What is difference between ARCH and GARCH models?

In the ARCH(q) process the conditional variance is specified as a linear function of past sample variances only, whereas the GARCH(p, q) process allows lagged conditional variances to enter as well. This corresponds to some sort of adaptive learning mechanism.

What does GARCH model do?

GARCH is a statistical modeling technique used to help predict the volatility of returns on financial assets. GARCH is appropriate for time series data where the variance of the error term is serially autocorrelated following an autoregressive moving average process.

How is GARCH model calculated?

The general process for a GARCH model involves three steps. The first is to estimate a best-fitting autoregressive model. The second is to compute autocorrelations of the error term. The third step is to test for significance.

Is GARCH stationary?

The GARCH(1,1) process is stationary if the stationarity condition holds. ARCH model can be estimated by both OLS and ML method, whereas GARCH model has to be estimated by ML method.

When to use an arch or GARCH model?

It’s usually easy to spot periods of increased variation sprinkled through the series. It can be fruitful to look at the ACF and PACF of both yt and y t 2. For instance, if yt appears to be white noise and y t 2 appears to be AR (1), then an ARCH (1) model for the variance is suggested.

How does the Arch ( 1 ) model work for yt?

The ARCH (1) model for the variance of model yt is that conditional on yt-1 , the variance at time t is We impose the constraints α 0 ≥ 0 and α 1 ≥ 0 to avoid negative variance. Note! The variance at time t is connected to the value of the series at time t – 1.

Which is a useful property of the ARCH model?

Two potentially useful properties of the useful theoretical property of the ARCH (1) model as written in equation line (2) above are the following: y t 2 has the AR (1) model y t 2 = α 0 + α 1 y t − 1 2 + error. y t is white noise when 0 ≤ α 1 ≤ 1.

When is the ARCH model appropriate for a time series?

The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model.