What is VAR, VECM, ARCH and GARCH modeling. How they differ from one another. When to use each of them.

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VAR, VECM, ARCH, and GARCH are different types of time series models used in econometrics to analyze and forecast data.

VAR (Vector Autoregression) models multiple time series variables as a system of equations, capturing the relationships between variables.
VECM (Vector Error Correction Model) is an extension of VAR that accounts for cointegration among variables, allowing for long-term relationships to be modeled.
ARCH (Autoregressive Conditional Heteroskedasticity) models the variance of a time series as a function of past values of the series, capturing volatility clustering.
GARCH (Generalized Autoregressive Conditional Heteroskedasticity) is an extension of ARCH that also includes lagged values of the conditional variance in the model, allowing for more flexibility in capturing volatility dynamics.
VAR is suitable for analyzing relationships between multiple time series variables, while VECM is used when variables are cointegrated. ARCH and GARCH are used to model and forecast volatility in financial time series data.

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