1. Gil Dafnai, Jonathan Sidi Research Department, Bank of Israel

2.  Motivation : GDP data is being published at a six week lag after the end of the relevant quarter (and it is needed sooner).  However : There is a lot of monthly data that is available before the policy meetings.  Therefore : We use real-time monthly data in order to Nowcast the GDP 3 weeks ahead of publication.

4.  General Data Set ( ): ◦ 170 monthly Indicators: 95% Domestic and 5% Global.  History: ◦ All series begin at least at 1998Q1.  Endpoints: ◦ All series have value for at least two month of the projected quarter.

5. 1. Seasonal adjustment by X12-ARIMA 2. Holt and Winters exponential smoother is applied where necessary 3. Convert to lower frequency (quarterly) by average observation 4. Convert to percent change 5. Standardize The resulting sample size is defined as

6. Conditional Selection Methods Unconditional Selection Methods Multiple Univariate LASSOElastic Net Sparse PCA 1.Two Component Norm 2.Iterated Component 3.Selected Loadings Stepwise Regression Intermediary Step Final Step

7. Benchmark Method

8. Conditional Selection Methods Unconditional Selection Methods Multiple Univariate LASSOElastic Net Stepwise Regression Intermediary Step Final Step

9. 1. RUN: 2. Calculate AIC i - and keep the top 25 (in Z) 3. Run Stepwise Backward regression on: 4. Calculate Static Forecast

10. PCA and SPCA

11. Conditional Selection Methods Unconditional Selection Methods Multiple Univariate LASSOElastic Net Sparse PCA 1.Two Component Norm 2.Iterated Component 3.Selected Loadings Stepwise Regression Intermediary Step Final Step

12. Principal Component Analysis Original DataCentered Data Rotated Centered Data Projection on max variance axis SC 1

13. Too many variables causes the inference to be extremely difficult What characteristic do PC1 or PC2 represent in the data???

14. Same Data Set!!! Retail Sales Indices 1.IL and US Consumer Confidence 2.Purchasing Manager’s Indices

15. The amount of variance in the data that is explained by the PCs decreases as sparsity increases

16. L2-normL1-norm Is the i th row of the data matrix

17. Application in Regression Three Methods 1. The classic approach (dimension reduction) 2. Two component norm (TCN) (variable selection) 3. Iterated component (IC) (Jolliffe 1973) (variable selection) Loadings Matrix

18. LASSO and Elastic Net

19. Conditional Selection Methods Unconditional Selection Methods Multiple Univariate LASSO Elastic Net Stepwise Regression Intermediary Step Final Step

23. 1. Advantages ◦ General form of algorithm makes it applicable to many problems in econometrics. ◦ Ability to produce decomposition of variable contribution of the forecast. 2. Shortcomings ◦ Can not select more then n variables ◦ If n>p then ridge is better ◦ No grouping LASSO Conclusions

24. Conditional Selection Methods Unconditional Selection Methods Multiple Univariate LASSO Elastic Net Stepwise Regression Intermediary Step Final Step

25. RIDGE LASSO L2-normL1-norm

26. 25%50% 75%

27. q75q50 Bias CBS

29. Results

30. Seasonally Adjusted, Annual Percent Change First Release will be used as control group

34. Comparison of Variable Selection Consistency (24 Periods)

36. Tomer Kriaf Research Department, Bank of Israel

37.  Consumption Equation: Import of Durables, VAT, Confidence Index, Revenue Index (L), Imports of Raw Materials, TA Stock Market Index.  Fixed Capital Formation Equation: Imports of investment Goods, Capital Utilization, PMI, lagged Inventories, TA Stock Market Index.  Inventories Equation: Exports of goods, Revenue Index, Industrial Production Index.  Exports Equation: Exports of Goods, PMI-USA.  Import Equation: Imports of Goods, Imports of Services.  GDP Equation: Derived GDP, Indirect Tax, Income Tax, TA Stock Market Index. Derived GDP

38. In SampleOut of SampleActual

39. Path Forecast Real Time Nowcast CBS Current Release CBS First Release

40. Gil Dafnai and Jonathan Sidi Research Department Bank of Israel