Showing papers on "Partial autocorrelation function published in 1980"
TL;DR: In this article, the authors studied the relationship between the maximum entropy spectrum and the reflection coefficient sequence characterizing the given subsurface model and derived the synthetic seismogram in terms of wave motion measured in units proportional to the square root of energy.
Abstract: A horizontally stratified half space bounded by a perfect reflector at the top gives rise to a seismogram which, when completed by the direct downgoing pulse at zero time and by symmetry about the origin for negative time, produces an autocorrelation function. If this autocorrelation is convolved with the corresponding prediction error operators of increasing length, we obtain a "gapped function," which deviates more and more from the perfect symmetry exhibited by the autocorrelation. This gapped function consists of the downgoing and upgoing waveforms at the top of each layer. The gap separates the two waveforms, and the gapwidth increases as deeper and deeper layers are reached. In particular, the width of the gap is a measure of the entropy of the seismogram at a given depth level-the deeper we go into the sub-surface, the higher the entropy of the corresponding gapped function. We explore the nature of the gapped function as it relates to the Toeplitz recursion generating the prediction error operators, and we re-derive the synthetic seismogram in terms of wave motion measured in units proportional to the square root of energy. We obtain an explicit relationship between the partial autocorrelation function on the one hand, and the reflection coefficient sequence on the other. This formulation allows us to generalize earlier results, so that we can treat the case for which the surface reflection coefficient is less than unity in magnitude. We investigate both the physical as well as the mathematical foundations of the stratified model, and the relation that this model bears to maximum entropy spectral analysis [1], [6]. In particular, we discuss Burg's fundamental result on the relationship of the maximum entropy spectrum to the reflection coefficient sequence characterizing the given subsurface model.
35 citations
TL;DR: In this paper, the behavior of the sample autocorrelation function, r(k), for an integrated autoregressive moving average time series is examined and the validity of the approximation in moderate-sized samples is examined.
Abstract: The behavior of the sample autocorrelation function, r(k), for an integrated autoregressive moving average time series is examined. The nonnormal asymptotic distribution of r(k) is characterized as a function of lag k and the parameters of the process. The validity of the approximation in moderate-sized samples is examined.
26 citations
TL;DR: In this article, a method of estimating the parameters of an autoregressive model with real and equal roots in its characteristic equation is developed, which uses the serial autocorrelation function in the estimation process.
20 citations
TL;DR: In this paper, the conditions for stationarity and invertibility are determined and the autocorrelation function and Yule-Walker equations are obtained for the general case, and as particular cases for special discrete values for various grids in plane and for orders 1 and 2 in time.
Abstract: Spatially dependent autoregressive models in m dimensions are defined. The conditions for stationarity and invertibility are determined. The autocorrelation function and Yule-Walker equations are obtained for the general case, and as particular cases for special discrete values for various grids in plane and for orders 1 and 2 in time. The spectra are obtained for these particular cases, and some results for the partial autocorrelation function. All results are new. The notation, definitions, and assumptions are those given by Voss et al. (1980). We assume stationarity of z over time t, where an m dimensional vec 12m tor. We assume the covariance structure as given by Hannan (1970), 2 with and all covariances existing. Nonstationary models will be considered in later papers.
14 citations
TL;DR: In this article, a general linear stochastic model was proposed, which assumes a time series to be generated by a linear aggregation of random shocks at various temporal and spatial locations.
Abstract: The paper describes a general linear stochastic model which supposes a time series to be generated by a linear aggregation of random shocks at various temporal and spatial locations. It is a combination of autoregressive and moving average models (ARMA). The autocorrelation functions and power spectra are determined,
5 citations
1 Dec 1980
TL;DR: In this article, a structure identification algorithm for linear multivariable systems is described that permits colored measurement and process noise as well as control inputs, and is made from operating records rather than responses to special inputs, is noniterative and thus termed direct identification.
Abstract: A structure identification algorithm for linear multivariable systems is described that permits colored measurement and process noise as well as control inputs. An apparently new canonical form for matrix fraction descriptions (MFD), the Structure Canonical form, is used to develop the algorithm. The identification is made from operating records rather than responses to special inputs, is noniterative and is thus termed direct identification. The algorithm requires testing a noise corrupted matrix for singularity and a threshold test for singularity using singular values is developed. The results extend those of previous studies which consider white measurement and process noise and do not allow control inputs. They can be interpreted as generalizing to the multivariable case partial autocorrelation techniques used in time series analysis.
2 citations
TL;DR: In this paper, the effect of system size and shape on the theoretical space-time autocorrelation function for first order STARMA models is described and an initial estimation for the STAR(11 and STMA(11) models is presented.
Abstract: The effect of system size and shape on the theoretical space-time autocorrelation function is described for first order STARMA models. Figures and tables are presented to assist in identification considerations which include model interpretation, patterns of the theoretical spacetime autocorrelation and partial autocorrelation functions, and initial estimation for the STAR(11) and STMA(11) models.