  The problem of non-stationarity in financial markets is discussed and related
to the dynamic nature of price volatility. A new measure is proposed for
estimation of the current asset volatility. A simple and illustrative
explanation is suggested of the emergence of significant serial
autocorrelations in volatility and squared returns. It is shown that when
non-stationarity is eliminated, the autocorrelations substantially reduce and
become statistically insignificant. The causes of non-Gaussian nature of the
probability of returns distribution are considered. For both stock and currency
markets data samples, it is shown that removing the non-stationary component
substantially reduces the kurtosis of distribution, bringing it closer to the
Gaussian one. A statistical criterion is proposed for controlling the degree of
smoothing of the empirical values of volatility. The hypothesis of smooth,
non-stochastic nature of volatility is put forward, and possible causes of
volatility shifts are discussed.
