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Journal ArticleDOI

Forecasting australian macroeconomic variables using a large dataset

01 Mar 2010-Social Science Research Network (Blackwell Publishing Asia)-Vol. 49, Iss: 1, pp 44-59

Abstract: This paper investigates the forecasting performance of the diffusion index approach for the Australian economy, and considers the forecasting performance of the diffusion index approach relative to composite forecasts Weighted and unweighted factor forecasts are benchmarked against composite forecasts, and forecasts derived from individual forecasting models The results suggest that diffusion index forecasts tend to improve on the benchmark AR forecasts We also observe that weighted factors tend to produce better forecasts than their unweighted counterparts We find, however, that the size of the forecasting improvement is less marked than previous research, with the diffusion index forecasts typically producing mean square errors of a similar magnitude to the VAR and BVAR approaches

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Melbourne Institute Working Paper Series
Working Paper No. 4/08
Forecasting Australian Macroeconomic
Variables Using a Large Dataset
Sarantis Tsiaplias and Chew Lian Chua

Forecasting Australian Macroeconomic Variables
Using a Large Dataset*
Sarantis Tsiaplias and Chew Lian Chua
Melbourne Institute of Applied Economic and Social Research
The University of Melbourne
Melbourne Institute Working Paper No. 4/08
ISSN 1328-4991 (Print)
ISSN 1447-5863 (Online)
ISBN 978-0-7340-3272-0
March 2008
* This research was funded by a grant from the Faculty of Economics and Commerce,
The University of Melbourne.
Melbourne Institute of Applied Economic and Social Research
The University of Melbourne
Victoria 3010 Australia
Telephone (03) 8344 2100
Fax (03) 8344 2111
Email melb-inst@unimelb.edu.au
WWW Address http://www.melbourneinstitute.com

Abstract
This paper investigates the forecasting performance of the diffusion index
approach for the Australian economy, and considers the forecasting performance of
the diffusion index approach relative to composite forecasts. Weighted and
unweighted factor forecasts are benchmarked against composite forecasts, and
forecasts derived from individual forecasting models. The results suggest that
diffusion index forecasts tend to improve on the benchmark AR forecasts. We also
observe that weighted factors tend to produce better forecasts than their unweighted
counterparts. We find, however, that the size of the forecasting improvement is less
marked than previous research, with the diffusion index forecasts typically producing
mean square errors of a similar magnitude to the VAR and BVAR approaches.
Keywords: Diffusion indexes; Forecasting; Australia.
JEL classification: C22; C53; E17

1 Introduction
Given the abundance of economic information available to forecasters, it is not
surprising that extensive research has been undertaken on methods aimed at rep-
resenting the information inherent in large datasets using a small number of vari-
ables. Stock and Watson (2002a,b) nd that the forecasts generated using a small
number of common factors outperform forecasts obtained from AR or VAR models
for US macroeconomic variables. Similarly, Forni et al. (2005) nd that factor-
based forecasts performed better than AR forecasts for European in‡ation and
production. Outside of the major North American and European economies, how-
ever, there is little evidence regarding the properties of forecasts generated using
di¤usion indexes or common factors.
This paper augments the existing literature in two ways. First, it investigates
the forecasting performance of the di¤usion index approach for the Australian
economy. And second, it considers the relative forecasting performance of the
di¤usion index approach relative to composite forecasts.
To evaluate the forecasting performance of the dusion index approach we
consider two methods for obtaining forecasts using common factors. The methods
are applied to principal components estimated using both unweighted and weighted
estimation methods. The factor-based forecasts are benchmarked against forecasts
derived from AR, VAR, Bayesian VAR and standard multivariate models. The
forecasting performance of the factor models is also compared to the performance
of composite forecasts generated using the individual forecasting models.
This paper is structured as follows. Section 2 de…nes the models employed to
generate forecasts. Section 3 describes the data used to estimate the forecasting
models. The fourth section presents and discusses the forecasting results. The
paper concludes with Section 5.
2 Forecasting models
We forecast the quarterly percentage changes in real and nominal GDP, the annual
unemployment rate observed at each quarter, and the quarterly headline in‡ation
rate. For each of these four variables, up to 4step ahead out of sample fore-
1

casts are generated using two di¤usion index approaches with both unweighted
and weighted factor estimates, an AR model, a multivariate forecasting approach
without a common factor component, a VAR and a BVAR. The AR and multivari-
ate approaches are chosen as popular single equation forecasting methods, while
the VAR and BVAR methods are chosen due to their popularity as macroeconomic
forecasting tools. Composite forecasts from the large set of available forecasts are
also constructed. The out of sample forecasts are generated for the 40 quarters
ending December 2006.
2.1 Unweighted PCA forecasts
The factors are extracted as the principal components of the available data set as
at time t (Stock and Watson, 2002a,b). Pursuant to this metho d, the variance-
covariance matrix of the T N data matrix X is decomposed as:
V (X) = V (F )
0
+ V (E) (1)
where V (F )
0
is the reduced-rank common component of the variance-covariance
matrix V (X) and V (E) is the idiosyncratic component. The principal components
are obtained as F =
0
X (see, Bai and Ng, 2002, and Stock and Watson, 2002a,
regarding the convergence prop erties of F ). Before undertaking the decomposition
in equation (1) for any given time period, the vectors in X are standardised as
zero mean, unit variance processes.
Two approaches are used to derive the forecasts by
t+hjt
. Pursuant to the rst
approach, the principal components of the data set X are extracted and regressed
on y using the factor equation
y
t+h
=
h
+
0
h
(L)F
t
+
h
(L)y
t
+ e
t+h
(2)
where e
t+h
iidN (0;
2
h
) ; F
t
= [f
1t
; :::; f
Kt
]
0
;
h
(L) =
h;0
+
h;1
L +:::+
h;n
1
L
n
1
,
h
(L) =
h;0
+
h;1
L + ::: +
h;n
2
L
n
2
and h = 1; 2; 3 or 4. For the second ap-
proach, the principal components are obtained from an augmented matrix X
?
.
The (T n
1
) (N n
1
) matrix X
?
is constructed by augmented each vector in
the data matrix X with up to n
1
lags of itself. The forecast by
t+hjt
is then obtained
2

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Abstract: Reflecting the importance of commodities for the Australian economy, we construct a dynamic stochastic general equilibrium (DSGE) model of the Australian economy with a commodity sector. We assess whether its forecasts can be improved by using it as a prior for an empirical Bayesian vector autoregression (BVAR). We find that the forecasts from the BVAR tend to be more accurate than those from the DSGE model. Nevertheless, for output growth these forecasts do not outperform benchmark models, such as a small open economy BVAR estimated using the standard priors for forecasting. A Bayesian factor augmented vector autoregression produces the most accurate near-term inflation forecasts.

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Cites background or result from "Forecasting australian macroeconomi..."

  • ...There is little literature providing estimates of for Australia, which governs the mobility of labour between sectors in response to real-wage differentials, and as we estimate the model without using labour market data we set ¼ 0:75.9 The depreciation rates are chosen with reference to annual national accounts data, which suggest that the depreciation rate in the mining sector is lower than in the rest of the economy at nearly 5 per cent per annum....

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  • ...For Australia, Tsiaplias and Chua (2010) study several factor-based forecasts and use a BVAR as a benchmark....

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  • ...26Abbas et al. (2016) also are critical of the New Keynesian Phillips curve as a model of inflation for Australia, although they focus on evaluating variants of the curve in Galí and Monacelli (2005), rather than the approach in this model which allows for incomplete short-run pass through in import prices, which is a common specification in empirical small-open economy DSGE models....

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  • ...Given the informational advantage that the FAVAR model has, it is somewhat surprising that it does not perform better than the autoregressive or SOE Minnesota VAR for output, although this aligns with the factor forecasts of Tsiaplias and Chua (2010) and the findings of Jiang et al. (2017)....

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de Silva1, Ashton J1Institutions (1)
13 Dec 2010
Abstract: Innovations state space time series models that encapsulate the exponential smoothing methodology have been shown to be an accurate forecasting tool. These models for the first time are applied to Australian macroeconomic data. In addition new multivariate specifications are outlined and demonstrated to be accurate.

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Cites methods from "Forecasting australian macroeconomi..."

  • ...A relatively recent study is Tsiaplias & Chua (2010) which examines the use of large data sets using the same approach as Stock & Watson (2002a,b)....

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References
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Jushan Bai1, Serena Ng2Institutions (2)
Abstract: In this paper we develop some econometric theory for factor models of large dimensions. The focus is the determination of the number of factors (r), which is an unresolved issue in the rapidly growing literature on multifactor models. We first establish the convergence rate for the factor estimates that will allow for consistent estimation of r. We then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria. The theory is developed under the framework of large cross-sections (N) and large time dimensions (T). No restriction is imposed on the relation between N and T. Simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice.

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Journal ArticleDOI
James H. Stock1, Mark W. WatsonInstitutions (1)
Abstract: This article considers forecasting a single time series when there are many predictors (N) and time series observations (T). When the data follow an approximate factor model, the predictors can be summarized by a small number of indexes, which we estimate using principal components. Feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both N and T grow large. The estimated factors are shown to be consistent, even in the presence of time variation in the factor model.

2,573 citations


Journal ArticleDOI
James H. Stock1, Mark W. Watson1Institutions (1)
Abstract: This article studies forecasting a macroeconomic time series variable using a large number of predictors. The predictors are summarized using a small number of indexes constructed by principal component analysis. An approximate dynamic factor model serves as the statistical framework for the estimation of the indexes and construction of the forecasts. The method is used to construct 6-, 12-, and 24-monthahead forecasts for eight monthly U.S. macroeconomic time series using 215 predictors in simulated real time from 1970 through 1998. During this sample period these new forecasts outperformed univariate autoregressions, small vector autoregressions, and leading indicator models.

2,518 citations


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  • ...These forecasts are typically better than the forecasts obtained by allowing the BIC to determine p (the BIC often selected p = 1; Stock and Watson (2002a) encountered a similar problem with respect to US macroeconomic data)....

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  • ...Instead of selecting the number of common factors to include in the forecasting model, and in contrast to previous work (Stock & Watson, 2002a,b; Boivin & Ng, 2006), the factors F are deduced by reference to the proportion of total variance explained by the principal components....

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  • ...The principal components are obtained as F = L′X (see Bai and Ng (2002) and Stock and Watson (2002a) regarding the convergence properties of F)....

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  • ...An iterative solution to the problem is proposed in Jones (2001) and implemented here (see also Forni et al., 2005; Boivin & 2 Evidence suggesting that the BIC may be used to determine the number of common factors is available in Stock and Watson (2002a)....

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  • ...The factors are extracted as the principal components of the available data set as at time t (Stock & Watson, 2002a, 2002b)....

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Abstract: In this paper we develop some econometric theory for factor models of large dimensions The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models We propose some panel C(p) criteria and show that the number of factors can be consistently estimated using the criteria The theory is developed under the framework of large cross-sections (N) and large time dimensions (T) No restriction is imposed on the relation between N and T Simulations show that the proposed criteria yield almost precise estimates of the number of factors for configurations of the panel data encountered in practice

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  • ...the lags of F in equation ( 2 ) (or, in the case of the second factor approach, the number of lags used to generate X�); and the lags of y in equation (2)....

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  • ...Unweighted 2 0 0 32 8 0 0 0 PCA( 2 ) 3 0 9 23 8 0 0 0 4 0 18 22 0 0 0 0...

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  • ...Unweighted 2 37 0 3 0 0 -1 0 PCA( 2 ) 3 29 0 11 0 0 -1 0 4 40 0 0 0 0 -1 0...

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  • ...Unweighted 2 0 40 0 0 0 -1 0 PCA( 2 ) 3 40 0 0 0 0 -1 0 4 40 0 0 0 0 -1 0...

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