Non-Gaussian series and series with non-zero means: Practical implications for time series analysis

Lusk, Eward J.; Wright, Haviland

doi:10.1016/0167-7152(82)90003-7

“…First, however, to see that the usual central limit theorem effects do not apply to (1.1) (in contrast with the conjecture of Lusk and Wright, 1982) consider the setting where {u,} is i.i.d. and nonnormal.…”

Section: Preliminariesmentioning

confidence: 99%

“…A , = A ) . Lusk and Wright (1982), Davies et al (1980) and Hart (1984) examine issues associated with symmetry and unimodality for the distribution of scalar stationary AR (and sometimes autoregressive moving-average (ARMA)) processes; Pemberton and Tong (1981) consider the same issues for a nonlinear generalization of stationary AR processes. Stigum (1975) and Tsay and Tiao (1990) examine the asymptotic distribution of AR processes with eigenvalues of A on the unit circle (e.g.…”

Section: Introductionmentioning

confidence: 99%

The Distribution of Nonstationary Autoregressive Processes Under General Noise Conditions

Spall

¹

1993

Journal Time Series Analysis

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In this paper we consider the long-run distribution of a multivariate autoregressive process of the form x, = An-,xn-, + noise, where the noise has an unknown (possibly nonstationary and nonindependent) distribution and A , is a (generally) time-varying transition matrix. It can easily be shown that the process x, need not have a known long-run distribution (in particular, central limit theorem effects do not generally hold). However, if the distribution of the noise approaches a known distribution as n gets large, we show that the distribution of x, may also approach a known distribution for large n. Such a setting might occur, for example, when transient effects associated with the early stages of a system's operation die out. We first present a general result that applies for arbitrary noise distributions and general A , . Several special cases are then presented that apply for noise distributions in the infinitely divisible class and/or for asymptotically constant coefficient A,. We illustrate the results on a problem in characterizing the asymptotic distribution of the estimation error in a Kalman filter.

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“…This section summarizes some basic results and introduces notation that will be used in the main results section. First, however, to see that the usual central limit theorem effects do not apply to (1.1) (in contrast with the conjecture of Lusk and Wright, 1982) consider the setting where {u,} is i.i.d. and nonnormal.…”

Section: Preliminariesmentioning

confidence: 99%

The distribution of nonstationary autoregressive processes under general noise conditions

Spall

¹

Proceedings of 32nd IEEE Conference on Decision and Control

0

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In this paper we consider the long-run distribution of a multivariate autoregressive process of the form x, = An-,xn-, + noise, where the noise has an unknown (possibly nonstationary and nonindependent) distribution and A , is a (generally) time-varying transition matrix. It can easily be shown that the process x, need not have a known long-run distribution (in particular, central limit theorem effects do not generally hold). However, if the distribution of the noise approaches a known distribution as n gets large, we show that the distribution of x, may also approach a known distribution for large n. Such a setting might occur, for example, when transient effects associated with the early stages of a system's operation die out. We first present a general result that applies for arbitrary noise distributions and general A , . Several special cases are then presented that apply for noise distributions in the infinitely divisible class and/or for asymptotically constant coefficient A,. We illustrate the results on a problem in characterizing the asymptotic distribution of the estimation error in a Kalman filter.

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Asymptotically most powerful rank tests for multivariate randomness against serial dependence

Hallin

¹

,

Ingenbleek

²

1989

Journal of Multivariate Analysis

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Non-Gaussian series and series with non-zero means: Practical implications for time series analysis

Cited by 10 publications

References 4 publications

The Distribution of Nonstationary Autoregressive Processes Under General Noise Conditions

The Distribution of Nonstationary Autoregressive Processes Under General Noise Conditions

The distribution of nonstationary autoregressive processes under general noise conditions

Asymptotically most powerful rank tests for multivariate randomness against serial dependence

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