Showing papers on "Autocorrelation published in 1987"

Time series regression with a unit root

Abstract: This paper studies the random walk, in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984).

Digital spectral analysis with applications

Abstract: This new book provides a broad perspective of spectral estimation techniques and their implementation. It concerned with spectral estimation of discretespace sequences derived by sampling continuousspace signals. Among its key features, the book: · Emphasizes the behavior of each spectral estimator for short data records. · Provides 35 computer programs, including fast algorithms. · Provides the theoretical background and review material in linear systems, Fourier transforms matrix algebra, random processes, and statics. · Summarizes classical spectral estimation as it is practiced today. · Covers Prony’s method, parametric methods, the minimum variance method, eigenanalysis-based estimators, multichannel methods, and twodimensional methods. · Includes problems. · Contains appendices that cover Sunspot Numbers, Complex Test Data, Temperature Data, and Program Conversion for Complex-to-Real Case. Of Special Interest A disk is included that has a double-sides 360kB format readable by any personal computer with an MS-DOS 2 or 3 operating system, such as the IBM XT or AT.

Determining the Order of Differencing in Autoregressive Processes

Abstract: One way of handling nonstationarity in time series is to compute first differences and fit a model to the differenced series unless the differenced series also looks nonstationary. In that case, second- or higher-order differencing is done. To decide if the current degree of differencing is sufficient, one can look at the autocorrelation function for slow decay. A formal statistical test for the need to difference further is available if one is willing to assume that at most one more difference will render the series stationary. In this article, we present a proper sequence of statistical tests that allows the practitioner to handle cases in which a high order of differencing may be needed. The proper sequence is not the traditional sequence, which begins with a test for a single unit root.

The Time Series Approach to Short Term Load Forecasting

Abstract: The application of time series analysis methods to load forecasting is reviewed. It is shown than Box and Jenkins time series models, in particular, are well suited to this application. The logical and organized procedures for model development using the autocorrelation function and the partial autocorrelation function make these models particularly attractive. One of the drawbacks of these models is the inability to accurately represent the nonlinear relationship between load and temperature. A simple procedure for overcoming this difficulty is introduced, and several Box and Jenkins models are compared with a forecasting procedure currently used by a utility company.

Statistical properties of radio-frequency and envelope-detected signals with applications to medical ultrasound.

Abstract: Both radio-frequency (rf) and envelope-detected signal analyses have lead to successful tissue discrimination in medical ultrasound The extrapolation from tissue discrimination to a description of the tissue structure requires an analysis of the statistics of complex signals To that end, first- and second-order statistics of complex random signals are reviewed, and an example is taken from rf signal analysis of the backscattered echoes from diffuse scatterers In this case the scattering form factor of small scatterers can be easily separated from long-range structure and corrected for the transducer characteristics, thereby yielding an instrument-independent tissue signature The statistics of the more economical envelope- and square-law-detected signals are derived next and found to be almost identical when normalized autocorrelation functions are used Of the two nonlinear methods of detection, the square-law or intensity scheme gives rise to statistics that are more transparent to physical insight Moreover, an analysis of the intensity-correlation structure indicates that the contributions to the total echo signal from the diffuse scatter and from the steady and variable components of coherent scatter can still be separated and used for tissue characterization However, this analysis is not system independent Finally, the statistical methods of this paper may be applied directly to envelope signals in nuclear-magnetic-resonance imaging because of the approximate equivalence of second-order statistics for magnitude and intensity

Conditional Heteroscedastic Time Series Models

Abstract: Under the traditional linear time series or regression setting, the conditional variance of one-step-ahead prediction is time invariant. Experience in conjunction with data analysis, however, suggests that the variability of a process might well depend on the available information. This reality has motivated extensive research to relax the constant variance assumption imposed by the traditional linear time series model, and several classes of generalized parametric models designed specifically for handling nonhomogeneity of a process have been proposed recently. In particular, the random coefficient autoregressive (RCA) models were widely investigated by time series analysts and the autoregressive conditional heteroscedastic (ARCH) models were investigated by econometricians. The interesting fact is that the ARCH processes can be regarded as special cases of the RCA model. In this article, I first give the relationship between these two types of models and show that the special feature of these t...

Cumulants: A powerful tool in signal processing

Abstract: The impulse response of a linear, time-invariant system is related in a simple closed-form solution to the output cumulants, when the input is assumed to be non-Gaussian and independent. This expression permits the use of one-dimensional processing of the output cumulants for identification of non-minimum-phase systems, and opens new directions in other signal processing applications.

The use of the Durbin–Watson d statistic in Rietveld analysis

Abstract: A weighted form of the Durbin–Watson d statistic [Durbin & Watson (1971). Biometrika, 58, 1–19] has been used to quantify the serial correlation between adjacent least-squares residuals in Rietveld refinements of step-scan powder diffraction data. Analyses of X-ray and neutron data from a range of materials have shown that the d statistic: provides a sensitive measure of the progress of a refinement and remains discriminating when other agreement indices fail, for example, when comparing results at different step widths; provides quantitative information about the significance of serial correlation present in the residuals; provides a convenient means of assessing the reliability of the estimates of the parameter variances; and provides a basis for the selection of values of step width and intensity corresponding to optimum and/or minimum use of experimental beam time.

Generalized stochastic subdivision

Abstract: Stochastic techniques have assumed a prominent role in computer graphics because of their success in modeling a variety of complex and natural phenomena. This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct high-quality random functions, including those with non-fractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique.

Autocorrelation of gene frequencies under isolation by distance.

Abstract: Spatial autocorrelation statistics are used for description of geographic variation of gene frequencies, but the relationship of these indices with the parameters describing the genetic structure of populations is not established. A simple relation is derived here between kinship coefficient and a measure of spatial autocorrelation, Moran9s I . The autocorrelation coefficient of gene frequencies at a given distance is a direct function of the kinship at that distance, and an inverse function of the standardized gene frequency variance, F st . Under isolation by distance, the expected values of Moran9s I for any allele may be calculated by means of Malkcot-Morton function, which predicts an exponential decline of genetic similarity in space. This allows comparison of observed gene frequency patterns with the patterns that should be caused by interaction of short range migration and random genetic drift.

A new modulation principle for incoherent scatter measurements

Abstract: A new method for measuring the ionosphere plasma autocorrelation function with an incoherent scatter radar is described. This method can be used in similar situations where multipulse methods have been used previously. In situations where the design of the transmitted signal is limited by a maximum allowed modulation time and a maximum radar peak power and where the signal to noise ratio is small, this method provides significantly more accurate ACF estimates than can be obtained by frequency commutated multiple pulse measurements. A simple explanation of the method is given, as well as a precise definition based on ambiguity functions. Computational algorithms are discussed, and it is shown that there are several possibilities to modify present algorithms so that this method can be implemented.

Automatic focusing by correlative methods

Abstract: The possibility of focusing images by the autocorrelation function is explained. It can be shown that these techniques are less sensitive to disturbances by noise than others. Furthermore, focusing criteria derived from autocorrelation functions have different responses to image contrast. It has been shown that these focusing criteria can be determined using binary images and applying the laws of stochastic ergodic metrology. This leads to a large reduction in computing time. Moreover, an attempt was made to focus by means of binary images determined by simple segmentation. The experimental results show that such a focus criterion operates quite well. The criterion offers the advantage that brightness levels in the image can be chosen selectively for focusing.

Test Consistency with Varying Sampling Frequency

Abstract: This Paper Considers the Consistency Property of Some Test Statistics Based on a Time Series of Data. While Th Eusual Consistency Criterion Is Based on Keeping the Sampling Interval Fixed, We Let the Sampling Interval Take Any Path As the Sample Size Increases to Infinity. We Consider Tests of the Null Hypotheses of the Random Walk and Randomness Against Positive Autocorrelation We Show That Tests of the Unit Root Hypothesis Based on the First-Order Correlation Coefficient of the Original Data Are Consistent As Long As the Span of the Data Is Increasing. Tests of the Same Hypothesis Based on the First-Order Correlation Coefficient Using the First-Differenced Data Are Consistent Only If the Span Is Increasing At a Rate Greater Than Square Root of 'T'. on the Other Hand Tests of the Randomness Hypotheses Based on the First-Order Correlation Coefficient Applied to the Original Data Are Consistent As Long As the Span Is Not Increasing Too Fast. We Provide Monte Carlo Evidence on the Power, in Finite Samples, of the Tests Studied Allowing Various Combinations of Span and Sampling Frequencies. It Is Found That the Consistency Properties Summarize Well the Behavior of the Power in Finite Samples. the Power of Tests for a Unit Root Is More Influenced by the Span Than the Number O Observations While Tests of Randomness Are More Powerfull When a Small Sampling Frequency Is Available.

A spectral autocorrelation method for measurement of the fundamental frequency of noise-corrupted speech

Abstract: A method for measurement of the fundamental frequency of a voiced speech signal corrupted by high levels of additive white Gaussian noise is described. The method is based on flattening the spectrum of the signal by a bank of bandpass lifters and extracting the pitch frequency from autocorrelation functions calculated at the output of the lifters. A smoothing modified median filter is applied to the calculated pitch frequency contour to result in an improvement in the accuracy of the method. A byproduct of the pitch tracker is a voiced/ unvoiced classifier. The maximum and the variance of the autocorrelation function maxima, over the bank of lifters, serve as the basis for voiced/unvoiced classification by making use of a two-dimensional, nearest-neighbor pattern recognition approach. Results are presented for fundamental frequency measurement and voiced/unvoiced classification for several signal-to-noise ratios.

Digital Simulation of Seismic Ground Motion

Abstract: The method of spectral representation for uni-variate, one-dimensional, stationary stochastic processes and multi-dimensional, uni-variate (as well as multi-dimensional, multi-variate) homogeneous stochastic fields has been reviewed in detail, particularly from the viewpoint of digitally generating their sample functions. This method of representation has then been extended to the cases of uni-variate, one-dimensional, nonstationary stochastic processes and multi-dimensional, uni-variate nonhomogeneous stochastic fields, again emphasizing sample function generation. Also, a fundamental theory of evolutionary stochastic waves is developed and a technique for digitally generating samples of such waves is introduced as a further extension of the spectral representation method. This is done primarily for the purpose of developing an analytical model of seismic waves that can account for their stochastic characteristics in the time and space domain. From this model, the corresponding sample seismic waves can be digitally generated. The efficacy of this new technique is demonstrated with the aid of a numerical example in which a sample of a spatially two-dimensional stochastic wave consistent with the Lotung, Taiwan dense array data is digitally generated.

Business Forecasting Methods

Abstract: Part 1 Time series techniques: smoothing methods methods for time series decomposition and analysis. Part 2 Casual or explanatory modeling techniques: linear regression and correlation multiple regression methods econometric models. Part 3 advanced topics in time series analysis: autocorrelation, autoregressive models and time series analysis additional time series models box-jenkins methods. Part 4 Qualitative Forecasting: Forecasting business conditions - some qualitative approaches. Part 5 Issue in forecasting: forecast evaluation, revison, and business planning and control.

A study of vibrational dephasing of the A 1 modes of CH3CN in a computer simulation of the liquid phase

Abstract: The vibrational dephasing of the four A 1 modes of CH3CN has been calculated for a simulation of the liquid phase at 288 K assuming that it is caused by generalized forces interacting with the cubic anharmonicities of each mode. The forces along each mode were resolved into electrostatic and Lennard-Jones components and the mean values, probability distributions and time autocorrelation functions were calculated. Line shifts in the liquid state were evaluated from the mean values. Line shapes are related to the shift-shift time correlation functions and hence to force-force correlation functions using the cumulant approximation. This was found to be a good approximation and the vibrational correlation functions (Fourier transforms of the line shapes) were computed using two sets of anharmonicity constants. The time scale of the shift fluctuations was never slow, so that the line shapes are nearly lorentzian in this model.

Continuous-time dynamics of asymmetrically diluted neural networks.

Abstract: We study the continuous-time dynamics of a strongly diluted Hopfield model with asymmetric synaptic connections. The model is exactly soluble for static as well as dynamic properties. The time evolution of the autocorrelation, the susceptibility, and the overlap function of two configurations are given in explicit form.

Spatial Autocorrelation among Errors and the Relative Efficiency of OLS in the Linear Regression Model

Abstract: The article considers the efficiency of ordinary least squares (OLS) coefficient estimates relative to generalized least squares (GLS) in a linear regression model where the disturbances follow a spatial autocorrelation pattern. The main result is that the limiting relative efficiency of OLS, as correlation among disturbances increases, tends to either zero or unity for most design matrices and correlation patterns encountered in practice. Which of these cases applies depends on the eigenvector corresponding to the largest eigenvalue of the spatial dependence matrix from the spatial autocorrelation scheme. In particular, the limiting relative efficiency of OLS is unity if this eigenvector lies in the column space of the design matrix. In practice, the relevant eigenvector will often be a column of ones. This implies that OLS is in the limit as good as GLS whenever there is a constant in the regression. We conclude, however, from several concrete examples that the loss in efficiency can still be s...

Methods for estimating the autocorrelation function of complex Gaussian stationary processes

Abstract: New methods for estimating the autocorrelation function (acf) of a complex Gaussian stationary process are presented. These methods are based on a general invariance property for the autocorrelation of a common class of the above processes. This property suggests estimation procedures based on magnitude hard limiting and phase quantization. The procedures are an extension of the relay estimator, currently employed for real processes. The computational cost and the general properties of the methods are discussed. In particular, some estimators especially suited for very simple implementations are considered. The performance of the complex hybrid sign estimator is evaluated and compared to that of the classical Direct estimator. The proposed methods are attractive for many applications in the field of digital signal processing.

Randomly Choosing Parameters from the Stationarity and Invertibility Region of Autoregressive–Moving Average Models

Abstract: SUMMARY Choice of appropriate parameter configurations for time series simulations is not always easy. One possible approach when simulating from autoregressive-moving average models is to choose parameter values from a uniform distribution on the stationarity and invertibility region associated with such models. In this paper, well-known time series results are applied to this problem to give a neat method which comprises generating partial autocorrelations independently distributed as appropriate beta variates and applying a standard transformation to obtain the parameters from these.

Fitting noncausal autoregressive signal plus noise models to noisy non-Gaussian linear processes

Abstract: The problem of estimating the parameters of a noncausal autoregressive signal model from noisy observations is considered. The signal is assumed to be non-Gaussian. The measurement noise is allowed to be non-Gaussian. Two techniques that use both autocorrelations and third-order autocumulants of the data are presented for parameter estimation. Knowledge of the probability distribution of the driving noise is not required. Several simulation examples are presented to illustrate the two methods. The problem of model order selection is also addressed.

Statistics of Rayleigh Backscatter From a Single-Mode Fiber

Abstract: This paper contains a detailed analysis of the statistical properties of the Rayleigh backscatter signal from a single-mode optical fiber. Derivations of the first- and second-order statistics, autocorrelation function, and power spectral density of the backscatter wave are given. The probability density functions of the amplitude and intensity of the backscatter signal are also calculated.

High resolution time delay estimation

Abstract: A new method is presented for estimating the arrival times of deterministic signal pulses that are separated by less than the duration of the signal autocorrelation function. The method is based on the observation that if the signal has a flat band-limited spectrum, then the maximum-likelihood estimator for the signal time of arrivals can be approximately implemented as an unweighted least-squares exponential fitting problem. An improved linear prediction algorithm for high resolution exponential parameter estimation is then used to estimate the time of arrivals. The proposed method is tested via computer simulation and it's performance is compared against the Cramer-Rao lower bound.

Urban travel demand: The impact of Box-Cox transformations with nonspherical residual errors

Abstract: We develop an algorithm for solving regression models with Box-Cox transformations on both the dependent and independent variables, while simultaneously taking into account corrections for serial correlation of several orders and for heteroscedasticity. The latter correction is of a general form which contains as special cases most specifications of heteroscedasticity found in practice. We apply the procedure to three urban travel demand functions, two of which are currently used in their linear form by the Montreal Transit Authority, and analyze more than 100 specifications. Our results show that taking into account nonsphericalness of the residuals has a major impact on model parameter estimates, notably on those which determine the functional form of the model, and that, conversely, modifications of the functional form have strong implications for both the structure of autocorrelation and the importance of heteroscedasticity; moreover, we find interactions between autocorrelation and heteroscedasticity structures. We introduce a special measure of elasticity for variables which contain zero observations, particularly dummy variables. Moreover, we find that elasticities of demand and implicit values of time depend to a large extent on the stochastic specification of the model.

Durbin–Watson and Generalized Durbin–Watson Tests for Autocorrelations and Randomness

Abstract: The Durbin–Watson (DW) test for lag 1 autocorrelation has been generalized (DWG) to test for autocorrelations at higher lags. This includes the Wallis test for lag 4 autocorrelation. These tests are also applicable to test for the important hypothesis of randomness. It is found that for small sample sizes a normal distribution or a scaled beta distribution by matching the first two moments approximates well the null distribution of the DW and DWG statistics. The approximations seem to be adequate even when the samples are from nonnormal distributions. These approximations require the first two moments of these statistics. The expressions of these moments are derived.

Fast adaptive least squares algorithms for power spectral estimation

Abstract: Power spectrum estimation is of great importance in various applications of signal processing, such as geophysics and communications. In this paper two new fast algorithms are presented that adaptively compute a least squares estimate of the power spectrum of a time series. This is achieved by modeling the input as an AR signal of order m and simultaneous minimization of the sum of the forward and backward prediction error energies. The first algorithm is of the 0 (m2) type, and the second of 0(m) requiring 9m multiplications and additions.

Voiceband signal classification

Abstract: A signal is classified as one among a plurality of classifications by employing the autocorrelation of a complex low-pass version of the signal, i.e., the complex autocorrelation. The normalized magnitude of the complex autocorrelation obtained at a prescribed delay interval, i.e., "lag", is compared to predetermined threshold values to classify the signal as having one of a plurality of baud rates.

Higher-order residual analysis for nonlinear time series with autoregressive correlation structures

Abstract: : The paper considers nonlinear time series whose second order autocorrelations satisfy autoregressive Yule-Walker equations. The usual linear residuals are then uncorrelated, but not independent, as would be the case for linear autoregressive processes. Two such types of nonlinear model are treated in some detail: random coefficient autoregression and multiplicative autoregression. The proposed analysis involves crosscorrelation of the usual linear residuals and their squares. This function is obtained for the two types of model considered, and allows differentiation between models with the same autocorrelation structure in the same class. For the random coefficient models it is shown that one side of the crosscorrelation function is zero, giving a useful signature of thes processes. The non-zero features of the other side of the crosscorrelations are informative of the higher order dependency structure. In applications this residual analysis requires only standard statistical calculations, and extends rather than replaces the usual second order analysis. Keywords: Nonlinear time series; Autoregressive; Linear residuals; Random coefficient autoregression; Multiplicative autoregression; Residual analysis.

A real-time high-resolution technique for angle-of-arrival estimation

Abstract: A new, fast method for angle-of-arrival estimation comparable in performance to modern eigen-decomposition based techniques is described. This method is well-suited to systolic array implementations. An adjunct to the method is an estimator for determining the most likely number of incident signal components.