A Novel Framework for Estimating Time-Varying Multivariate Autoregressive Models and Application to Cardiovascular Responses to Acute Exercise

2019 ◽  
Vol 66 (11) ◽  
pp. 3257-3266 ◽  
Author(s):  
Kyriaki Kostoglou ◽  
Andrew D. Robertson ◽  
Bradley J. MacIntosh ◽  
Georgios D. Mitsis
Keyword(s):  
Acute Exercise ◽  
Cardiovascular Responses ◽  
Autoregressive Models ◽  
Time Varying ◽  
Multivariate Autoregressive Models ◽  
Multivariate Autoregressive

On Asymptotic Prediction Problems for Multivariate Autoregressive Models in the Unstable Nonexplosive Case

1987 ◽  
Vol 36 (1-2) ◽  
pp. 29-38 ◽  
Author(s):  
A. K. Basu ◽  
S. Sen Roy
Keyword(s):  
Autoregressive Process ◽  
Autoregressive Models ◽  
Multivariate Autoregressive Models ◽  
Prediction Problems ◽  
Dependent Error ◽  
Meansquare Error ◽  
Multivariate Autoregressive

This paper considers the prediction problems of a k-dimensional, pth order autoregressive process with unstable but non-explosive roots and dependent error variables. The estimated predictor has been shown to be asymptotically equivalent to the optimal predictor. An expression for the meansquare error of the estimated predictor has also been derived .

Using the Eigenvalues of Multivariate Spectral Matrices to Achieve Cutting Direction and Sensor Orientation Independence

2005 ◽  
Vol 128 (1) ◽  
pp. 350-354 ◽  
Author(s):  
John T. Roth
Keyword(s):  
Cutting Tools ◽  
Autoregressive Models ◽  
Triaxial Accelerometer ◽  
Industrial Environment ◽  
Monitoring Techniques ◽  
Monitoring Technique ◽  
Sensor Orientation ◽  
Multivariate Autoregressive Models ◽  
Cutting Direction ◽  
Multivariate Autoregressive

There is a strong need for monitoring techniques capable of tracking the health of cutting tools under varying conditions. Unfortunately, most monitoring techniques are dependent on the cutting direction and/or the sensor orientation, limiting their effectiveness in the typical industrial environment. With this in mind, this research develops a monitoring technique that is independent of both of these factors. This is accomplished by using multivariate autoregressive models that are fit to the output from a triaxial accelerometer. The work shows that the eigenvalues of multivariate spectral matrices, calculated at the machining frequencies, are not only sensitive to the condition of the tool but are also independent of the direction of cutting and the orientation of the sensor. This independence is verified experimentally through tests conducted under a variety of cutting directions and sensor orientations.

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