My Finance

Now it is time to apply our new tool, the Yeo-Johnson transform, to monthly average CBOE VIX 1986-2025 as opposed to annual volatility. We discussed such autoregression of order 1 on the log scale in our previous manuscript. But the innovations are IID and not Gaussian. We tried (unsuccessfully) to fit the variance-gamma distribution. The new Python file is in the old GitHub repository together with the data file.

But we are interested only in the time series modeling of volatility, since the normalized monthly returns are already IID Gaussian. Thus we apply the autoregression of order 1 to the transformed log VIX and analyze innovations of this autoregression.

Results: Shapiro-Wilk and Jarque-Bera for transformed log volatility, with However, autoregression innovations are IID but not Gaussian, both normality tests give extremely low values.