Optimal Sampling Rates for Auto Regressive Models

摘要

In time series analysis a particular model for a linear system is an auto-regression model. Auto-regression models are particularly well suited to structural linear systems which have been persistently excited by white noise. The white noise is assumed to be unmeasurable and it is assumed that there is no measurement noise. The variability of the results obtained in practice tends to depend on the sampling rates used. This memo examines in detail the asymptotic convariance matrix for estimates of the damping rate and frequency for a fixed length of record and variable sampling rates in a linear system which is completely described, in continuous time, by a single second order differential equation. It is shown that the selection of sampling rate plays an extremely important role in the quality of estimates.