Accuracy measurements

Model selection in regression models is addressed through the use metrics such as aic, bic, and so on. Though we have earlier used such models for selecting the models, it is important to note that the general purpose of time series is forecasting. Thus, time series modeling has some customized metrics, which are useful for forecasting purpose. Here, a comparison is made between the actual values and the fitted values.

To get the perspective, we have the time series in Y_t, 1 < t < T and suppose that the forecast values by virtue of using a certain model, say AR(p), MA(q), or ARIMA(p,d,q), for the time series is

. We can then capture the fit of the model by comparing

. The residuals due to the model is defined by

. The accuracy measurements are then defined as follows:

The computations would be performed using raw codes.

Getting ready

The R object osv would be required in the current R environment. The reader will require the ARIMA objects osv_arima_1, osv_arima_2...