An exponential moving-average sequence and point process (EMA1)
- 1 March 1977
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 14 (1) , 98-113
- https://doi.org/10.2307/3213263
Abstract
A construction is given for a stationary sequence of random variables {Xi} which have exponential marginal distributions and are random linear combinations of order one of an i.i.d. exponential sequence {εi}. The joint and trivariate exponential distributions ofXi−1,XiandXi+ 1are studied, as well as the intensity function, point spectrum and variance time curve for the point process which has the {Xi} sequence for successive times between events. Initial conditions to make the point process count stationary are given, and extensions to higher-order moving averages and Gamma point processes are discussed.Keywords
This publication has 4 references indexed in Scilit:
- A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1)Advances in Applied Probability, 1977
- On Conditional and Partial CorrelationThe American Statistician, 1976
- Bivariate Exponential Distributions in Reliability TheoryJournal of the Royal Statistical Society Series B: Statistical Methodology, 1970
- The Statistical Analysis of Series of EventsPublished by Springer Nature ,1966