4. When serial correlation is detected in the model, AR model should be used. However, before using AR model, time series must be tested for Covariance Stationarity.

· If time series has a linear trend and covariance nonstationary; it can be transformed into covariance stationary by taking the first difference of the data.

· If time series has exponential trend and covariance nonstationary; it can be transformed into covariance stationary by taking natural log of the time series and then taking the first difference.

· If the time series exhibits structural change, two different time-series model (i.e. before & after the shift) must be estimated.

· When time series exhibits seasonality, seasonal lags must be included in the AR model.

5. When time series is converted into Covariance Stationarity, AR model can be used i.e.

· Estimate AR (1) model;

· Test serial correlation in the regression errors; if no serial correlation is found only then AR (1) model can be used. When serial correlation is detected in AR (1), then AR (2) should be used and tested for serial correlation. When no serial correlation is found, AR (2) can be used. If serial correlation is still present, order of AR is kept on increasing until all serial correlation is removed.

6. Plot the data and detect any seasonality. When seasonality is present, add seasonal lags in the model.

7. Test the presence of autoregressive conditional heteroskedasticity in the residuals of the model i.e. using ARCH (1) model.

8. In order to determine the better forecasting model, calculate out-of-sample RMSE of each model and select the model with the lowest out of-sample RMSE.

· If time series has a linear trend and covariance nonstationary; it can be transformed into covariance stationary by taking the first difference of the data.

· If time series has exponential trend and covariance nonstationary; it can be transformed into covariance stationary by taking natural log of the time series and then taking the first difference.

· If the time series exhibits structural change, two different time-series model (i.e. before & after the shift) must be estimated.

· When time series exhibits seasonality, seasonal lags must be included in the AR model.

5. When time series is converted into Covariance Stationarity, AR model can be used i.e.

· Estimate AR (1) model;

· Test serial correlation in the regression errors; if no serial correlation is found only then AR (1) model can be used. When serial correlation is detected in AR (1), then AR (2) should be used and tested for serial correlation. When no serial correlation is found, AR (2) can be used. If serial correlation is still present, order of AR is kept on increasing until all serial correlation is removed.

6. Plot the data and detect any seasonality. When seasonality is present, add seasonal lags in the model.

7. Test the presence of autoregressive conditional heteroskedasticity in the residuals of the model i.e. using ARCH (1) model.

8. In order to determine the better forecasting model, calculate out-of-sample RMSE of each model and select the model with the lowest out of-sample RMSE.

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