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## Autoregressive Process (autoregressive + process)
Kinds of Autoregressive Process
## Selected Abstracts## Maximum Likelihood Estimation for a First-Order Bifurcating Autoregressive Process with Exponential Errors JOURNAL OF TIME SERIES ANALYSIS, Issue 6 2005J. ZhouAbstract., Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter. [source] ## First-Order Autoregressive Processes with Heterogeneous Persistence JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2003JOANN JASIAKAbstract. We propose a semi-nonparametric method of identification and estimation for Gaussian autoregressive processes with stochastic autoregressive coefficients. The autoregressive coefficient is considered as a latent process with either a moving average or regime switching representation. We develop a consistent estimator of the distribution of the autoregressive coefficient based on nonlinear canonical decomposition of the observed process. The approach is illustrated by simulations. [source] ## Fractional Bayesian Lag Length Inference in Multivariate Autoregressive Processes JOURNAL OF TIME SERIES ANALYSIS, Issue 1 2001Mattias VillaniThe posterior distribution of the number of lags in a multivariate autoregression is derived under an improper prior for the model parameters. The fractional Bayes approach is used to handle the indeterminacy in the model selection caused by the improper prior. An asymptotic equivalence between the fractional approach and the Schwarz Bayesian Criterion (SBC) is proved. Several priors and three loss functions are entertained in a simulation study which focuses on the choice of lag length. The fractional Bayes approach performs very well compared to the three most widely used information criteria, and it seems to be reasonably robust to changes in the prior distribution for the lag length, especially under the zero-one loss. [source] ## Autoregressive processes with data-driven regime switching JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2009Joseph Tadjuidje KamgaingAbstract., We develop a switching-regime vector autoregressive model in which changes in regimes are governed by an underlying Markov process. In contrast to the typical hidden Markov approach, we allow the transition probabilities of the underlying Markov process to depend on past values of the time series and exogenous variables. Such processes have potential applications in finance and neuroscience. In the latter, the brain activity at time t (measured by electroencephalograms) will be modelled as a function of both its past values as well as exogenous variables (such as visual or somatosensory stimuli). In this article, we establish stationarity, geometric ergodicity and existence of moments for these processes under suitable conditions on the parameters of the model. Such properties are important for understanding the stability properties of the model as well as for deriving the asymptotic behaviour of various statistics and model parameter estimators. [source] ## A statistical model for unwarping of 1-D electrophoresis gels ELECTROPHORESIS, Issue 22 2005Chris Glasbey ProfessorAbstract A statistical model is proposed which relates density profiles in 1-D electrophoresis gels, such as those produced by pulsed-field gel electrophoresis (PFGE), to databases of profiles of known genotypes. The warp in each gel lane is described by a trend that is linear in its parameters plus a first-order autoregressive process, and density differences are modelled by a mixture of two normal distributions. Maximum likelihood estimates are computed efficiently by a recursive algorithm that alternates between dynamic time warping to align individual lanes and generalised-least-squares regression to ensure that the warp is smooth between lanes. The method, illustrated using PFGE of Escherichia coli O157 strains, automatically unwarps and classifies gel lanes, and facilitates manual identification of new genotypes. [source] ## Modelling the effects of air pollution on health using Bayesian dynamic generalised linear models ENVIRONMETRICS, Issue 8 2008Duncan LeeAbstract The relationship between short-term exposure to air pollution and mortality or morbidity has been the subject of much recent research, in which the standard method of analysis uses Poisson linear or additive models. In this paper, we use a Bayesian dynamic generalised linear model (DGLM) to estimate this relationship, which allows the standard linear or additive model to be extended in two ways: (i) the long-term trend and temporal correlation present in the health data can be modelled by an autoregressive process rather than a smooth function of calendar time; (ii) the effects of air pollution are allowed to evolve over time. The efficacy of these two extensions are investigated by applying a series of dynamic and non-dynamic models to air pollution and mortality data from Greater London. A Bayesian approach is taken throughout, and a Markov chain monte carlo simulation algorithm is presented for inference. An alternative likelihood based analysis is also presented, in order to allow a direct comparison with the only previous analysis of air pollution and health data using a DGLM. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Consumer,resource interactions and cyclic population dynamics of Tanytarsus gracilentus (Diptera: Chironomidae) JOURNAL OF ANIMAL ECOLOGY, Issue 5 2002Árni EinarssonSummary 1Tanytarsus gracilentus population dynamics in Lake Myvatn show a tendency to cycle, with three oscillations occurring between 1977 and 1999 having periods of roughly 7 years. The population abundance fluctuated over four orders of magnitude. 2A partial autocorrelation function (PACF) accounting for measurement error revealed a strong positive lag-1 autocorrelation and a moderate negative lag-2 partial autocorrelation. This suggests that the dynamics can be explained by a simple second-order autoregressive process. 3We tested the alternative hypotheses that the cyclic dynamics of T. gracilentus were driven by consumer,resource interactions in which T. gracilentus is the consumer, or predator,prey interactions in which T. gracilentus is the prey. We analysed autoregressive models including both consumer,resource interactions and predator,prey interactions. 4Wing length of T. gracilentus was used as a surrogate for resource abundance and/or quality, because body size is known to fluctuate with resource abundance and quality in dipterans. Furthermore, the wing lengths of Micropsectra lindrothi , a species ecologically similar to T. gracilentus , fluctuated synchronously with T. gracilentus wing lengths, thereby indicating that the shared resources of these two species were indeed cycling. Wing lengths of other chironomid species were not synchronized. 5The predators of T. gracilentus included midges in the genera Procladius and Macropelopia , and the fish Gasterosteus aculeatus (three-spined stickleback). 6The autoregressive models supported the hypothesis that T. gracilentus dynamics were driven by consumer,resource interactions, and rejected the hypothesis that the dynamics were driven by predator,prey interactions. 7The models also revealed the consequences of consumer,resource interactions for the magnitude of fluctuations in T. gracilentus abundance. Consumer,resource interactions amplified the exogenous variability affecting T. gracilentus per capita population growth rates (e.g. temperature, rainfall, etc.), leading to variability in abundance more than two orders of magnitude greater than the exogenous variability. [source] ## Unemployment and liquidity constraints JOURNAL OF APPLIED ECONOMETRICS, Issue 3 2007Vassilis A. HajivassiliouWe present a dynamic framework for the interaction between borrowing (liquidity) constraints and deviations of actual hours from desired hours, both measured by discrete-valued indicators, and estimate it as a system of dynamic binary and ordered probit models with panel data from the Panel Study of Income Dynamics. We analyze a household's propensity to be liquidity constrained by means of a dynamic binary probit model. We analyze qualitative aspects of the conditions of employment, namely whether the household head is involuntarily overemployed, voluntarily employed, or involuntarily underemployed or unemployed, by means of a dynamic ordered probit model. We focus on the possible interaction between the two types of constraints. We estimate these models jointly using maximum simulated likelihood, where we allow for individual random effects along with an autoregressive process for the general error term in each equation. A novel feature of our method is that it allows for the random effects to be correlated with regressors in a time-invariant fashion. Our results provide strong support for the basic theory of constrained behavior and the interaction between liquidity constraints and exogenous constraints on labor supply. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Identification of Persistent Cycles in Non-Gaussian Long-Memory Time Series JOURNAL OF TIME SERIES ANALYSIS, Issue 4 2008Mohamed BoutaharAbstract., Asymptotic distribution is derived for the least squares estimates (LSE) in the unstable AR(p) process driven by a non-Gaussian long-memory disturbance. The characteristic polynomial of the autoregressive process is assumed to have pairs of complex roots on the unit circle. In order to describe the limiting distribution of the LSE, two limit theorems involving long-memory processes are established in this article. The first theorem gives the limiting distribution of the weighted sum, is a non-Gaussian long-memory moving-average process and (cn,k,1 , k , n) is a given sequence of weights; the second theorem is a functional central limit theorem for the sine and cosine Fourier transforms [source] ## A superharmonic prior for the autoregressive process of the second-order JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2008Fuyuhiko TanakaAbstract., The Bayesian estimation of the spectral density of the AR(2) process is considered. We propose a superharmonic prior on the model as a non-informative prior rather than the Jeffreys prior. Theoretically, the Bayesian spectral density estimator based on it dominates asymptotically the one based on the Jeffreys prior under the Kullback,Leibler divergence. In the present article, an explicit form of a superharmonic prior for the AR(2) process is presented and compared with the Jeffreys prior in computer simulation. [source] ## Maximum Likelihood Estimation for a First-Order Bifurcating Autoregressive Process with Exponential Errors JOURNAL OF TIME SERIES ANALYSIS, Issue 6 2005J. ZhouAbstract., Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter. [source] ## The adjustment of prediction intervals to account for errors in parameter estimation JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2004Paul KabailaAbstract., Standard approximate 1 , , prediction intervals (PIs) need to be adjusted to take account of the error in estimating the parameters. This adjustment may be aimed at setting the (unconditional) probability that the PI includes the value being predicted equal to 1 , ,. Alternatively, this adjustment may be aimed at setting the probability that the PI includes the value being predicted equal to 1 , ,, conditional on an appropriate statistic T. For an autoregressive process of order p, it has been suggested that T consist of the last p observations. We provide a new criterion by which both forms of adjustment can be compared on an equal footing. This new criterion of performance is the closeness of the coverage probability, conditional on all of the data, of the adjusted PI and 1 , ,. In this paper, we measure this closeness by the mean square of the difference between this conditional coverage probability and 1 , ,. We illustrate the application of this new criterion to a Gaussian zero-mean autoregressive process of order 1 and one-step-ahead prediction. For this example, this comparison shows that the adjustment which is aimed at setting the coverage probability equal to 1 , , conditional on the last observation is the better of the two adjustments. [source] ## Efficient use of higher-lag autocorrelations for estimating autoregressive processes JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2002LAURENCE BROZEThe Yule,Walker estimator is commonly used in time-series analysis, as a simple way to estimate the coefficients of an autoregressive process. Under strong assumptions on the noise process, this estimator possesses the same asymptotic properties as the Gaussian maximum likelihood estimator. However, when the noise is a weak one, other estimators based on higher-order empirical autocorrelations can provide substantial efficiency gains. This is illustrated by means of a first-order autoregressive process with a Markov-switching white noise. We show how to optimally choose a linear combination of a set of estimators based on empirical autocorrelations. The asymptotic variance of the optimal estimator is derived. Empirical experiments based on simulations show that the new estimator performs well on the illustrative model. [source] ## Exact expected values of variance estimators for simulation NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2007Tûba Aktaran-KalaycAbstract We formulate exact expressions for the expected values of selected estimators of the variance parameter (that is, the sum of covariances at all lags) of a steady-state simulation output process. Given in terms of the autocovariance function of the process, these expressions are derived for variance estimators based on the simulation analysis methods of nonoverlapping batch means, overlapping batch means, and standardized time series. Comparing estimator performance in a first-order autoregressive process and the M/M/1 queue-waiting-time process, we find that certain standardized time series estimators outperform their competitors as the sample size becomes large. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007 [source] ## Granger's representation theorem: A closed-form expression for I(1) processes THE ECONOMETRICS JOURNAL, Issue 1 2005Peter Reinhard HansenSummary, The Granger representation theorem states that a cointegrated vector autoregressive process can be decomposed into four components: a random walk, a stationary process, a deterministic part, and a term that depends on the initial values. In this paper, we present a new proof of the theorem. This proof enables us to derive closed-form expressions of all terms of the representation and allows a unified treatment of models with different deterministic specifications. The applicability of our results is illustrated by examples. For example, the closed-form expressions are useful for impulse response analyses and facilitate the analysis of cointegration models with structural changes. [source] ## Nonlinear dynamics in high-frequency intraday financial data: Evidence for the UK long gilt futures market THE JOURNAL OF FUTURES MARKETS, Issue 11 2002David G. McMillanRecent research investigating the properties of high-frequency financial data has suggested that the stochastic nonlinearity widely present in such data may be characterized by heterogeneous components in conditional volatility, and nonlinear dependence of threshold autoregressive form due to market frictions. This article tests for the presence of such effects in intraday long gilt futures returns on the UK LIFFE market. Tests against the null of linearity indicate the significance of smooth transition autoregressive nonlinearities in such returns at the 5-min frequency, which entails a first-order autoregressive process with switching intercept. This nonlinear structure is robust to the presence of asymmetric and component structures in conditional variance, and consistent with the existence of heterogeneous traders facing different levels of transaction costs, noise trader risk, or capital constraints. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:1037,1057, 2002 [source] ## A test of homogeneity for autoregressive processes INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2002Rafael Martínez Pedro GómezAbstract In this paper, we introduce a new hypothesis test to determine whether or not two spectral densities are proportional. We deliberately limit our study to autoregressive processes and derive the asymptotic behaviour of the test. A test for autoregressive coefficient nullity or randomness is deduced. We derive asymptotic behaviour for these tests and show the usefulness of our test to detect speech in a noisy environment. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Maximum likelihood estimation of higher-order integer-valued autoregressive processes JOURNAL OF TIME SERIES ANALYSIS, Issue 6 2008Ruijun BuAbstract., In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701,722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) specification with binomial thinning and Poisson innovations, we examine both the asymptotic efficiency and finite sample properties of the ML estimator in relation to the widely used conditional least squares (CLS) and Yule,Walker (YW) estimators. We conclude that, if the Poisson assumption can be justified, there are substantial gains to be had from using ML especially when the thinning parameters are large. [source] ## First-Order Autoregressive Processes with Heterogeneous Persistence JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2003JOANN JASIAKAbstract. We propose a semi-nonparametric method of identification and estimation for Gaussian autoregressive processes with stochastic autoregressive coefficients. The autoregressive coefficient is considered as a latent process with either a moving average or regime switching representation. We develop a consistent estimator of the distribution of the autoregressive coefficient based on nonlinear canonical decomposition of the observed process. The approach is illustrated by simulations. [source] ## Efficient use of higher-lag autocorrelations for estimating autoregressive processes JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2002LAURENCE BROZEThe Yule,Walker estimator is commonly used in time-series analysis, as a simple way to estimate the coefficients of an autoregressive process. Under strong assumptions on the noise process, this estimator possesses the same asymptotic properties as the Gaussian maximum likelihood estimator. However, when the noise is a weak one, other estimators based on higher-order empirical autocorrelations can provide substantial efficiency gains. This is illustrated by means of a first-order autoregressive process with a Markov-switching white noise. We show how to optimally choose a linear combination of a set of estimators based on empirical autocorrelations. The asymptotic variance of the optimal estimator is derived. Empirical experiments based on simulations show that the new estimator performs well on the illustrative model. [source] |