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

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Gil Dafnai, Jonathan Sidi Research Department, Bank of Israel

 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.

 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.

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

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

Benchmark Method

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

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

PCA and SPCA

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

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

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

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

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

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

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

LASSO and Elastic Net

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

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

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

RIDGE LASSO L2-normL1-norm

25%50% 75%

q75q50 Bias CBS

Results

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

Comparison of Variable Selection Consistency (24 Periods)

Tomer Kriaf Research Department, Bank of Israel

 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

In SampleOut of SampleActual

Path Forecast Real Time Nowcast CBS Current Release CBS First Release

Gil Dafnai and Jonathan Sidi Research Department Bank of Israel

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