Autoregressive modelling includes a model identification procedure, that is, it is necessary to choose the order of the autoregressive (AR) process that best fit the data.
There are two criteria: An information-theoretic criterion, minimum description length criterion. You may get the details in the following books:
Adaptive filter theory by Simon Haykin
Spectral analysis and time series, vols.1 and 2, Academic press, New York. 1981
S.M.Kay Modern Spectral estimation:theory and application, Prentice-Hall, Englewood Cliffs, NJ, 1988
Dear Anjana P Das,
In statistics and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it describes certain time-varying processes in nature, economics, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation.
Order of Autoregressive Process (p) :
Specifically, for an AR(1) process, the sample autocorrelation function should have an exponentially decreasing appearance. However, higher-order AR processes are often a mixture of exponentially decreasing and damped sinusoidal components.
For higher-order autoregressive processes, the sample autocorrelation needs to be supplemented with a partial autocorrelation plot. The partial autocorrelation of an AR(p) process becomes zero at lag p+1 and greater, so we examine the sample partial autocorrelation function to see if there is evidence of a departure from zero. This is usually determined by placing a 95 % confidence interval on the sample partial autocorrelation plot (most software programs that generate sample autocorrelation plots will also plot this confidence interval). If the software program does not generate the confidence band, it is approximately ±2/N0.5, with N denoting the sample size.
Here attached file of Identification and Estimation Process.
Best regards
Dear Anjana,
To select the ideal degree of AR model manually is a cumbersome task.I recommend you to use SPSS.
After entering your data in SPSS, select Time Series from Analyze option menu. In this section, you can find an option which allows you to find the best fit for your model. Since you are looking for the degree of your AR model, don't forget to filter your model to show only for Auto Regressive. SPSS will offer you the best degree of AR model with high accuracy. It also provides you its error, confidence interval, and p-value to show how significant this suggestion is.
Kind regards
Dear Anjana P Das
Singular Value Decomposition(SVD) is one of the methods you could apply to determine the order of an AR model.
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