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Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
THE BRAZILIAN QUARTERLY REAL
GDP:TEMPORAL DISAGGREGATION AND
NOWCASTING.
André Nunes Maranhão - University of Brasília and Bank of BrazilAndré Minella - Central Bank of Brazil
Cleomar Gomes da Silva - Federal University of Uberlandia.
II Seminário em Macroeconomia Aplicada - EESP-FGV
19 - October - [email protected]
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Presentation
1 IntroductionMonitoring of Economic Activity
2 Temporal Disaggregation MethodsInternational ReviewAggregation and Disaggregation Methods
3 Model Selection Criteria and Data DescriptionModel Selection CriteriaData Description and Variable Selection
4 ResultsResults of Model SelectionNowcasting Exercises
5 ConclusionConclusion and Research Agenda
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Monitoring of Economic Activity
Nowcasting Problem
Economic variables and diferent frequencies:industrial production (PIM), retail survey (PMC) Monthly, 2months lag (t +2);Average Electric Energy Consumption Monthly, 1 month lag(t +1);
GDP frequency: Quarterly with Lag;IBC-Br: The Central Bank of Brazil Economic ActivityIndex;IBC-Br frequency: Monthly, 2 months lag (t +2);IBC-Br : Weaknesses and questions;Is there any room for advancement and improvement?
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
International Review
Literature
Article ThemeBoot, Feibes & Lisma (1965) Interpolation methods
Denton (1971) Interpolation methodsChow & Lin (1971) Parametric modelFernandez (1981) Unit root case
Gregoir (1995) Dynamic modelSalazar et al. (1997, 1998) Dynamic model
Santos, Silva & Cardoso (2001) Dynamic modelMonch & Uhlig (2005) State-Space (SS) model
Cardoso (1981) Fisrt brazilian caseNotini et alli. (2012) SS Coincident index for brazilian GDP
Table : Time evolution of the disaggregation models
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Aggregation and Disaggregation Methods
Concepts and Definitions
yl,t =s∑
i=1
ciyh,i
Yl = CYh
Yh = AYl
Ct×3t =13
1 1 1 0 0 0 0 · · · 00 0 0 1 1 1 0 · · · 0...
......
......
......
. . ....
0 0 0 0 0 0 0 · · · 1
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Aggregation and Disaggregation Methods
First Model
Chow & Lin (1971):
Yl = X ′l β + ul ul ∼ N(0,Vl)
Yh = X ′hβ + uh uh ∼ N(0,Vh)
uh,t = ρuh,t−1 + εt
ε ∼ N(0, σ2ε )
Yh = A(X ′l β + ul)⇔ Yh = AYl
minβ,ρ
COV (Yh − Yl)
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Aggregation and Disaggregation Methods
A Disaggregation Model using Kalman Filter
Monch & Uhlig (2005):
y+ = (0 0 y3 0 0 y6 0 0 y9...)
y+l,t =
13
2∑i=0
yh,t−i , t=3,6,9,...
0, otherwise
y+l,t = Htξt
Ht =
{[1/3 1/3 1/3 0], para, t = 3,6,9, ...
[0 0 0 0], otherwise
ξt =
yh,t
yh,t−1yh,t−2uh.t
=
φ 0 0 ρ1 0 0 00 1 0 00 0 0 ρ
×
yh,t−1yh,t−2yh,t−3uh,t−1
+
X ′h,tβ
000
+
εt00εt
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Aggregation and Disaggregation Methods
State-Space Models for Disaggregation
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Model Selection Criteria
Methods of Evaluation
In-Sample CriteriaMonch & Uhlig (2005):
R2diff =
Var(∆y+t |T )
Var(∆y+t |T ) + Var(∆ut |T )
Out-of-Sample CriteriaProietti (2006):
MAPE =1T
T∑t=1
∣∣∣∣∣ y+t − y+
t
y+t
∣∣∣∣∣RMSE =
√√√√ 1T
T∑t=1
(y+t − y+
t )2
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Data Description and Variable Selection
Variable Selection
1st quarter of 2003 to the 2rd quarter of 2017 (Real GDP);54 variables were tested;Unit root tests: ADF, MADFgls, with and without structuralbreaks - Perron (1989), determinist trend with structuralbreaks;Cross correlation in first difference: Monch & Uhlig (2005),Notini & Issler (2008) and Notini et alli. (2012);Causality tests;Principal Component Analysis in time series context;
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Data Description and Variable Selection
Selected Variables
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Results of Model Selection
Models Selected
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Nowcasting Exercises
Model t+1
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Nowcasting Exercises
Model t+2 without IBC-Br
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Nowcasting Exercises
Model t+2
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Nowcasting Exercises
Predictive Ability
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Conclusion and Research Agenda
Final Considerations
Main Contribuitions1 Model (t+1) and GDP disaggregation;
Same predictive capacity of the IBC-Br, however withvariables t + 1;The quarterly average coincides with the values of realGDP, in this sense it is literally a coincident indicator.
2 Model (t+2) without IBC-Br and Model (t+2);Both models have a better predictive performance than theIBC-Br;The quarterly average coincides with the values of realGDP.In all models of the nowcasting exercise, we have themonthly estimate of real GDP for the periods prior tonowcasting. (Temporal disaggregation of real GDP).
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Conclusion and Research Agenda
Final Considerations
Research Agenda1 Possibility of testing variables from the big data context;2 Use of high-dimensional time series models;3 Extended temporal sample for the purpose of using
predictability tests as presented by Giacomini and White(2006);
4 Study of turning points and economic cycles.
Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion
Conclusion and Research Agenda
Article Presented:
THE BRAZILIAN QUARTERLY REAL GDP:TEMPORAL
DISAGGREGATION AND NOWCASTING.
André Nunes Maranhão.
THANK YOU ALL.