Forecasting GDP growth

Transcription

1 Forecasting GDP growth Torsten Lisson (contact: Emanuel Gasteiger (contact: Note: This talk was given at the class Economic Forecasting of Prof. Robert. M. Kunst at the University of Vienna, Austria on January the 9 th 2007.

2 Introduction Model-free forecast Model-based univariate forecast Model-based multivariate forecast Discussion of results Exhibit 2

3 Basic idea to this study steams from the Keynesian economy How close are our forecasts of model-free and model-based procedures to forecasts of leading research institutions? How do forecasts develope if we use the components of the GDP according to a Keynesian economy? Y = C + G + I + (EX " IM Exhibit 3

4 We use public data of the Austrian GDP and its components on quarterly basis Data source: Data set: Country: Period: Variables: GDP (Y t Statistical Office of the European Communities (EUROSTAT Austria 1988q01 to 2006q03 (75 observations Household and non-profit sector consumption (C t Government expenditures (G t Gross investment (I t Exports of goods and services (EX t Imports of goods and services (IM t Unit: mio. EURO fixed prices (base year is 1995 Exhibit 4

5 GDP over time shows clear cyclical patterns and trending Cyclical patterns: q1 to q2 Trends: q2 to q3 q3 to q4 q4 to q1 More ressources Technological progress (Inflation in nominal GDP Exhibit 5

6 The time series of GDP growth rate appears to be stable but cyclical patterns remain The growth rate: y ˆ t = (Y "Y t t"1 Y t"1 Exhibit 6

7 Introduction Model-free forecast Model-based univariate forecast Model-based multivariate forecast Discussion of results Exhibit 7

8 We choose the Holt-Winters Seasonal Smoothing method Why Holt-Winters method? Which parameter shall one choose? Which form shall one choose? Exhibit 8

9 Recall the Holt-Winters method Multiplicative version: L t = " X t S t#s + (1#"(L t#1 + T t#1 Additive version: L t = "(X t # S t#s + (1#"(L t#1 + T t#1 T t = "(L t # L t#1 + (1# "T t#1 T t = "(L t # L t#1 + (1# "T t#1 S t = " X t L t + (1# "S t#s S t = " X t L t + (1# "S t#s X^ N (h = (L N + T N hs N +h"s X^ N (h = L N + T N h + S N +h"s Note: Stata derives the starting value from the mean of the first half of the samples observations by default Exhibit 9

10 We evaluate the procedures by the predicted mean squared error (PRMSE Idea: we want a good forecast, not the best model fit Evaluation method: benchmark observations Y t used observations for prediction predictions PRMSE = 1 n "( Y ˆ i #Y i 2 n i= 72 ˆ Y t 88 q1 05 q3 06 q3 forecast Note: For all further analysis we use the sub-sample of 71 observations Exhibit 10

11 Evaluation results favour the additive (0.3; 0.3; 0.3 method Evaluation results: Multiplicative Additive Course (0,3; 0,1; 0,1 0, ,01250 Literature maximum (0,3; 0,3; 0,3 0, ,01138 Stata (0,?; 0,?; 0,? 0, ,01214 We choose (0,3; 0,3; 0,3 Exhibit 11

12 Best multiplicative Holt-Winters prediction appears to be explosive Exhibit 12

13 Best additive Holt-Winters prediction appears to be more realistic Exhibit 13

14 Introduction Model-free forecast Model-based univariate forecast Model-based multivariate forecast Discussion of results Exhibit 14

15 The time series ˆ y t is not first order integrated We perform a Dickey-Fuller test: ˆ H 0 : y t is I(1 vs. H 1 : y t is stationary ˆ Critical values: Dickey-Fuller Value: 1%-level: -3,548 5%-level: -2,912 10%-level: -2,591 > -11,811 ˆ y t is stationary Exhibit 15

16 We use 4 methods to find the right lag-order Correlation functions Information criteria Residual diagnostics Hypotheses testing Exhibit 16

17 The correlation functions do not converge to zero and point in the direction of seasonal adjustment Exhibit 17

18 We can not be sure about a seasonal pattern from the correlation functions of 4 ˆ y t We focus on ARMA models Exhibit 18

19 Akaike and Schwarz Information Criterion both recommend a ARMA (3,3 model Akaike criterion Schwarz criterion MA(q AR(p MA(q AR(p , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,0382 Exhibit 19

20 We analyse the residuals by the Portmanteau Test We perform the test for all of the 20 models We plot the 4 models where the Q-Statistic is lower than the critical value of the chi-squared distribution We choose our favourite model by eyeball analysis Exhibit 20

21 Residuals of ARMA (2,4 Exhibit 21

22 Residuals of ARMA (3,2 Exhibit 22

23 Residuals of ARMA (3,4 Exhibit 23

24 Residuals of ARMA (3,3 Exhibit 24

25 The general to specific approach of hypothesis testing recommends a ARMA (3,3 model y ˆ t = * " ˆ 1 y t#1 + * " ˆ 2 y t#2 + * " ˆ 3 y t#3 + $ t + % * 1$ t#1 + % * 2$ t#2 + % * 3$ t#3 + % 4 $ t#4 ˆ y t = " * 1 ˆ y t#1 + " * 2 ˆ y t#2 + " * 3 ˆ y t#3 + $ t + % * 1$ t#1 + % * 2 $ t#2 + % * 3 $ t#3 Exhibit 25

26 The ARMA (3,3 comes close to the data Exhibit 26

27 We receive similar models for the sum of the components of the GDP Sum up the components + Calculate the growth rate + Iterate procedures Y t = C t + G t + I t + (EX t " IM t y ˆ t = (Y "Y t t"1 Y t"1 Model-free / model-based univariate approach Receive similar models Exhibit 27

28 Y t and the sum of its components is almost the same Exhibit 28

29 Introduction Model-free forecast Model-based univariate forecast Model-based multivariate forecast Discussion of results Exhibit 29

30 Multivariate analysis is based on the components of the GDP We estimate a multivariate VAR model of the components of Y t : " ln(c t % " ln(c t(1 % " ln(c t(2 % " ln(c t(3 % " ln(c t(4 % $ ' $ ' $ ' $ ' $ ' $ ln(g t ' $ ln(g t(1 ' $ ln(g t(2 ' $ ln(g t(3 ' $ ln(g t(4 ' $ ln(i t ' = A 1 $ ln(i t(1 ' + A 2 $ ln(i t(2 ' + A 3 $ ln(i t(3 ' + A 4 $ ln(i t(4 ' + t $ ' $ ' $ ' $ ' $ ' $ ln(ex t ' $ ln(ex t(1 ' $ ln(ex t(2 ' $ ln(ex t(3 ' $ ln(ex t(4 ' # $ ln(im t &' # $ ln(im t(1 &' # $ ln(im t(2 &' # $ ln(im t(3 &' # $ ln(im t(4 &' Exhibit 30

31 The information criterias suggest a VAR(4 model We compare VAR(. models: Akaike Schwarz HQ VAR (0-13, , ,5647 VAR (1-22, , ,0562 VAR (2-23, , ,7482 VAR (3 VAR (4 VAR (5-23, ,3994* -25, , ,0266* -21, , ,0597* -23,6622 We check whether VAR(4 is stable by the stability condition below: det(i K " #z $ 0 det(i K " # 1 z " # 2 z 2 " # 3 z 3 " # 4 z 4 $ 0, for z 1 Exhibit 31

32 Before calculating the growth rate one has to remove the logarithm and sum up the predicted values Finally we calculate the growth rate: y ˆ t +h = ( C ˆ t +h + G ˆ t +h + I ˆ t +h + B ˆ t +h " ( C ˆ t +h"1 + G ˆ t +h"1 + I ˆ t +h"1 + B ˆ t +h"1 ( C ˆ t +h"1 + G ˆ t +h"1 + I ˆ t +h"1 + B ˆ t +h"1 y ˆ t +h = ( Y ˆ t +h " Y ˆ t +h"1 Y ˆ t +h"1, where B:= (EX-IM Exhibit 32

33 The VAR(4 seems to be close to the data Exhibit 33

34 Introduction Model-free forecast Model-based univariate forecast Model-based multivariate forecast Discussion of results Exhibit 34

35 The differences in the forecast results are quiet high H.-W. M. Univariate H.-W. M. Univariate Multivar. Wifo ( IHS ( q4 4,4% 2,1% 2,5% 3,1% 1,1% 2007q1-11,3% - 7,3% -7,4% - 9,3% -8,8% 2007q2 6,1% 5,1% 4,1% 6,2% 7,5% 2007q3 4,5% 3,0% 2,9% 3,0% 1,9% 2007q4 4,9% 2,1% 2,5% 3,1% 0,9% ,7% 2,7% 2,2% 2,3% 1,1% 2,7% 2,6% Y t Y t = C t +G t +I t +EX t -IM t The univariate ARMA (3,3 model is in line with the forecasts of the research institutions Exhibit 35

36 Thank you! Exhibit 36

37 Back up Exhibit 37

38 Nominal versus real GDP Why to correct for inflation? Uncover the true trend of GDP Stabilize variance, i.e. eliminate price-shocks Exhibit 38

39 Complete output for ACF and PACF of Y t Exhibit 39

40 Complete output for ACF and PACF of 4 Y t Exhibit 40