Showing papers on "STAR model published in 1986"

Generalized autoregressive conditional heteroscedasticity

Abstract: A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.

On estimating thresholds in autoregressive models

Abstract: The problem of estimating the threshold parameter, ie, the change point, of a threshold autoregressive model is studied By introducing smoothness into the model, sampling properties of the conditional least-squares estimate may be obtained Artificial and real data are used for illustrations

A portmanteau test for self-exciting threshold autoregressive-type nonlinearity in time series

Abstract: SUMMARY A portmanteau test to detect self-exciting threshold autoregressive-type nonlinearity in time series data is proposed. The test is based on cumulative sums of standardized residuals from autoregressive fits to the data. Significance levels for the test under the hypothesis of linearity are obtain from the asymptotic distribution of the cumulative sums as Brownian motion. The performance of the test is evaluated for simulated data from linear, bilinear and self-exciting threshold autoregressive models. It is also compared with another test which has been suggested for detecting general nonlinearity. Features of the proposed test, which make it useful in identifying the autoregressive order and the lag in threshold models, are discussed.

Infrence for non-negative autoregressive schemes

Abstract: The object of this paper is the statistical analysis of Several Closely related models arising in water quality analysis. In particular, concern is with the autoregressive scheme Xr = ρXr−1 + Yr where 0 < ρ < 1 and Y's are i.i.d, and non-negative. The estimation and testing problem is considered for three parametric models - Gaussian, uniform and exponential - as well as for the nonparametric case where it is assumed that the Y's have a positive continuous distribution.

Periodic Gamma Autoregressive Processes for Operational Hydrology

Abstract: A number of models have been suggested for hydrologic time series in general and streamflow series in particular. Most of them are normal autoregressive (AR) of order 1 with either constant or periodic parameters. Since generally hydrologic time series are nonnormal (skewed), transformations have been suggested to make the series approximately normal. A new class of univariate models is proposed herein which incorporates skewed and correlation properties within the model structure without the necessity of transformations. Such models assume a gamma marginal distribution and a constant or periodic autoregressive structure. The models may be additive gamma, multiplicative gamma, or a mixed model which incorporates properties of both additive and multiplicative models. The gamma models were tested and compared in relation to (transformed) normal AR models by computer simulation studies based on five weekly streamflow series with samples varying from 35 to 40 years of record. The results show that the new class of gamma models compares favorably with respect to the normal models in reproducing the basic statistics usually analyzed for streamflow simulation. It is expected that the proposed gamma models will be of interest to other researchers for further developments and applications to hydrologic and geophysical time series.

Asymptotic properties of some preliminary estimators for autoregressive moving average time series models

Abstract: . Some simple preliminary estimators for the coefficients of mixed autoregressive moving average time series models are considered. As the first step the estimators require the fitting of a long autoregression to the data. The first two methods of the paper are non-iterative and generally inefficient. The estimators are Yule-Walker type modifications of the least squares estimators of the coefficients in auxiliary linear regression models derived, respectively, for the coefficients of the long autoregression and for the coefficients of the corresponding long moving average approximation of the model. Both of these estimators are shown to be strongly consistent and their asymptotic distributions are derived. The asymptotic distributions are used in studying the loss in efficiency and in constructing the third estimator of the paper which is an asymptotically efficient two-step estimator. A numerical illustration of the third estimator with real data is given.

The criterion autoregressive transfer function of parzen

Abstract: . A mathematical derivation of the Criterion Autoregressive Transfer Function (CAT) of Parzen (1974) is given and a generalization of this criterion is introduced. The asymptotic distribution of the orders selected by CAT, this generalized criterion, and a new version of CAT introduced by Parzen (1977a) are derived. The joint finite sample behaviour of these three criteria and of the FPEα,-criterion of Bhansali and Downham (1977) is examined by means of a simulation study.

On an Autoregressive Model with Time Dependent coefficients

Abstract: As one of the non-stationary time series model, we consider a firstorder autoregressive model in which the autoregressive coefficient is assumed to be a function,f t (θ), of timet. We establish several assumptions onf t (θ), not on the terms in the Taylor expansion of log-likelihood function, and show that the estimators of unknown parameters involved inf t (θ) have strong consistency and asymptotic normality under these assumptions when sample size tends to infinity.

Mixture autoregressive hidden Markov models for speaker independent isolated word recognition

Abstract: In this paper a signal modeling technique based upon finite mixture autoregressive probabilistic functions of Markov chains is developed and applied to the problem of speech recognition, particularly speaker-independent recognition of isolated digits. Two types of mixture probability densities are investigated: finite mixtures of Gaussian autoregressive densities (GAM) and nearest-neighbor partitioned finite mixtures of Gaussian autoregressive densities (PGAM). In the former (GAM), the observation density in each Markov state is simply a (stochastically constrained) weighted sum of Gaussian autoregressive densities, while in the latter (PGAM) it involves nearest-neighbor decoding which, in effect, defines a set of partitions on the observation space. In this paper we discuss the signal modeling methodology and give experimental results on speaker independent recognition of isolated digits.

The Multiple Outlier Problem in Time Series Analysis

Abstract: Summary In this paper we consider the multiple outlier problem in time series analysis. The underlying undisturbed time series is assumed to be an autoregressive process. The location of the suspicious values is supposed to be known. We introduce conditional least squares estimators for the parameters. The estimates are shown to be strongly consistent. Using similar arguments as in the theory of linear models, we get a test statistic for the general linear hypothesis. Its asymptotic distribution is derived.

Performance of multichannel autoregressive spectral estimators

Abstract: This paper compares and contrasts the performance of multichannel periodogram and autoregressive spectrum analysis techniques periodogram when processing sunspot and world air temperature data, a first order autoregressive process, and an artificial data set of sinusoids in colored noise. It is shown that the high resolution benefit of autoregressive analysis must be tempered by an awareness of a severe feed across effect among the autospectral autoregressive estimates that may prevent multichannel autoregressive spectral estimation from being a viable spectral estimation approach. The feed across effect manifests itself as very sharp spikes in the autospectrum where there should be no spectral energy. The cause is known to be inexact pole-zero cancellation in the autoregressive coeffieient matrix estimates. Performing single channel autoregressive spectral estimates will provide indications of where the feed across effect is occurring. The astronomical literature has applied these multichannel autoregressive techniques to correlate sunspot activity with terrestrial activity such as tides, earth rotation variations, air temperature variations, and drought cycles. High correlation has alledgedly been found. However, the findings of the literature is now in doubt because this author believes that the astrophysical researchers were misled by the feed across anomaly. This paper also serves to correct some errors reported on examples in reference [3].

On Some Asymptotic Results for Multivariate Autoregressive Models with Estimated Parameters

Abstract: In this paper the asymptotic equivalence of the estimated predictor and the optimal predictor of k-dimensional pth order autoregressive process in the stable case with dependent error variables bas been shown. An expression for the mean square error of the estimated predictor has also been derived.

On the identification of systems from data measurements using ARMA lattice models

Abstract: Methods for the autoregressive moving average (ARMA) modeling of digital systems using a two-channel autoregressive (AR) lattice are presented. One method has the advantage that one-half of the lattice parameters are zero when the system's excitation signal is white noise.

An algorithm for solving the extended Yule- Walker equations of an autoregressive moving-average time series (Corresp.)

Abstract: A new form of the extended Yule-Walker equations of a stationary autoregressive moving-average (ARMA) scheme is proposed. An algorithm using the new form is also given for calculating the parameters of the ARMA process from its autocovariance function without a proof of its convergence.

A stochastic process that is autoregressive in two directions of time.

Abstract: A continuous time stationary process is discussed that is maxautoregressive in one direction of time and sum–autoregressive in the other direction. A discrete time version of the process was discussed in Chemick (1981). A related continuous time process is discussed in Weiss (1980).

The Box-Jenkins approach to random coefficient autoregressive modelling

Abstract: Recent time series research has been directed towards the relaxation of the assumption that time series models have constant coefficients. One class of models to emerge as a result of this has been that of random coefficient autoregressive models. This paper demonstrates how the Box-Jenkins three-step approach of model specification, estimation and diagnostic checking may be applied to this class of models.

Efficiencies of weighted averages in stationary autoregressive processes

Abstract: The criterion of second-order efficiency is used to distinguish among estimators, which have the same asymptotic variance, of the mean of a stationary autoregressive process. The best linear unbiased estimator is typically unknown, since it depends on the parameters of the process. It is demonstrated by second-order efficiency that the sample mean performs poorly under certain conditions, whereas some weighted averages maintain a more consistent performance as the parameters of the underlying process are allowed to vary. Numerical examples are shown for second-and third-order autoregressive processes.

ARMA Spectral Estimation via Model Reduction

Abstract: In this paper we study how to estimate autoregressive moving average (ARMA) processes via a high order autoregressive (AR) estimate and model reduction. The model reduction techniques considered are based on the L2-norm. internally balanced realizations, or the Hankelnorm. We apply this estimation technique to the problem of finding narrow-band signals in white noise.

Autoregressive model identification for multivariate time series

Abstract: A procedure is developed for the identification of autoregressive models for stationary invertible multivariate Gaussian time series. Model selection is based on either the AIC information criterion or on a statistic called CVR, cross-validatory residual sum of squares. An example is given to show that the forecasts generated by these models compare favorably with those generated by other common time series modeling techniques.

Detection of unknown-frequency sinusoids in noise via autoregressive modeling

Abstract: A family of autoregressive (AR) detection statistics is introduced and their potential for enhanced detection of unknown-frequency sinusoids in noise is illustrated AR models applied to both the time data and the correlation data are addressed and compared The computational complexity of the resulting decision rules is also incorporated in the analysis

Comments, with reply, on "ARMA spectral estimation of time series with missing observations" by B. Porat and B. Friedlander

Abstract: A variant to a recently proposed autoregressive moving average (ARMA) spectrum estimation technique for time series with gapped data is suggested. It is based on the partial fraction expansion of the power spectrum and exhibits some computational and operational advantages.

A frequency domain approach to lagrange multiplier test for autoregressive moving average models

Abstract: . The paper derives a goodness of fit test for autoregressive moving average models using the frequency domain approximation to the log likelihood and the Lagrange multiplier approach. The test statistic is based on the sample autocovariances and can be quickly computed through a recursive procedure.

Bayesian Analyses of Nonhomogeneous Autoregressive Processes

Abstract: : This paper considers nonhomogeneous autoregressive processes which are special cases of the vector-valued autoregressive processes considered by Anderson (1978) for the analysis of panel survey data. The authors point out that, for a nonhomogeneous autoregressive process of order higher than one, the least-squares estimates cannot be obtained unless repeated measurements are made on the time series. Presented are two Bayesian approaches based on Kalman filter models which alleviate the above difficulty and result in an alternative strategy for the analyses of nonhomogeneous autoregressive processes. In the first approach the notion of exchangeability plays a key role, whereas for the second approach, which results in an adaptive Kalman filter model, an approximation due to Lindley facilitates the necessary computations for inference.

Non-stationary 2D estimation: An application to turbulence field analysis

Abstract: A two-dimensional (2D) nonstationary (NS) autoregressive (AR) model is proposed for the characterization of non-homogeneous textural patterns in images. The approach taken in this paper leads to the extension of a fast estimation technique to the 2D nonstationary case. The procedure which is used for estimating the parameters of the space-varying model is described in detail. This procedure is based on a relation between several 2D autoregressive models and on AR vector model. Next we give some preliminary experimental results and we discuss the applicability of this approach to modelling the vorticity field of a turbulent flow.

AUTOREGRESSIVE MODEL FOR 1/f NOISE

Abstract: We use a Monte Carlo simulation to generate noise that approaches 1/f over a certain frequency range. A superposition of a small number of noise terms with Lorentzian spectra, for the cases of one rate and two rate kinetics is considered. An autoregressive model is used to calculate the characteristic times. The advantages of this time domain analysis are discussed.