Temporal Disaggregation of Time Series_ An ARIMA-Based Approach

Victor M. Guerrero
Instituto Tecnol6gico de Mkxico (ITAM), Mhico 01000, D.F.
Summary
Many economic time series are only available in temporally aggregated form. When the analysis
requires disaggregated data, the analyst faces the problem of deriving these data in the most
reasonable way. In this paper a data-based method is developed which produces an optimal
estimator of the disaggregated series. The method requires a preliminary estimate of the series,
which is adjusted to fulfil the restrictions imposed by the aggregated data. Empirical selection of the
preliminary estimate is discussed and a statistic is developed for testing its adequacy. Some
comparisons with other methods, as well as numerical illustrations, are presented.
Key words: Adjustment to annual totals; Benchmarking; Best linear unbiased estimation;
Distribution; Interpolation; Minimum mean-square error; Time series models.

1 Introduction
In this paper a new method is presented for disaggregating a time series which
combines the aggregated (say annual) data, with preliminary estimates of the disaggregated
(say monthly) values, in an optimal manner. The present approach views the
disaggregated series as estimated values of an unobserved time series. The optimality
criterion employed is that of minimizing the generalized conditional variance of the
estimation error.