When we do GARCH, we make time series stationary.
Stationary means constant mean and variance.
Then how are we modelling variance with GARCH when its stationary?
What am I missing here.
Also, can I find daily standard deviation for a stationary time series, using the rolling window method? Same logic, why am I getting different daily S.D. for a stationary time series using rolling window method?
If a time series is stationary (constant mean and variance), we can model volatility with GARCH. According to a source, we can use an ARCH model to forecast volatility. We can also take a time series of daily volatility measures and forecast that directly via a standard ARIMA method. Here one could take differences until arriving at a stationary series.
Autoregressive models can be developed for univariate time series data that is stationary (AR), has a trend (ARIMA), and has a seasonal component (SARIMA). One aspect of a univariate time series that these autoregressive models do not model is a change in the variance over time. This is where ARCH and GARCH models come in. ARCH models are used to model the changing variance of a time series. GARCH models are an extension of ARCH models that also model the changing variance of a time series.
GARCH models are used to model the volatility of a time series. They are often used in finance to model the volatility of stock prices, for example. Even if a time series is stationary, it can still have time-varying volatility. GARCH models are designed to capture this time-varying volatility. The Johansen test is used to test cointegrating relationships between several non-stationary time series data. Compared to the Engle-Granger test, the Johansen test allows for more than one cointegrating relationship. The number of cointegrating vectors that are possible when applying the Johansen test depends on the number of variables in the system and whether they all have unit roots. If there are three variables each with unit roots, there are at most two cointegrating vectors. More generally, if there are n variables which all have unit roots, there are at most n-1 cointegrating vectors.
If the time series is stationary (constant mean and variance), you can still model volatility with GARCH. GARCH models are used to capture the time-varying volatility of a time series, even if the mean is constant. The GARCH model estimates the conditional variance of a time series as a function of its past values and past variances. The model assumes that the variance of the error term is a function of its past values and past variances. Therefore, even if the mean is constant, the variance can still change over time.
If a time series is stationary (constant mean and variance), then we can model the volatility with GARCH. GARCH models are used to model the volatility of time series data that is not stationary. However, if the time series is stationary, then we can use GARCH models to model the volatility of the time series.
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