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Descriptor realizations of autoregressive representations
 IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
, 2004
"... ... In this paper, it is shown how to reduce an ARrepresentation to a fundamental equivalent realization in descriptor form. ..."
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... In this paper, it is shown how to reduce an ARrepresentation to a fundamental equivalent realization in descriptor form.
order moving average and autoregressive representations
"... Abstract. An invertible causal linear process is a process which has infinite order moving average and autoregressive representations. We assume that the coefficients in these representations depend on a Euclidean parameter, while the corresponding innovations have an unknown centered distribution ..."
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Abstract. An invertible causal linear process is a process which has infinite order moving average and autoregressive representations. We assume that the coefficients in these representations depend on a Euclidean parameter, while the corresponding innovations have an unknown centered distri
Stationary space–time Gaussian fields and their time autoregressive representation
, 2002
"... We compare two different modelling strategies for continuous space discrete time data. The first strategy is in the spirit of Gaussian kriging. The model is a general stationary space–time Gaussian field where the key point is the choice of a parametric form for the covariance function. In the main, ..."
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Cited by 7 (0 self)
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, covariance functions that are used are separable in space and time. Nonseparable covariance functions are useful in many applications, but construction of these is not easy. The second strategy is to model the time evolution of the process more directly. We consider models of the autoregressive type where
Stationary space–time Gaussian elds and their time autoregressive representation
"... Abstract: We compare two different modelling strategies for continuous space discrete time data. The rst strategy is in the spirit of Gaussian kriging. The model is a general stationary space–time Gaussian eld where the key point is the choice of a parametric form for the covariance function. In the ..."
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. In the main, covariance functions that are used are separable in space and time. Nonseparable covariance functions are useful in many applications, but construction of these is not easy. The second strategy is to model the time evolution of the process more directly. We consider models of the autoregressive
Stationary Space Time Gaussian Fields and their time autoregressive representation
, 2002
"... We compare two different modelling strategies for continuous space discrete time data. The first strategy is in the spirit of Gaussian kriging. The model is a general stationary spacetime Gaussian field where the key point is the choice of a parametric form for the covariance function. Mostly, cova ..."
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We compare two different modelling strategies for continuous space discrete time data. The first strategy is in the spirit of Gaussian kriging. The model is a general stationary spacetime Gaussian field where the key point is the choice of a parametric form for the covariance function. Mostly, covariance functions which are used are separable in space and time. Nonseparable covariance functions are useful in many applications, but construction of such is not easy.
Testing for Common Trends
 Journal of the American Statistical Association
, 1988
"... Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix ..."
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Cited by 464 (7 self)
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matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic
Common Persistence in Conditional Variances
 ECONOMETRIC REVIEWS
, 1993
"... Since the introduction of the autoregressive conditional heteroskedastic (ARCH) model in Engle (1982), numerous applications of this modeling strategy have already appeared. A common finding in many of these studies with high frequency financial or monetary data concerns the presence of an approxima ..."
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Cited by 347 (20 self)
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of an approximate unit root in the autoregressive polynomial in the univariate time series representation for the conditional second order moments of the process, as in the socalled integrated generalized ARCH (IGARCH) class of models proposed in Engle and Bollerslev (1986). In the IGARCH models shocks
Movingaverage representation for autoregressive approximations
, 1995
"... We study the properties of an MA(1)representation of an autoregressive approximation for a stationary, realvalued process. In doing so we give an extension of Wiener's Theorem in the deterministic approximation setup. When dealing with data, we can use this new key result to obtain insight i ..."
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Cited by 12 (3 self)
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We study the properties of an MA(1)representation of an autoregressive approximation for a stationary, realvalued process. In doing so we give an extension of Wiener's Theorem in the deterministic approximation setup. When dealing with data, we can use this new key result to obtain insight
ON THE RANGE OF VALIDITY OF THE AUTOREGRESSIVE SIEVE BOOTSTRAP
"... Abstract. We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the ARsieve bootstrap is valid for stationary processes possessi ..."
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Cited by 10 (2 self)
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possessing a general Woldtype autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is everywhere positive. Our main theorem provides a simple and effective tool in assessing whether the AR
Results 1  10
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368