incorporating uncertainties into economic forecasts: an application to forecasting economic activity...
DESCRIPTION
1. INTRODUCTION 2. METHODOLOGY 3. RESULTS 4. CONCLUSIONTRANSCRIPT
Incorporating Uncertainties into Economic Forecasts: an Application to Forecasting
Economic Activity in Croatia
Dario RukeljMinistry of Finance of the Republic of Croatia
Barbara UlloaCentral Bank of Chile
Young Economists’ Seminar (YES)Dubrovnik Economic Conference
June 23, 2010
Uncertainty is the only certainty there is, and knowing how to live with insecurity is the only security...
John Allen Paulos
1. INTRODUCTION
2. METHODOLOGY
3. RESULTS
4. CONCLUSION
MOTIVATION
Source: European Commission
-5
-4
-3
-2
-1
0
1
2
3
4
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
%
Projection in the current year Projection one year aheadProjection two years ahead Outturn
FORECASTS OF THE EUROZONE REAL GDP GROWTH
DEALING WITH UNCERTAINTY
Point forecasts Mode of distribution
Interval forecasts Consists of an upper and a lower limit
Density forecasts The whole probability distribution of the forecasts
1. INTRODUCTION
2. METHODOLOGY
3. RESULTS
4. CONCLUSION
STOCHASTIC SIMULATION APPROACH*
Data generating process assumed to be VAR model, estimated in the finite sample:
tit
p
iit tyy
10
1
ˆˆˆ
Forecasts incorporating future uncertainties:
)(10
)(
1
)( )(ˆˆˆˆ xhT
xihT
p
ii
xhT uhTyy
Forecasts incorporating future and parameter uncertainties: Simulate s in sample values of y
For each of these estimated models, r replications of the forecasts are calculated
)(10
)(
1
)( ˆˆˆˆ st
sit
p
ii
st utyy
),(),(
1
)(),( )(ˆˆˆˆ10
sxhT
sssxihT
p
i
ssxhT uhTyy
i
* Garrat, Pessaran and Shin (2003 and 2006)
SIMULATED SHOCKS Parametric approach :
),()(),( ˆ srht
ssrht vPu
)'()()( ˆˆˆ sss PP
),0(),( IIINv srht
Non-parametric approach: random draws with replacements from the in sample residuals
Unbalanced risks:
xforxC
xforxCvf sr
ht
,2
1exp
,2
1exp),,,'(
222
221
21),(
121
kC /2k
CALCULATION
Future uncertainty Obtain the set of simulated shocks Generate the forecasts using the simulated shocks Sort the forecasted values of the variable of interest Determine probability bands by the deciles
Future and parameter uncertainty Using initial values for the number of lags determined by the order of the VAR, calculate
forecasts ahead using estimated parameters of the initial model, as well as applying a shock to each observation in each period
Re estimate the models with each set of time series obtained in this way Based on these models forecasts are made like under only future uncertainty
PRESENTATION
5.15
5.17
5.19
5.21
5.23
5.25
5.27
5.29
2007 I IV VII X 2008 I IV VII X 2009 I IV
Prob
abili
ty d
ensi
ty
90%
80%
70%
50%
60%
Probability Distribution Fanchart
EVALUATION
In Sample Fancharts
5.120
5.140
5.160
5.180
5.200
5.220
5.240
5.260
5.280
5.300
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Probability Integral Transform
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1 2 3 4 5 6
KOLMOGOROV – SMIRNOV TEST
Kolmogorov – Smirnov test can be used for comparing two distributions
Comparing Probability Integral Transform of outturns with uniform distribution
Let F(a) be the cumulative distribution function of uniform distribution
Cumulative distribution function of empirical distribution is given by:
tn
baF 1,ˆ
aFbaFD i ,ˆmax
where t is the number of observations of variable b such that
If variable b comes from uniform distribution then D should be small
b a
1. INTRODUCTION
2. METHODOLOGY
3. RESULTS
4. CONCLUSION
Reduced form VECM from Rukelj (2010) considered:
ttttt uxxctbxx 661111ˆ...ˆˆ)1(ˆ'
where xt is vector of endogenous variables (m, g and y).
Rewritten in a VAR form:
titi
it utyx 10
7
1
ˆˆˆ
PORTMANTEAU TEST (H0:Rh=(r1,...,rh)=0)
Tested order: 10
Adjusted test statistic 66.884
p-Value: 0.151
JARQUE-BERA TEST
Variable Test Statistic p-Value Skewness Kurtosis
u1 1.074 0.585 0.052 3.421
u2 14.798 0.001 0.745 3.609
u3 1.066 0.587 0.060 3.415
BENCHMARK MODEL
FUTURE UNCERTAINTY
Fanchart – Parametric Approach PIT – Parametric Approach
5.10
5.15
5.20
5.25
5.30
2006I
IV VII X 2007I
IV VII X 2008I
IV VII X 2009I
IV0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1 2 3 4 5 6 7 8 9 10 11 12
FUTURE UNCERTAINTY
Fanchart – Non Parametric Approach PIT – Non Parametric Approach
5.10
5.15
5.20
5.25
5.30
2006I
IV VII X 2007I
IV VII X 2008I
IV VII X 2009I
IV 0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1 2 3 4 5 6 7 8 9 10 11 12
FUTURE UNCERTAINTY
Fanchart – Skewed Distribution PIT – Skewed Distribution
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1 2 3 4 5 6 7 8 9 10 11 12
5.10
5.15
5.20
5.25
5.30
2006I
IV VII X 2007I
IV VII X 2008I
IV VII X 2009I
IV
FUTURE AND PARAMETER UNCERTAINTY
Fanchart – Parametric Approach PIT – Parametric Approach
4.90
5.00
5.10
5.20
5.30
5.40
5.50
2006I
IV VII X 2007I
IV VII X 2008I
IV VII X 2009I
IV 0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1 2 3 4 5 6 7 8 9 10 11 12
FUTURE AND PARAMETER UNCERTAINTY
Fanchart – Non Parametric Approach PIT – Non Parametric Approach
4.90
5.00
5.10
5.20
5.30
5.40
5.50
2006I
IV VII X 2007I
IV VII X 2008I
IV VII X 2009I
IV 0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1 2 3 4 5 6 7 8 9 10 11 12
KOLMOGOROV – SMIRNOV TEST RESULTS
Kolmogorov (D) 1 2 3 4 5 6 7 8 9 10 11 12
Value (D) 0.14 0.20 0.24 0.18 0.30 0.26 0.21 0.24 0.22 0.22 0.21 0.19Adjusted value 0.83 1.25 1.47 1.13 1.83 1.60 1.30 1.49 1.34 1.38 1.26 1.17Probability 0.49 0.09 0.03 0.16 0.00 0.01 0.07 0.02 0.06 0.04 0.08 0.13
Value (D) 0.17 0.22 0.26 0.22 0.29 0.28 0.24 0.28 0.25 0.24 0.22 0.20Adjusted value 1.06 1.33 1.62 1.37 1.79 1.69 1.49 1.73 1.52 1.45 1.37 1.24Probability 0.21 0.06 0.01 0.05 0.00 0.01 0.02 0.00 0.02 0.03 0.05 0.09
Value (D) 0.20 0.17 0.19 0.17 0.23 0.29 0.26 0.30 0.30 0.27 0.29 0.27Adjusted value 1.22 1.06 1.16 1.04 1.39 1.79 1.60 1.86 1.86 1.67 1.79 1.66Probability 0.10 0.21 0.14 0.23 0.04 0.00 0.01 0.00 0.00 0.00 0.00 0.01
Value (D) 0.41 0.42 0.41 0.43 0.40 0.42 0.39 0.38 0.38 0.37 0.38 0.37Adjusted value 2.53 2.61 2.52 2.65 2.45 2.59 2.42 2.35 2.33 2.30 2.35 2.28Probability 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Value (D) 0.35 0.38 0.38 0.35 0.39 0.38 0.36 0.39 0.33 0.35 0.35 0.32Adjusted value 2.18 2.35 2.35 2.15 2.42 2.33 2.22 2.39 2.01 2.15 2.15 1.96Probability 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Future and parameter uncertainty, non - parametric
Future uncertainty, parametric
Future uncertainty, non - parametric
Future uncertainty, skewed (σ1=1, σ2=2)
Future and parameter uncertainty, parametric
1. INTRODUCTION
2. METHODOLOGY
3. RESULTS
4. CONCLUSION
FORECASTING WITH UNCERTAINTY
Probability Forecasts for the Real GDP Growth
2010 Q1 2010 Q2 2010 Q3 2010 Q4 2011 Q1 2011 Q2 2011 Q3 2011 Q4
Central Projection -2.50 -0.50 0.50 1.00 2.50 2.00 1.50 1.00
Probability that distribution will be between specified interval, %
Pr. {<0%} 95 62 43 35 32 34 37 41Pr. {0% - 2%} <5 34 32 31 29 27 22 19Pr. {2% - 4%} <5 <5 22 21 20 20 18 16Pr. {>6%} <5 <5 <5 <5 19 19 23 24
CONCLUSION
In this paper we have shown how to calculate, present and evaluate density forecasts by stochastic simulation approach
An application of this methodological framework to the chosen benchmark model showed that: parametric and non-parametric approach yielded similar results incorporating parameter uncertainty results in a much wider probability
bands of the forecasts evaluation of the density forecasts indicate a better performance when
only future, without parameter uncertainties are considered
Future research in this topic should incorporate model uncertainty and additional goodness of fit tests
Thank you for your attention!