Some Basic and Asymptotic Properies in INMA(q) Processes

  • Park, You-Sang (Department of Statistics, Korea University, Seoul, 136-701) ;
  • Kim, Myung-Jin (Department of Statistics, Korea University, Seoul, 136-701)
  • Published : 1997.06.01

Abstract

We propose an integer-valued MA(q) process with Poisson disturbance. Its various properties are discussed such as the joint distribution, time reversibility and regression. We derive the asymptotic distribution of autocovariance function and estimators of the parameters in the suggested model. We also consider the relationship between INMA(q) and M/D/.infty. processes.

Keywords

References

  1. Statistical Papers v.29 Integer-valued moving average (INMA) process Al-Osh, M. A.;Alzaid, A. A.
  2. Communication in Statistics A: Theory and Methods v.21 First-order autorgressive time series with negative binomial and geometric marginals Ao-Osh, M. A.;Aly, A. A.
  3. Journal of Applied Probability v.27 An integer-valued pth-order autoregressive structure(INAR(p)) process Alzaid, A. A.;Ao-Osh, M. A.
  4. Journal of Multivariate Analysis v.50 On some integer-valued autorgressive moving average models Aly. A. A.;Bouzar, N.
  5. Time Series: Theory and Methods Brockweel, P. J.;Davis, R. A.
  6. Journal of the Royal Statistical Society, Series B, Methodological v.40 Discrete time series generated by mixtures I : correlational and runs properties Jacobs, P. A.;Lewis, P A. W.
  7. Journal of the Royal Statistical Society, Series B, Methodological v.40 Discrete time series generated by mixtures Ⅱ: asymptotic properties Jacobs, P. A.;Lewis, P. A. W.
  8. Journal of Time Series Analysis v.4 Stationary discrete autoregressivemoving average time series generated by mixtures Jacobs, P. A.;Lewis, P. A. W.
  9. Advances in Applied Probabilty v.18 Autoregressive moving-average processes with negativebinomial and geometric marginal distributions McKenzie, E.
  10. Advances in Applied Probability v.20 Some ARMA models for dependent sequences of Poisson counts McKenzie, E.
  11. 1995 proceedings of the International statistical Institute Some asymptotic properties in INAR(1) process with negative binomial marginals Park, Y.S.;Kim, K.
  12. Statistical Papers On autocovariance function in INAR(1) process with Poisson marginals Park, Y.S.;Oh, C.
  13. Introduction to Probability Models(3rd ed.) Ross, S.M.