Time series formed from the superposition of discrete renewal processes. (English) Zbl 0669.62086
The superposition of independent, discrete renewal processes produces a counting process which is also a discrete time series. The conditional distribution and correlation structure of this kind of time series may be obtained. In suitable conditions the conditional distribution has a spectrum which is exactly or approximately rational. When this is so, an ARMA can be found which matches the spectrum of the superposition.
MSC:
62M15 | Inference from stochastic processes and spectral analysis |
62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
60K05 | Renewal theory |