Limited memory predictors based on polynomial approximation of periodic exponents

Nikolai Dokuchaev

doi:10.1002/for.2843

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arXiv · 2002.04386

Limited memory predictors based on polynomial approximation of periodic exponents

Nikolai Dokuchaev

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Abstract

The paper presents transfer functions for limited memory time-invariant linear integral predictors for continuous time processes such that the corresponding predicting kernels have bounded support. It is shown that processes with exponentially decaying Fourier transforms are predictable with these predictors in some weak sense, meaning that convolution integrals over the future times can be approximated by causal convolutions over past times. For a given predicting horizon, the predictors are based on polynomial approximation of a periodic exponent (complex sinusoid) in a weighted $L_2$-space.

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Nikolai Dokuchaev. 2021-10-08. Limited memory predictors based on polynomial approximation of periodic exponents. https://doi.org/10.1002/for.2843

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