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 di¤usion 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