On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

Abstract

Abstract-In this work, we investigate the relationship between continuous-time autoregressive (AR) models and their sampled version. We consider uniform sampling and derive criteria for uniquely determining the continuous-time parameters from sampled data; the model order is assumed to be known. We achieve this by removing a set of measure zero from the collection of all AR models and by investigating the asymptotic behavior of the remaining set of autocorrelation functions. We provide necessary and sufficient conditions for uniqueness of general AR models, and we demonstrate the usefulness of this result by considering particular examples. We further exploit our theory and introduce an estimation algorithm that recovers continuous-time AR parameters from sampled data, regardless of the sampling interval. We demonstrate the usefulness of our algorithm for various Gaussian and non-Gaussian AR processes.

Modified dam deformation monitoring model considering periodic component contained in residual sequence

“…Specifically, the model form can be classified as AR ( p ), MA ( q ), or ARMA ( p , q ) model. When the model form is identified, the model order can be determined with AIC criterion 45 . AIC standard criterion can be expressed as where L is the upper limit of order given in advance; is the variance estimation of residual sequence in the ARIMA model; and N is the sample size.…”

“…When the model form is identified, the model order can be determined with AIC criterion. 45 AIC standard criterion can be expressed as…”

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“…ARIMA model is the combination of the autoregressive and moving average (ARMA) model with the differential operation. The model is an important method for forecasting non-stationary time series with high precision in a short period, 39,40 which is usually written as ARIMA ( p, d, q ) model. The basic idea of modeling is that non-stationary time series can be processed smoothly with the difference method and then the time series is forecasted and analyzed by observing characteristics of correlation function truncation and tailing, such as auto-regression order ( p ), differential times ( d ), and moving average order ( q ).…”

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