Integer-valued autoregressive processes with periodic structure

In this paper the periodic integer-valued autoregressive model of order one with period T, driven by a periodic sequence of independent Poisson-distributed random variables, is studied in some detail. Basic probabilistic and statistical properties of this model are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the method of moments, least squares-type and likelihood-based ones. Their performance is compared through a simulation study.

[1]  Christian H. Weiß,et al.  The combined INAR(p) models for time series of counts , 2008 .

[2]  A. V. Vecchia.  PERIODIC AUTOREGRESSIVE‐MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES , 1985 .

[3]  Kurt Brännäs,et al.  A New Approach to Modelling and Forecasting Monthly Guest Nights in Hotels , 2001 .

[4]  Harry L. Hurd,et al.  Periodically correlated random sequences : spectral theory and practice , 2007 .

[5]  Eric R. Ziegel,et al.  Developments in Time Series Analysis , 1993 .

[6]  Niels Haldrup,et al.  Common Periodic Correlation Features and the Interaction of Stocks and Flows in Daily Airport Data , 2005 .

[7]  W. Bennett.  Statistics of regenerative digital transmission , 1958 .

[8]  Robert Lund,et al.  A new look at time series of counts , 2009 .

[9]  Harry L. Hurd,et al.  Climatological time series with periodic correlation , 1995 .

[10]  J. Franke,et al.  Conditional maximum likelihood estimates for INAR(1) processes and their application to modelling epileptic seizure counts , 1993 .

[11]  David R. Maidment,et al.  Handbook of Hydrology , 1993 .

[12]  Robert Lund,et al.  Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models , 2000 .

[13]  Kurt Brännäs,et al.  Tourist Accommodation Effects of Festivals , 2006 .

[14]  R. Lund,et al.  Changepoint Detection in Periodic and Autocorrelated Time Series , 2007 .

[15]  E. G. Gladyshev.  Periodically and Almost-Periodically Correlated Random Processes with a Continuous Time Parameter , 1963 .

[16]  K. Hipel,et al.  Time series modelling of water resources and environmental systems , 1994 .

[17]  Q. Shao.  Mixture periodic autoregressive time series models , 2006 .

[18]  Gael M. Martin,et al.  Bayesian predictions of low count time series , 2005 .

[19]  A. M. M. Shahiduzzaman Quoreshi,et al.  Bivariate Time Series Modeling of Financial Count Data , 2006 .

[20]  Philip Hans Franses,et al.  A multivariate approach to modeling univariate seasonal time series , 1994 .

[21]  Robert Lund,et al.  PARSIMONIOUS PERIODIC TIME SERIES MODELING , 2006 .

[22]  Magda Monteiro,et al.  Optimal Alarm Systems for Count Processes , 2008 .

[23]  P. Hall,et al.  Martingale Limit Theory and its Application. , 1984 .

[24]  Qin Shao,et al.  Least-squares estimation and ANOVA for periodic autoregressive time series , 2004 .

[25]  Philip Hans Franses,et al.  Multivariate periodic time series models , 2004 .

[26]  Marc Hallin,et al.  On the invertibility of periodic moving-average models , 1994 .

[27]  B. McCabe,et al.  Asymptotic properties of CLS estimators in the Poisson AR(1) model , 2005 .

[28]  Mark M. Meerschaert,et al.  Identification of periodic autoregressive moving average models and their application to the modeling of river flows , 2006 .

[29]  Robert Lund,et al.  Large Sample Properties of Parameter Estimates for Periodic ARMA Models , 2001 .

[30]  Harry L. Hurd,et al.  PERIODIC CORRELATION IN STRATOSPHERIC OZONE DATA , 1994 .

[31]  Soohan Ahn,et al.  Analysis of the M/D/1-type queue based on an integer-valued first-order autoregressive process , 2000, Oper. Res. Lett..

[32]  Christian H. Weiß.  Controlling jumps in correlated processes of Poisson counts , 2009 .

[33]  Antonio Napolitano,et al.  Cyclostationarity: Half a century of research , 2006, Signal Process..

[34]  H. Hurd,et al.  Periodically Correlated Random Sequences , 2007 .

[35]  Alain Latour,et al.  The Multivariate Ginar(p) Process , 1997, Advances in Applied Probability.

[36]  I. V. Basawa,et al.  Least-squares estimation for bifurcating autoregressive processes , 2005 .

[37]  R. Lund,et al.  First-order seasonal autoregressive processes with periodically varying parameters , 2004 .