Page 351 - Special Topic Session (STS) - Volume 3

STS550 Angelia L. Grant et al.
models and the use of models that perform differently across different time
horizons. It is often the case that when forecasts from a variety of different
models are appropriately combined, the forecast combination approach
outperforms individual forecasts (see, e.g., Timmermann, 2006; Guidolin and
Timmermann, 2009; Rapach et al., 2010).
This paper develops a forecast combination approach for the components
of household consumption expenditure using autoregressive models,
regressions on relative prices and the almost ideal demand system developed
by Deaton and Muellbauer (1980). The autoregressive models capture the
1
persistence and longer-term trends in the consumption components, while
the relative price regressions and the almost ideal system capture shifts in
consumption components that are driven by relative price changes. At shorter
forecasting horizons, models that capture short-run dynamics perform well,
while at longer horizons models with trend terms and relative prices generally
perform better based on root mean squared forecast errors.
Two forecast combinations are constructed – one based on equal weights
and the other weighted based on forecasting performance according to rolling
2
squared forecast errors. The advantage of combining forecasts based on past
forecast performance is that the forecast combination is robust to changes in
modelling performance. That is, it accounts for the fact that certain models
can improve or diminish in performance over particular time periods. However,
it is also often found that equal weights perform strongly (see, e.g.,
Timmermann, 2006).
The forecast combinations generally perform better than the almost ideal
demand system, which is the model currently used for estimating the
household final consumption components. The fuels and lubricants and the
electricity and gas components are the components where the forecast
combination performance is closest to that of the almost ideal demand
system. The forecast combination based on past forecast performance
performs better than the equal weights model for all components.

2. Individual Forecasting Models
The first models considered are autoregressive models. These models take
into account the persistence of the shares of consumption components, with
the share of consumption on a particular component modelled to be a linear
combination of past shares. The implicit assumption within autoregressive

1 There are, of course, other factors that might affect household consumption, such as changes
in tax policy, income uncertainty and changes in wealth.
For density forecasts of Australian output growth, inflation and interest rates, Gerard and
2
Nimark (2008) use the predictive likelihood for combining forecasts from different vector
autoregression models.
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