Detection of Logical-and-Probabilistic Correlation in Time Series

An application of the heterogeneous variables system prediction method to solving the time series analysis problem with respect to the sample size is considered in this work. It is created a logical-and-probabilistic correlation from the logical decision function class. Two ways is considered. When the information about event is kept safe in the process, and when it is kept safe in depending process.

Application of the Multivariate Prediction Method to Time Series

* This work was financially supported by RFBR-04-01-00858.

Extreme Situations Prediction by MultidimenSional Heterogeneous Time Series Using Logical Decision Functions

* The work is supported by RFBR, grant 04-01-00858-a

Sensitivity Analysis of the Risk of Forecasting for Autoregressive Time Series with Missing Values

2000 Mathematics Subject Classification: 62M20, 62M10, 62-07.

Branching Processes with Immigration and Integer-valued Time Series

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes to stationary Ginar(d) and get consistency and asymptotic normality for the corresponding estimators. The technique covers autoregressive moving average time series as well.