A recipe is provided for producing, from a sequence of procedures in the Gaussian regression model, an asymptotically equivalent sequence in the density estimation model with i. i. d. observations. The recipe is, to put it roughly, to calculate square roots of normalised frequencies over certain...

In this paper the asymptotic behaviour of the maximum likelihood and Bayesian estimators of a delay parameter is studied. The observed process is supposed to be the solution of a linear stochastic differential equation with one time delay term. It is shown that these estimators are consistent...

We consider a two-scaled diffusion system, when drift and diffusion parameters of the “slow” component are contaminated by the "fast" unobserved component. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the "slow" component w.r.t. the...

This paper proposes a procedure for testing alternative specifications of the short term interest rate's dynamics which takes into account that according to some restrictions the interest rate is nonstationary, i.e. the traditional test statistic has a non-standard distribution. Moreover, we do...

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 investigate a new separable nonparametric model for time series, which includes many ARCH models and AR models already discussed in the literature. We also propose a new estimation procedure based on a localization of the econometric method of instrumental variables. Our method has...