□ Time Series Summary
- Time Series can be classified to stationary and non stationary. Stationary means the co variance are stationary.
- Some models that are of common use to model stationary series are the autoregressive moving average (ARMA) models. The conditions are given for the stability of AR models and the invertibility condition, we can write it as infinite autoregression.
- AR models can be estimated by the OLS, but the estimation of MA models is somewhat complex. In practice, however, the MA part does not involve too many parameters. A grid search procedure is described for the estimation of MA models.
- Then after the estimation of the ARMA model, one has to apply tests for the serial correlation to check that the errors are white noise. Tests for this are described. Also, different ARMA models can be compared using the AIC and BIC criteria. For comparing different AR models, Akaike's FPE criterion can also be used.
- Now, another goodness of fit measure R ^ 2. However, time series data usually have strong trends and seasonals, and the R ^ 2's that we get are often high. It is difficult to judge the usefulness of a model by just looking at the high R ^ 2. Some alternative measures have been discussed, and those should be used.
To be contd...
Aditya Pokhrel
MBA, MA Economics, MPA
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