Loss of Fitting and Distance Prediction in Fixed vs Updated ARIMA Models
In many cases, it might be advisable to keep an operational time series model fixed for a given span of time, instead of updating it as a new datum becomes available. One common case, is represented by model–based deseasonalization procedures, whose time series models are updated on a regular basis by National Statistical Offices. In fact, in order to minimize the extent of the revisions and grant a greater stability of the already released figures, the interval in between two updating processes is kept “reasonably” long (e.g. one year). Other cases can be found in many contexts, e.g. in engineering for structural reliability analysis or in all those cases where model re–estimation is not a practical or even a viable options, e.g. due to time constraints or computational issues. Clearly, the inevitable trade–off between a fixed models and its updated counterpart, e.g. in terms of fitting performances, out–of–sample prediction capabilities or dynamics explanation should be always accounted for. This paper is devoted at presenting a procedure for the prediction of the loss in terms of fitting ability of a fixed model of the type autoregressive integrated moving average versus its updated version – according to a suitable quadratic cost function – and at giving a quantitative measure of the discrepancy between them. Being the updating frequency customizable, the presented approach can also be employed for simulations purposes, according to the updating intervals, the degree of complexity of the chosen model and the available computing resources. Finally, an empirical experiment involving both computer simulated and macroeconomic time series will be presented and the related outcomes discussed.
