The effect of temporal aggregation on ARIMA models is investigated. The paper discusses the change of model form resulting from aggregation. For the IMA model it is noted that reduction of model order may occur, due to aggregation, which takes an arbitrarily high order IMA (d, q) process to an IMA ( 4 0) process for the aggregates. For the AR process, we derive the exact order for the aggregate model and show that aggregation of an AR ( p ) series does not necessarily produce an ARMA (p, q ) aggregate series as has been suggested in the literature. In particular, the AR order of AR (p) and ARIMA (p, d, q) can be reduced upon aggregation. The paper gives the general conditions under which this reduction of order may occur.
SUMMARY
We develop a model disaggregation method to derive a disaggregate model from a given aggregate model, which is then used to perform data disaggregation. Since a time series model and its autocovariance structure are closely related, we approach the problem by exploring the possibility of estimating the autocovariance structure for the unobserved disaggregated series from the available autocovariances of an aggregate model. Let the time series aggregates be the non‐overlapping sums of m consecutive disaggregated observations. Given an aggregate autoregressive integrated moving average ARIMA(p, d, r) model with r ≤ p + d + 1, assume that there is no hidden periodicity of order m. It is shown that, if m is odd or if m is even but all the real roots of the autoregressive polynomial of the given aggregate model are positive, then there exists a disaggregate model whose autocovariances can be uniquely derived from the autocovariances of the given aggregate model. Both non‐seasonal and seasonal models are discussed. Empirical examples are presented to illustrate the method.
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