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least-squares extrapolation
We derive a formula for $m$-step least-squares extrapolation in non-linear AR$(p)$ processes and compare it with the naïve extrapolation. The least- squares extrapolation depends on the distribution of white noise. Some bounds for it are derived that depend only on the expectation of white noise. An example shows that in general case the difference between both types of extrapolation can be very large. Further, a formula for least-squares extrapolation in multidimensional non-linear AR($p$) process is derived.
[1] Anděl J.: A remark on least–squares and naïve extrapolations in non–linear AR(1) processes. J. Forecasting 15 (1996), 549–552 DOI 10.1002/(SICI)1099-131X(199612)15:7<549::AID-FOR630>3.0.CO;2-F
[2] Kall P., Wallace S. W.: Stochastic Programming. Wiley, Chichester 1994 MR 1315300 | Zbl 0812.90122
[3] Tong H.: Non–linear Time Series. Clarendon Press, Oxford 1990 Zbl 0835.62076
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