Evaluating forecasting accuracy of the temporally aggregated space–time autoregressive model

Abstract

This article aims at analysing the effect of temporal aggregation in space–time autoregressive models. By means of a simulation experiment, it is shown that, the greater the spatial dependence in time series, the lower the bias due to temporal aggregation. However, the ratio between the average mean squared forecasting errors for daily data and that for yearly data seems to decrease for high parameter values.

Acknowledgements

The author would like to thank Giuseppe Arbia, Sandy Dall’erba, Cem Ertur, Carlo Fiorio, Raffaella Giacomini, Wilfried Koch, Julie LeGallo and Gianfranco Piras for useful comments on earlier drafts. Financial support from Bocconi University (Ricerca di Base) is also gratefully acknowledged.

Notes

¹ In this article, we focus only on temporal aggregation and do not consider spatial aggregation.

² In particular, let us consider two semi-annual STAR models:

where ζ, ξ are error terms. The annual process, given by the sum of y _t and z _t , shares the same properties of the original processes, i.e. it is still a STAR model:

³ Examples of spatial–temporal models used for forecasting can be found in Pace et al . (1999) and, in a Bayesian framework, in LeSage and Pan (1995). In particular, LeSage and Pan (1995) make use of a Bayesian VAR model where the contiguity matrix is assumed to be the prior.

⁴ We assume that a year has 360 days and all months have 30 days.

⁵ Notice that there are only two exceptions, i.e. when β = 0.25 and ρ = 0.25 for N = 81 and N = 256.