Abstract
For \(1<p\leqslant 2\), random processes that are stationary in the sense of pth-order means are studied. Bounds are obtained for the coefficients of finite autoregressive and moving average representations; convergence of finite predictors is investigated; and attention is given to the special cases of filtered i.i.d. white noise and symmetric stable noise. These results are made possible by an extension of the Pythagorean theorem to \(L^p\).
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The author tenders his heartfelt thanks to the referee, whose close reading yielded numerous recommendations for improving the manuscript.
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Cheng, R. On the prediction of p-stationary processes. Period Math Hung 85, 481–505 (2022). https://doi.org/10.1007/s10998-022-00451-z
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DOI: https://doi.org/10.1007/s10998-022-00451-z