1,720,954 research outputs found
Modified Durbin Method for Accurate Estimation of Moving-Average Models
Full text linkSpectra with narrow valleys can accurately be described with moving-average (MA) models by using only a small number of parameters. Durbin's MA method uses the estimated parameters of a long autoregressive (AR) model to calculate the MA parameters. Probably all the pejorative remarks on the quality of Durbin's method in the literature are based on suboptimal or wrong choices for the method of AR estimation or for the order of the intermediate AR model. Generally, the AR order should considerably be higher than the order of the best predicting AR model, and it should grow with the sample size. Furthermore, the Burg estimates for the AR parameters give the best results because they have the smallest variance of all the AR methods with a small bias. A modified Durbin MA method uses a properly defined number of AR parameters, which was estimated with Burg's method, and outperforms all the other known MA estimation methods, asymptotically as well as in finite samples. The accuracy is generally close to the Cramer-Rao bound.Multi-Scale PhysicsApplied Science
Finite-Sample Bias Propagation in Autoregressive Estimation With the Yule–Walker Method
No full textThe Yule-Walker (YW) method for autoregressive (AR) estimation uses lagged-product (LP) autocorrelation estimates to compute an AR parametric spectral model. The LP estimates only have a small triangular bias in the estimated autocorrelation function and are asymptotically unbiased. However, using them in finite samples with the YW method for AR estimation can give a strong distortion in the weak parts of the power spectral density. The distortion is shown to be influential in an example without strong spectral peaks. The true biased AR model, which is computed by applying the triangular bias to the true autocorrelation function, has an infinite order. A new objective measure is introduced to determine the smallest sample size for which the unbiased asymptotic theory can be considered as a fair approximation.Multi-Scale PhysicsApplied Science
Spectral Analysis of Irregularly Sampled Data with Time Series Models
No full textSlotted resampling transforms an irregularly sampled process into an equidistant missing-data problem. Equidistant resampling inevitably causes bias, due to aliasing and the shift of the irregular observation times to an equidistant grid. Taking a slot width smaller than the resampling time can diminish the shift bias. A dedicated estimator for time series models of multiple slotted data sets with missing observations has been developed for the estimation of the power spectral density and of the autocorrelation function. The algorithm estimates time series models and selects the order and type from a number of candidates. It is tested with benchmark data. Spectra can be estimated until frequencies higher than 100 times the mean data rate.Applied Science
Evaluation of railway systems dynamics by model adjustment
No full textMechanical, Maritime and Materials Engineerin
- …
