On the asymptotic behavior of the Durbin-Watson statistic for ARX processes in adaptive tracking
نویسندگان
چکیده
A wide literature is available on the asymptotic behavior of the Durbin-Watson statistic for autoregressive models. However, it is impossible to find results on the Durbin-Watson statistic for autoregressive models with adaptive control. Our purpose is to fill the gap by establishing the asymptotic behavior of the Durbin Watson statistic for ARX models in adaptive tracking. On the one hand, we show the almost sure convergence as well as the asymptotic normality of the least squares estimators of the unknown parameters of the ARX models. On the other hand, we establish the almost sure convergence of the Durbin-Watson statistic and its asymptotic normality. Finally, we propose a bilateral statistical test for residual autocorrelation in adaptive tracking.
منابع مشابه
Tracking Interval for Doubly Censored Data with Application of Plasma Droplet Spread Samples
Doubly censoring scheme, which includes left as well as right censored observations, is frequently observed in practical studies. In this paper we introduce a new interval say tracking interval for comparing the two rival models when the data are doubly censored. We obtain the asymptotic properties of maximum likelihood estimator under doubly censored data and drive a statistic for testing the ...
متن کاملWeighted estimation and tracking for Bienaym e Galton Watson processes with adaptive control
For Bienaym e–Galton–Watson processes in adaptive tracking situations, we establish asymptotic results for weighted estimators of the mean and the variance of the o spring distribution. c © 1999 Elsevier Science B.V. All rights reserved MSC: 60J80; 93E24; 60F05; 60F15
متن کاملControlling Nonlinear Processes, using Laguerre Functions Based Adaptive Model Predictive Control (AMPC) Algorithm
Laguerre function has many advantages such as good approximation capability for different systems, low computational complexity and the facility of on-line parameter identification. Therefore, it is widely adopted for complex industrial process control. In this work, Laguerre function based adaptive model predictive control algorithm (AMPC) was implemented to control continuous stirred tank rea...
متن کاملAdaptive Robust Control for Trajectory Tracking of Autonomous underwater Vehicles on Horizontal Plane
This manuscript addresses trajectory tracking problem of autonomous underwater vehicles (AUVs) on the horizontal plane. Adaptive sliding mode control is employed in order to achieve a robust behavior against some uncertainty and ocean current disturbances, assuming that disturbance and its derivative are bounded by unknown boundary levels. The proposed approach is based on a dual layer adaptive...
متن کاملSpatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression
In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson'...
متن کامل