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The Identification of ARMA Models
Biometrika, 1990SUMMARY We present a new powerful method for determining the order of ARMA (p, q) models having small sets of observations. The procedure is based on an autoregressive order determination criterion and on linear estimation methods. Simulated data are used to demonstrate the capabilities of the approach. for a survey.
TARMO PUKKILA +2 more
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ARMA MODELLING WITH NON‐GAUSSIAN INNOVATIONS
Journal of Time Series Analysis, 1988Abstract.The problem of modelling time series driven by non‐Gaussian innovations is considered. The asymptotic normality of the maximum likelihood estimator is established under some general conditions. The distribution of the residual autocorrelations is also obtained. This gives rise to a potentially useful goodness‐of‐fit statistic.
McLeod, AI, Li, WK
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Arma models with bilinear innovations
Communications in Statistics. Stochastic Models, 1999Summary: It is well known that any purely non-deterministic stationary process \((X_t)\) with finite variance can be written as an infinite moving average in terms of its innovation process. This property is widely used in the linear methods of estimation and prediction of time series but these methods may give poor results when the innovations are not
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ON EMBEDDING A DISCRETE‐PARAMETER ARMA MODEL IN A CONTINUOUS‐PARAMETER ARMA MODEL
Journal of Time Series Analysis, 1989Abstract. It is shown that a real‐valued discrete‐parameter Gaussian ARMA (p. q) model with q < p can be embedded in a real‐valued continuous‐parameter Gaussian ARMA(p', q') model with q' < p'. The problem of embedding a real‐valued discrete‐parameter Gaussian AR(p) into a real‐valued continuous‐parameter Gaussian AR(p) is also discussed.
He, S. W., Wang, J. G.
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Journal of Time Series Analysis, 1984
Abstract.This paper considers the class of ARMA models with ARCH errors. Maximum Likelihood and Least Squares estimates of the parameters of the model and their covariance matrices are noted and incorporated into techniques for model building based upon the application of the usual Box‐Jenkins methodology of identification, estimation and diagnostic ...
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Abstract.This paper considers the class of ARMA models with ARCH errors. Maximum Likelihood and Least Squares estimates of the parameters of the model and their covariance matrices are noted and incorporated into techniques for model building based upon the application of the usual Box‐Jenkins methodology of identification, estimation and diagnostic ...
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Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181), 2002
We present some aspects of non-Gaussian H-ARMA models. After recalling that an H-ARMA process is obtained by passing an ARMA process through a Hermite polynomial nonlinearity, we describe the theoretical analysis of their cumulants and cumulant spectra. The main advantage of this kind of model is that the cumulant structure of the output can be deduced
D. Declercq, P. Duvaut
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We present some aspects of non-Gaussian H-ARMA models. After recalling that an H-ARMA process is obtained by passing an ARMA process through a Hermite polynomial nonlinearity, we describe the theoretical analysis of their cumulants and cumulant spectra. The main advantage of this kind of model is that the cumulant structure of the output can be deduced
D. Declercq, P. Duvaut
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The Misspecification of Arma Models
Statistica Neerlandica, 1989The object of this paper is to assess the effects of fitting a model of the wrong order to a time series which is generated by an autoregressive moving–average process. The method is to examine the spectral density functions which are indicated by the probability limits of the least–squares estimators of the misspecified models.
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Context dependent ARMA modeling
21st IEEE Convention of the Electrical and Electronic Engineers in Israel. Proceedings (Cat. No.00EX377), 2002We propose to extend the use of Risannen's (1983) "tree source"-a relative of the partial hidden Markov model-to continuous signals. While the original algorithm is dedicated to modeling the context in which each symbol can occur in a discrete symbol space, we propose to match a specific ARMA model with each identified context. An example is presented.
A. Shmilovici, I. Ben-Gal
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