Publication: Predicción en modelos de componentes inobservables condicionalmente heteroscedásticos
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2009-04
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2009-06
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Abstract
During the last two decades, there has been an increasing interest in the academic and practitioner
world on modelling the volatility clustering observed in many economic and financial
series. This research was pioneered by Engle (1982) and Bollerslev (1986), with the introduction
of GARCH models. It is also common to observe stochastic trends in many economic and
financial time series. In this case, a popular practice is to take differences in order to obtain
a stationary transformation. Then, an ARMA model is fitted to this transformation to represent
the transitory dependence. Alternatively, the dynamic properties of series with stochastic
trends may be represented by unobserved component models. It is well known that both models
are equivalent when the disturbances are Gaussian. In this case, the reduced form of an
unobserved component model is an ARIMA model with restrictions on the parameters; see,
for example, Harvey (1989). The main difference between both specifications is that while the
ARIMA model includes only one disturbance, the corresponding unobserved component model
incorporates several disturbances. Consequently, working with the ARIMA specification is usually
simpler. However, using the unobserved components model may lead to discover features of
the series that are not apparent in the reduced form model because they arise when estimating
the components.
When combining both, stochastic trends and volatility clustering, the ARIMA and unobserved
component models are not in general Gaussian. This implies that they are no longer
equivalent when allowing for conditional heteroscedasticity in the noises. Among the large number
of works devoted to studying and applying models that combine these features, almost
none of them made a comparative analysis between the two alternatives. This important issue
remains somewhat unexplored. Therefore, we think that more effort should be placed in this
respect, specially in what regards to forecasting performance. The study of this issue represents
the main goal of this thesis
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Keywords
Análisis de series temporales, Volatilidad, Inflación, Econometría, Modelo econométrico, Previsión, Finanzas