Unit root indicates a stochastic trend in the time series. Sometimes it is known as “random walk with drift”. A time series dataset will show a systematic unpredictable pattern if it has the unit root.
To test cointegration, Johansen cointegration test is widely used which determines the number of independent linear combinations (k) for (m) time series variables set that yields a stationary process. The test gives the rank of cointegration.
Granger causality is a method to examine the causality between two variables in a time series. “Causality” is related to cause and effect notion, although it is not exactly the same. It is a statistical concept which is based on the prediction.
The present article shows extensions of ARCH, i.e. GARCH model in STATA. Like ARCH model, ARCH extensions like Generalised ARCH (GARCH) model too need squared residuals as determinants of the equation’s variance.
After performing Autoregressive Integrated Moving Average (ARIMA) modelling in the previous article: ARIMA modeling for time series analysis in STATA, the time series GDP can be modelled through ARIMA (9, 2, 1) .
Autoregressive Integrated Moving Average (ARIMA) is popularly known as Box-Jenkins method. The emphasis of this method is on analyzing the probabilistic or stochastic properties of a single time series. Unlike regression models where Y is explained by X1 X2….XN regressor (like the introductory case where GDP is explained by GFC and PFC), ARIMA allows Y (GDP) to be explained by its own past or lagged values.