bluuebunny/crossref_metadata_2025 huggingface dataset:
A COMPARATIVE STUDY OF VARIOUS UNIVARIATE TIME SERIES MODELS FOR CANADIAN LYNX DATA
Authors: Lim K. S.
Published: May 2008

Abstract.This paper describes the results of a simulation study aimed at comparing the various time series models, both linear and non‐linear, fitted to the annual Canadian lynx trappings for the years 1821–1934.
THE APPROXIMATE DENSITIES OF SOME QUADRATIC FORMS OF STATIONARY RANDOM VARIABLES
Authors: Abril Juan Carlos
Published: May 2008

Abstract. First we obtain a convenient way of expressing the determinant of the difference between an identity matrix and some products of Toeplitz matrices. Then, using these results, we show that for a large number of normal processes there exist some quadratic forms whose matrices are of Toeplitz type such that their joint density admits an Edgeworth expansion.
A NOTE ON EMBEDDING A DISCRETE PARAMETER ARMA MODEL IN A CONTINUOUS PARAMETER ARMA MODEL
Authors: Chan K. S. , Tong H.
Published: May 2008

Abstract. We have shown that it is not always possible to embed a real‐valued discrete parameter Gaussian AR(1) model in a real‐valued continuous parameter Gaussian AR(1). The problem with general ARMA models is also discussed.
ESTIMATION IN MULTIPLE AUTOREGRESSIVE‐MOVING AVERAGE MODELS USING PERIODICITY
Authors: Cipra Tomáš , Tlustý Pavel
Published: May 2008

Abstract. An estimation procedure for multiple autoregressive‐moving average models is suggested which takes advantage of the possibility of transferring these multiple models to univariate periodic autoregressive‐moving average models. The procedure is simple enough to be practicable using less efficient computers and it should give acceptable estimates for longer time series. By using this method for shorter time series, the obtained estimates may serve as the initial estimates for more complicated estimation procedures.
MARGINALS OF MULTIVARIATE FIRST‐ORDER AUTOREGRESSIVE TIME SERIES MODELS
Authors: Stam Antonie , Hillmer Steven C.
Published: May 2008

This paper is concerned with the marginal models associated with a given multivariate first‐order autoregressive model. A general theory is developed to determine when reductions in the known orders of the marginal models will occur. When the auto‐regressive coefficient matrix has repeated eigenvalues, there may be global reductions in the marginal models. Zeros in the eigenvectors and generalized eigenvectors of the auto‐regressive coefficient matrix lead to local reductions in the marginal models. The case when the autoregressive parameter matrix has systematic zeros is also investigated.
A SCORE TEST FOR DETECTION OF TIME SERIES OUTLIERS
Authors: Abraham Bovas , Yatawara Nihal
Published: May 2008

Abstract.Two characterizations, the aberrant observation and innovation models, for outliers in time series are considered. A procedure based on the well‐known score‐test is discussed for detection of outliers and distinguishing between the outlier types. Significance levels of the tests are also obtained and the method is illustrated with simulated examples.
ARMA MODELLING WITH NON‐GAUSSIAN INNOVATIONS
Authors: Li W. K. , McLeod A. I.
Published: May 2008

Abstract.The problem of modelling time series driven by non‐Gaussian innovations is considered. The asymptotic normality of the maximum likelihood estimator is established under some general conditions. The distribution of the residual autocorrelations is also obtained. This gives rise to a potentially useful goodness‐of‐fit statistic. Applications of the results to two important cases are discussed. Two real examples are considered.
EFFICIENT ESTIMATION OF NONSTATIONARY TIME SERIES REGRESSION
Authors: Harvey A. C. , Robinson P. M.
Published: May 2008

Abstract. A multiple time series regression model with trending regressors has residuals that are believed to be not only serially dependent but nonstationary. Assuming the residuals can be decomposed as a stationary autoregressive process of known order multiplied by an unknown time‐varying scale factor, we propose estimators of the regression coefficients and show them to be as efficient as estimators based on known scale factors. Our estimators have features in common with adaptive estimators proposed by Carroll (1982) and Hannan (1963) for different regression problems, involving respectively independent residuals with heteroskedasticity of unknown type, and stationary residuals with unknown serial dependence structure.
SOME PROPERTIES OF CONDITIONAL QUASI‐LIKELIHOOD FUNCTIONS FOR TIME SERIES MODEL FITTING
Authors: Huzii Mituaki
Published: May 2008

Abstract. We consider fitting a parametric model to a time series and obtain the maximum likelihood estimates of unknown parameters included in the model by regarding the time series as a Gaussian process satisfying the model. We evaluate the asymptotic value of the conditional quasi‐likelihood function when the number of observations tends to infinity. We show what properties of the time series we can find by examining the behaviour of the conditional quasi‐likelihood function, even when the time series does not necessarily satisfy the model and is not necessarily Gaussian.
A LIMITING PROPERTY OF SAMPLE AUTOCOVARIANCES OF PERIODICALLY CORRELATED PROCESSES WITH APPLICATION TO PERIOD DETERMINATION
Authors: Tian C. J.
Published: May 2008

Abstract. It is shown that the sample autocovariance of a periodically correlated process converges to a limit which reveals the same periodicity as the process. A theorem is proved relating to the rate of almost sure convergence, which is uniform in the lag up to some orders of observation length. Based on the limiting property, a strongly consistent estimate of hidden period is proposed.
NON‐NEGATIVE AUTOREGRESSIVE PROCESSES
Authors: Anděl Jiří
Published: May 2008

Abstract. Consider a stationary autoregressive process given by Xt=b1Xt‐1+…+bpXt‐p+Yt, where the Yt are independent identically distributed positive variables and b1,…,bp are non‐negative parameters. Let the variables X1,…,Xn be given. If p= 1 then it is known that b1*= min(Xt/Xt‐1) is a strongly consistent estimator for b1 under very general conditions. In this paper the case p= 2 is analysed in detail. It is proved that min(Xt/Xt‐1)→b1 almost surely (a.s.) and min(Xt/Xt‐2)→b2+b12 a.s. as n→ 8. The convergence is very slow. Denote by b1* and b2* values of b1 and b2 respectively which maximize b2+b2 under the conditions Xt‐b1Xt‐1‐b2Xt‐2≥ 0 for t= 3,…, n. We prove that b1*b1 and b2*b2 a.s. Simulations show that b1* and b2* are better than the least‐squares estimators of the autoregressive coefficients when the distribution of Yt is exponential.
THE RESOLUTION OF CLOSELY ADJACENT SPECTRAL LINES
Authors: Hannan E. J. , Quinn B. G.
Published: May 2008

Abstract. The problem is that of determining the parameters in a trigonometric polynomial when it is observed with added stationary noise. The frequencies, in particular, must be determined and the situation especially considered is that where these are close together. A similar problem arises if an angular frequency is close to zero or π. The method of estimation is the maximization of the regression sum of squares as a function of the unknown frequencies. In the asymptotic theory, the closely adjacent frequencies are separated by an amount that is of the order T‐1, where T is the length of the series. Simulations show that this asymptotic treatment gives a better approximation in cases where the separation is of this magnitude than that obtained by treating the frequencies as fixed.
ESTIMATING THE NUMBER OF TERMS IN A SINUSOIDAL REGRESSION
Authors: Quinn B. G.
Published: May 2008

Abstract.A procedure based on the automatic information criterion procedure of Akaike is presented for estimating the number of sinusoidal terms present in a time series. The procedure is shown to produce a strongly consistent estimator.
FORECASTING EXPONENTIAL AUTOREGRESSIVE MODELS OF ORDER 1
Authors: Al‐Qassam M. S. , Lane J. A.
Published: May 2008

Abstract.Exact forecasting of the non‐linear EXPAR(1) model for several steps ahead involves a sequence of numerical integrations, thus motivating the search for reasonable approximations. A method based on the assumption of approximately normal forecast errors is shown to give forecasts which perform well in both qualitative and numerical comparisons with two alternative approximations based on naive extrapolation and linearization of the autoregression function.
ESTIMATION AND INTERPOLATION OF MISSING VALUES OF A STATIONARY TIME SERIES
Authors: Pourahmadi Mohsen
Published: May 2008

Abstract. A complete solution of the important problem of estimating (interpolating) the missing values of a stationary time series is obtained by decomposing it into a prediction plus regression problem. This makes it possible to estimate the missing values by finding the multistep‐ahead predictors and using the existing computer packages for time series analysis. Such a solution is vital for the E step of the EM algorithm, and it is shown how this algorithm can be used to develop a simultaneous procedure for estimating the parameters and missing values of a time series.
THE PREDICTIVE PERFORMANCE OF THREE AUTOREGRESSIVE MOVING‐AVERAGE MODELS:A MONTE CARLO INVESTIGATION
Authors: Batts John T. , McNown Robert F.
Published: May 2008

Abstract.The relative accuracy of point and interval forecasts from three related autoregressive moving‐average (ARMA) models—multivariate, univariate, and transfer function—is evaluated in this study. It is found that the multivariate models produce the most accurate one‐ and three‐step‐ahead point forecasts of nonindependent series. However, the most accurate point forecasts of independent series are generated by the univariate models. Compared with the multivariate models, the transfer function predictions are relatively unreliable, but with the appropriate restrictions they are superior to the univariate forecasts in certain cases. Interval forecasts from the correctly specified models are reliable indicators of forecast dispersion.
ON EMBEDDING A DISCRETE‐PARAMETER ARMA MODEL IN A CONTINUOUS‐PARAMETER ARMA MODEL
Authors: He S. W. , Wang J. G.
Published: May 2008

Abstract. It is shown that a real‐valued discrete‐parameter Gaussian ARMA (p. q) model with q < p can be embedded in a real‐valued continuous‐parameter Gaussian ARMA(p', q') model with q' < p'. The problem of embedding a real‐valued discrete‐parameter Gaussian AR(p) into a real‐valued continuous‐parameter Gaussian AR(p) is also discussed.
SIMULTANEOUS CONFIDENCE BANDS FOR THE SPECTRAL ESTIMATE OF TWO‐CHANNEL AUTOREGRESSIVE PROCESSES
Authors: Sakai Hideaki , Sakaguchi Fuminori
Published: May 2008

Abstract. In this paper we derive simultaneous confidence bands for the maximum entropy method spectral estimate of two‐channel autoregressive (AR) processes by using the asymptotic theory of the estimation of periodic AR processes.
MULTIVARIATE WALSH‐FOURIER ANALYSIS
Authors: Stoffer David S.
Published: May 2008

Abstract. In this paper we establish a statistical methodology for the spectral analysis of stationary multivariate time series via the Walsh‐Fourier transform. Theoretical results pertaining to the definition and estimation of the Walsh‐Fourier spectral matrix and functions of that matrix including cross‐spectra, coherency and phase are given. An example of the statistical techniques developed in this paper is given; in particular, the methodologies are applied to neonatal sleep data collected from a study of the effect of maternal substance use during pregnancy.
ESTIMATION AND TESTING OF A MULTIVARIATE EXPONENTIAL SMOOTHING MODEL
Authors: Fernández F. Javier
Published: May 2008

Abstract.The form of the spectral likelihood function of a multivariate stochastic process permits straightforward construction of a scoring algorithm for maximum likelihood estimation using first derivatives only and a score test statistic for hypothesis testing. These techniques are applied to the analysis of a multivariate exponential smoothing model for which the homogeneity hypothesis is also discussed.
SELECTING ORDER FOR GENERAL AUTOREGRESSIVE MODELS BY MINIMUM DESCRIPTION LENGTH
Authors: Huang Dawei
Published: May 2008

Abstract.In this paper we put forward some criteria for estimating the order for general autoregressive (AR) models (i.e. AR models without any constraint about the roots of the characteristic polynomial) according to the minimum description length. Different criteria are given for different kinds of AR models because the convergence rates are different. It is proved that all the estimates for the order are strongly consistent.
THE ZERO‐CROSSING RATE OF AUTOREGRESSIVE PROCESSES AND ITS LINK TO UNIT ROOTS
Authors: He Shuyuan , Kedem Benjamin
Published: May 2008

Abstract. The asymptotic zero‐crossing rate (ZCR) of the general second‐order autoregressive process is investigated. When the associated characteristic polynomial has a unit root eiθ (0 ≤θ≤π), the ZCR converges in mean square to θ/π and the rate of convergence is very fast regardless of the noise level.
ESTIMATION FOR THE FIRST‐ORDER DIAGONAL BILINEAR TIME SERIES MODEL
Authors: Kim Won Kyung , Billard L. , Basawa I. V.
Published: May 2008

Abstract.The problem of estimation of the parameterbin the simple diagonal bilinear model {Xt},Xt=et+bet‐1Xt‐1, is considered, where {et} is Gaussian white noise with zero mean and possibly unknown variance s̀2. The asymptotic normality of the moment estimator ofbis established for the two cases when s̀2is known and s̀2is unknown. It is noted that the limit distribution of the least‐squares cannot easily be derived analytically. A bootstrap comparison of the sampling distributions of the least‐squares and moment estimates shows that both are asymptotically normal with the least‐squares estimate being the more efficient.
FISHER'S INFORMATION MATRIX FOR SEASONAL AUTOREGRESSIVE‐MOVING AVERAGE MODELS
Authors: Klein André , Mélard Guy
Published: May 2008

Abstract.Two procedures are described for obtaining Fisher's information matrix of a multiplicative seasonal autoregressive‐moving average process. They can be useful in determining the asymptotic covariance matrix of Gaussian maximum likelihood estimators of the parameters. Components of the information matrix are expressed in the first procedure as integrals of rational functions. The second procedure makes use of the autocorrelation function of several autoregressive processes.
LEVINSON‐TYPE RECURSIVE ALGORITHMS FOR LEAST‐SQUARES AUTOREGRESSION
Authors: Huang Dawei
Published: May 2008

Abstract. A set of formulae for calculating the least‐squares autoregressive coefficients is given. It can be used for stable, unstable and explosive models. The calculations needed by this algorithm are less than those of the Burg and Marple algorithms. The method used to deduce these formulae has general significance. For example, it is also used to improve the Marple algorithm. Simulation shows that the estimates given by this algorithm are better than those given by the Levinson and Burg recursions.
OUTLIER DIAGNOSTICS IN TIME SERIES ANALYSIS
Authors: Ledolter Johannes
Published: May 2008

Abstract.Cook's likelihood displacement is a convenient measure of the impact of a model perturbation on parameter estimates. A commonly used model perturbation in regression is the deletion of acase, or equation. A natural model perturbation in the time series context is the deletion of anobservation, or a group of observations. Diagnostics that measure the impact of individual observations on the time series estimates are explored in this paper. A diagnostic that compares the estimates of the innovation variance with and without a particular observation is studied in detail.
ON THE PROBABILITY OF ESTIMATING A DETERMINISTIC COMPONENT IN THE LOCAL LEVEL MODEL
Authors: Shephard N. G. , Harvey A. C.
Published: May 2008

Abstract. A local level model has a deterministic level when the signal‐to‐noise ratio q is zero. In this paper we investigate the properties of the maximum likelihood estimator of q, paying particular attention to the case where its true value is zero. These properties are shown to be crucially dependent on the initial conditions employed.
STRONG CONSISTENCY AND ASYMPTOTIC NORMALITY OF /1 ESTIMATES OF THE AUTOREGRESSIVE MOVING‐AVERAGE MODEL
Authors: Dunsmuir William T. M. , Spencer Nancy M.
Published: May 2008

Abstract. The strong consistency and central limit theorem for least absolute deviation estimates of the parameters in a scalar autoregressive‐moving average model are established under general conditions on the innovations.
ITERATIVE AND RECURSIVE ESTIMATION OF TRANSFER FUNCTIONS
Authors: Grillenzoni Carlo
Published: May 2008

Abstract.A unified treatment of non‐linear estimation, pseudolinear regression and stochastic approximation for open‐loop transfer function models is provided. Pseudolinear regression techniques are used to derive the recursive non‐linear least‐squares estimator, avoiding the methodological problems implicit in traditional derivations. Stochastic approximation analysis is used to investigate in a direct manner the conditions of convergence and consistency of both iterative and recursive algorithms. The various methods are compared using data for an industrial process.
ESTIMATION OF THE PARAMETERS OF AN EAR(p) PROCESS
Authors: Billard L. , Mohamed Fouad Y.
Published: May 2008

Abstract.Gaver and Lewis and Lawrance and Lewis have described an autoregressive process of orderp, EAR(p), which is such that the marginal distribution of the observations follows an exponential distribution. There is now a rich class of exponential and related distributions time series models. Such models are of importance in queuing and network processes, for example. The properties of these and related models have been well explored, but so far little work has been done toward the important problem of estimation. We attempt here to address this question for the EAR(p) models. Because of inherent discontinuities in some of the relevant underlying distributions, the standard theory cannot be applied. However, by utilizing a general theory developed by Klimko and Nelson, conditional least‐squares estimators are derived. Further, it is shown that these estimators are strongly consistent and asymptotically normally distributed. Small‐sample properties are investigated. The results suggest that these estimators are to be preferred compared with those suggested by Lawrance and Lewis.
NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES
Authors: Granger C. W. J. , Hallman Jeff
Published: May 2008

Abstract. In this paper we consider the effects of nonlinear transformations on integrated processes and unit root tests performed on such series. A test that is invariant to monotone data transformations is proposed. It is shown that series are generally not cointegrated with nonlinear transformations of themselves, but the same transformation applied to a pair of cointegrated series can result in cointegration between the transformed series.
A RELATION FOR ‘LINEARITY’ OF THE BISPECTRUM
Authors: Sakaguchi Fuminori
Published: May 2008

Abstract. A relation is presented which is a necessary and sufficient condition for the bispectrum to be of the linear process type.
AN EXPLICIT NEARLY UNBIASED ESTIMATE OF THE AR(1) PARAMETER FOR REPEATED MEASUREMENTS
Authors: Azzalini A. , Frigo A. C.
Published: May 2008

Abstract.It is assumed thatn(n≥ 1) independent time series, each of lengthT.have the same autocorrelation function of the AR(1) type, but they may differ in mean value, with the mean value of theith series equal to a linear combination of a set of covariates associated with the series. To estimate the common autoregressive parameter, Daniels' method is extended to the present case. As, for smallT, this gives a severely biased estimate, a formula for its mean value is obtained. A modified estimate which has a substantially smaller bias is found using this formula.
LONG‐RANGE DEPENDENCE, NON‐LINEARITY AND TIME IRREVERSIBILITY
Authors: Cox D. R.
Published: May 2008

Abstract. A rather general class of stationary processes with long‐range dependence is introduced by mixing independent processes with short‐range dependence. The class is used to study the relation between non‐linearity and time irreversibility of the long‐range dependence process and the corresponding features of the component processes.
A METHODOLOGY FOR SELECTING SUBSET AUTOREGRESSIVE TIME SERIES MODELS
Authors: Yu Gwo‐Hsing , Lin Yow‐Chang
Published: May 2008

Abstract. In time series modelling, subset models are often desirable, especially when the data exhibit some form of periodic behaviour with a range of different natural periods in terms of days, weeks, months and years. Recently, Hokstad proposed a method based on personal judgement for selecting the first tentative model to obtain the best subset autoregressive model. The subjective approach adopted in the Hokstad method is a disadvantage in building up a computer program which could automatically select the appropriate model of a given time series. In this paper, we propose overcoming this disadvantage by employing the inverse autocorrelation function to select the first tentative model. In addition to sets of synthetic data, some well‐known real series such as the D, E and F series of Box and Jenkins and the Canadian lynx data are analysed to validate the proposed method. The results indicate that the method can successfully detect the true model for a given time series.
NONPARAMETRIC TESTS FOR SERIAL DEPENDENCE
Authors: Chan Ngai Hang , Tran Lanh Tat
Published: May 2008

Abstract. A nonparametric test statistic based on the distance between the joint and marginal densities is developed to test for the serial dependence for a given sequence of time series data. The key idea lies in observing that, under the null hypothesis of independence, the joint density of the observations is equal to the product of their individual marginals. Histograms are used in constructing such a statistic which is nonparametric and consistent. It possesses high power in capturing subtle or diffuse dependence structure. A bilinear time series model is used to illustrate its performance with the classical correlation approach.
TESTS FOR SEASONAL COINTEGRATION USING PRINCIPAL COMPONENTS
Authors: Joyeux Roselyne
Published: May 2008

Abstract. Precise definitions of integrations at frequencies other than zero are given. New cointegration tests, which do not present the problems encountered in existing tests, are developed. They are a generalization of the latent root tests developed by Phillips and Ouliaris.
ALGORITHMS FOR ESTIMATION OF POSSIBLY NONSTATIONARY VECTOR TIME SERIES
Authors: Zhou Guofu
Published: May 2008

Abstract.This paper presents efficient algorithms for evaluating the likelihood function and its gradient of possibly nonstationary vector autoregressive moving‐average (VARMA) processes.
‘PURIFYING’ NOISY SIGNALS
Authors: Rabinovitch A. , Thieberger R.
Published: May 2008

Abstract. A method is presented for obtaining the set of all possible pure origins of a given noisy ARMA(2,2) signal. By a transformation to a new set of variables the locus of this set becomes a straight line.
NON‐NEGATIVE AUTOREGRESSIVE MODELS
Authors: Hong‐zhi An
Published: May 2008

Abstract. Consider a stationary non‐negative autoregressive (AR) model given xt=b1xt‐1, +…+bpxt‐p+et, where the et are independent identically distributed non‐negative variables and b1, …, bp are non‐negative parameters, and all the roots of the equation 1 –b1u–…–bpup= 0 are outside the unit circle. The stationary solution of the above AR model is called a stationary non‐negative AR process. Let x1, x2, …xn be an example of a stationary non‐negative AR process. Under very general conditions strongly consistent estimators of the AR parameters b1, b2, …, bp have been studied. In this paper a new procedure is proposed to estimate not only b1, b2, …, bp but also bo which is the essential lower bound of the variable et. We shall show that the new estimators obtained using the new procedure are consistent estimators of bo, b1, …, bp under the weakest condition which guarantees that the stationary non‐negative AR model has a stationary non‐degenerative solution.
SPECTRAL RADIUS, KRONECKER PRODUCTS AND STATIONARITY
Authors: Liu Jian
Published: May 2008

Abstract. We provide a stochastic proof of the inequality ρ(A⊗A+B⊗B) ≥ρ(A⊗A), where ρ(M) denotes the spectral radius of any square matrix M, i.e. max{|eigenvalues| of M}, and M⊗N denotes the Kronecker product of any two matrices M and N. The inequality is then used to show that stationarity of the bilinear model

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will imply stationarity of the linear part, i.e. the linear ARMA model

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for r= 1 and q= 1. Furthermore, it is shown that stationarity of the subdiagonal model, i.e. the bilinear model with bij=0 for i< j, again implies stationarity of its linear part, provided that the stationarity condition given by Bhaskara Rao and his colleagues is met. Interestingly, the conclusion that stationarity of the subdiagonal models, implies that the linear component models cannot be extended to the general non‐subdiagonal bilinear models. The last observation is demonstrated via a simple example with p=m= 1, r= 0 and q= 2.
COMPUTATION OF CANONICAL CORRELATION BETWEEN PAST AND FUTURE OF A TIME SERIES
Authors: Pourahmadi Mohsen , Miamee A. G.
Published: May 2008

Abstract. The canonical correlation between the past and future of a stationary time series is shown to be the limit of the canonical correlation between the infinite past and finite future, and computation of the latter is reduced to an eigenvalue problem invovling finite matrices. This provides a convenient finite‐dimensional algorithm for computing canonical correlations and components of a time series. An upper bound is conjectured for the largest canonical correlation.
TIME‐REVERSIBILITY, IDENTIFIABILITY AND INDEPENDENCE OF INNOVATIONS FOR STATIONARY TIME SERIES
Authors: Breidt F. J. , Davis R. A.
Published: May 2008

Abstract. Weiss (J. Appl. Prob. 12 (1975) 831–36) has shown that for causal autoregressive moving‐average (ARMA) models with independent and identically distributed (i.i.d.) noise, time‐reversibility is essentially unique to Gaussian processes. This result extends to quite general linear processes and the extension can be used to deduce that a non‐Gaussian fractionally integrated ARMA process has at most one representation as a moving average of i.i.d. random variables with finite variance. In the proof of this uniqueness result, we use a time‐reversibility argument to show that the innovations sequence (one‐step prediction residuals) of an ARMA process driven by i.i.d. non‐Gaussian noise is typically not independent, a result of interest in deconvolution problems. Further, we consider the case of an ARMA process to which independent noise is added. Using a time‐reversibility argument we show that the innovations of the ARMA process with added independent noise are independent if and only if both the driving noise of the process and the added noise are Gaussian.
STATE SPACE MODELS WITH DIFFUSE INITIAL CONDITIONS
Authors: Marshall Pablo
Published: May 2008

Abstract. A state space model with diffuse initial conditions is considered. A simple and direct proof of the algorithm for computing the likelihood function and minimum mean square estimators of the state is given
ORDER IDENTIFICATION STATISTICS IN STATIONARY AUTOREGRESSIVE MOVING‐AVERAGE MODELS:VECTOR AUTOCORRELATIONS AND THE BOOTSTRAP
Authors: Paparoditis Efstathios , Streitberg Bernd
Published: May 2008

Abstract. In this paper we consider the vector autocorrelation approach for identifying ARMA (p, q) models and use a bootstrap procedure in order to evaluate the distribution of the corresponding sample statistics by means of a resampling scheme for the residuals when p and q are unknown. The asymptotic validity of the bootstrap procedure applied to the vector autocorrelation estimates is established. Some simulations and examples demonstrating the appropriateness of the proposed bootstrap procedure in comparison with large‐sample Gaussian approximations are included.
SPECTRAL ANALYSIS OF STATIONARY POINT PROCESSES USING THE FAST FOURIER TRANSFORM ALGORITHM
Authors: Rigas A. G.
Published: May 2008

Abstract.In this paper we consider techniques of spectral analysis for stationary point processes in order to study the behaviour of a complex physiological system. The estimates of the power spectrum are obtained by smoothing the periodogram which is computed very rapidly with the help of the fast Fourier transform algorithm. In the computation of the estimates we can use either the whole record of the data or a number of disjoint records.
PARTIAL AUTOCORRELATION PROPERTIES FOR NON‐STATIONARY AUTOREGRESSIVE MOVING‐AVERAGE MODELS
Authors: Anderson O. D.
Published: May 2008

Abstract. We are primarily interested in relating the partial autocorrelation behaviour of an autoregressive integrated moving‐average process of order (p, d, q), {Zi} say, with those of its D‐differenced processes {(1 ‐ B)DZi} (D= 1, …, d). To this end, we evaluate the early partial correlations corresponding to serial correlations which initially follow a slow linear decline from unity. These partials, to a first approximation, take a small constant negative value from lag 2 onwards. We also demonstrate a relationship between the theoretical partials πk and πk(Δ) for a once‐integrated process {Zi} and its first‐differenced process {(1 ‐ B)Zi} respectively. These results carry over to cases where the non‐stationary zeros are at ‐1, and differencing is replaced by the corresponding ‘simplifying’ transformation implicit in the operator 1 +B.
ESTIMATION OF THE NON‐STATIONARY FACTOR IN ARUMA MODELS
Authors: Huang D. , Anh V. V.
Published: May 2008

Abstract. Two methods for the estimation of the non‐stationary factor in ARUMA models are given. Both methods yield strongly consistent estimators and the roots of the corresponding filters lie on the unit circle.
ON‐LINE FREQUENCY ESTIMATION
Authors: Hannan E. J. , Huang D.
Published: May 2008

Abstract.An algorithm is presented for on‐line estimation of the frequency ω from dataxj=Acos(jω+φ) +μjwhereμjis generated by a stationary process. The algorithm requires only about 20 calculations at each time point. Theorems justifying the algorithm as asymptotically efficient are presented. Simulations show the algorithm working well at reasonably low signal‐to‐noise ratios. A feature of the algorithm is that it must not be run for too long without reinitiation with a new initial value. A rule for choosing these reinitiation times is given.
REGRESSION OF SPECTRAL ESTIMATORS WITH FRACTIONALLY INTEGRATED TIME SERIES
Authors: Hassler Uwe
Published: May 2008

Abstract. Assuming a normal distribution we supplement the proof of periodogram regression suggested by Geweke and Porter‐Hudak (J. Time Ser. Anal. 4 (1983) 221–38) in order to estimate and test the difference parameter of fractionally integrated autoregressive moving‐average models. The procedure proposed by Kashyap and Eom (J. Time Ser. Anal. 9 (1988) 35–41) arises as a special case and is found to be correct if the true parameter value is negative. Regression of the smoothed periodogram yields estimators for the difference parameter with much faster vanishing variance; no asymptotic distribution can be derived, however. In computer experiments we find that the smoothed periodogram regression may be superior to pure periodogram regression when we have to discriminate between autoregression and fractional integration
AN AIC TYPE ESTIMATOR FOR THE NUMBER OF COSINUSOIDS
Authors: Wang Xiaobao
Published: May 2008

Abstract. An AIC type estimator for the number of cosinusoids is studied. The estimator is proved to be strongly consistent in the presence of colored noise.
THE RECURSIVE FITTING OF SUBSET VARX MODELS
Authors: Penm Jack H. W. , Penm Jammie H. , Terrell R. D.
Published: May 2008

Abstract. A vector time series model of the form A(L)y(t) + B(L)x(t) =ε(t) is known as a vector autoregressive model with exogenous variables (VARX model) and involves a regressand vector y(t) and a regressor vector x(t). This paper provides a method for the recursive fitting of subset VARX models. It suggests the use of ascending recursions in conjunction with an order selection criterion to choose an ‘optimum’ subset VARX model.
RECOGNIZING OVERDIFFERENCED TIME SERIES
Authors: Chang Ming Chun , Dickey David A.
Published: May 2008

Abstract. Differencing is often used to render a time series stationary. The decision of how much differencing to do is usually based on plots of data, the autocorrelation function or a statistical test. Hence, it may happen that an analyst mistakenly differences a stationary series. When that happens, the inverse autocorrelation function takes on a specific pattern. We characterize this pattern and discuss the behavior of sample estimates of the inverse autocorrelation function for such overdifferenced series.
DISCRIMINANT ANALYSIS FOR STATIONARY VECTOR TIME SERIES
Authors: Zhang Guoqiang , Taniguchi Masanobu
Published: May 2008

Abstract. In this paper, we shall consider the case where a stationary vector process {Xt} belongs to one of two categories described by two hypotheses π1 and π2. These hypotheses specify that {Xt} has spectral density matrices f(Λ) and g(Λ) under π1 and π2, respectively. Although Gaussianity of {Xt} is not assumed, we can formally make the Gaussian likelihood ratio (GLR) based on X(1),…X(T). Then an approximation I(f:g) of the GLR is given in terms of f(Λ) and g(Λ). If f(Λ) and g(Λ) are known, we can use I(f:g) as a classification statistic. It is shown that I(f:g) is a consistent classification criterion in the sense that the misclassification probabilities converge to zero as T→∝. When g is contiguous to f, we discuss non‐Gaussian robustness of I(f:g). A sufficient condition for the non‐Gaussian robustness will be given. Also a numerical example will be given.
PERIODIC CORRELATION IN STRATOSPHERIC OZONE DATA
Authors: Bloomfield Peter , Hurd Harry L. , Lund Robert B.
Published: May 2008

Abstract. A 50‐year time series of monthly stratospheric ozone readings from Arosa, Switzerland, is analyzed. The time series exhibits the properties of a periodically correlated (PC) random sequence with annual periodicities. Spectral properties of PC random sequences are reviewed and a test to detect periodic correlation is presented. An autoregressive moving‐average (ARMA) model with periodically varying coefficients (PARMA) is fitted to the data in two stages. First, a periodic autoregressive model is fitted to the data. This fit yields residuals that are stationary but non‐white. Next, a stationary ARMA model is fitted to the residuals and the two models are combined to produce a larger model for the data. The combined model is shown to be a PARMA model and yields residuals that have the correlation properties of white noise.
COMPARISON OF TIME AND CROSS‐SECTIONAL AGGREGATION UNDER A TIME SERIES RANDOM COMPONENT MODEL
Authors: Eltinge John L.
Published: May 2008

Abstract. Small‐area estimation under a stationary time series random component model is considered. Cross‐sectional aggregation and varying degrees of time aggregation are treated as competing prediction methods. An estimated mean‐squared prediction error criterion is used to compare these methods. Some exact and asymptotic properties of this criterion are developed, a consistent estimator of the associated asymptotic variance is presented and simultaneous approximate confidence intervals for the mean‐squared prediction errors are discussed. Time aggregation of a single series is considered as a special case. In addition, an extension to the assessment of mean‐squared prediction errors of synthetic small‐area predictors is outlined.
DIAGNOSTIC CHECKING OF PERIODIC AUTOREGRESSION MODELS WITH APPLICATION
Authors: McLeod A. I.
Published: May 2008

Abstract.An overview of model building with periodic autoregression (PAR) models is given emphasizing the three stages of model development:identification, estimation and diagnostic checking. New results on the distribution of residual autocorrelations and suitable diagnostic checks are derived. The validity of these checks is demonstrated by simulation. The methodology discussed is illustrated with an application. It is pointed out that the PAR approach to model development offers some important advantages over the more general approach using periodic autoregressive moving‐average models.
LAGRANGE MULTIPLIER TESTS FOR FRACTIONAL DIFFERENCE
Authors: Agiakloglou Christos , Newbold Paul
Published: May 2008

Abstract.This paper develops Lagrange multiplier tests of ARMA(p, q) models against fractional ARIMA(p, d, q) alternatives. The performance of the tests is investigated for moderate‐sized samples. It is concluded that fractional difference will be difficult to detect when the orders (p, q) are over‐specified in an autoregressive moving‐average (ARMA) analysis. The importance of distinguishing between the mean known and mean estimated cases in fractional difference models is illustrated in the context of these tests.
ON THE INVERTIBILITY OF PERIODIC MOVING‐AVERAGE MODELS
Authors: Bentarzi Mohamed , Hallin Marc
Published: May 2008

Abstract. A sufficient condition for the invertibility of univariate periodic moving‐average models has been given by Cipra and Ghysels and Hall. We show that this condition is not a necessary one, and provide a necessary and sufficient condition for the general m‐variate, d‐periodical moving‐average MA(q) case.
SYMMETRIC STABLE SEQUENCES WITH MISSING OBSERVATIONS
Authors: Nassiuma Dankit K.
Published: May 2008

Abstract. A procedure for evaluating optimal linear estimates of missing values in the minimum dispersion sense is proposed for stationary symmetric stable processes. Analytical expressions for the estimates are obtained for the autoregressive moving‐average process and it is shown that the finite variance setting results are special cases. Cases of one and more than one missing value are considered.
ON VECTOR AUTOCORRELATIONS AND GENERALIZED SECOND‐ORDER FUNCTIONS FOR TIME SERIES
Authors: Paparoditis Efstathios
Published: May 2008

Abstract. Some structural properties of certain vector generalizations of second‐order functions of a stationary stochastic process based on determinantial functions of autocovariances are discussed. In particular, a generalized autocovariance function which retains all properties of the ordinary autocovariance function is considered and the linear dependence structure of certain scalar stochastic processes associated with this function is investigated. Properties of the normalized function are discussed and a duality property is found, according to which this function also generalizes in a natural way the ordinary partial autocorrelation function of stochastic processes.
SOME SIMPLE TESTS OF THE MOVING‐AVERAGE UNIT ROOT HYPOTHESIS
Authors: Breitung Jorg
Published: May 2008

Abstract. This paper deals with three test statistics for a moving‐average (MA) unit root. The spectral test is based on the estimate of the spectral density at frequency zero. The variance difference statistic compares the sample variance of the integrated series with the estimated variance imposing the MA unit root constraint. Furthermore, Tanaka's score type test statistic is modified to improve the power in higher order models. The asymptotic power of the tests is considered and Monte Carlo experiments are performed to investigate the small sample properties of the tests. Finally, the tests are applied to a number of economic time series to determine the degree of integration.
USING THE MUTUAL INFORMATION COEFFICIENT TO IDENTIFY LAGS IN NONLINEAR MODELS
Authors: Granger Clive , Lin Jin‐Lung
Published: May 2008

Abstract. Two alternative methods are considered for identifying what lags to use in a nonlinear model relating a pair of series. One is based on a mutual information function, the other is Kendall's r. They both have the property that if each variable is instantaneously transformed, such that ranks are preserved, then the functions are unchanged. Simulations find properties of the functions and allow application to generated nonlinear series. In simple cases, the methods appear to find frequently the correct lags.
THE DETECTION OF A SINGLE ADDITIVE OUTLIER OF UNKNOWN POSITION
Authors: Kabaila Paul
Published: May 2008

Abstract.Kudo (On the testing of outlying observations.Sankhya17 (1956), 67–73) has derived an optimal invariant detector of a single additive outlier of unknown position in the context of an underlying Gaussian process consisting of independent and identically distributed random variables. We show how this author's arguments can be extended to derive an invariant detector of an additive outlier of unknown position for an underlying zero‐mean Gaussian stochastic process. This invariant detector depends on the parameters of this process; its properties are analysed further for the particular case of an underlying zero‐mean Gaussian AR(p) process. It provides an upper bound on the performance of any invariant detector based solely on the data and it may be ‘bootstrapped’ to provide an invariant detector based solely on the data. A plausibility argument is presented in favour of the proposition that the bootstrapped detector is nearly optimal for sufficiently large data lengthn.The truth of this proposition has been confirmed by simulation results for zero‐mean Gaussian AR(1) and AR(2) processes (for certain sets of possible outlier positions). The bootstrapped detector is shown to be closely related to the detector based on the approximate likelihood ratio criteria of Fox (Outliers in time series.J. Roy. Statist. Soc. Ser. B34 (1972), 350–63) and the leave‐one‐out diagnostic of Bruce and Martin (Leave‐k‐out diagnostics in time series.J. Roy. Statist. Soc. Ser B51 (1989), 363–424). It is also shown how the case of an underlying Gaussian process with arbitrary mean can be reduced to the case of an underlying zero‐mean Gaussian process.
STATISTICAL ANALYSIS OF ECONOMIC TIME SERIES VIA MARKOV SWITCHING MODELS
Authors: McCulloch Robert E. , Tsay Ruey S.
Published: May 2008

Abstract.In this paper we develop a very general Markov switching model for analysis of economic time series. Our general set‐up allows us to assess the effects of a variety of model and prior assumptions on the results. The growth rates of US quarterly real gross national product are used to illustrate the proposed analysis. We find that although the evidence is not strong the analysis does not support the model in which the dynamic behavior is constant and that allowing the dynamic structure to change affects the results. We also find that the results are sensitive to the prior specification.
A GOODNESS‐OF‐FIT TEST FOR AUTOREGRESSIVE MOVING‐AVERAGE MODELS BASED ON THE STANDARDIZED SAMPLE SPECTRAL DISTRIBUTION OF THE RESIDUALS
Authors: Velilla Santiago
Published: May 2008

Abstract. A stochastic process derived from the standardized sample spectral density of the residuals of a causal and invertible ARMA(p, q) model is introduced to construct a goodness‐of‐fit procedure. The test statistics considered have a proper limiting distribution which is free of unknown parameters and which, unlike some well‐known goodness‐of‐fit statistics based on the residuals, does not depend on the sample size.
LARGE SAMPLE ANALYSIS OF AUTOREGRESSIVE MOVING‐AVERAGE MODELS WITH ERRORS IN VARIABLES
Authors: Chanda Kamal C.
Published: May 2008

Abstract. We consider estimation of parameters of an unobservable ARMA(p, q) process {Ut; t= 1,2,…} based on a set of n observables, X1, …, Xn, where Xt=Ut, +εt, 1 ≤t≤n, it being assumed that {εt} is independent of {Ut}. We examine the asymptotic properties of these ARMA estimators under a set of weak regularity conditions on {εt}.
BIAS‐CORRECTED NONPARAMETRIC SPECTRAL ESTIMATION
Authors: Politis Dimitris N. , Romano Joseph P.
Published: May 2008

Abstract.The theory of nonparametric spectral density estimation based on an observed stretchX1,…,XNfrom a stationary time series has been studied extensively in recent years. However, the most popular spectral estimators, such as the ones proposed by Bartlett, Daniell, Parzen, Priestley and Tukey, are plagued by the problem of bias, which effectively prohibits ✓N‐convergence of the estimator. This is trueevenin the case where the data are known to bem‐dependent, in which case ✓N‐consistent estimation is possible by a simple plug‐in method.

In this report, an intuitive method for the reduction in the bias of a nonparametric spectral estimator is presented. In fact, applying the proposed methodology to Bartlett's estimator results in bias‐corrected estimators that are related to kernel estimators with lag‐windows of trapezoidal shape. The asymptotic performance (bias, variance, rate of convergence) of the proposed estimators is investigated; in particular, it is found that the trapezoidal lag‐window spectral estimator is ✓N‐consistent in the case of moving‐average processes, and ✓(N/log/N)‐consistent in the case of autoregressive moving‐average processes. The finite‐sample performance of the trapezoidal lag‐window estimator is also assessed by means of a numerical simulation.
ON THE SELECTION OF RANDOM SAMPLING SCHEMES FOR THE SPECTRAL ESTIMATION OF CONTINUOUS TIME PROCESSES
Authors: Lii Keh‐Shin , Masry Elias
Published: May 2008

Abstract. Let X={X(t), ‐∝<t<∝} be a continuous time stationary process with spectral density φx(Λ) and {φk} be a stationary point process independent of X. The problem of selecting the sampling point process {τk} for the estimation of φx(Λ) based on the discrete time observations {X(τk), τk} is considered. Sufficient conditions are established for the admittability of a broad class of delayed renewal point processes. Examples are given for delayed renewal point processes {τk} which have a mixture of Gamma densities for their inter‐arrival times. Guidelines are given for the selection of specific point processes in the estimation of broadband and narrowband spectral density functions.
LONG‐RANGE DEPENDENCE AND MIXING FOR DISCRETE TIME FRACTIONAL PROCESSES
Authors: Viano M. C. , Deniau Cl. , Oppenheim G.
Published: May 2008

Abstract. A large class of discrete time stationary processes, an extension of the well‐known fractionally integrated autoregressive moving‐average models, is investigated. For a suitable choice of parameters, these processes are long‐range dependent. After a detailed study of the asymptotic behaviour of their correlations, we investigate their mixing properties and then give some simulated examples.
LOGSPLINE ESTIMATION OF A POSSIBLY MIXED SPECTRAL DISTRIBUTION
Authors: Kooperberg Charles , Stone Charles J. , Truong Young K.
Published: May 2008

Abstract.Cubic splines and indicator functions are used to estimate the spectral density function and line spectrum, respectively, for a stationary time series. A fully automatic procedure involving maximum likelihood, stepwise addition and deletion of basis functions, and the Bayes information criterion (BIC) is used to select the final model.
A NOTE ON THE EMBEDDING OF DISCRETE‐TIME ARMA PROCESSES
Authors: Brockwell Peter J.
Published: May 2008

Abstract. Let {Xn, n= 0, 1, 2,…} be a discrete‐time ARMA(p, q) process with q < p whose autoregressive polynomial has r (not necessarily distinct) negative real roots. According to a recent result of He and Wang (On embedding a discrete‐parameter ARMA model in a continuous‐parameter ARMA model. J. Time Ser. Anal. 10 (1989), 315–23) there exists a continuous‐time ARMA (p', q') process {Y(t), t≥0} with q' < p'=p+r such that {Y(n), n= 0, 1, 2,…} has the same autocorrelation function as {Xn}. In this paper we show that this result is false by considering the case when {Xn} is a discrete‐time AR(2) process whose autoregressive polynomial has distinct complex conjugate roots. We identify the proper subset of such processes which are embeddable in a continuous‐time ARMA(2, 1) process. We show that every discrete‐time AR(2) process with distinct complex conjugate roots can be embedded in either a continuous‐tie ARMA(2, 1) process or a continuous‐time ARMA(4, 2) process, or in some cases both. We derive an expression for the spectral density of the process obtained by sampling a general continuous‐time ARMA(p, q) process (with distinct autoregressive roots) at arbitrary equally spaced time points. The expression clearly shows that the sampled process is a discrete‐time ARMA (p', q') process with q' < p.