Finite-Sample Bias Propagation in Autoregressive Estimation With the Yule–Walker Method

The 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...

Five Separate Bias Contributions in Time Series Models for Equidistantly Resampled Irregular Data

The use of time series models for irregular data requires resampling of the data on an equidistant grid. Slotted resampling transforms an irregular randomly sampled process into an equidistant signal where data are missing. An approximate maximum-likelihood time series estimator has been developed to estimate the power spectral density and the...

Modified Durbin Method for Accurate Estimation of Moving-Average Models

Spectra 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...

Likelihood-Based Hypothesis Tests for Brain Activation Detection From MRI Data Disturbed by Colored Noise: A Simulation Study

Functional magnetic resonance imaging (fMRI) data that are corrupted by temporally colored noise are generally preprocessed (i.e., prewhitened or precolored) prior to functional activation detection. In this paper, we propose likelihood-based hypothesis tests that account for colored noise directly within the framework of functional activation...

Noise in multivariate GPS position time-series

A methodology is developed to analyze a multivariate linear model, which occurs in many geodetic and geophysical applications. Proper analysis of multivariate GPS coordinate time-series is considered to be an application. General, special, and more practical stochastic models are adopted to assess the noise characteristics of multivariate time...

Sign Language Recognition by Combining Statistical DTW and Independent Classification

To recognize speech, handwriting, or sign language, many hybrid approaches have been proposed that combine Dynamic Time Warping (DTW) or Hidden Markov Models (HMMs) with discriminative classifiers. However, all methods rely directly on the likelihood models of DTW/HMM. We hypothesize that time warping and classification should be separated...

Calibration of transient groundwater models using time series analysis and moment matching

A comprehensive and efficient approach is presented for the calibration of transient groundwater models. The approach starts with the time series analysis of the measured heads in observation wells using all active stresses as input series, which may include rainfall, evaporation, surface water levels, and pumping. The time series analysis...

Assessment of noise in GPS coordinate time series: Methodology and results

We propose a methodology to assess the noise characteristics in time series of position estimates for permanent Global Positioning System (GPS) stations. Least squares variance component estimation (LS?VCE) is adopted to cope with any type of noise in the data. LS?VCE inherently provides the precision of (co)variance estimators. One can also...

Fast error analysis of continuous GPS observations

It has been generally accepted that the noise in continuous GPS observations can be well described by a power-law plus white noise model. Using maximum likelihood estimation (MLE) the numerical values of the noise model can be estimated. Current methods require calculating the data covariance matrix and inverting it, which is a significant...

Constrained stochastic simulation: Generation of time series around some specific event in a normal process

The method of so-called constrained stochastic simulation is introduced. This method specifies how to efficiently generate time series around some specific event in a normal process. All events which can be expressed by means of a linear condition (constraint) can be dealt with. Two examples are given in the paper: the generation of stochastic...