ESTIMATION AND INTERPOLATION OF MISSING VALUES OF A STATIONARY TIME SERIES

Abstract. A complete solution of the important problem of estimating (interpolating) the missing values of a stationary time series is obtained by decomposing it into a prediction plus regression problem. This makes it possible to estimate the missing values by finding the multistep-ahead predictors and using the existing computer packages for time series analysis. Such a solution is vital for the E step of the EM algorithm, and it is shown how this algorithm can be used to develop a simultaneous procedure for estimating the parameters and missing values of a time series.     

INVERSE AUTOCOVARIANCES AND A MEASURE OF LINEAR DETERMINISM FOR A STATIONARY PROCESS

Abstract. The inverse autocorrelations and autocovariances of a stationary stochastic process are generally used in the identification of ARMA models and linear systems, but they are also useful for studying linear relations inside the process as a whole.
Using inverse autocovariances, for any stationary process an 'inverse process' may be defined which may be considered a minimum variance linear filter, and turns out to be the best linear two-sided interpolator for one unknown value.
Basing on these results an index of linear determinism is introduced to measure to what degree a stationary process satisfies a linear deterministic constraint. The behaviour of the index for ARMA processes is finally examined.     

ASYMPTOTIC EFFICIENCY OF THE SAMPLE COVARIANCES IN A GAUSSIAN STATIONARY PROCESS

Abstract. This paper deals with the asymptotic efficiency of the sample autocovariances of a Gaussian stationary process. The asymptotic variance of the sample autocovariances and the Cramer–Rao bound are expressed as the integrals of the spectral density and its derivative. We say that the sample autocovariances are asymptotically efficient if the asymptotic variance and the Cramer–Rao bound are identical. In terms of the spectral density we give a necessary and sufficient condition that they are asymptotically efficient. This condition is easy to check for various spectra.     

THE ZERO-CROSSING RATE OF AUTOREGRESSIVE PROCESSES AND ITS LINK TO UNIT ROOTS

Abstract. The asymptotic zero-crossing rate (ZCR) of the general second-order autoregressive process is investigated. When the associated characteristic polynomial has a unit root e ^iθ (0 ≤θ≤π), the ZCR converges in mean square to θ/π and the rate of convergence is very fast regardless of the noise level.     

MODELING SIMULATION AND CONTROL OF THE WOOD DRYING PROCESS Part 1. A Set of PDE's as an Internal Model

Abstract

The internal model proposed is a nonlinear system of a few partial differential equations. The boundary conditions for the differential equations are specified at the lumber board entrance and between the wood and air. The initial conditions are calibrated by solving the static model and by the technical experiment. In conclusion, it can be said that the consistency of the model with experimental results seems to be reasonably good and can be used for process simulation and control     

Relative entropy and spectral constraints: some invariance properties of the ARMA class

Abstract. We determine the form of spectral densities of multidimensional scalar processes which minimize a relative entropy under a finite number of general moment‐type constraints. The obtained theoretical results are applied to spectral densities of weakly stationary processes under covariances, inverse covariances and cepstral or impulse response constraints. Invariance properties of the class of autoregressive moving‐average (ARMA) processes are shown to hold under the relative entropy minimization principle for many choices of entropy.