Learn to build a GARCH(1,1) model in R using rugarch. The tutorial covers specifying the model, estimating parameters like alpha and beta with maximum likelihood, and forecasting volatility. An S&P 500 example shows alpha at 0.08 and beta at 0.91, with recent volatility of 0.48% expected to rise to 0.5-0.54%.
Chapters
The parameters alpha and beta drive the volatility series denoted by sigma. In this video you will learn to use the package autogarch to estimate them. You need to first specify the GARCH model that you want to estimate. For simplicity. We assume here that the return is normally distributed with constant mean, mu and time varying variance sigma squared table the variance follows the GARG equation. You then have four parameters to estimate the mean parameter mu and the GARCH variance parameters omega, alpha and beta. You can estimate those parameters by maximum likelihood. This means finding parameter values such that the estimated GARCH model is most likely to have generated the observed return series. Maximum likelihood estimation of GARG models is straightforward when you use the R package rigar of Alexios Galanos. It requires to first use the ugarchspec function to specify the GARG model assumptions for the mean, the variance and the distribution. Then you use the function uguardsfit to estimate the model. Finally, to make predictions about future returns you you need to use the function youguideforecast. Here you see the corresponding R code. First, the arguments meanmodel, variancemull and distributionmodel are set in uguard spec. For meanmul we specify that the mean is constant. We don't use an ARMA model and thus set the ARMA order equal to the vector 00 for the variance. We take a stamp card model as distribution model. We specify here to use the normal distribution. Then we estimate the model by applying Ugarch's fit function with as arguments the returns used to estimate the model and the garage specification used in ugaudge forecast. We use the estimated GARCH model and set the argument nahead to specify for how many days ahead we make the prediction. The results of the gauche estimation are available in the ugash fit object. You can use the methods cov, incvariance fitted and sigma to extract useful information regarding the GARCH coefficient estimates. The unconditional variance the predicted mean and volatility you see here the estimation output for the daily S&P 500 returns. The estimate alpha and beta are 0.08 and 0.91 since their sum is less than 1. The estimated volatility is mean reverting with long run value equal to the square root of its unconditional variance. For the daily S&P 500 returns you can see that the long run standard deviation equals 1%. You obtain a time series of estimated fallabilities by applying the sigma method to the RREGARCHFIT object. The volatility is clearly mean diverting around a long run value of 1%. Note that the last value is 0.48% which is only half of the long term value of 1%. You can thus expect the future volatility to gradually increase over the next days. This is indeed the case. As you can see by applying the sigma method to the output from Dugard's forecast function, the volatility steadily increases from 0.5% to 0.54% over the next five days. Applying the method fitted gives the predicted mean. This prediction is constant here since the mean model used assumes a constant mean. At the end of the chapter you will use the GARCH model to solve the technical allocation problem of deciding how to split your wealth between an investment in a risky asset and an investment in risk free assets. A popular approach called volatility targeting solves this problem by setting the weight such that the portfolio volatility equals a constant target level like 5%. Under this approach the optimal weight equals 5% times the inverse of the Garge volatility. Let's do some exercises and play with the R garden.
