Monitoring with Detecting Changes in Model Parameters

2 Monitoring with Detection of Changes in Model Parameters 

An alternative SPM framework for autocorrelated data is developed by monitoring variations in time series model parameters that are updated at each new measurement instant. Parameter change detection with recursive weighted least squares was used to detect changes in the parameters and the order of a time series model that describes stock prices in financial markets [263]. Here, the recursive least squares is extended with adaptive forgetting. 

Consider an autocorrelated process described by an autoregressive model AR p), 

Assume that n observations are available to form the calibration data set. The parameter estimates o n) and the variance estimate d1 of the noise process e k) are computed. Under the null hypothesis Hq, the distribution of the parameter estimates after time n becomes k) N o n), Po n)a ), 

If the alternate hypothesis is accepted at the detection phase, estimation of change by PCD method is initiated by reducing the forgetting factor to a small value at the detection instant. This will cause the filter to converge quickly to the new values of model parameters. Shewhart charts for each model parameter are used for observing the new identified values of the model parameters. At this point the out-of-control decision made at the detection phase can be reassessed. If the identified values of the parameters are inside the range defined by the null hypothesis, then the detection decision can be reversed and the alarm is declared false. 

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