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The Quality of Lagged Products and Autoregressive Yule–Walker Models as Autocorrelation Estimates

Broersen, P.M.T. (author)

The sample autocorrelation function is defined by the mean lagged products (LPs) of random observations. It is the inverse Fourier transform of the raw periodogram. Both contain the same information, and the quality of the full-length sample autocorrelation to represent random data is as poor as that of a raw periodogram. The autoregressive (AR)...

journal article 2009

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Vector Autoregressive Order Selection in Practice

Broersen, P.M.T. (author)

Vector time series analysis takes the same model order and model type for the different signals involved. Selection criteria have been developed to select the best order to simultaneously predict the different components of the vector. The prediction of single channels might require a different order or type for the best accuracy of each...

journal article 2009

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

Broersen, P.M.T. (author)

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...

journal article 2009

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

Broersen, P.M.T. (author)

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...

journal article 2009

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Modified Durbin Method for Accurate Estimation of Moving-Average Models

Broersen, P.M.T. (author)

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...

journal article 2009

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Practical Aspects of the Spectral Analysis of Irregularly Sampled Data With Time-Series Models

Broersen, P.M.T. (author)

Several algorithms for the spectral analysis of irregularly sampled random processes can estimate the spectral density for a low frequency range. A new time-series method extended that frequency range with a factor of thousand or more. The new algorithm has two requirements to give useful results. First, at least ten closest pairs of neighboring...

journal article 2009

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Spectral Analysis of Irregularly Sampled Data with Time Series Models

Broersen, P.M.T. (author)

Slotted 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...

journal article 2008

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ARMAsel for Detection and Correction of Outliers in Univariate Stochastic Data

Broersen, P.M.T. (author)

For stationary random data, an automatic estimation algorithm can now select a time series model with a spectral accuracy close to the Cramér–Rao lower bound. The parameters of that selected time series model accurately represent the spectral density and the autocovariance function of the data. That is all the possible information for Gaussian...

journal article 2008

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Time series models for spectral analysis of irregular data far beyond the mean data rate

Broersen, P.M.T. (author)

journal article 2008

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Time-series analysis if data are randomly missing

Broersen, P.M.T. (author), Bos, R. (author)

journal article 2006

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Estimating time-series models from irregularly spaced data

Broersen, P.M.T. (author), Bos, R. (author)

journal article 2006

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Automatic identification of time-series models from long autoregressive models

Broersen, P.M.T. (author), de Waele, S. (author)

journal article 2005

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Finite sample properties of ARMA order selection

Broersen, P.M.T. (author), de Waele, S. (author)

journal article 2004

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Application of autoregressive spectral analysis to missing data problems

Broersen, P.M.T. (author), de Waele, S. (author), Bos, R. (author)

journal article 2004

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Order selection for vector autoregressive models

de Waele, S. (author), Broersen, P.M.T. (author)

journal article 2003

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Time series analysis in a frequency subband

Broersen, P.M.T. (author), de Waele, S. (author)

journal article 2003

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Generating data with prescribed power spectral density

Broersen, P.M.T. (author), de Waele, S. (author)

journal article 2003

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Automatic spectral analysis with time series models

Broersen, P.M.T. (author)

journal article 2002

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Autoregressive spectral estimation by application of the Burg algorithm to irregularly sampled data

Bos, R. (author), de Waele, S. (author), Broersen, P.M.T. (author)

journal article 2002

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Finite sample effects in vector autoregressive modeling

de Waele, S. (author), Broersen, P.M.T. (author)

journal article 2002