Closed-form expression for finite predictor coefficients of multivariate ARMA processes
Autor: | Akihiko Inoue |
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Jazyk: | angličtina |
Rok vydání: | 2020 |
Předmět: |
Statistics and Probability
Multivariate statistics Statistics::Theory 02 engineering and technology 01 natural sciences law.invention 010104 statistics & probability Sieve law FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Applied mathematics Statistics::Methodology 0101 mathematics Multivariate ARMA processes Mathematics Numerical Analysis Numerical analysis Probability (math.PR) Univariate 020206 networking & telecommunications Probability and statistics Linear-time algorithm Expression (mathematics) Autoregressive model Finite predictor coefficients Closed-form expression Statistics Probability and Uncertainty Mathematics - Probability |
Popis: | We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of the number of observations. The significance of the expression is that it provides us with a linear-time algorithm to compute the finite predictor coefficients. In the proof of the expression, a correspondence result between two relevant matrix-valued outer functions plays a key role. We apply the expression to determine the asymptotic behavior of a sum that appears in the autoregressive model fitting and the autoregressive sieve bootstrap. The results are new even for univariate ARMA processes. Journal of Multivariate Analysis, to appear |
Databáze: | OpenAIRE |
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