Abstract
Let X 1 ..., X N be a non-stationary p-dimensional autoregressive series of the order n, where n < N. Suppose that m and k are integers such that 1 ≤ m ≤ N - n, 0 ≤ k ≤ m - 1. It is proved that the best linear extrapolation of X m-k based on X m + 1 , ..., X N does not depend on X m + n + 1 , ..., X N . Some formulas for the covariance function of the non-stationary autoregressive series are given. Several special stationary cases are discussed as a consequence of the presented general theorem.
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References
J. Anděl: On the multiple autoregressive series. Ann. Math. Statist. 42 (1971), 755–759.
J. Anděl: Symmetric and reversed multiple stationary autoregressive series. Ann. Math. Statist. 43 (1972), 1197–1203.
J. Anděl: On multiple random sequences. In: Proc. Prague Conf. on Asympt. Methods of Statist., Vol. I (1974), 15–23.
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© 1977 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Anděl, J. (1977). On the Backward Extrapolation of Non-Stationary Autoregressive Series. In: Kožešnik, J. (eds) Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, vol 7A. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9910-3_3
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DOI: https://doi.org/10.1007/978-94-010-9910-3_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9912-7
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