Short-term forecasts of GDP from dynamic factor models

Short-term forecasts of GDP from dynamic factor models Gerhard Rünstler gerhard.ruenstler@wifo.ac.at Austrian Institute for Economic Research November 16, 2011

1 Introduction Forecasting GDP from large unbalanced monthly data sets Dynamic factor models (DFMs) have become a common tool Latest development: Giannone, Reichlin and Small (JME, 2010) Explicit modelling of factor dynamics Implemented with Kalman lter Nowadays widely used in CB world

DFM (Giannone et al., 2010) x t = f t + t ; t N(0; ), px f t = A i f t i + t, i=1 t = B t ; t N(0; I q )

Introducing monthly GDP growth by t = 0 f t by (3) t = by t + by t 1 + by t 2 y Q 3k = 1 3 (y(3) 3k + y(3) 3k 1 + y(3) 3k 2 )

State space form xt y Q t = 0 0 0 0 1 2 4 f t y (3) t Q t 3 5 + t 0 2 4 I r 0 0 0 1 0 1 0 3 1 3 2 5 4 f t+1 y (3) t+1 Q t+1 3 5 = 2 4 A 1 0 0 0 0 0 0 0 t 3 2 5 4 f t y (3) t Q t 3 2 5 + 4 B t " t+1 0 3 5

2 Features E cient handling of unbalanced data Good forecasting performance Integration of interpolation and forecasting Contributions for forecast can be obtained Weights may be used for series selection

3 Forecast performance 1 Angelini et al. (EJ, 2010): DFM vs ECB BEQs for euro area Data set: 85 series from 1991 Q1 Fcst evaluation: 1999 Q1-2007 Q2 Pseudo-real time forecast design recursive estimates replicate real-time data availability but nal data vintages

Table 1. Bridge equations for euro area GDP growth (BES model). Equation Explanatoryvariables 1 2 3 4 5 6 7 8 9 10 11 12 Industrial production (total) Ind. production construction Retail sales New car registrations Service confidence Unemployment rate Money M1 Business confidence EuroCoin (CEPR) OECD leading indicator

Euro area data set Real activity 32 Industrial production 6 weeks Retail sales 6 weeks Labour market 6-8 weeks Surveys (EC) 22 0 weeks Business Consumer Retail & construction Financial data 22 0 weeks Exchange & interest rates Stock price indices Other US data 10 various

FORECAST EVALUATION Example Real activity Surveys Financial Q2 (Oct) (Nov) (Dec) 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun 7 Jul

FORECAST EVALUATION Example Real data Surveys Financial Q2 (Oct) (Nov) (Dec) 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun 7 Jul

FORECAST EVALUATION Example Real data Surveys Financial Q2 (Oct) (Nov) (Dec) 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun 7 Jul

FORECAST EVALUATION Example Real data Surveys Financial Q2 (Oct) (Nov) (Dec) 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun 7 Jul

Short-term forecasts of euro area GDP growth C

4 Forecast performance 2 Rünstler et al. (JoF, 2009): Forecast evaluation for 8 countries Compare Fcst avg from bivariate quarterly VARS Fcst avg from bridge equations (single indicators) DFM by Giannone et al (2010) Di usion index (Stock and Watson, 1997) Generalized dynamic factor model (Forni et al, 2002)

No of series Production and sales Table 1: Datasets of which Surveys Financial Prices Other Sample start Euro area EA 85 25 25 24 0 11 1991 Belgium BE 393 25 262 50 42 14 1991 Germany DE 111 55 19 32 4 1 1991 France FR 118 19 96 0 2 1 1991 Italy IT 84 27 24 10 20 3 1991 Netherlands NL 76 8 33 8 23 4 1991 Portugal PT 141 32 78 12 10 9 1991 Lithuania LT 103 35 21 12 33 1 1995 Hungary HU 80 33 9 12 11 15 1998 Poland PL 81 16 30 10 11 14 1997

Table 3: Results overview Forecasts 2000 Q1 2005 Q4 for euro area countries and 2002 Q1 2005 Q4 for NMS Average RMSE for preceding, current and one-quarter-ahead forecasts relative to the naive forecast EA BE DE FR IT NL PT LT HU PL EuroA NMS AR 5 5 5 6 3 6 6 5 2 3 5.2 3.3 VAR 4 6 6 5 5 1 5 1 5 1 4.7 2.3 BEQ 3 4 4 4 6 4 4 2 3 4 4.3 3.0 KF 1 1 1 2 1 2 1 4 4 5 1.3 4.3 PC 2 3 2 1 2 5 2 6 6 6 2.5 6.0 GPC 6 2 3 3 4 3 3 3 1 2 3.0 2.0

4 Forecast weights Express forecasts as the weighted sum of observations by Q t+hjt = P t 1 k=0! k;t(h)z t k Algorithm due to Harvey and Koopman (2003) Weights are invariant for pseudo-real-time fcst Inspect Cumulative forecast weights P t 1 k=0! k;i(h) for series i, Historical contributions of series i to the forecast

Cumulative forecast weights R e a l a c t v i t y S u r v e y s F i n a n c i a l M ai n B al a n ce d 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

Cumulative forecast weights 1.0 Main data Forecast 1 1.0 12 Balanced data Forecast 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 1.0 Forecast 4 1.0 Forecast 4 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 1.0 Forecast 7 1.0 Forecast 7 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0.

5 Variable selection Bai and Ng (2007): Smaller data sets may be more e cient Use robust versions of stepwise regressions (LARS, LASSO) Rünstler (2010) compares KF weights with LARS Selections obtained from pre-sample KF weights tend to be more robust

Euro area 0,3 0,2 Out-of-sample RMSE Gains against naive fcst Average across horizons AR(1) KFW Lars 0,3 Out-of-sample RMSE Optimal selections 0,1 0,0 0,2-0,1-0,2 All Weights 20-0,3 AR(1) All 60 50 40 30 20 15 10 0,1 LARS 30 7 6 5 4 3 2 1

Germany 0,2 0,1 Out-of-sample RMSE Gains against naive fcst Average across horizons AR(1) KFW Lars 0,5 Out-of-sample RMSE Optimal selections 0,0 0,4-0,1-0,2 AR(1) All 60 50 40 30 20 15 10 0,3 All Weights 20 LARS 30 7 6 5 4 3 2 1

France 0,3 0,2 Out-of-sample RMSE Gains against naive forecast Average across horizons AR(1) KFW Lars 0,4 Out-of-sample forecast Optimal selections 0,1 0,0 0,3-0,1-0,2-0,3 AR(1) All 60 50 40 30 20 15 10 0,2 All Weights 50 LARS 30 7 6 5 4 3 2 1