Adaptive estimation for a time inhomogeneous stochastic-volatility model

Let a process SI , ... ,ST obey the conditionally heteroskedastic equation St = Vt Et whcrc Et is a random noise and Vt is the volatility coefficient which in turn obeys an autoregression type equation log v t = w + a S t- l + nt with an additional noise nt. We consider the situation which the parameters w and a might also depend on the time t, and we study the problem of online estimation of current values of w = w(T) and a = a(T) from the observations SI , ... ,ST. We propose an adaptive method of estimation which does not use any information about time homogenity of the obscured process. We apply this model to two series of FX daily returns on DEM/USD and GBP/USD.