Random Coefficient Autoregressive Models: An Introduction

Nicholls, D. F.; Quinn, Barry

doi:10.1007/978-1-4684-6273-9

Cited by 326 publications

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“…The AR with conditional heteroscedasticity (ARCH, Engle, 1982) model has recursion X n = θ n ξ 2 1 + ξ 2 X 2 n−1 . Random coefficient model assumes (Nicholls and Quinn, 1982).…”

Section: Geometric-moment Contractionmentioning

confidence: 99%

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Limit theorems for iterated random functions

Shao

2004

J. Appl. Probab.

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We study geometric-moment contracting properties of nonlinear time series that are expressed in terms of iterated random functions. Under Dini-continuity condition, a central limit theorem for additive functionals of such systems is established. The empirical processes of sample paths are shown to converge to Gaussian processes in the Skorokhod space. An exponential inequality is established. We present a bound for joint cumulants, which ensures the applicability of several asymptotic results in spectral analysis of time series. Our results provide a vehicle for statistical inferences for fractals and many nonlinear time series models.

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“…The AR with conditional heteroscedasticity (ARCH, Engle, 1982) model has recursion X n = θ n ξ 2 1 + ξ 2 X 2 n−1 . Random coefficient model assumes (Nicholls and Quinn, 1982).…”

Section: Geometric-moment Contractionmentioning

confidence: 99%

“…Some special models have been discussed earlier; see for example, Petruccelli and Woolford (1984), Nicholls and Quinn (1982). See WW (2000) and Herkenrath et al (2003) for some recent work.…”

Section: Geometric-moment Contractionmentioning

confidence: 99%

Limit theorems for iterated random functions

Shao

2004

J. Appl. Probab.

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“…Some ARCH processes can be viewed as random coefficient autoregressions (RCA, see Nicholls and Quinn, 1982) and the stability properties of those processes can be applied. For example, consider the simple non-Engle ARCH model of type (2.4)…”

Section: Strict Stationarity In Arch Generalizationsmentioning

confidence: 99%

Augmented ARCH models for financial time series: stability conditions and empirical evidence

Kunst

1997

Applied Financial Economics

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The class of conditionally heteroskedastic models known as 'augmented ARCH' encompasses most linear 'ARCH'-type models found in the literature and, in particular, two basic ARCH variants for autocorrelated series: Engle (1982) explains conditional variance by lagged errors, Weiss (1984) also by lagged observations. The framework permits an evaluation of whether the restrictions evolving from the Engle or the Weiss models are valid in practice. Time series of stock market indexes for some major stock exchanges yield empirical examples. In most cases, the statistical approximation to actual dynamic behavior is improved substantially by considering augmented ARCH structures.

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“…The work of Nicholls and Quinn [13] on random-coefficient autoregressive models is relevant to the NLAR(2) process. They have given the necessary and sufficient conditions for the existence of the unique covariance stationary solution to the following class of univariate random-coefficient autoregressive (RCA) models of order k, RCA(k), zn = t {Vi + Bn(i>}Zn-i + cn, (3.3) i=l n = 0, fl, *2,-a., where the following conditions hold.…”

Section: A Second-order Autoregressive Laplace Time-series Modelmentioning

confidence: 99%

“…It is shown that a convex combination of three-scaled Laplace variables can be combined with an independent pair of Laplace variables to obtain another Laplace variable. Necessary and sufficient conditions for the existence of the NLAR(2) model are given using results of Nicholls and Quinn [13].…”

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confidence: 99%

A new Laplace second-order autoregressive time-series model--NLAR(2)

Dewald

Lewis

1985

IEEE Trans. Inform. Theory

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Abstract-A time-series model for Laplace (double-exponential) variables having second-order autoregressive structure (NLAR(2)) is presented. The model is Markovian and extends the second-order process in exponential variables, NEAR(2), to the case where the marginal distribution is Laplace. The properties of the Laplace distribution make it useful for modeling in some cases where the normal distribution is not appropriate. The time-series model has four parameters and is easily simulated. The autocorrelation function for the process is derived as well as third-order moments to further explore dependency in the process. The model can exhibit a broad range of positive and negative correlations and is partially time reversible. Joint distributions and the distrfbution of differences are presented for the first-order case NLAR(l).

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Random Coefficient Autoregressive Models: An Introduction

Cited by 326 publications

References 0 publications

Limit theorems for iterated random functions

Limit theorems for iterated random functions

Augmented ARCH models for financial time series: stability conditions and empirical evidence

A new Laplace second-order autoregressive time-series model--NLAR(2)

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