Spectral Analysis of Non-Stationary Time Series

Nonparametric spectrum estimation for spatial data

“…Anderson (1971, p.520), Grenander andRosenblatt (1957, p.134), Hannan (1970, p.280), Parzen (1957); see also Brillinger's (1970) and Zhurbenko's (1986) discussion of spectral estimates for random …elds). Thus the proof is omitted.…”

The distance between rival nonstationary fractional processes

“…Tapers of any chosen order p > 0 can be generated by the proposal of Kolmogorov (see Zhurbenko (1986)): when n is of form n = (p + 1)(r − 1) + 1 we choose h t proportional to the coefficient of…”

Limit Theorems for Large Deviations

“…As it is known, estimates of the cumulants of random variables related to a Markov chain (StatuleviCius, 1969 (or satisfying the more general condition RMT (Zhurbenko, 1972(Zhurbenko, , 1982, (Zuev, 1981), (StatuleviCius, , 1979(StatuleviCius, , 1983, (Rosenblatt, 1979)) are expressed by the product of mixing functions. In the case of arbitrary variables it is impossible to achieve this.…”