Baxter’s Inequality for Triangular Arrays
نویسندگان
چکیده
A central problem in time series analysis is prediction of a future observation. The theory of optimal linear prediction has been well understood since the seminal work of A. Kolmogorov and N. Wiener during World War II. A simplifying assumption is to assume that one-step-ahead prediction is carried out based on observing the infinite past of the time series. In practice, however, only a finite stretch of the recent past is observed. In this context, Baxter’s inequality is a fundamental tool for understanding how the coefficients in the finite-past predictor relate to those based on the infinite past. We prove a generalization of Baxter’s inequality for triangular arrays of stationary random variables under the condition that the spectral density functions associated with the different rows converge.
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