Periodic Time Series Models
Chris Chatfield · Journal of the Royal Statistical Society Series A (Statistics in Society) · 2005
This advanced text looks at a special class of seasonal models that are suitable for describing and forecasting some economic time series. The reader might reasonably expect that any seasonal model could be regarded as ‘periodic’, but this term is customarily reserved, as here, for stochastic models where the model parameters vary across the seasons. For example, a first-order periodic autoregressive (PAR(1)) model is one where the autoregressive parameter varies through the year, as might be needed, for example, if the autocorrelation from April to May is say 0.5, whereas that from October to November is say −0.4. This means that the processes are not strictly stationary (as the authors note on page 31), but the book devotes much effort to looking for unit roots in the characteristic equation as such roots indicate a different type of non-stationarity and are also of interest for other reasons. This book is essentially a second edition of the first author's earlier book ( Franses, 1996) with some general lower level material on seasonal models removed, a survey of recent research added and an up-to-date list of references provided. Without loss of generality, the book restricts attention to quarterly data.