Autoregressive models with epsilon-skew-normal innovations

We consider the problem of modelling asymmetric near-Gaussian correlated signals by autoregressive models with epsilon-skew normal innovations. Moments and maximum likelihood estimators of the parameters are proposed and their limit distributions are derived. Monte Carlo simulation results are analyzed and the model is fitted to a real time series.

[1]  Mohamed Alosh,et al.  FIRST‐ORDER INTEGER‐VALUED AUTOREGRESSIVE (INAR(1)) PROCESS , 1987 .

[2]  Hocine Fellag,et al.  Bayesian estimation of an AR(1) process with exponential white noise , 2003 .

[3]  F. Quintana,et al.  Statistical inference for a general class of asymmetric distributions , 2005 .

[4]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[5]  Moti L. Tiku,et al.  ESTIMATING PARAMETERS IN AUTOREGRESSIVE MODELS IN NON-NORMAL SITUATIONS: ASYMMETRIC INNOVATIONS , 1999 .

[6]  N. Shephard,et al.  Likelihood analysis of a first‐order autoregressive model with exponential innovations , 1999 .

[7]  G. S. Mudholkar,et al.  The epsilon-skew-normal distribution for analyzing near-normal data , 2000 .

[8]  Peter A. W. Lewis,et al.  STATIONARY DISCRETE AUTOREGRESSIVE‐MOVING AVERAGE TIME SERIES GENERATED BY MIXTURES , 1983 .

[9]  G. Janacek,et al.  A CLASS OF MODELS FOR NON-NORMAL TIME SERIES , 1990 .

[10]  A. I. McLeod,et al.  ARMA MODELLING WITH NON-GAUSSIAN INNOVATIONS , 1988 .

[11]  J. Andel.  On ar(1) processes with exponential white noise , 1988 .

[12]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .

[13]  E. McKenzie,et al.  Autoregressive moving-average processes with negative-binomial and geometric marginal distributions , 1986, Advances in Applied Probability.

[14]  Wing-Keung Wong,et al.  Time Series Models with Asymmetric Innovations , 2018 .

[15]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[16]  A. Hutson.  Utilizing the Flexibility of the Epsilon-Skew-Normal Distribution for Common Regression Problems , 2004 .

[17]  Carlo Novara,et al.  of nonlinear time series , 2001 .

[18]  Wing-Keung Wong,et al.  Estimating parameters in autoregressive models with asymmetric innovations , 2005 .

[19]  A. W. Kemp,et al.  Kendall's Advanced Theory of Statistics. , 1994 .

[20]  M. Tiku,et al.  Time Series Models in Non‐Normal Situations: Symmetric Innovations , 2000 .