Short-term forecasts of GDP from dynamic factor models

Transcription

1 Short-term forecasts of GDP from dynamic factor models Gerhard Rünstler Austrian Institute for Economic Research November 16, 2011

2 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

3 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 )

4 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 )

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

6 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

7 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 Q Q2 Pseudo-real time forecast design recursive estimates replicate real-time data availability but nal data vintages

8 Table 1. Bridge equations for euro area GDP growth (BES model). Equation Explanatoryvariables Industrial production (total) Ind. production construction Retail sales New car registrations Service confidence Unemployment rate Money M1 Business confidence EuroCoin (CEPR) OECD leading indicator

9 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

10 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

11 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

12 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

13 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

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17 Short-term forecasts of euro area GDP growth C

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19 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)

20 No of series Production and sales Table 1: Datasets of which Surveys Financial Prices Other Sample start Euro area EA Belgium BE Germany DE France FR Italy IT Netherlands NL Portugal PT Lithuania LT Hungary HU Poland PL

21 Table 3: Results overview Forecasts 2000 Q Q4 for euro area countries and 2002 Q 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 VAR BEQ KF PC GPC

22 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

23 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

24 Cumulative forecast weights 1.0 Main data Forecast Balanced data Forecast Forecast Forecast Forecast Forecast

25 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

26 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 ,1 LARS

27 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 ,3 All Weights 20 LARS

28 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 ,2 All Weights 50 LARS