| Abstract [eng] |
The most popular proxy variables, used to describe the financial volatility, are squared and absolute returns. These two proxy variables are widely discussed in recent studies. In this paper we proposed the extension of existing studies analysing absolute returns in some positive degree as volatility proxy variable. Some statistical properties of this new proxy variable were investigated using four main discrete volatility models as a basis for our investigation: Generalized ARCH, Stochastic Volatility, Exponential GARCH and Asymmmetric Power ARCH. We applied these definitions to daily data of S&P 500 stock market closing prices ranging from 1928.01.01 till 2007.12.31. In order to estimate the best degree, the modeled volatility was compared with the volatility proxy variable. We used our volatility proxy as volatility estimate to find degree, which minimizes mean squared error. We have shown that the best degree for volatility proxy variable is ranging from 2 to 3. The second method we have used was analysis of the autocorrelation function. We obtained that degree ranges from 1 to 1.5. |
