables utilized: 166 variables.
- Estimation sample period: 2007Q2 to 2019Q4 using rolling-window regression.
- Out-of-sample nowcast evaluation period: 2020Q1 to 2023Q1.
- Nowcasting models evaluated: Bridge, MIDAS, U-MIDAS, DFMs (DFM-1 uses one factor and DFM-2 uses two factors), and ML techniques such as Ridge Regression, LASSO, and Elastic Net.
- Noted comparison: LASSO method outperforms all other models, but only when guided by economic judgment and sign restrictions.
- Simpler models like the Bridge model provide reliable estimates nearly comparable to those from LASSO when effective variable selection is applied.

### Selected variables and method-specific patterns (summary)
- AS-ARIMAX selection:
  - Identifies variables related to macroeconomics, firms production, and government indicators.
  - Largely overlooks many financial and prices indicators, except for deposit rates and sector loans.
  - Pattern similar to dimensionality reduction achieved through PCA.
- PCA selection:
  - Treats all variables as a weighted average, potentially diluting impact of more relevant predictors.
  - Demonstrated weakest forecasting performance among the three approaches.
- ML Lasso regularization:
  - Includes a wide range of variables from almost all categories, except for real estate indicators.
  - Performs best when combined with economic judgment and sign restrictions.

### Representative selected variables (examples preserved from source table)
- Target and lags:
  - China: Gross Domestic Product (SA, Bil.2020.Yuan) DLOG_RGDP(-1), DLOG_RGDP(-2)
- Consumption:
  - China: Retail Sales (SA, 100 Mil.Yuan) DLOG(RETAIL)
- Firm and production indicators (selected examples):
  - Index of Industrial Value Added (SA, 2005=100) DLOG(II)
  - China: Fixed Investment: Manufacturing [Revised] (NSA, 100 Mil.Yuan) DLOG(FI_MAN)
  - China: Output: Motor Vehicles (NSA, 10,000.Units) DLOG(OUT_MV)
  - China: Output: Cement (NSA, 10,000.Metric Tons) DLOG(OUT_CMT)
  - China: IP: Natural Gas (NSA, 100 Mil Cubic M) DLOG(IP_NAT_GAS)
- Survey/forward-looking and external indicators:
  - China PMI: Services Business Activity (SA, 50+=Expansion) PMI_SERV_CAIXIN
  - Developed Markets PMI: Composite (SA, 50+=Expansion) PMI_AE
  - Global PMI: Services Business Activity (SA, 50+=Expansion) GPMI_SERV
- Financial variables and principal components:
  - China: Uses of Funds by Sector Loans (EOP,SA, 100 Mil Yuan) DLOG(UF_SL)
  - DEP_R_PC1 (principal component of deposit rates)
  - SP_PC1 (principal component of stock price indices)
  - SHIBOR_PC1 (principal component of Shibor rates)
  - NLR_PC1 (principal component of nominal lending rates)
- Prices and external:
  - China: PPI: Consumer Goods (SA, 2020=100) DLOG(PPI_CG)
  - China: Producer Prices: All Industry Products (SA, 2020=100) DLOG(PP_ALL)
  - CBOE VIX Volatility Index [VVIX] (AVG, Index) VVIX_USA

### Key conclusions and policy-relevant takeaways
- Parameter proliferation and the "curse of dimensionality" are material concerns for nowcasting:
  - Excessive numbers of high-frequency predictors relative to observations can introduce noise and lead to overfitting, reducing forecasting accuracy.
- Effective approaches to mitigate parameter proliferation (evaluated):
  - (i) Variable selection using AS-ARIMAX.
  - (ii) Regularization techniques in ML models (Ridge, LASSO, Elastic Net).
  - (iii) Dimensionality reduction through PCA.
- Practical guidance from findings:
  - Variable selection guided by economic judgment and sign restrictions materially improves ML regularization outcomes (notably LASSO).
  - Simple models (e.g., Bridge) with careful variable selection (AS-ARIMAX plus economic judgment and sign restrictions) can yield forecasting results comparable to, and sometimes superior to, more complex regularization methods.
  - PCA is less desirable for nowcasting because it may dilute the impact of more relevant predictors by treating all variables as weighted averages.

*Source: IMF Working Paper excerpt — Parameter Proliferation in Nowcasting: Issues and Approaches*

### Annex I. Data Description

### Annex I. Data Description

### Overview
- Provides itemized metadata for indicators used in the analysis, including: Description, Deflation Method, Seasonal adjustment, Aggregation, Start Date, End Date, and Source.
- Entries include financial market indices, China macroeconomic and sectoral series, policy rates, price indices (CPI/PPI), production and trade series, balance-sheet aggregates, sentiment and PMI measures, and international indices.

### Deflation methods (as reported)
- Series deflated using:
  - CPI
  - PPI
  - Export price index
  - CPI of goods
  - CPI of goods (appears for retail/consumer series)
- Many series report "No" under Deflation Method (i.e., not deflated).

### Seasonal adjustment (as reported)
- Seasonal adjustment statuses include:
  - Yes--regular X13
  - Yes--CHN SA
  - No
  - Not Allowed
- Examples of "Yes--regular X13": CBOE Market Volatility Index: VIX (Index).
- Examples of "Yes--CHN SA": China: Export Volume Index (NSA, 2010=100) and many China National Bureau of Statistics series.
- Several series explicitly flagged as "Not Allowed" for seasonal adjustment or aggregation (e.g., China: Monthly ECRI Peaks/Troughs (+1 or -1); China: Purchasing Price Index of Raw Materials (NSA, M/M %Chg); China: Real Industrial Value Added (SA, M/M %Chg); China: Services Sector Production Index (NSA, Y/Y %Chg)).

### Aggregation and timing conventions (as reported)
- Aggregation types shown:
  - Average
  - Sum
  - End of Period
  - End of Period (EOP) or EOP noted in Description
  - Not Allowed (for series where aggregation is not allowed)
- Examples:
  - "Average" for indices and yield averages (e.g., China: Government Bond Yield: 10 Year (AVG, % p.a)).
  - "Sum" for flow or volume measures (e.g., China: Electricity Consumption (SA, Bil.KWH)).
  - "End of Period" for stock or level series (e.g., China: Money Supply: M1 (EOP,SA, Bil.Yuan)).

### Time coverage patterns
- Start dates range from as early as Jan-1970 (China: JP Morgan Broad Nominal Effective Exchange Rate (2010=100)) and Dec-1969 (Hong Kong: Stock Price Index: Hang Seng Bank (Jul-31-64=100)) to many series starting in the 1990s and 2000s.
- End dates mostly end in Feb-2023 or Mar-2023; some extend to Apr-2023 and Dec-2022/Dec-2023 where noted.
- Date precision is monthly unless otherwise indicated in the Description (e.g., Q1-66 reference for University of Michigan: Consumer Sentiment; YTD or quarterly/annual specifications in some series).

### Sources represented (selected)
- China National Bureau of Statistics
- People's Bank of China
- Haver Analytics (where indicated in combination with national sources)
- General Administration of Customs, China
- JP Morgan
- Chicago Board Options Exchange
- Wall Street Journal
- Shanghai Stock Exchange / Shenzhen Stock Exchange
- PolicyUncertainty.com
- Economic Cycle Research Institute
- Yicai Research Institute
- University of Michigan
- Ministry of Finance of China
- Ministry of Commerce

### Representative entries (first 20 rows exactly as reported)
- 1 — CBOE Market Volatility Index: VIX (Index) | Deflation Method: No | Seasonal adjustment: Yes--regular X13 | Aggregation: Average | Start Date: Jan-1990 | End Date: Mar-2023 | Source: Wall Street Journal
- 2 — CBOE VIX Volatility Index [VVIX] (AVG, Index) | Deflation Method: No | Seasonal adjustment: Yes--regular X13 | Aggregation: Average | Start Date: Jan-2007 | End Date: Mar-2023 | Source: Chicago Board Options Exchange
- 3 — China PMI: Manufacturing (SA, 50+=Expansion) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Apr-2004 | End Date: Mar-2023 | Source: Caixin/S&P Global
- 4 — China: Acquisition of Land by Real Estate Developers (SA, Mil.Sq.Meters) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Sum | Start Date: Jan-2001 | End Date: Dec-2022 | Source: China National Bureau of Statistics/Haver Analytics
- 5 — China: Aggregate Social Financing to the Real Economy (EOP, SA, Tril.Yuan) | Deflation Method: CPI | Seasonal adjustment: No | Aggregation: End of Period | Start Date: Dec-2002 | End Date: Mar-2023 | Source: People's Bank of China/Haver Analytics
- 6 — China: Composite PMI Output Index (SA, 50+=Expansion) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Jan-2017 | End Date: Mar-2023 | Source: China Federation of Logistics & Purchasing/CNBS
- 7 — China: Consumer Confidence (SA, 100+=Optimistic) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Jan-1990 | End Date: Feb-2023 | Source: China National Bureau of Statistics/Haver Analytics
- 8 — China: Consumer Price Index (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Jan-1984 | End Date: Mar-2023 | Source: China National Bureau of Statistics
- 9 — China: CPI Excluding Food and Energy (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Jan-2005 | End Date: Mar-2023 | Source: China National Bureau of Statistics
- 10 — China: CPI: Clothing (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
- 11 — China: CPI: Food (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
- 12 — China: CPI: Housing (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
- 13 — China: CPI: Medicine (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
- 14 — China: CPI: Recreation, Education & Cultural Services (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
- 15 — China: CPI: Transportation and Communications (SA, 2020=100) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: Dec-2000 | End Date: Mar-2023 | Source: China National Bureau of Statistics
- 16 — China: Deposit Rates: 3-Month Certificates of Deposit (% per annum) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: May-1990 | End Date: Mar-2023 | Source: People's Bank of China
- 17 — China: Deposit Rates: 6-Month Certificates of Deposit (% per annum) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Average | Start Date: May-1990 | End Date: Mar-2023 | Source: People's Bank of China
- 18 — China: Electricity Consumption (SA, Bil.KWH) | Deflation Method: No | Seasonal adjustment: No | Aggregation: Sum | Start Date: Jul-2008 | End Date: Mar-2023 | Source: China Electricity Council
- 19 — China: Export Volume Index (NSA, 2010=100) | Deflation Method: No | Seasonal adjustment: Yes--CHN SA | Aggregation: Average | Start Date: Jan-2005 | End Date: Feb-2023 | Source: General Administration of Customs, China
- 20 — China: Exports: Mechanical & Electrical Products (NSA, Bil.USD) | Deflation Method: Export price index | Seasonal adjustment: Yes--CHN SA | Aggregation: Sum | Start Date: Jan-2001 | End Date: Mar-2023 | Source: General Administration of Customs, China

*Annex I. Data Description (as provided in the source document)*

### References

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### Applications to Country Nowcasts and Policy-Relevant Studies
- Akepanidtaworn, K. and Akepanidtaworn, K. (2025). GDP Nowcasting Performance of Machine Learning versus non-Machine Learning Models. IMF Working Paper (forthcoming).
- Heenan, G.M., Lui, K., Nield, I., Muaulu, E., Reupena, V., Sabuga, I., and Tolovaa, A. (2025). Nowcasting Real GDP in Samoa. IMF Working Paper 25/92, International Monetary Fund.
- Heng, D., Han, F., Chey, S., Uch, R., Kuchsa, D., and Phork, P. (2024). Nowcasting and Near-Term Forecasting Cambodia’s Economy. IMF Working Paper 24/247, International Monetary Fund.
- Kuzin, V., Marcellino, M., and Schumacher, C. (2011). MIDAS vs. mixed-frequency VAR: Nowcasting GDP in the euro area. International Journal of Forecasting, 27(2), 529-542.
- Ouliaris, S., and Rochon, C. (2023). Assessing the Impact of Policy Changes on a Nowcast. IMF Working Paper 23/153, International Monetary Fund.

### Tools, Seasonal Adjustment, and Additional Methodological References
- Roberts, I. and White, G. (2015). “Seasonal Adjustment of Chinese Economic Statistics,” Research Discussion Paper, RDP 2015-13, Reserve Bank of Australia.
- United States Census Bureau, 2023. “X-13ARIMA-SEATS Seasonal Adjustment Program,” retrieved from https://www.census.gov/data/software/x13as.html.
- Ghysels, E., Santa-Clara, P., and Valkanov, R. (2004). Predicting Volatility: Getting the Most Out of Return Data Sampled at Different Frequencies. Journal of Econometrics, 131(1-2), 59-95.
- Chan, J., Koop, G., Poirier, D. J., and Tobias, J. L. (2019). "Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure." Journal of Econometrics, 212(1), 97-115.
- Matteson, D. S., Tsay, R. S., and Preve, D. (2019). "Factor Modeling for High-Dimensional Time Series: Inference and Model Selection." Journal of Time Series Analysis, 40(2), 241-264.

*Parameter Proliferation in Nowcasting: Issues and Approaches - An Application to Nowcasting China’s Real GDP, Working Paper No. WP/2025/217*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025217-source-pdf.pdf_