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

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)...

Vector Autoregressive Order Selection in Practice

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...

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...

ARMAsel for Detection and Correction of Outliers in Univariate Stochastic Data

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...

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