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 necessary3. Convert to lower frequency (quarterly) by

average observation 4. Convert to percent change 5. Standardize

The resulting sample size is defined as ̂

ˆ d

Conditional Selection Methods

Unconditional Selection Methods

Multiple Univariate

LASSO Elastic Net

SparsePCA

PCA

1. Two Component Norm2. Iterated Component3. Selected Loadings Stepwise

Regression

Stepwise Regression

dIntermediary

StepFinalStep

Benchmark Method

Conditional Selection Methods

Unconditional Selection Methods

Multiple Univariate

LASSO Elastic Net

Stepwise Regression

Stepwise Regression

Intermediary Step

FinalStep

ˆ d

d

1. RUN:2. Calculate AICi - and keep the top 25 (in Z)

3. Run Stepwise Backward regression on:

4. Calculate Static Forecast

,ˆ ˆ;d i i d iGDP c

25

1

ˆd i i

i

GDP c Z

PCA and SPCA

Conditional Selection Methods

Unconditional Selection Methods

Multiple Univariate

LASSO Elastic Net

SparsePCA

PCA

1. Two Component Norm2. Iterated Component3. Selected Loadings Stepwise

Regression

Stepwise Regression

Intermediary Step

FinalStep

ˆ d

d

Original Data Centered Data

Rotated Centered Data Projection on max variance axis

SC1

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

22

, , 1, ,ˆ1 1 1

ˆ argmini

p pn

i spca i i i j j i ji j j

SC X

L2-norm L1-norm

2 2`, 1, ,ˆ

1 1 1

ˆˆ , argmini

p pn

i i i j j i ji j j

X X

Is the ith row of the data matrix XiX

Three Methods1. The classic approach

(dimension reduction)2. Two component norm (TCN)

(variable selection)

3. Iterated component (IC) (Jolliffe 1973)

(variable selection)

Loadings Matrix

1,1 1,2 1,

2,1 2,2 2,

,1 ,2 ,

p pL

p

p

p p p p

l l l

l l l

l l l

LASSO and Elastic Net

Conditional Selection Methods

Unconditional Selection Methods

Multiple Univariate

LASSO Elastic Net

Stepwise Regression

Stepwise Regression

Intermediary Step

FinalStep

ˆ d

d

1

ˆ. :p

jj

s t t

21

ˆ. :p

jj

s t t

2ˆ1

ˆ ˆargminj

n

i

Y X

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

Stepwise Regression

Intermediary Step

FinalStep

ˆ d

d

2 2

ˆ1 1

ˆ argmin 1j

pn

EN j ji j

Y X

RIDGE LASSO

L2-norm L1-norm

25% 50% 75%

q75 q50

Bias

CBS

2 2

ˆ1 1

ˆ argmin 1j

pn

EN j ji j

Y X

2 2

ˆ1 1

ˆ argmin 1j

pn

EN j ji j

Y X

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.

De

riv

ed

GD

P

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2

2004 2005 2006 2007 2008 2009 2010

תחזית מוץ למדגם התוצר הנאמד בתוך המדגם In Sampleתמ"ג בפועל Out of Sample Actual

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

2009Q2 2009Q3 2009Q4 2010Q1 2010Q2

תחזית נאיבית NOWCAST בזמן אמת I אומדן למ"ס אומדן למ"ס אחרוןPath Forecast

Real Time Nowcast CBS Current Release

CBS First Release

Gil Dafnai and Jonathan Sidi

Research Department

Bank of Israel