Abstract
In this article, we propose an interval estimation method to trace an unknown disaggregate series within certain bandwidths. First, we consider two model-based disaggregation methods called the GLS disaggregation and the ARIMA disaggregation. Then, we develop iterative steps to construct AR-sieve bootstrap prediction intervals for model-based temporal disaggregation. As an illustration, we analyze the quarterly total balances of U.S. international trade in goods and services between the first quarter of 1992 and the fourth quarter of 2020.
Highlights
Based on the bootstrap approach, we present a modified procedure for constructing bootstrap prediction intervals of temporal disaggregation
Step 1: Using the disaggregation method introduced in Section 2.2, we identify an autoregressive integrated moving-average (ARIMA)( p, d, q) expression for the unknown disaggregate series xt and find the autocovariance estimates, γu (0), γu (1), . . ., γu ( p + d + 1), and the coefficient estimates, φ1, . . . , φp and θ1, . . . , θq, of the disaggregate model
We have developed a modified procedure for constructing AR-sieve bootstrap prediction intervals of an unknown disaggregate series xt
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. It is inevitable that temporal aggregation causes a significant loss of information as a time series of relatively high frequency is compressed into periodic totals of relatively low frequency (see [1,2,3]). [9,10] estimated unknown consecutive observations in a disaggregate series based on the model structure of a given aggregate series. [14,15,16] introduced an AR-sieve bootstrap procedure to construct nonparametric prediction intervals for linear time series models such as stationary and invertible autoregressive integrated moving-average (ARIMA) processes. AR-sieve bootstrap interval estimation provides a theoretical basis for solving the model-based disaggregation problems of [9,10].
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