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Heterogeneity and aggregation in seasonal time series.

Tripodis, Georgios (2007) Heterogeneity and aggregation in seasonal time series. PhD thesis, London School of Economics and Political Science (United Kingdom).

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Abstract

Seasonality is an important part of many real time series. While issues of seasonal heteroscedasticity and aggregation have been a cause of concern for data users, there has not been a great deal of theoretical research in this area. This thesis concentrates on these two issues. We consider seasonal time series with single season heteroscedasticity. We show that when only one month has different variability from others there are constraints on the seasonal models that can be used. We show that both the dummy and the trigonometric models are not effective in modelling seasonal series with this type of variability. We suggest two models that permit single season heteroscedasticity as a special case. We show that seasonal heteroscedasticity gives rise to periodic autocorrelation function. We propose a new class, called periodic structural time series models (PSTSM) to deal with such periodicities. We show that PSTSM have correlation structure equivalent to that of a periodic integrated moving average (PIMA) process. In a comparison of forecast performance for a set of quarterly macroeconomic series, PSTSM outperform periodic autoregressive (PAR) models both within and out of sample. We also consider the problem of contemporaneous aggregation of time series using the structural time series framework. We consider the conditions of identifiability for the aggregate series. We show that the identifiability of the models for the component series is not sufficient for the identifiability of the model for the aggregate series. We also consider the case where there is no estimation error as well as the case of modeling an unknown process. For the case of the unknown process we provide recursions based on the Kalman filter that give the asymptotic variance of the estimated parameters.

Item Type: Thesis (PhD)
Uncontrolled Keywords: Statistics
Sets: Collections > ProQuest Etheses
Departments > Statistics
URI: http://etheses.lse.ac.uk/id/eprint/2933

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