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Autoregressive Processes
, 1987
"... Suppose {X n} is a pth order autoregressive process with. innovations in the domain of attraction of a stable law and the true order p unknown. The estimate of p, P, is chosen to minimize Akaike's Information Criterion over the integers 0, 1,..., K. It is shown that p is weakly consistent and ..."
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Suppose {X n} is a pth order autoregressive process with. innovations in the domain of attraction of a stable law and the true order p unknown. The estimate of p, P, is chosen to minimize Akaike's Information Criterion over the integers 0, 1,..., K. It is shown that p is weakly consistent
Autoregressive process.
, 2008
"... The performance of NeymanPearson detection of correlated random signals using noisy observations is considered. Using the large deviations principle, the performance is analyzed via the error exponent for the miss probability with a fixed falsealarm probability. Using the statespace structure of ..."
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The performance of NeymanPearson detection of correlated random signals using noisy observations is considered. Using the large deviations principle, the performance is analyzed via the error exponent for the miss probability with a fixed falsealarm probability. Using the statespace structure of the signal and observation model, a closedform expression for the error exponent is derived using the innovations approach, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signaltonoise ratio (SNR) ≥ 1, the error exponent is monotonically decreasing as the correlation becomes strong while for SNR < 1 there is an optimal correlation that maximizes the error exponent for a given SNR.
An Extension of Cointegration to Fractional Autoregressive Processes
, 2010
"... An extension of cointegration to fractional autoregressive processes Søren Johansen ..."
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An extension of cointegration to fractional autoregressive processes Søren Johansen
Testing and modeling threshold autoregressive processes.
 Journal of the American Statistical Association
, 1989
"... ..."
Survival probabilities of autoregressive processes
, 2014
"... Given an autoregressive processX of order p (i.e.Xn = a1Xn−1+ · · ·+apXn−p+ Yn where the random variables Y1, Y2,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time N (survival or persistence probability). Depending o ..."
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Cited by 2 (0 self)
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Given an autoregressive processX of order p (i.e.Xn = a1Xn−1+ · · ·+apXn−p+ Yn where the random variables Y1, Y2,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time N (survival or persistence probability). Depending
StickBreaking Autoregressive Processes
"... This paper considers the problem of defining a timedependent nonparametric prior for use in Bayesian nonparametric modelling of time series. A recursive construction allows the definition of priors whose marginals have a general stickbreaking form. The processes with PoissonDirichlet and Dirichle ..."
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Cited by 8 (0 self)
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This paper considers the problem of defining a timedependent nonparametric prior for use in Bayesian nonparametric modelling of time series. A recursive construction allows the definition of priors whose marginals have a general stickbreaking form. The processes with Poisson
Multiscale autoregressive processes
 IEEE Trans. Signal Processing
, 1915
"... In many applications (e.g. recognition of geophysical and biomedical signals and multiscale analysis of images), it is of interest to analyze and recognize phenomena occuring at different scales. The recently introduced wavelet transforms provide a timeandscale decomposition of signals that offer ..."
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Cited by 4 (1 self)
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naturally to models of signals on trees, and this provides the framework for our investigation. In particular, in this paper we describe the class of isotropic processes on homogenous trees and develop a theory of autoregressive models in this context. This leads to generalizations of Schur and Levinson
Spatially Varying Autoregressive Processes
 Technometrics
, 2011
"... We develop a class of models for processes indexed in time and space that are based on autoregressive (AR) processes at each location. We use a Bayesian hierarchical structure to impose spatial coherence for the coefficients of the AR processes. The priors on such coefficients consists of spatial pr ..."
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Cited by 2 (0 self)
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We develop a class of models for processes indexed in time and space that are based on autoregressive (AR) processes at each location. We use a Bayesian hierarchical structure to impose spatial coherence for the coefficients of the AR processes. The priors on such coefficients consists of spatial
The Law of Iterated Logarithm for Autoregressive Processes
"... This paper mainly discusses some dynamics asymptotic properties of autoregressive processes. By using the dependence of random variables, we prove the least squares (LS) estimator of the unknown parameters satisfies the law of iterated logarithm. ..."
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This paper mainly discusses some dynamics asymptotic properties of autoregressive processes. By using the dependence of random variables, we prove the least squares (LS) estimator of the unknown parameters satisfies the law of iterated logarithm.
Results 1  10
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2,448