On the Statistical Properties of Impulse Response Function Estimators

Abstract: Estimating stochastic linear systems using Impulse Response Functions (IRFs) is a fundamental problem with broad relevance across multiple disciplines. IRFs describe how a system responds to external inputs, providing essential insights into system behavior and control. Such analyses have important applications in signal processing, control theory, econometrics, oceanography, and related fields. In this talk, I will focus on the estimation of IRFs for Single-Input Single-Output (SISO) systems. We consider a time-invariant continuous linear system driven by zero-mean stationary Gaussian input processes. The aim of the study is to develop a method for estimating the unknown IRF based on observations of both the system’s input and output signals. Our approach is based on a cross-correlogram estimator, which computes the correlation between the input and output processes. We establish conditions for asymptotic unbiasedness and consistency, analyze the rate of convergence, and propose a statistical goodness-of-fit test for validating the estimated IRF. The theoretical results are supported by numerical simulations.

probabilitystatistics theorydata analysis, statistics and probability

Audience: researchers in the topic

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Asymptotic Methods in Statistics

Series comments: One can find video files and slides of talks at the seminar on Asymptotic Methods in Statistics here: www.youtube.com/@SeminarforAsymptoticMethods

A link to a slide is below the description of the video, namely shorturl.at/jUAhL and shorturl.at/6wjUA shorturl.at/rdpqs

Alas the links do not work in one click: you should emphasize them with a mouse and select, e.g., "Go to shorturl.at/rdpqs".

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