Complete 6 page APA formatted essay: Statistical Models for Forecasting milk production.In time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an aut

Complete 6 page APA formatted essay: Statistical Models for Forecasting milk production.

In time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. In theory, the most general class of models for forecasting a time series are stationary and can be made stationary by transformations such as differencing and logging. ARIMA models form an important part of the Box-Jenkins approach to time-series modeling. A non-seasonal ARIMA model is classified as an ARIMA (p, d, q) model, where: p is the number of autoregressive terms, d is the number of non-seasonal differences and q is the number of moving average terms.

Estimation

At the identification stage one or more models are tentatively chosen that seem to provide statistically adequate representations of the available data. The parameters are estimated by modified least squares or the maximum likelihood techniques appropriate to time series data.

Diagnostic

For adequacy of the model, the residuals are examined from the fitted model and alternative models are considered. Different models can be obtained for various combinations of AR and MA individually and collectively. The satisfactory model is considered which adequately fits the data.

Method selection

The best model is obtained on the basis of minimum value of Akaike Information Criteria (AIC) which is given by:

&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp. AIC = -2 log L + 2m

&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp. Where m = p + q

&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp.&nbsp. L is the likelihood function

p& q are orders of Auto-Regressive and Moving Average models respectively - number of parameters, Akaike (1974)