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

Accounting for conditional leptokurtosis and closing days effects in FIGARCH models of daily exchange rates

This paper, estimates FIGARCH models introduced by Baillie et al. (1996a) for the four major daily exchange rates against the USD (DEM, FRF, YEN and the GBP). The former contributions are extended by accounting for the observed kurtosis through a Student- t based maximum likelihood estimation and by including variables capturing the effect of closing days. These estimations suggest that the introduction of these features improves the goodness of fit properties of the model on the one hand, and may lead to different interest parameters estimates on the other hand. In particular, it is shown that in the case of the DEM, volatility shocks may display much less persistence than documented by previous studies. Finally, it is shown that an ARFIMA-FIGARCH framework turns out to be relevant for all the currencies (except the GBP), without inducing any significant changes in the inference of the stochastic volatility process.

Empirical wavelet analysis of tail and memory properties of LARCH and FIGARCH models

Heavy tails, Long memory, Volatility, Wavelets, 62M10, 42C40,

Bubbles and long-range dependence in asset prices volatilities

A model for a financial asset is constructed with two types of agents. The agents differ in terms of their beliefs. The proportions of the two types change over time according to a stochastic process which models the interaction between the agents. Thus, unlike other models, agents do not persist in holding "wrong" beliefs. Bubble-like phenomena in the asset price occur. We consider several tests for detecting long range dependence and change-points in the conditional variance process. Although the model seems to generate long-memory properties of the volatility series, we show that this is due to the switching of regimes which are detected by the tests we propose