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Modelling and forecasting time series sampled at different frequencies
Author(s) -
Casals José,
Jerez Miguel,
Sotoca Sonia
Publication year - 2009
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1112
Subject(s) - unobservable , observability , series (stratigraphy) , observable , computer science , interpolation (computer graphics) , sampling (signal processing) , time series , state space , multivariate statistics , econometrics , mathematics , statistics , artificial intelligence , detector , machine learning , motion (physics) , paleontology , telecommunications , physics , quantum mechanics , biology
This paper discusses how to specify an observable high‐frequency model for a vector of time series sampled at high and low frequencies. To this end we first study how aggregation over time affects both the dynamic components of a time series and their observability, in a multivariate linear framework. We find that the basic dynamic components remain unchanged but some of them, mainly those related to the seasonal structure, become unobservable. Building on these results, we propose a structured specification method built on the idea that the models relating the variables in high and low sampling frequencies should be mutually consistent. After specifying a consistent and observable high‐frequency model, standard state‐space techniques provide an adequate framework for estimation, diagnostic checking, data interpolation and forecasting. An example using national accounting data illustrates the practical application of this method. Copyright © 2008 John Wiley & Sons, Ltd.