Forecasting GDP growth - Zentraler Informatikdiensthomepage.univie.ac.at/robert.kunst/070107_efc.pdf · Forecasting GDP growth Torsten Lisson ... We use public data of the Austrian

Forecasting GDP growth

Torsten Lisson (contact: torsten.lisson@gmail.com)Emanuel Gasteiger (contact: emanuel.gasteiger@gmail.com)

Note: This talk was given at the class „Economic Forecasting“ of Prof. Robert. M. Kunst at the University of Vienna, Austria on January the 9th 2007.

Exhibit 2

Introduction

Model-free forecast

Model-based univariate forecast

Model-based multivariate forecast

Discussion of results

Exhibit 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 ofleading research institutions?

!

Y = C +G + I + (EX " IM)

How do forecasts develope if we use the components of the GDP according to a Keynesianeconomy?

Exhibit 4

We use public data of the Austrian GDP and its components onquarterly basis

Data source: Statistical Office of the European Communities (EUROSTAT)http://ec.europa.eu/eurostat

Data set: Country: Austria Period: 1988q01 to 2006q03 (75 observations) Variables:

GDP (Yt) Household and non-profit sector consumption (Ct) Government expenditures (Gt) Gross investment (It) Exports of goods and services (EXt) Imports of goods and services (IMt)

Unit: mio. EURO fixed prices (base year is 1995)

Exhibit 5

GDP over time shows clear cyclical patterns and trending

Cyclical patterns:

q1 to q2 ⇑

q2 to q3 ⇑

q3 to q4 ⇑

q4 to q1 ⇓

Trends: More ressources Technological progress (Inflation in nominal

GDP)

Exhibit 6

The time series of GDP growth rate appears to be stable butcyclical patterns remain

!

ˆ y t =(Yt "Yt"1

)

Yt"1

The growth rate:

Exhibit 7

Introduction

Model-free forecast

Model-based univariate forecast

Model-based multivariate forecast

Discussion of results

Exhibit 8

We choose the Holt-Winters Seasonal Smoothing method

Why Holt-Winters method?

Which parameter shall one choose?

Which form shall one choose?

Exhibit 9

Recall the Holt-Winters method

Multiplicative version: Additive version:

!

Lt="(X

t# S

t#s) + (1#")(Lt#1 + T

t#1)

!

Tt

= "(Lt# L

t#1) + (1#")Tt#1

!

St= "

Xt

Lt

+ (1# ")St#s

!

X

^

N (h) = LN

+ TNh + S

N +h"s

!

Lt="

Xt

St#s

+ (1#")(Lt#1 + T

t#1)

!

Tt

= "(Lt# L

t#1) + (1#")Tt#1

!

St= "

Xt

Lt

+ (1# ")St#s

!

X

^

N (h) = (LN

+ TNh)S

N +h"s

Note: Stata derives the starting value from the mean of the first half of the samples’ observations by default

Exhibit 10

We evaluate the procedures by the predicted mean squarederror (PRMSE)

!

ˆ Y t

!

Yt

88q1 05q3!

PRMSE =1

n( ˆ Y

i

i= 72

n

" #Yi)

2

06q3

used observations forprediction

Evaluation method:

benchmarkobservations

forecast

predictions

Idea: we want a good forecast, not the best model fit

Note: For all further analysis we use the sub-sample of 71 observations

Exhibit 11

Evaluation results favour the additive (0.3; 0.3; 0.3) method

0,012500,011380,01214

Multiplicative Additive(0,3; 0,1; 0,1)(0,3; 0,3; 0,3)(0,?; 0,?; 0,?)

0,266340,012300,01312

Course

Evaluation results:

StataLiterature maximum

We choose (0,3; 0,3; 0,3)

Exhibit 12

Best multiplicative Holt-Winters prediction appears to beexplosive

Exhibit 13

Best additive Holt-Winters prediction appears to be morerealistic

Exhibit 14

Introduction

Model-free forecast

Model-based univariate forecast

Model-based multivariate forecast

Discussion of results

Exhibit 15

We perform a Dickey-Fuller test:

H0: is I(1) vs. H1: is stationary

The time series is not first order integrated

1%-level: -3,548

5%-level: -2,912

10%-level: -2,591

> -11,811

Critical values: Dickey-Fuller Value:

is stationary

!

ˆ y t

!

ˆ y t

!

ˆ y t

!

ˆ y t

Exhibit 16

We use 4 methods to find the right lag-order

Correlation functions

Information criteria

Residual diagnostics

Hypotheses testing

Exhibit 17

The correlation functions do not converge to zero and point inthe direction of seasonal adjustment

Exhibit 18

We can not be sure about a seasonal pattern from thecorrelation functions of ∆4

We focus on ARMA models

!

ˆ y t

Exhibit 19

Akaike and Schwarz Information Criterion both recommend aARMA (3,3) model

Akaike criterion

0 1 2 3

0

AR(p)

MA(q)

-225,2912 -230,4085 -246,6321 -385,382

1 -260,3076 -258,3298 -276,264 -414,176

2 -275,2224 -256,7264 -310,5073 -419,3524

3 -281,6136 -279,678 -336,7877 -435,191

4 -281,1353 -283,1412 -272,3503 -434,2746

0 1 2 3

0

AR(p)

MA(q)

-220,7943 -223,663 -237,6381 -374,1395

1 -253,5621 -249,3358 -265,0216 -400,6856

2 -266,2284 -245,484 -297,0163 -403,6129

3 -270,3711 -266,187 -323,2968 -417,203

4 -267,6443 -269,9202 -254,3624 -414,0382

Schwarz criterion

Exhibit 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-squareddistribution

We choose our favourite model by eyeball analysis

Exhibit 21

Residuals of ARMA (2,4)

Exhibit 22

Residuals of ARMA (3,2)

Exhibit 23

Residuals of ARMA (3,4)

Exhibit 24

Residuals of ARMA (3,3)

Exhibit 25

The general to specific approach of hypothesis testingrecommends a ARMA (3,3) model

!

ˆ y t ="*

1ˆ y t#1

+"*

2ˆ y t#2

+"*

3ˆ y t#3

+ $t +%*

1$t#1+%

*

2$t#2+%

*

3$t#3+%

4$t#4

!

ˆ y t ="*

1ˆ y t#1

+"*

2ˆ y t#2

+"*

3ˆ y t#3

+ $t +%*

1$t#1+%

*

2$t#2+%

*

3$t#3

Exhibit 26

The ARMA (3,3) comes close to the data

Exhibit 27

Calculate the growth rate

We receive similar models for the sum of the components of theGDP

!

Yt= C

t+G

t+ I

t+ (EX

t" IM

t)Sum up the components

+

Receive similar models!

ˆ y t =(Yt "Yt"1

)

Yt"1

Iterate procedures

+Model-free / model-based univariate approach

Exhibit 28

Yt and the sum of its components is almost the same

Exhibit 29

Introduction

Model-free forecast

Model-based univariate forecast

Model-based multivariate forecast

Discussion of results

Exhibit 30

Multivariate analysis is based on the components of the GDP

!

ln(Ct)

ln(Gt)

ln(It)

ln(EXt)

ln(IMt)

"

#

$ $ $ $ $ $

%

&

' ' ' ' ' '

= A1

ln(Ct(1)

ln(Gt(1)

ln(It(1)

ln(EXt(1)

ln(IMt(1)

"

#

$ $ $ $ $ $

%

&

' ' ' ' ' '

+ A2

ln(Ct(2)

ln(Gt(2)

ln(It(2)

ln(EXt(2)

ln(IMt(2)

"

#

$ $ $ $ $ $

%

&

' ' ' ' ' '

+ A3

ln(Ct(3)

ln(Gt(3)

ln(It(3)

ln(EXt(3)

ln(IMt(3)

"

#

$ $ $ $ $ $

%

&

' ' ' ' ' '

+ A4

ln(Ct(4 )

ln(Gt(4 )

ln(It(4 )

ln(EXt(4 )

ln(IMt(4 )

"

#

$ $ $ $ $ $

%

&

' ' ' ' ' '

+ )t

We estimate a multivariate VAR model of the components of Yt:

Exhibit 31

The information criterias suggest a VAR(4) model

Akaike SchwarzVAR (0)

VAR (2)VAR (1)

-13,5647-22,0562-22,7482-22,9124-24,0597*-23,6622

HQ

VAR (3)VAR (4)

We compare VAR(.) models:

-13,6285-22,4389-23,4499-23,9331-25,3994*-25,3208

-13,4679-21,4753-21,6832-21,3634-22,0266*-21,1451VAR (5)

We check whether VAR(4) is stable by the stability condition below:

!

det(IK" #z) $ 0

det(IK" #1z " #2z

2" #3z

3" #4z

4) $ 0, for |z|≤1

Exhibit 32

Before calculating the growth rate one has to remove thelogarithm and sum up the predicted values

, where B:= (EX-IM)

Finally we calculate the growth rate:

!

ˆ y t +h =( ˆ C t +h + ˆ G t +h + ˆ I t +h + ˆ B t +h " ( ˆ C t +h"1

+ ˆ G t +h"1+ ˆ I t +h"1

+ ˆ B t +h"1))

( ˆ C t +h"1+ ˆ G t +h"1

+ ˆ I t +h"1+ ˆ B t +h"1

)

!

ˆ y t +h =( ˆ Y t +h "

ˆ Y t +h"1)

ˆ Y t +h"1

Exhibit 33

The VAR(4) seems to be close to the data

Exhibit 34

Introduction

Model-free forecast

Model-based univariate forecast

Model-based multivariate forecast

Discussion of results

Exhibit 35

The differences in the forecast results are quiet high

2,1%- 7,3% 5,1% 3,0% 2,1% 2,7%

1,1%-8,8% 7,5% 1,9% 0,9% 1,1% 2,7% 2,6%

H.-W. M. Univariate Multivar. Wifo (21.12.06) IHS (21.12.06)

2006q42007q12007q22007q32007q4

2007

4,4%- 11,3% 6,1% 4,5% 4,9% 5,7%

3,1%- 9,3% 6,2% 3,0% 3,1% 2,3%

H.-W. M. Univariate

2,5%-7,4%4,1%2,9%2,5%2,2%

Yt Yt = Ct+Gt+It+EXt-IMt

The univariate ARMA (3,3) model is in line with the forecasts of the researchinstitutions

Exhibit 36

Thank you!

Exhibit 37

Back up

Exhibit 38

Nominal versus real GDP

Why to correct for inflation?

Uncover the true trendof GDP

Stabilize variance, i.e.eliminate price-shocks

Exhibit 39

Complete output for ACF and PACF of Yt

Exhibit 40

Complete output for ACF and PACF of ∆4Yt