Subodh Kant

Auto-Regressive Integrated Moving Average Also known as Box-Jenkins methodology A type of linear model Capable of representing stationary and non-stationary time series Rely heavily on autocorrelation pattern of data It can produce accurate forecast based on a description of historical pattern in the data Do not involve independent variables in its construction

Does not assume any particular pattern in the historical data Uses an iterative approach to identify a possible model Residuals are small, Randomly distributed and Contain no useful information Repeats the process till a satisfactory model is obtained

Postulate general class of models Identify models to be tentatively entertained Estimate parameters in tentatively entertained models Diagnostic checking (is this model correct?) Use model for forecasting Yes No

Based on examining the time series plot and Stationary Seasonality / repeating pattern Autocorrelation for several time lags Dying gradually or Dying after 1 / 2 or some spikes Partial autocorrelation for several time lags Dying gradually or Dying after 1 / 2 or some spikes

Autocorrelation Cut off after order q of the process Die out Partial Autocorrelation Cut off after order p of the process Either AR(p) or MA (q) Check both AR(p) Die outMA(q)ARMA (p, q) (value of p and q rarely exceed 2)

It is not a good practice to include AR and MA parameters to cover all possibilities Start with a model containing few rather than many parameters Examine residual autocorrelation and partial autocorrelation and check its behavior If MA behavior is apparent add MA parameter or if AR behavior is apparent add AR parameter We may delete one parameter at a time if it is not significant (as judged by t-ratios)

Models are selected based on looking at plot of series and matching sample autocorrelation and sample partial autocorrelation patterns with known theoretical patterns of ARIMA process If two or more models represent the data then – Parsimony principle leads to selection of simple model having fewer parameters If model contains same number of parameters then model with smallest mean square error s 2 is ordinarily preferred