EWMA, GARCH ...

Q: What EWMA and GARCH stand for?

A: EWMA is Exponentially Weighted Moving Average. While GARCH is Generalised Autoregressive Conditional Heteroscedasticity. These are models for estimating current and future levels of volatilities and correlations of assets for calculating VaR of a portfolio and valuing derivatives respectively.

Q: Among EWMA and GARCH, which is a better model for estimating volatilities and correlations?

A: Both model estimate present volatility using value of previous day's volatility and previous day's % change in market variable. Moreover, the weights assigned to observations decrease exponentially as observations become older. But in GARCH model additional weight is given to long run average variance rate, LRAV. Thus, theoretically GARCH is more appealing than EWMA model. The weights (model parameters) are estimated using MLM. Finally, a model is judged by how well it removes autocorrelation from the historical data using Ljung Box Statistics.