The paper deals with the power and robustness of the R/S type tests under contiguous alternatives. We briefly review the long memory models in levels and volatility, and describe the R/S-type tests used to test for the presence of long memory. The empirical power of the tests is investigated...

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...

We show that the empirical process of the squared residuals of an ARCH(p) sequence converges in distribution 1,0 a Gaussirm process B(F(t)) +t f(t) e, where F is the distribution function of the squared innovations, f its derivative, {B(tl, 0 <; t>1} a Brownian bridge and e a normal random variable.

We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991) and Kirman (1993), can replicate the empirical long-memory properties of the two first-conditional moments of financial time series. The essence of these models is that the forecasts and...

We introduce a new statistic written as a sum of certain ratios of second-order increments of partial sums process of observations, which we call the increment ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d-integrated () behavior of time series Xt,...