bluuebunny/crossref_metadata_2025 huggingface dataset:
SPECTRAL ESTIMATION AND DECONVOLUTION FOR A LINEAR TIME SERIES MODEL
Authors: Pawitan Yudianto , Shumway R. H.
Published: May 2008

Abstract. A vector linear time series model is observed as the sum of a convolution of an unknown signal and an additive noise process. The main objective is the estimation or deconvolution of the signal when the spectra of the signal and noise processes are unknown. We prove the strong consistency of a class of nonparametric spectral estimators derived by maximizing a particular Gaussian likelihood function. We also study the mean square convergence of the finite‐sample deconvolution estimators as a function of the sample length T, the filter length M and the spectral bandwidth BT=LT/T.
REFERENCE ANALYSIS OF THE DYNAMIC LINEAR MODEL
Authors: Pole Andy , West Mike
Published: May 2008

Abstract.We consider the analysis of normal dynamic linear models subject to reference (vague or uninformative) initial priors on the state parameters and observational variance. New sequential updating equations and the related smoothing or filtering recurrences are derived for such reference analyses. The case of no evolution noise is highlighted, as this is of key practical importance and interest. Practical questions concerning prediction and collinearity are discussed, as are particular features of special models.
A COMPOSITE LINEAR MODEL GENERATING A STATIONARY STOCHASTIC PROCESS WITH GIVEN THIRD‐ORDER AUTOCORRELATION FUNCTION
Authors: Sakaguchi Fuminori , Sakai Hideaki
Published: May 2008

Abstract. A composite linear model is proposed which generates a non‐Gaussian stationary stochastic process with a given third‐order autocorrelation function and a white power spectrum. The design of the model is based on the fact that a type of finite‐impulse‐response linear system with a non‐Gaussian white input series produces an output process whose third‐order correlations exist only for special time lags. An arbitrary third‐order autocorrelation function can be constructed by superposing output processes of this type. The model requires at most 2L2+ 4L+ 1 independent identically distributed (i.i.d.) input processes for the third‐order autocorrelation function with the largest time lag L. Results of numerical experiments confirm the validity of the model.
THE ESTIMATION OF SPECTRUM, INVERSE SPECTRUM AND INVERSE AUTOCOVARIANCES OF A STATIONARY TIME SERIES
Authors: Rao T. Subba , Gabr M. M.
Published: May 2008

Abstract. In this paper we consider the method of spectral estimation proposed by Pisarenko, and interpret its form through the properties of circular symmetric matrices. This interpretation helps us to redefine Capon's ‘high resolution’ estimation for time series defined on the real line. Using the properties of the eigenvalues and eigenvectors of Wishart matrices, we study the sampling properties of these matrices, applying a method of derivation different from that given by Pisarenko. We also show how Capon's high resolution estimator can be used to estimate the inverse spectrum and the inverse autocovariances, and we derive the asymptotic sampling properties of these estimates. The methods are illustrated with examples.
SPECTRAL DISCRIMINATION FOR TWO GROUPS OF TIME SERIES
Authors: Alagón Javier
Published: May 2008

Abstract. The problem of discriminating in the frequency domain between two groups of Gaussian stationary time series is examined. A test aimed at detecting differences between the windowed spectra of the two groups is used. The effect of windows on the resulting quadratic discriminant function is considered. Two examples taken from seismology and neurology are given.
ESTIMATION OF THE MOVING‐AVERAGE REPRESENTATION OF A STATIONARY PROCESS BY AUTOREGRESSIVE MODEL FITTING
Authors: Bhansali R. J.
Published: May 2008

Abstract.The Hannan‐Rissanen procedure for recursive order determination of an autoregressive moving‐average process provides ‘non‐parametric’ estimators of the coefficientsb(u), say, of the moving‐average representation of a stationary process by auto‐regressive model fitting, and also that of the cross‐covariances,c(u), between the process and its linear innovations. An alternative ‘autoregressive’ estimator of theb(u) is obtained by inverting the autoregressive transfer function. Some uses of these estimators are discussed, and their asymptotic distributions are derived by requiring that the orderkof the fitted autoregression approaches infinity simultaneously with the lengthTof the observed time series. The question of bias in estimating the parameters is also examined.
ESTIMATION OF AUTOREGRESSIVE MOVING‐AVERAGE MODELS VIA HIGH‐ORDER AUTOREGRESSIVE APPROXIMATIONS
Authors: Wahlberg Bo
Published: May 2008

Abstract. In this paper the problem of estimating autoregressive moving‐average (ARMA) models is dealt with by first estimating a high‐order autoregressive (AR) approximation and then using the AR estimate to form the ARMA estimate. We show how to obtain an efficient ARMA estimate by allowing the order of the AR estimate to tend to infinity as the number of observations tends to infinity. This approach is closely related to the work of Durbin. By transforming the approach into the frequency domain, we can view it as an L2‐norm model approximation of the relative error of the spectral factors. It can also be seen as replacing the periodogram estimate in the Whittle approach by a high‐order AR spectral density estimate. Since L2‐norm approximation is a difficult task, we replace it by a modification of a recent model approximation technique called balanced model reduction. By an example, we show that this technique gives almost efficient ARMA estimates without the use of numerical optimization routines.
IDENTIFYING MULTIVARIATE TIME SERIES MODELS
Authors: Tsay Ruey S.
Published: May 2008

Abstract.This paper is concerned with how canonical variate analysis can be used to identify the structure of a linear multivariate time series model. The procedure used is based on that of Akaike and Cooper and Wood. A correction and a refinement are made, however. The correction is on the testing statistic and the refinement on the allowed order (p, q). Appropriate asymptotic distributions for testing zero canonical correlations are also given.
A CENTRAL LIMIT THEOREM OF FOURIER TRANSFORMS OF STRONGLY DEPENDENT STATIONARY PROCESSES
Authors: Yajima Yoshihiro
Published: May 2008

Abstract. We consider a limiting distribution of the finite Fourier transforms of observations drawn from a strongly dependent stationary process. It is proved that the finite Fourier transforms at different frequencies are asymptotically independent and normally distributed. Our result can apply to a fractional autoregressive integrated moving‐average process and a fractional Gaussian noise, two examples of strongly dependent stationary processes.
ESTIMATION OF AUTOREGRESSIVE MOVING‐AVERAGE ORDER GIVEN AN INFINITE NUMBER OF MODELS AND APPROXIMATION OF SPECTRAL DENSITIES
Authors: Pötscher B. M.
Published: May 2008

Abstract.A modification of the minimum Akaike information criterion (AIC) procedure (and of related procedures like the Bayesian information criterion (BIC)) for order estimation in autoregressive moving‐average (ARMA) models is introduced. This procedure has the advantage that consistency for the order estimators obtained via this procedure can be established without restricting attention to only a finite number of models. The behaviour of these newly introduced order estimators is also analysed for the case when the data‐generating process is not an ARMA process (transfer function/spectral density approximation). Furthermore, the behaviour of the order estimators obtained via minimization of BIC (or of related criteria) is investigated for a non‐ARMA data‐generating process.
GENERAL LINEAR PROCESSES:A PROPERTY OF THE EMPIRICAL PROCESS APPLIED TO DENSITY AND MODE ESTIMATION
Authors: Chanda K. C. , Ruymgaart F. H.
Published: May 2008

Abstract. General linear processes do not usually satisfy strong mixing conditions. Therefore, we investigate the empirical process based on samples from such a general linear process by using a truncation argument and derive a local fluctuation inequality. It is well known that such a fluctuation inequality is of basic importance in the study of the empirical process. Here it is applied to obtain a rate of almost sure (a.s.) convergence for certain density estimators in the supremum norm. This extends a local result obtained by Chanda. As a direct corollary a rate of a.s. convergence for a mode estimator is obtained.
BIASES OF ESTIMATORS IN MULTIVARIATE NON‐GAUSSIAN AUTOREGRESSIONS
Authors: Pope Alun Lloyd
Published: May 2008

Abstract. Expressions for the bias of the least‐squares and modified Yule‐Walker estimators in a correctly specified multivariate autoregression of arbitrary order are obtained without assuming that the innovations are Gaussian. Instead, the innovations are assumed to form a martingale difference sequence which is stationary up to sixth order and which has finite sixth moments. The errors in the expressions are shown to be O(n‐3/2), as the sample size n under some moment conditions. The expressions obtained are the same in the Gaussian and non‐Gaussian cases.
FILTERING AND SMOOTHING IN STATE SPACE MODELS WITH PARTIALLY DIFFUSE INITIAL CONDITIONS
Authors: Ansley Craig F. , Kohn Robert
Published: May 2008

Abstract.Ansley and Kohn (Annals of Statistics, 1985) generalized the Kalman filter to handle state space models with partially diffuse initial conditions and used this filter to compute the marginal likelihood of the observations efficiently. In this paper we simplify the algorithm and make it numerically more accurate and operationally more efficient. Based on this filtering algorithm we obtain a corresponding smoothing algorithm for the state vector.
SOME PROPERTIES OF AUTOREGRESSIVE ESTIMATES FOR PROCESSES WITH MIXED SPECTRA
Authors: Mackisack M. S. , Poskitt D. S.
Published: May 2008

Abstract. A formal justification for the use of the method of autoregressive spectral estimation for time series consisting of a sinusoidal signal in additive noise is given in this paper. The analytical properties of the autoregressive approximation to the generalized spectral density of the process are presented, and the operational characteristics of the statistical estimation procedure are discussed. In particular, strong convergence of the autoregressive parameters and the autoregressive transfer function approximation is shown.
ORDERS AND INITIAL VALUES OF NON‐STATIONARY MULTIVARIATE ARMA MODELS
Authors: Swift A. L.
Published: May 2008

Abstract. Akaike's stepwise canonical correlations procedure identifies each autoregressive (AR) order (assuming a lesser moving‐average (MA) order) and gives initial parameter estimates of a stationary multivariate autoregressive moving‐average model. We show that a similar procedure is valid for the non‐stationary model when this can be approximated by a large‐order AR‐only model which has consistent least‐squares estimators.

The procedure can also be adapted for all MA orders by fixing the overall maximum of any MA order less its corresponding AR order. We perform the canonical correlations procedure on a succession of values of this maximum and compare the results to obtain one or more prospective model structures.
DIFFERENCE EQUATIONS FOR HIGHER‐ORDER MOMENTS AND CUMULANTS FOR THE BILINEAR TIME SERIES MODEL BL(p, 0,p, 1)
Authors: Sesay S. A. O. , Rao T. Subba
Published: May 2008

Abstract.In this paper we obtain difference equations for higher‐order moments and cumulants for the time series {Xt} satisfying the bilinear model BL(p, 0,p, 1). These equations are similar to the well‐known Yule‐Walker equations for the autoregressive moving‐average model which are in terms of the second‐order covariances. Thus they can be used for the tentative identification of bilinear models. Another application of these equations is in the computation of preliminary estimates of the parameters of the model. We shall illustrate this by means of simulations for two simple examples of bilinear models.
ON THE ASYMPTOTIC DISTRIBUTION OF THE GENERALIZED PARTIAL AUTOCORRELATION FUNCTION IN AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES
Authors: Choi Byoung Seon
Published: May 2008

Abstract.It has been conjectured and illustrated that the estimate of the generalized partial autocorrelation function (GPAC), which has been used for the identification of autoregressive moving‐average (ARMA) models, has a thick‐tailed asymptotic distribution. The purpose of this paper is to investigate the asymptotic behaviour of the GPAC in detail. It will be shown that the GPAC can be represented as a ratio of two functions, known as the θ function and the Λ function, each of which itself has a useful pattern for ARMA model identification. We shall show the consistencies of the extended Yule‐Walker estimates of the three functions and present their asymptotic distributions.
FORECASTING GLOBAL ICE VOLUME
Authors: Newton H. Joseph , North Gerald R. , Crowley Thomas J.
Published: May 2008

Abstract. Forecasts and associated probability limits of total ice volume for the next 100 000 years are found based upon a historical record of 440 000 years of oxygen‐18 from deep sea cores. The forecasts are found using two different time series models, one based on the assumption that ice volume contains deterministic sinusoids, and one assuming that the record contains ‘disturbed periodicities’, i.e. the sinusoids do not have the same cycle length and amplitude from one cycle to another. The results for the two models are seen to be very similar, with both predicting a small probability for a future ice volume event to be as large as the last ice age, which was one of the largest glaciations of the last 2 million years.
APPROXIMATE DISTRIBUTION OF PARAMETER ESTIMATORS FOR FIRST‐ORDER AUTOREGRESSIVE MODELS
Authors: Tuan Dinh Pham
Published: May 2008

Abstract. Formulae for the exact bias and mean square error for the least squares for forward‐backward least squares estimators are obtained based on the explicit expressions for the moment‐generating and characteristic functions of quadratic form in the first‐order autoregressive process. Asymptotic expressions for their cumulants and the maximum likelihood estimator are given. Approximations of the distributions of the above estimators are proposed based on the Ornstein‐Ulenbeck process. A simple computational procedure for the exact distribution is developed, and some numerical comparisons are given which support the overall good accuracy of the approximation and confirm that the maximum likelihood estimator performs better than the others.
DATA‐DEPENDENT ESTIMATION OF PREDICTION FUNCTIONS
Authors: Burman P. , Nolan D.
Published: May 2008

Abstract.The technique of cross‐validation for model selection where the observations have martingale‐like structure is developed. It is argued that cross‐validation works, unaltered, in this more general setting. The specific example of the stationary Markov process is considered in detail. An estimate of the one‐step prediction function of this process is selected from a collection of splines by minimizing the cross‐validatory version of the prediction error. Asymptotic optimality of the estimate is established.
A NEW DIAGNOSTIC TEST OF MODEL INADEQUACY WHICH USES THE MARTINGALE DIFFERENCE CRITERION
Authors: Hinich Melvin J. , Patterson Douglas M.
Published: May 2008

Abstract. Let {x(t)} denote a discrete‐time random process. Given a sample of increments e(t) = x(t) ‐ x(t ‐ 1) from the time series, we wish to test formally whether the sample is consistent with the assumption that {e(t)} is a martingale difference. It is shown that the martingale criterion is more general than the white noise criterion in analyzing fitted residuals for signs of model inadequacy. In this paper we present such a test which approximately achieves a given type 1 error probability for samples. We assume that (1) the process is strictly stationary, (2) all its kth‐order cumulant functions exist and (3) the kth‐order cumulants are absolutely summable and satisfy a mixing condition. The martingale assumption implies that most third‐order cumulants of the increment process are zero, and thus the third‐order cumulant sequence is sparse. This result is used to derive test statistics based on a modified sample bispectrum. The test can be regarded as a two‐dimensional portmanteau test of serial dependence. The large‐sample results are demonstrated through the use of artificial data. Finally, the test is applied to a daily financial series.
REVERSED RESIDUALS IN AUTOREGRESSIVE TIME SERIES ANALYSIS
Authors: Lawrance A. J. , Lewis P. A. W.
Published: May 2008

Abstract.Both linear and non‐linear time series can have directional features which can be used to enhance the modelling and investigation of linear or non‐linear autoregressive statistical models. For this purpose, reversedpth‐order residuals are introduced. Cross‐correlations of residuals and squared reversed residuals allow extensions of current model identification ideas. Quadratic types of partial autocorrelation functions are introduced to assess dependence associated with non‐linear models which nevertheless have linear autoregressive correlation structures. The use of these residuals and their cross‐correlation functions is exemplified empirically on some deseasonalized river flow data for which a first‐order autoregressive model is a satisfactory second‐order fit. Parallel theoretical computations are undertaken for the non‐linear first‐order random coefficient autoregressive model and comparisons are made. While the data are shown to be strongly non‐linear, their correlational signatures are found to be convincingly different from those of a first‐order autoregressive model with random coefficients.
EMPIRICAL EVIDENCE ON DICKEY‐FULLER‐TYPE TESTS
Authors: Agiakloglou C. , Newbold P.
Published: May 2008

Abstract. The empirical performance of tests of the Dickey–Fuller type for unit autoregressive roots in the generating model of a time series is studied. In particular, the case where the true generating model structure is unknown and may involve a substantial moving‐average component is examined.
A TEST FOR CONDITIONAL HETEROSKEDASTICITY IN TIME SERIES MODELS
Authors: Bera A. K. , Higgins M. L.
Published: May 2008

Abstract. When testing for conditional heteroskedasticity and nonlinearity, the power of the test in general depends on the functional forms of conditional heteroskedasticity and nonlinearity that are allowed under the alternative hypothesis. We suggest a test for conditional heteroskedasticity and nonlinearity with the nonlinear autoregressive conditional heteroskedasticity model of Higgins and Bera as the alternative. Standard testing procedures are not applicable since our nonlinear autoregressive conditional heteroskedasticity (ARCH) parameter is not identified under the null hypothesis. To resolve this problem, we apply the procedure recently proposed by Davies. Power and size of the suggested test are investigated through simulation, and an empirical application of testing for ARCH in exchange rates is also discussed.
FREQUENCY‐DOMAIN ESTIMATION OF BILINEAR TIME SERIES MODELS
Authors: Sesay S. A. O. , Rao T. Subba
Published: May 2008

Abstract.Two frequency‐domain methods of estimation of the parameters of linear time series models–one based on maximum likelihood, called the ‘Whittle criterion’, and the other based on least squares, called the ‘Taniguchi criterion’–are discussed in this paper. A heuristic justification for their use in models such as bilinear models is given. The estimation theory and associated asymptotic theory of these methods are numerically illustrated for the bilinear model BL(p,0,p, 1). For that purpose, an approach based on the calculus of Kronecker product matrices is used to obtain the derivatives of the spectral density function of the state‐space form of the model.
CLASSIFICATION OF TEXTURES USING SECOND‐ORDER SPECTRA
Authors: Yuan J. , Rao T. Subba
Published: May 2008

Abstract. We consider the classification of textures as realizations of stationary random fields using non‐parametric estimates of their second‐order spectra. The random fields in each class are assumed to be stationary with the same spectrum, which we estimate from a finite sample by smoothing its periodogram. The classification rule can be interpreted as maximizing a mean square convergent approximation to the averaged log‐likelihood if the random fields are Gaussian, and in general as minimizing the discrepancy of the periodogram from the spectrum of the class. The limiting behaviour of the probability of misclassification as the sample size tends to infinity is studied under certain cumulant conditions. The classification rule is illustrated with real texture data.
ESTIMATION FOR NONNEGATIVE AUTOREGRESSIVE PROCESSES WITH AN UNKNOWN LOCATION PARAMETER
Authors: McCormick William P. , Mathew George
Published: May 2008

Abstract. Consider an AR(1) process given by Xt=γ+øXt+Zt≥ 1. where 0 ≤γ, 0 ≤ø 1 are unknown parameters and the innovations Zt, ≥ 1, are independently and identically distributed positive random variables. We propose estimates of (γø) which are obtained as the solution to a linear programming problem and establish their strong consistency. When the Zts have the exponential distribution. our estimate becomes the conditional maximum likelihood estimate given X0. Under the assumption of regular variation of the innovation distribution at its left and right endpoints (assumed to be 0 and ∝ respectively), we establish asymptotic limit laws for the estimates. Consistent estimators for a class of moving‐average processes with heavy‐tailed innovation distribution are also presented.
GEOMETRIC ERGODICITY OF A DOUBLY STOCHASTIC TIME SERIES MODEL
Authors: Meyn Sean P. , Guo Lei
Published: May 2008

Abstract. We demonstrate that a large class of doubly stochastic time series models are geometrically ergodic, and hence admit second‐order stationary solutions.

We also establish a version of the strong law of large numbers, the law of the interated logorithm and the central limit theorem for the stochastic processes under consideration.
A COMPUTATIONAL METHOD FOR ESTIMATING DENSITIES OF NON‐GAUSSIAN NONSTATIONARY UNIVARIATE TIME SERIES
Authors: Hodges P. E. , Hale D. F.
Published: May 2008

Abstract. Kitagawa's (1987a) numerical integration formulae used to approximate the filtering, prediction and smoothing densities of nonlinear non‐Gaussian state‐space models are modified. The method involves integration by parts which permits the integration of the conditional system density and, possibly, the observational density prior to and independently of the computation of the filtering, prediction and smoothing densities. In addition to a substantial reduction in computing time and an increase in accuracy, this approach eliminates the necessity of incorporating dynamic adjustments to the filtering, prediction and smoothing processes to accommodate difficult noise densities.

Three numerical examples are presented. One example replicates Kitagawa's non‐Gaussian state‐space model; the second is a linear Gaussian model; and the third is a nonlinear non‐Gaussian model. Comparisons of speed and accuracy between alternative methods and between three computers (personal computer, minicomputer and supercomputer) are made.
ESTIMATION FOR REGRESSIVE AND AUTOREGRESSIVE MODELS WITH NON‐NEGATIVE RESIDUAL ERRORS
Authors: Hong‐Zhi An , Fuchun Huang
Published: May 2008

Abstract. The parameter estimation problems for regressive and autoregressive models are investigated. A new procedure is proposed which differs from the least squares method. Theorems relating to the rate of almost sure convergence of the new estimators are formulated. Some simulation results are also shown. With these convergent rates and simulation results a clear comparison of the new estimator with the least squares estimator is obtained.
ESTIMATION OF THE PERIOD OF PERIODICALLY CORRELATED SEQUENCES
Authors: Martin Donald E. K. , Kedem Benjamin
Published: May 2008

Abstract.In this paper we consider the problem of estimating the periodTof periodically correlated sequences. A method is developed which uses the periodogram of the average magnitude difference function (AMDF). It will be shown that this method alleviates problems associated with other methods.
A NOTE ON ARMA MODEL PARAMETER REDUNDANCY
Authors: McLeod A. I.
Published: May 2008

Abstract. A simple condition expressed directly in terms of the autoregressive moving‐average model parameters is given for determining autoregressive moving‐average model redundancy.
POWER OF THE NEURAL NETWORK LINEARITY TEST
Authors: Teräsvirta Timo , Lin Chien‐Fu , Granger Clive W. J.
Published: May 2008

Abstract. Recently, a new linearity test for time series was introduced based on concepts from the theory of neural networks. Lee et al. have already studied the power properties of this test and they are further investigated here. They are compared by simulation with those of a Lagrange multiplier (LM) type test that we derive from the same single‐hidden‐layer neural network model. The auxiliary regression of our LM type test is a simple cubic ‘dual’ of the Volterra expansion of the original series, and the power of the test appears superior overall to that of the other test.
BIAS IN AN ESTIMATOR OF THE FRACTIONAL DIFFERENCE PARAMETER
Authors: Agiakloglou Christos , Newbold Paul , Wohar Mark
Published: May 2008

Abstract. An estimator of the difference parameter in a class of long‐memory time series models is examined. It is shown that, in particular circumstances, the estimator can be badly biased, and tests based on it consequently seriously misleading. The source of this bias is identified, and it is shown that its magnitude can readily be predicted through straightforward analytical arguments.
A CORRECTED AKAIKE INFORMATION CRITERION FOR VECTOR AUTOREGRESSIVE MODEL SELECTION
Authors: Hurvich Clifford M. , Tsai Chih‐Ling
Published: May 2008

Abstract. We develop a small‐sample criterion (AICC) for the selection of the order of vector autoregressive models. AICC is an approximately unbiased estimator of the expected Kullback‐Leibler information. Furthermore, AICC provides better model order choices than the Akaike information criterion in small samples.
VARIANCE ESTIMATION FOR QUADRATIC STATISTICS
Authors: Smith B. , Field C.
Published: May 2008

Abstract. A frequency domain smoothing procedure is presented which provides variance estimates for linear functions of the periodogram. The method provides consistent estimates of the true asymptotic variance, has good small‐sample efficiency properties in the Gaussian case and reflects non‐Gaussian structure. The relationship of the estimates to frequency domain bootstrap algorithms is discussed.
ON BOOTSTRAP PREDICTIVE INFERENCE FOR AUTOREGRESSIVE PROCESSES
Authors: Kabaila Paul
Published: May 2008

Abstract. In this paper we consider bootstrap‐based predictive inference for autoregressive processes of order p. We consider both unconditional inference and inference conditional on the last p observed values. We make two contributions. Our first contribution is to point out the best way to apply the bootstrap to unconditional predictive inference when the process is Gaussian. Now, it may be argued that predictive inference for autoregressive processes of order p should be carried out conditional on the last p observed values. When the process is Gaussian, a bootstrap predictive inference conditional on the last p observed values is conveniently computed by ‘running’ the same autoregressive process backwards in time. This procedure is inappropriate for non‐Gaussian autoregressive processes. Our second (and more important) contribution is to present a method (which is not computationally burdensome) for the computation of a bootstrap predictive inference for a non‐Gaussian autoregressive process of order p conditional on the last p observed values.
EXACT GENERAL‐LAG SERIAL CORRELATION MOMENTS AND APPROXIMATE LOW‐LAG PARTIAL CORRELATION MOMENTS FOR GAUSSIAN WHITE NOISE
Authors: Anderson Oliver D.
Published: May 2008

Abstract.Given series realizations of lengthngenerated by a Gaussian white noise process, we use formulae for the moments about zero of the serial covariances to obtain all the non‐centred and central moments up to order 4 for, first, the serial correlations exactly (all lags) and, then, the low‐lag partial correlations approximately (mainly to O(n‐3)). The results agree with empirical values obtained by simulation forn= 100.
AN INNOVATION STATE SPACE APPROACH FOR TIME SERIES FORECASTING
Authors: Libert Gaëtan , Wang Liang , Liu Bao
Published: May 2008

Abstract.An innovation state space modelling approach is presented in which the structures and parameters of a model are determined by an identification algorithm proposed by Tse and Weinert (IEEE Trans. Automat. Contr.120 (1975), 603–13) and the singular value decomposition technique. This approach is applied to two typical data series to illustrate its use, and its forecasting accuracy is compared with other time series approaches.
MAXIMUM LIKELIHOOD ESTIMATION FOR AUTOREGRESSIVE PROCESSES DISTURBED BY A MOVING AVERAGE
Authors: Shin Dong Wan
Published: May 2008

Abstract. Maximum likelihood estimation for stationary autoregressive processes when the signal is subject to a moving‐average sampling error is discussed. A modified maximum likelihood estimator is proposed. An algorithm for computing derivatives of the modified likelihood is suggested. Maximum likelihood estimators of the parameter vector are shown to be strongly consistent and to have a multivariate normal limiting distribution. A Monte Carlo simulation shows that the modified maximum likelihood estimator performs better than other available estimators. US current labour force data are analysed as an example.
(MIS)SPECIFICATION OF LONG MEMORY IN SEASONAL TIME SERIES
Authors: Hassler Uwe
Published: May 2008

Abstract. We present a complete generalization of fractional differencing with seasonal processes. The contribution of each seasonal frequency to the variance of a process may be modelled by separate difference parameters. The regression of the log‐periodogram allows estimation of the difference parameters. We approximate the bias and the variance of these estimators with large samples. Numerical examples illustrate the risk of fractional misspecification.
AN ITERATIVE FILTERING ALGORITHM FOR NON‐FOURIER FREQUENCY ESTIMATION
Authors: Kedem Benjamin , Troendle James
Published: May 2008

Abstract. We study an iterative filtering method to estimate frequencies of random Gaussian sinusoids in white noise. The method uses higher order crossings and takes advantage of a fixed point to guide the use of bandpass filtering in an attempt effectively to increase the signal‐to‐noise ratio. At each iteration the expected zero‐crossing rate is estimated from independent time series. Convergence occurs with any prespecified probability less than one.
NON‐LINEAR TIME SERIES MODELLING AND DISTRIBUTIONAL FLEXIBILITY
Authors: Lye Jenny N. , Martin Vance L.
Published: May 2008

Abstract.Most of the existing work in non‐linear time series analysis has concentrated on generating flexible functional models by specifying non‐linear specifications for the mean of a particular process, without much, if any, attention given to the distributional properties of the model. However, as Martin (J. Time Ser. Anal.13 (1992), 79–94) has shown, greater flexibility in perhaps a more natural way can be achieved by consideration of distributions from the generalized exponential class. This paper represents an extension of the earlier work of Martin by introducing a flexible class of non‐linear time series models which can capture a wide range of empirical behaviour such as skewed, fat‐tailed and even multimodal distributions. This class of models is referred to as generalized exponential non‐linear time series. A maximum likelihood algorithm is given for estimating the parameters of the model and the framework is applied to estimating the distribution of the movements of the exchange rate.
DATA AUGMENTATION AND DYNAMIC LINEAR MODELS
Authors: Frühwirth‐Schnatter Sylvia
Published: May 2008

Abstract.We define a subclass of dynamic linear models with unknown hyperpara‐meter calledd‐inverse‐gamma models. We then approximate the marginal probability density functions of the hyperparameter and the state vector by the data augmentation algorithm of Tanner and Wong. We prove that the regularity conditions for convergence hold. For practical implementation a forward‐filtering‐backward‐sampling algorithm is suggested, and the relation to Gibbs sampling is discussed in detail.
INFINITE VARIANCE STABLE ARMA PROCESSES
Authors: Kokoszka Piotr S. , Taqqu Murad S.
Published: May 2008

Abstract. The asymptotic dependence structure of autoregressive moving‐average processes with stable innovations is analyzed. The analysis is carried out by means of a measure of dependence which extends the covariance function and is applicable to stochastic processes with infinite variance.
AUTOMATIC SEMIPARAMETRIC ESTIMATION OF THE MEMORY PARAMETER OF A LONG‐MEMORY TIME SERIES
Authors: Hurvich Clifford M. , Beltrao Kaizo I.
Published: May 2008

Abstract. In Geweke and Porter‐Hudak's estimator ωd(GPH) of the memory parameter of a long‐memory process, a critical choice the user must make is the number of frequencies, M, to be used in the regression of the log periodogram on log frequency. This choice is critical in practice because by simply varying M for a given data set it is often possible to obtain a very wide range of values of the estimator. Although Geweke and Porter‐Hudak have found that choosing M to be the square root of the sample size gave good results in simulation, they gave no theoretical justification for this choice. Here, we propose automatic criteria for selecting M, and another tuning constant used in related estimates of the memory parameter, based on frequency domain cross‐validation. We provide some theoretical and heuristic justification for the proposed criteria. In a simulation study, we compare some of the resulting automatic methods of estimating the memory parameter with existing non‐automatic ones.
ASYMPTOTIC EFFICIENCY OF THE SAMPLE COVARIANCES IN A GAUSSIAN STATIONARY PROCESS
Authors: Kakizawa Yoshihide , Taniguchi Masanobu
Published: May 2008

Abstract. This paper deals with the asymptotic efficiency of the sample autocovariances of a Gaussian stationary process. The asymptotic variance of the sample autocovariances and the Cramer–Rao bound are expressed as the integrals of the spectral density and its derivative. We say that the sample autocovariances are asymptotically efficient if the asymptotic variance and the Cramer–Rao bound are identical. In terms of the spectral density we give a necessary and sufficient condition that they are asymptotically efficient. This condition is easy to check for various spectra.
SEMIPARAMETRIC TIME SERIES REGRESSION
Authors: Truong Young K. , Stone Charles J.
Published: May 2008

Abstract.Let (Xi,Yi),i= 0, pL 1,… denote a bivariate stationary time series withXibeing Rd‐valued andYibeing real‐valued. We consider the regression modelYi=θ(Xi) +Zi, where θ(·) is an unknown function and Ziis an autoregressive process. Given a realization of lengthn, we examine the problem of estimating the nonparametric function θ(·) and the parametric componentZi. Under appropriate regularity conditions, it is shown that both components can be optimally estimated.
LAG WINDOW ESTIMATION OF THE DEGREE OF DIFFERENCING IN FRACTIONALLY INTEGRATED TIME SERIES MODELS
Authors: Chen Gemai , Abraham Bovas , Peiris Shelton
Published: May 2008

Abstract. In this paper we consider the estimation of the degree of differencing d in the fractionally integrated autoregressive moving‐average time series model ARFIMA (p, d, q). Using lag window spectral density estimators we develop a regression type estimator of d which is easy to calculate and does not require prior knowledge of p and q. Some large sample properties of the estimator are studied and the performance of the estimator for small samples is investigated using the simulation method for a range of commonly used lag windows. Some practical recommendations on the choice of lag windows and the choice of the window parameters are provided.
ON GENERALIZED FRACTIONAL PROCESSES – A CORRECTION
Authors: Gray Henry L. , Zhang Nien‐Fan , Woodward Wayne A.
Published: May 2008

Abstract. A sign error in the proof of Theorem 3 of the paper by Gray et al. (1989) slightly changes a result of that theorem. In this correction we note the error along with the resulting changes that should be made in the results and the proof of the theorem. Additionally, another minor error in the proof is noted which does not effect the result.
ON THE PITMAN NON‐ADMISSIBILITY OF CORRELOGRAM‐BASED METHODS
Authors: Hallin Marc
Published: May 2008

Abstract. A classical result of Chernoff and Savage (Asymptotic normality and efficiency of certain nonparametric tests. Ann. Math. Statist. 29 (1958), 972–94) on lower bounds for the local asymptotic power of normal‐score rank tests, and the resulting Pitman non‐admissibility of classical Gaussian testing procedures in general linear models with independent observations, are shown to hold also for linear autoregressive moving‐average time series models. The Pitman non‐admissibility of usual correlogram‐based methods follows.
ESTIMATION OF THE MEMORY PARAMETER FOR NONSTATIONARY OR NONINVERTIBLE FRACTIONALLY INTEGRATED PROCESSES
Authors: Hurvich Clifford M. , Ray Bonnie K.
Published: May 2008

Abstract. We consider the asymptotic characteristics of the periodogram ordinates of a fractionally integrated process having memory parameter d≥ 0.5, for which the process is nonstationary, or d≤ ‐.5, for which the process is noninvertible. Series having d outside the range (‐.5,.5) may arise in practice when a raw series is modeled without preliminary consideration of the stationarity and invertibility of the series or when a wrong decision is made concerning the stationarity and invertibility of the series. We find that the periodogram of a nonstationary or noninvertible fractionally integrated process at the jth Fourier frequency ωj= 2πj/n, where n is the sample size, suffers from an asymptotic relative bias which depends on j. We also examine the impact of periodogram bias on the regression estimator of d proposed by Geweke and Porter‐Hudak (1983) in finite samples. The results indicate that the bias in the periodogram ordinates can strongly affect the GPH estimator even when the number of Fourier frequencies used in the regression is allowed to depend on the length of the series. We find that data tapering and elimination of the first periodogram ordinate in the regression can reduce this bias, at the cost of an increase in variance for nonstationary series. Additionally, we find for nonstationary series that the GPH estimator is more nearly invariant to first‐differencing when a data taper is used.
STOCHASTIC ORDERS OF MAGNITUDE ASSOCIATED WITH TWO‐STAGE ESTIMATORS OF FRACTIONAL ARIMA SYSTEMS
Authors: Wright J. H.
Published: May 2008

Abstract. Two‐stage estimators have been proposed in fractional autoregressive integrated moving‐average (ARIMA) systems which first estimate the long‐run features of the system semi‐parametrically and then estimate the short‐run features by usual methods in a second stage. Although asymptotic theory is available for the estimates in the first stage of such a procedure, we are aware of no results concerning the estimates in the second stage. In this paper we provide a stochastic order of magnitude associated with an estimator in this class and discuss this result.
PARAMETER ESTIMATION FOR PERIODIC ARMA MODELS
Authors: Adams G. J. , Goodwin G. C.
Published: May 2008

Abstract. In time series analysis of data sequences, the estimation of the parameters of an identified autoregressive moving‐average (ARMA) model is a well‐known and straightforward exercise. However, if the parameters of the model are periodic (i.e. a periodic ARMA (PARMA) model) then the estimation process becomes more difficult. This paper describes an on‐line parameter estimation technique, based on methods from automatic control, which is demonstrated to provide consistent estimates of PARMA model parameters.
TESTING FOR TREND STATIONARITY VERSUS DIFFERENCE STATIONARITY
Authors: Arellano Consuelo , Pantula Sastry G.
Published: May 2008

Abstract. Testing the null hypothesis that a process is difference stationary has received considerable attention in the past decade. Recently, there has been some interest in testing the null hypothesis that a process is a sum of a linear trend and a stationary invertible noise sequence. In this paper we present procedures for testing the null hypothesis that a process is trend stationary against the alternative that the process is difference stationary. A Monte Carlo study is presented to study the behavior of the proposed test criteria. Average global temperature data are used to illustrate the test criteria.
TESTING EQUALITY OF VARIANCES FOR PAIRED TIME SERIES
Authors: Beran Jan , Gasser Theo
Published: May 2008

Abstract. We develop a simple test for testing equality of variances for paired stationary Gaussian time series. The test statistic is a modified z statistic. It is based on the periodograms of the two series and consistent estimation of the difference between the two spectral densities. Simulations illustrate the validity of the asymptotic results for finite samples. An application to EEG data is discussed.
IMPROVED BOOTSTRAP PREDICTION INTERVALS FOR AUTOREGRESSIONS
Authors: Breidt F. Jay , Davis Richard A. , Dunsmuir William T. M.
Published: May 2008

Abstract. We consider bootstrap construction and calibration of prediction intervals for nonGaussian autoregressions. In particular, we address the question of prediction conditioned on the last p observations of the process, for which we offer an exact simulation technique and an approximate bootstrap approach. In simulations for a variety of first‐order autoregressions, we compare various nonparametric prediction intervals and find that calibration gives reasonably narrow prediction intervals with the lowest coverage probability mean squared error among the methods used.
STOCHASTIC MODELING AND IDENTIFICATION OF SEISMIC RECORDS BASED ON ESTABLISHED DETERMINISTIC FORMULATIONS
Authors: Dargahi‐Noubary G. R.
Published: May 2008

Abstract. Stochastic modeling on the basis of established deterministic formulations is stressed and some examples from seismology are presented. Using well‐known deterministic models for a source time function, a single parameter stochastic difference equation (autoregressive model) is derived for seismic records of P‐waves from nuclear explosions and natural earthquakes. A model‐evaluation technique other than statistical goodness‐of‐fit is considered, and its application is illustrated using available data. The interdependency between the characteristic polynomial of the difference equation, its complementary solution (signal), its particular integral (noise) and some physical variables are explained. Variables included in the discussion are duration, intensity and the so‐called corner frequency. Utilizing these dependencies, the signal‐generated character of noise is also illustrated.

To fit the model an estimation procedure is described, and its statistical properties are derived. It is shown that the proposed model fits the records of P‐waves from underground nuclear explosions and natural earthquakes as well as the records of Rayleigh waves from atmospheric explosions. Applications of the model to depth‐ and reflection‐parameter estimation and to event discrimination are discussed, and some representative numerical examples are presented.
ON RESULTS OF PORAT CONCERNING ASYMPTOTIC EFFICIENCY OF SAMPLE COVARIANCES OF GAUSSIAN ARMA PROCESSES
Authors: Walker A. M.
Published: May 2008

Abstract. An alternative derivation is given of results first obtained by Porat (1987) concerning the asymptotic efficiencies of sample autocovariances of a stationary Gaussian ARMA process. This is based on an approximation to the likelihood of these autocovariances.
CONFIDENCE REGIONS FOR PARAMETERS IN THE AR(1) MODEL
Authors: Hamilton David , Wu Ka Ho
Published: May 2008

Abstract.The construction of approximate joint and marginal confidence regions for parameters in the first‐order autoregressive time series model is discussed. These regions are based on the large sample distributions of the likelihood ratio (and approximations to it), of the maximum likelihood estimates and of the score statistics. All these approaches are illustrated using a well‐known example from Box and Jenkins (Time Series Analysis:Forecasting and Control, revised edn. San Francisco:Holden Day, 1976) and some simulated series. In addition, a simulation study is provided for comparing the coverage properties of the various procedures.
SPURIOUS REGRESSIONS BETWEEN I(d) PROCESSES
Authors: Marmol Francesc
Published: May 2008

Abstract. This paper develops an analytical study for the nonsense or spurious regressions that are generated by quite general integrated (of order d) random processes. In doing this, we generalize the work of Phillips (Understanding spurious regressions in econometrics. J. Econ. 33 (1986), 311–40) who provided an analytical study of linear regressions involving only I(1) stochastic processes. Our generalization of Phillips' work to the I(d) case is made employing fractional differencing techniques.
RESULTS ON ESTIMATION AND TESTING FOR A UNIT ROOT IN THE NONSTATIONARY AUTOREGRESSIVE MOVING‐AVERAGE MODEL
Authors: Yap Sook Fwe , Reinsel Gregory C.
Published: May 2008

Abstract. We review the limiting distribution theory for Gaussian estimation of the univariate autoregressive moving‐average (ARMA) model in the presence of a unit root in the autoregressive (AR) operator, and present the asymptotic distribution of the associated likelihood ratio (LR) test statistic for testing for a unit root in the ARMA model. The finite sample properties of the LR statistic as well as other unit root test procedures for the ARMA model are examined through a limited simulation study. We conclude that, for practical empirical work that relies on standard computations, the LR test procedure generally performs better than other standard procedures in the presence of a substantial moving‐average component in the ARMA model.
RATE OF CONVERGENCE FOR LOGSPLINE SPECTRAL DENSITY ESTIMATION
Authors: Kooperberg Charles , Stone Charles J. , Truong Young K.
Published: May 2008

Abstract. The logarithm of the spectral density function for a stationary process is approximated by polynomial splines. The approximation is chosen to maximize the expected log‐likelihood based on the asymptotic properties of the periodogram. Estimates of this approximation are shown to possess the usual nonparametric rate of convergence when the number of knots suitably increases to infinity.
AN APPLICATION OF THE SCHUR‐COHN ALGORITHM TO TIME SERIES ANALYSIS
Authors: Barnard Roger W. , Chanda Kamal C.
Published: May 2008

Abstract. Standard least squares analysis of autoregressive moving‐average (ARMA) processes with errors‐in‐variables entails the construction of a new set of parameters which are functions of the original ARMA parameters, and requires that derivatives of these new parameters of order three or less with respect to the ARMA parameters exist and be bounded. The boundedness of these derivatives in turn depends critically on the nonsingularity of a matrix B which is a function of the ARMA parameters via the new parameters in the model. A particular version of the classical Schur–Cohn algorithm enables us to establish this nonsingularity.