Home About us Contact
|
Home About us Contact | ||
|
|
||
Stationary Time Series (stationary + time_series)
Selected AbstractsInfluence of Missing Values on the Prediction of a Stationary Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2005Pascal Bondon Primary 62M10; secondary 60G25 Abstract., The influence of missing observations on the linear prediction of a stationary time series is investigated. Simple bounds for the prediction error variance and asymptotic behaviours for short and long-memory processes respectively are presented. [source] Recursive Relations for Multistep Prediction of a Stationary Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2001Pascal Bondon Recursive relations are established between the coefficients of the finite past multistep linear predictors of a stationary time series. These relations generalize known results when the prediction is based on infinite past and permit simplification of the numerical calculation of the finite past predictors. [source] A missing values imputation method for time series data: an efficient method to investigate the health effects of sulphur dioxide levelsENVIRONMETRICS, Issue 2 2010Swarna Weerasinghe Abstract Environmental data contains lengthy records of sequential missing values. Practical problem arose in the analysis of adverse health effects of sulphur dioxide (SO2) levels and asthma hospital admissions for Sydney, Nova Scotia, Canada. Reliable missing values imputation techniques are required to obtain valid estimates of the associations with sparse health outcomes such as asthma hospital admissions. In this paper, a new method that incorporates prediction errors to impute missing values is described using mean daily average sulphur dioxide levels following a stationary time series with a random error. Existing imputation methods failed to incorporate the prediction errors. An optimal method is developed by extending a between forecast method to include prediction errors. Validity and efficacy are demonstrated comparing the performances with the values that do not include prediction errors. The performances of the optimal method are demonstrated by increased validity and accuracy of the , coefficient of the Poisson regression model for the association with asthma hospital admissions. Visual inspection of the imputed values of sulphur dioxide levels with prediction errors demonstrated that the variation is better captured. The method is computationally simple and can be incorporated into the existing statistical software. Copyright © 2009 John Wiley & Sons, Ltd. [source] The variance ratio and trend stationary model as extensions of a constrained autoregressive modelJOURNAL OF FORECASTING, Issue 5 2010Shlomo Zilca Abstract This paper shows that a constrained autoregressive model that assigns linearly decreasing weights to past observations of a stationary time series has important links to the variance ratio methodology and trend stationary model. It is demonstrated that the proposed autoregressive model is asymptotically related to the variance ratio through the weighting schedules that these two tools use. It is also demonstrated that under a trend stationary time series process the proposed autoregressive model approaches a trend stationary model when the memory of the autoregressive model is increased. These links create a theoretical foundation for tests that confront the random walk model simultaneously against a trend stationary and a variety of short- and long-memory autoregressive alternatives. Copyright © 2009 John Wiley & Sons, Ltd. [source] A hybrid forecasting approach for piece-wise stationary time seriesJOURNAL OF FORECASTING, Issue 7 2006Minxian Yang Abstract We consider the problem of forecasting a stationary time series when there is an unknown mean break close to the forecast origin. Based on the intercept-correction methods suggested by Clements and Hendry (1998) and Bewley (2003), a hybrid approach is introduced, where the break and break point are treated in a Bayesian fashion. The hyperparameters of the priors are determined by maximizing the marginal density of the data. The distributions of the proposed forecasts are derived. Different intercept-correction methods are compared using simulation experiments. Our hybrid approach compares favorably with both the uncorrected and the intercept-corrected forecasts.,,Copyright © 2006 John Wiley & Sons, Ltd. [source] A self-normalized approach to confidence interval construction in time seriesJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2010Xiaofeng Shao Summary., We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning-parameter-dependent approaches, our method has the attractive convenience of being free of any user-chosen number or smoothing parameter. The interval is constructed on the basis of an asymptotically distribution-free self-normalized statistic, in which the normalizing matrix is computed by using recursive estimates. Under mild conditions, we establish the theoretical validity of our method for a broad class of statistics that are functionals of the empirical distribution of fixed or growing dimension. From a practical point of view, our method is conceptually simple, easy to implement and can be readily used by the practitioner. Monte Carlo simulations are conducted to compare the finite sample performance of the new method with those delivered by the normal approximation and the block bootstrap approach. [source] Wavelet processes and adaptive estimation of the evolutionary wavelet spectrumJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2000G. P. Nason This paper defines and studies a new class of non-stationary random processes constructed from discrete non-decimated wavelets which generalizes the Cramér (Fourier) representation of stationary time series. We define an evolutionary wavelet spectrum (EWS) which quantifies how process power varies locally over time and scale. We show how the EWS may be rigorously estimated by a smoothed wavelet periodogram and how both these quantities may be inverted to provide an estimable time-localized autocovariance. We illustrate our theory with a pedagogical example based on discrete non-decimated Haar wavelets and also a real medical time series example. [source] Range Unit-Root (RUR) Tests: Robust against Nonlinearities, Error Distributions, Structural Breaks and OutliersJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2006Felipe Aparicio Abstract., Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series. In this paper, we propose a completely different method to test for the type of long-wave patterns observed not only in unit-root time series but also in series following more complex data-generating mechanisms. To this end, our testing device analyses the unit-root persistence exhibited by the data while imposing very few constraints on the generating mechanism. We call our device the range unit-root (RUR) test since it is constructed from the running ranges of the series from which we derive its limit distribution. These nonparametric statistics endow the test with a number of desirable properties, the invariance to monotonic transformations of the series and the robustness to the presence of important parameter shifts. Moreover, the RUR test outperforms the power of standard unit-root tests on near-unit-root stationary time series; it is invariant with respect to the innovations distribution and asymptotically immune to noise. An extension of the RUR test, called the forward,backward range unit-root (FB-RUR) improves the check in the presence of additive outliers. Finally, we illustrate the performances of both range tests and their discrepancies with the Dickey,Fuller unit-root test on exchange rate series. [source] Computer Algebra Derivation of the Bias of Linear Estimators of Autoregressive ModelsJOURNAL OF TIME SERIES ANALYSIS, Issue 2 2006Y. Zhang Abstract., A symbolic method which can be used to obtain the asymptotic bias and variance coefficients to order O(1/n) for estimators in stationary time series is discussed. Using this method, the large-sample bias of the Burg estimator in the AR(p) for p = 1, 2, 3 is shown to be equal to that of the least squares estimators in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for the Burg estimator's bias because this problem is too intractable without using computer algebra. The asymptotic bias coefficient to O(1/n) of Yule,Walker as well as least squares estimates is also derived in AR(3) models. Our asymptotic results show that for the AR(3), just as in the AR(2), the Yule,Walker estimates have a large bias when the parameters are near the nonstationary boundary. The least squares and Burg estimates are much better in this situation. Simulation results confirm our findings. [source] Influence of Missing Values on the Prediction of a Stationary Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2005Pascal Bondon Primary 62M10; secondary 60G25 Abstract., The influence of missing observations on the linear prediction of a stationary time series is investigated. Simple bounds for the prediction error variance and asymptotic behaviours for short and long-memory processes respectively are presented. [source] Recursive Relations for Multistep Prediction of a Stationary Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2001Pascal Bondon Recursive relations are established between the coefficients of the finite past multistep linear predictors of a stationary time series. These relations generalize known results when the prediction is based on infinite past and permit simplification of the numerical calculation of the finite past predictors. [source] Robust Automatic Bandwidth for Long MemoryJOURNAL OF TIME SERIES ANALYSIS, Issue 3 2001Marc Henry The choice of bandwidth, or number of harmonic frequencies, is crucial to semiparametric estimation of long memory in a covariance stationary time series as it determines the rate of convergence of the estimate, and a suitable choice can insure robustness to some non-standard error specifications, such as (possibly long-memory) conditional heteroscedasticity. This paper considers mean squared error minimizing bandwidths proposed in the literature for the local Whittle, the averaged periodogram and the log periodogram estimates of long memory. Robustness of these optimal bandwidth formulae to conditional heteroscedasticity of general form in the errors is considered. Feasible approximations to the optimal bandwidths are assessed in an extensive Monte Carlo study that provides a good basis for comparison of the above-mentioned estimates with automatic bandwidth selection. [source] Prediction Variance and Information Worth of Observations in Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2000Mohsen Pourahmadi The problem of developing measures of worth of observations in time series has not received much attention in the literature. Any meaningful measure of worth should naturally depend on the position of the observation as well as the objectives of the analysis, namely parameter estimation or prediction of future values. We introduce a measure that quantifies worth of a set of observations for the purpose of prediction of outcomes of stationary processes. The worth is measured as the change in the information content of the entire past due to exclusion or inclusion of a set of observations. The information content is quantified by the mutual information, which is the information theoretic measure of dependency. For Gaussian processes, the measure of worth turns out to be the relative change in the prediction error variance due to exclusion or inclusion of a set of observations. We provide formulae for computing predictive worth of a set of observations for Gaussian autoregressive moving-average processs. For non-Gaussian processes, however, a simple function of its entropy provides a lower bound for the variance of prediction error in the same manner that Fisher information provides a lower bound for the variance of an unbiased estimator via the Cramer-Rao inequality. Statistical estimation of this lower bound requires estimation of the entropy of a stationary time series. [source] | ||||||||||