Showing papers on "Moving-average model published in 2000"

Reply to "Comments on 'Theory and Application of Covariance Matrix Tapers for Robust Adaptive Beamforming'"

Abstract: We consider the autoregressive estimation for periodically correlated processes, using the parameterization given by the partial autocorrelation function. We propose an estimation of these parameters by extending the sample partial autocorrelation method to this situation. The comparison with other methods is made. Relationships with the stationary multivariate case are discussed.

A Course in Time Series Analysis

Abstract: Introduction (D. Pe?a & G. Tiao). BASIC CONCEPTS IN UNIVARIATE TIME SERIES. Univariate Time Series: Autocorrelation, Linear Prediction, Spectrum, State Space Model (G. Wilson). Univariate Autoregressive Moving Average Models (G. Tiao). Model Fitting and Checking, and the Kalman Filter (G. Wilson). Prediction and Model Selection (D. Pe?a). Outliers, Influential Observations and Missing Data (D. Pe?a). Automatic Modeling Methods for Univariate Series (V. Gomez & A. Maravall). Seasonal Adjustment and Signal Extraction in Economic Time Series (V. Gomez & A. Maravall). ADVANCED TOPICS IN UNIVARIATE TIME SERIES. Heteroscedatic Models (R. Tsay). Nonlinear Time Series Models (R. Tsay). Bayesian Time Series Analysis (R. Tsay). Nonparametric Time Series Analysis: Nonparametric Regression, Locally Weighted Regression, Autoregression and Quantile Regression (S. Heiler). Neural Networks (K. Hornik & F. Leisch). MULTIVARIATE TIME SERIES. Vector ARMA Models (G. Tiao). Cointegration in the VAR Model (S. Johansen). Multivariate Linear Systems (M. Deistler). References. Index.

The sample autocorrelation function of non-linear time series

Abstract: When studying a real-life time series, it is frequently reasonable to assume, possibly after a suitable transformation, that the data come from a stationary time series (Xt). This means that the finite-dimensional distributions of this sequence are invariant under shifts of time. Various stationary time series models have been studied in detail in the literature. A standard assumption is that the time series is Gaussian or, more generally, that it has a probability distribution with light tails, in the sense that P(lXtl > x) decays to zero at least exponentially. Zie: Summary

Asymptotics for the partial autocorrelation function of a stationary process

Abstract: The purpose of this paper is to study the long-time behaviour of the partial autocorrelation function of a stationary process. Let {Xn} = {Xn : n ∈ Z} be a real, zero-mean, weakly stationary process, defined on a probability space (Ω,F , P ), which we shall simply call a stationary process . Throughout this paper, we assume that {Xn} is purely nondeterministic (see §2). The autocovariance function γ(·) of {Xn} is defined by

System, device and method for time-domain equalizer training using an auto-regressive moving average model

Abstract: A system, device, and method for time-domain equalizer (TEQ) training determines the TEQ order and TEQ coefficients by applying the multichannel Levinson algorithm for auto-regressive moving average (ARMA) modeling of the channel impulse response. Specifically, the TEQ is trained based upon a received training signal. The received training signal and knowledge of the transmitted training signal are used to derive an autocorrelation matrix that is used in formulating the multichannel ARMA model. The parameters of the multichannel ARMA model are estimated via a recursive procedure using the multichannel Levinson algorithm. Starting from a sufficiently high-order model with a fixed pole-zero difference, the TEQ coefficients corresponding to a low-order model are derived from those of a high-order model.

Moments and the Autocorrelation Structure of the Exponential GARCH(p,q) Process

Abstract: In this paper the autocorrelation structure of the Exponential GARCH(p,q) process of Nelson (1991) is considered. Conditions for the existence of any arbitrary unconditional moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of squared observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard GARCH(p,q) process. In particular, it is seen that, the EGARCH(p,q) model has a richer autocorrelation structure than the standard GARCH(p,q) one. The statistical theory is further illustrated by a few special cases such as the symmetric and the asymmetric EGARCH(2,2) models under the assumption of normal errors or non-normal errors. The autocorrelations computed from an estimated EGARCH(2,1) model of Nelson (1991) are highlighted.

On periodic autoregressive processes estimation

Abstract: We consider the autoregressive estimation for periodically correlated processes, using the parametrization given by the partial autocorrelation function. We propose an estimation of these parameters by extending the sample partial autocorrelation method to this situation. A comparison with other methods is made. Relationships with the stationary multivariate case are discussed.

Prediction Intervals Based on Autoregression Forecasts

Abstract: The variability of parameter estimates is commonly neglected when constructing prediction intervals based on a parametric model for a time series. This practice is due to the complexity of conditioning the inference on information such as observed values of the underlying stochastic process. In this paper, conditional prediction intervals when using autoregression forecasts are proposed whose simple implementation will hopefully enable wide use. A simulation study illustrates the improvement over classical intervals in terms of empirical coverage.

Threshold Autoregressive Model for a Time Series Data

Abstract: In this paper we try to fit a threshold autoregressive (TAR) model to time series data of monthly coconut oil prices at Cochin market. The procedure proposed by Tsay [7] for fitting the TAR model is briefly presented. The fitted model is compared with a simple autoregressive (AR) model. The results are in favour of TAR process. Thus the monthly coconut oil prices exhibit a type of non-linearity which can be accounted for by a threshold model.

Parametric modeling of blurred images for image restoration

Abstract: Almost all of parameter estimation schemes for image restoration to date, attempt to model the true image as a autoregressive model and the point spread function as a moving average model and assume the symmetry of the point spread function in order to reduce the computational complexity The autoregressive process builds the true image bypassing a Gaussian white noise process through a filter and may result in unstable systems and optimization of parameters could be trapped in local minima In this article a different approach is presented with simulation results where initial white Gaussian process is replaced by scaled degraded image avoiding optimization problems

Spectral analysis of segmented data

Abstract: Time series analysis is reformulated to allow processing of segmented data. This involves the reformulation of parameter estimation and order selection. Parameter estimation for autoregressive (AR) models is done by fitting a single model to all segments simultaneously. Parameter estimation for moving average (MA) and the combined ARMA models can be derived entirely from long autoregressive models. The finite sample theory required for order selection of AR models has been generalized to segments of data. The resulting algorithm can also deal effectively with segments of unequal length.

Graphical and phase space models for univariate time series

Abstract: There are various approaches to model time series data. In the time domain ARMA-models and state space models are frequently used, while phase space models have been applied recently, too. Each approach has got its own strengths and weaknesses w.r.t. parameter estimation, prediction and coping with missing data. We use graphical models to explore and compare the structure of time series models, and focus on interpolation in e.g. seasonal models.