Informatica

The paper defines the decomposition problem of a mixture of time series into homogeneous components. First part deals with a solution based on Bayesian approach in the case of independent observations, the other part is devoted to a solution of on-line decomposition for a time series consisting of weakly stationary components.

A likelihood approach is considered to the problem of making inferences about the point t = ν in a Gaussian autoregressive sequence {Xt, t = 1 ÷ N} at which the underlying AR(p) parameters undergo a sudden change. The statistics of a loglikelihood function L(n, ν) is investigated over the admissible values n ∈ (p + 1, $\dots$ , N - 1) of a change point ν under validity of hypothesis of a change and no change. The expressions of L(n, ν) implying the loss of plausibility when moving away from the true change point ν are presented, and the probabilities P{$\bar{v}_{N}$ = ν± r}, r = 0,1,2, $\dots$, where $\bar{v}_{N}$ is the MLH estimate of a change point ν from the available realization x1,x2,…,xN of {Xt, t = 1 ÷ N} are considered.