Multivariate Approach to Time Series Model Identification
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– Multivariate Approach to Time Series Model Identification –
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This work suggests an exact and systematic model identification approach which is entirely new and addresses most of the challenges of existing methods. We developed quadratic discriminant functions for various orders of autoregressive moving average (ARMA) models.
An Algorithm that is to be used alongside our functions was also developed. In achieving this, three hundred sets of time series data were simulated for the development of our functions.
Another twenty five sets of simulated time series data were used in testing out the classifiers which correctly classified twenty three out of the twenty five sets.
The two cases of misclassification merely imply that our Algorithm will require a second iteration to correctly identify the model in question. The Algorithm was also applied to some real life time series data and it correctly classified it in two iterations
Model identification is a crucial part of Time Series model development. The main task of Time Series Modeling is to first examine the series at hand so as to establish the theoretical model that generates the Series.
This task seems to be the most challenging and most ambiguous in Time Series Modeling. It has been approached from different perspectives over time. One of the most popular approach is the Box and Jenkins approach presented in Box and Jenkins (1976).
Their method involves going through some iterative steps before a final model is selected. The initial step involves calculating the sample autocorrelation function (ACF) and partial autocorrelation function (PACF) of the series at various lags and comparing their behaviour with known behaviour of some theoretical model and the model that best approximates the sample behavior is tentatively selected.
There are two serious problems with their method. First is the fact that one will need to fit several models or do several adjustments to arrive at the final model.
This makes the method computationally expensive. Another serious problem is the inability of the method to accurately differentiate between some classes of models.
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