Showing papers on "Autocorrelation published in 1982"

Techniques of trend analysis for monthly water quality data

Abstract: Some of the characteristics that complicate the analysis of water quality time series are non-normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as ‘less than’: the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow-adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow-adjusted concentrations, which may also be seasonal and non-normal, can then be tested for trend by using the seasonal Kendall test.

Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation

Abstract: Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.

Serial Correlation and the Fixed Effects Model

Abstract: This paper generalizes the Durbin-Watson type statistics to test the OLS residuals from the fixed effects model for serial independence. Also generalized are the tests proposed by Sargan and Bhargava for the hypothesis that the residuals form a random walk. A method for efficient estimation of the parameters is also developed. Finally, an earnings function is estimated using the Michigan Survey of Income Dynamics in order to illustrate the uses of the tests and the estimation procedures developed in this paper.

Spectral estimation: An overdetermined rational model equation approach

Abstract: In seeking rational models of time series, the concept of approximating second-order statistical relationships (i.e., the Yule-Walker equations) is often explicitly or implicitly invoked. The parameters of the hypothesized rational model are typically selected so that these relationships "best represent" a set of autocorrelation lag estimates computed from time series observations. One of the objectives of this paper will be that of establishing this fundamental approach to the generation of rational models. An examination of many popular contemporary spectral estimation methods reveals that the parameters of a hypothesized rational model are estimated upon using a "minimal" set of Yule-Walker equation evaluations. This results in an undesired parameter hypersensitivity and a subsequent decrease in estimation performance. To counteract this parameter hypersensitivity, the concept of using more than the minimal number of Yule-Walker equation evaluations is herein advocated. It is shown that by taking this overdetermined parametric evaluation approach, a reduction in data-induced model parameter hypersensitivity is obtained, and a corresponding improvement in modeling performance results. Moreover, upon adapting a singular value decomposition representation of an extended-order autocorrelation matrix estimate to this procedure, a desired model order determination method is obtained and a further significant improvement in modeling performance is achieved. This approach makes possible the generation of low-order high-quality rational spectral estimates from short data lengths.

Time delay estimation via cross-correlation in the presence of large estimation errors

Abstract: The estimate of the difference in time of arrival of a common random signal received at two sensors, each of which also receives uncorrelated noise, is examined for both small and large estimation errors. It is shown that as the post-integration signal-to-noise ratio decreases, the correlator exhibits a thresholding effect; that is, the probability of a large error (an anomalous estimate) increases rapidly. Approximate theoretical results for the probability of an anomaly are presented and are verified experimentally. The variance of the time delay estimate is examined for both a gated mode, in which the time delay corresponding to the correlation peak closest to the true time delay is used as the estimate of time delay, and an ungated mode, in which the time delay corresponding to the largest peak over the full range of the correlator delay times is used as the estimate. The observed variance for both modes is compared with the theoretical variance based on a small error analysis. For the gated modes, the signal-to-noise ratio below which the observed variance begins to differ significantly from the small error theory can be reliably predicted from a linearity criterion. It is shown, however, that the expected variance for the ungated mode can depart from the small error theory at a higher signal-to-noise ratio than for the gated modes; thus the variance due to anomalies can be the most important factor in determining the region of applicability of the small error analysis.

A Mathematical Basis for the Random Decrement Vibration Signature Analysis Technique

Abstract: The mathematical basis for the Random Decrement Technique of vibration signature analysis is established. The general relationship between the autocorrelation function of a random process and the Randomdec signature is derived. For the particular case of a linear time invariant system excited by a zero-mean, stationary, Gaussian random process, a Randomdec signature of the output is shown to be proportional to the auto-correlation of the output. Example Randomdec signatures are computed from acceleration response time histories from an offshore platform.

Transport properties of stochastic Lorentz models

Abstract: Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed waiting time. In the stochastic Lorentz gas the light particle moves at constant speed and is scattered stochastically at collisions with the scatterers. For the waiting time Lorentz models the Green's function of the diffusion process is calculated exactly. The diffusion coefficient is found to be the same as for a corresponding random walk on a regular lattice, the velocity autocorrelation function exhibits a long-time tail proportional to ${t}^{\ensuremath{-}\frac{3}{2}}$ and super Burnett and higher-order transport coefficients are found to diverge. For the stochastic Lorentz gas similar results are found for the diffusion coefficient and the velocity autocorrelation function, but the generalized super Burnett coefficient, as introduced by Alley and Alder, is convergent in this case. For a special case of the waiting time Lorentz models some other aspects are considered, such as periodic boundary conditions, steady-state diffusion and fluctuations of the velocity autocorrelation function about its average value, due to the initial conditions and to the stochastic distribution of scatterers.

Reconstruction of the support of an object from the support of its autocorrelation

Abstract: The phase-retrieval problem consists of the reconstruction of an object from the modulus of its Fourier transform or, equivalently, from its autocorrelation. This paper describes a number of results relating to the reconstruction of the support of an object from the support of its autocorrelation. Methods for reconstructing the object’s support are given for objects whose support is convex and for certain objects consisting of collections of distinct points. The uniqueness of solutions is discussed. In addition, for the objects consisting of collections of points, a simple method is shown for completely reconstructing the object functions.

Two-Dimensional Discrete Properties of Random Surfaces

Abstract: Recent work has shown that it is possible to predict surface parameters measured digitally from a surface profile by means of three points on the autocorrelation function. The weakness of this work has been that only one-dimensional parameters have been evaluated. The present contribution extends the theory to include two-dimensional parameters of the surface which are expressed in terms of between four and seven points on the autocorrelation function depending on the type of surface. It is shown that this technique provides an alternative to traditional mapping methods. It is shown also that as a general rule results obtained from the discrete analysis do not converge to those obtained from the continuous theory. The nature and magnitude of the differences between the two approaches are discussed in detail. Finally, the theoretical results are confirmed experimentally and the general significance of discrete methods reviewed.

ARMA Model identification of hydrologic time series

Abstract: In recent years, ARMA models have become popular for modeling geophysical time series in general and hydrologic time series in particular. The identification of the appropriate order of the model is an important stage in ARMA modeling. Such model identification is generally based on the autocorrelation and partial autocorrelation functions, although recently improvements have been obtained using the inverse autocorrelation and the inverse partial autocorrelation functions. This paper demonstrates the use of the generalized partial autocorrelation function (GPAF) and the R and S functions of Gray et al. (1978) for ARMA model identification of hydrologic time series. These functions are defined, and some recursive relations are given for ease of computation. All three functions, when presented in tabular form, have certain characteristic patterns that are useful in ARMA model identification. Several examples are included to demonstrate the usefulness of the proposed identification technique. Actual applications are made using the Saint Lawrence River and Nile River annual streamflow series.

Adaptive acquisition of multiple access codes

Abstract: An adaptive acquisition technique is disclosed for enabling the initial acquisition of a received coded signal in a direct sequence spread spectrum system using multiple access codes for code division multiplexing. In order to obtain code synchronization by initial acquisition, correlation of a received code with a reference code is performed by an adaptive serial search over the code phase uncertainty which compares the measured signal correlation levels with two thresholds fixed to have a constant difference. During code signal acquisition, the thresholds are increased each time the measured correlation level exceeds the upper threshold, by an amount which equals the difference between the correlation level and the current upper threshold. Initial code signal acquisition is indicated when the detected correlation level raises the threshold levels to a point after which no further correlation measurements exceed the lower threshold. In this manner, false code signal synchronizations normally caused by autocorrelation sidelobes during strong signal reception, are reduced with little degradation in the low signal performance of the system.

Dipole autocorrelation function for molecular pressure broadening: A quantum theory which satisfies the fluctuation-dissipation theorem

Abstract: The dipole autocorrelation function for spectral line broadening is treated in a quantum theory which rigorously satisfies the fluctuation-dissipation theorem on a microscopic level. The basic approximation in the theory is the binary-collision approximation. In the present paper, the two-body interaction is decomposed into one part which commutes with the internal coordinates and another part which does not. The theory, as developed, is appropriate for broadening mechanisms for which the noncommuting term may be treated within the framework of perturbation theory, while the commuting term is to be treated exactly. The theory gives, at long times, a result for the dipole autocorrelation function consistent with the well-known impact approximation. At short times, an autocorrelation function of Gaussian form, with renormalization of the initial-state occupancy is obtained. It is found that the qualitative features discussed above are unaltered in higher-order perturbation theory. The results are consistent with the requirement that all time derivatives of the autocorrelation function at $t=0$ exist. This further satisfies the requirement that all moments of the line-shape function in the frequency domain exist, hence that the line-shape function decays "exponentially" sufficiently far in the wings.

Intensity fluctuations in a multiple scattering medium. Solution of the fourth moment equation

Abstract: The intensity fluctuations arising when a wave propagates through a medium containing weak random inhomogeneities of refractive index are described by a parabolic equation for the fourth moment of the wave field. The present paper obtains an analytical solution for this equation when an initially plane wave is normally incident on a half-space containing such a medium. The solution is in the form of a multiple convolution and is valid even for multiple scatter. The multiple convolution is evaluated to yield an expression for the spatial frequency spectrum of intensity fluctuations. This spectrum is valid for any autocorrelation function of refractive index irregularities. Media with a Gaussian autocorrelation function and a Kolmogorov-type autocorrelation function of refractive index irregularities are treated as examples. Finally the spatial frequency spectra of intensity fluctuations are integrated to give the scintillation index curves as functions of distance of propagation in the medium. The regions of validity of the different approximations are discussed and the limits of error associated with the solutions are given.

Robust detection by autoregressive spectrum analysis

Abstract: The problem of detecting a signal with an unknown Doppler shift and random phase in white noise is essentially a problem in spectral analysis. This paper examines the merits of a detector based upon the autoregressive spectral estimator. Some advantages of the auto-regressive detector are that the detection performance is independent of Doppler shift and phase and the false alarm rate is independent of noise level. Also, the performance does not depend upon the exact signal form but only upon its autocorrelation function, leading to a robust detector. For the first order autoregressive model investigated, the computational and storage requirements of the autoregressive detector are less than that for a conventional bank of matched filters detector. It is shown by example that when the actual received signal departs appreciably from the signal assumed in a conventional detector, i.e., a bank of matched filters, the AR detection performance exceeds that of the conventional detector.

Molecular dynamics simulation of liquid anisotropy. II. Rise and fall transients on a picosecond time scale

Abstract: The behavior of a liquid sample subjected to an external torque of picosecond duration is investigated by molecular dynamics simulation, using 108 C2v triatomics interacting with a 3×3 site–site Lennard‐Jones potential. The resulting rise and fall transients are computed and their behavior is such as to fall on Langevin’s functions from the linear response region to saturation, i.e., when the energetic perturbation (E) is less than kT to the point at which it is about 10 times kT. The breakdown of the fluctuation–dissipation theorem is investigated at the point E/kT = 12, where the normalized fall transients no longer decay as the equilibrium autocorrelation functions but considerably faster. The simulation does not support the conventional view of rise and fall transients, which is based on Debye’s theory of rotational diffusion.

Detecting Outliers in Time Series Data

Abstract: Occasional large errors in data can have drastic effects on estimates for such quantities as correlation coefficients, regression coefficients, and spectral density estimates. In this article we investigate the effect of outliers on time series data by considering the influence function for the autocorrelations p(k) of a stationary time series. This influence function matrix is applied to simulated data, to power plant data, and to inventory data on nuclear materials.

Adaptive analysis of speech based on a pole-zero representation

Abstract: Two analysis methods are proposed to estimate the orders as well as the parameter values of an autoregressive moving-average (ARMA) process with a white Gaussian noise or a train of impulses as input. This process is adopted as a model for the process of speech production. The estimation is accomplished directly from the signal waveform using recursive formulas and is optimum in the sense that the variance of errors in the estimated waveform is minimized. This method is less vulnerable to fluctuations in the fundamental period of the source than the previously proposed methods based on the auto-correlation function. In order to trace the trajectories of the poles and zeros in the vocal tract transfer function, it is required to develop a method for adapting to the temporal variations of the acoustic characteristics of speech. A method is also proposed for adaptive control of the analysis interval based on the detection of convergence of the estimated values of the parameters. The validity of the proposed methods is tested by analysis of both synthetic and natural speech sounds.

An Evaluation of Ultrasound NDE Correlation Flaw Detection Systems

Abstract: The advantages and limitations of correlation flaw detec- tion systems are studied with a new system which uses a digital delay Line to replace the acoustic delay line of our original random signal flaw detection system. A general signal-to-noise ratio (SNR) formula is derived for correlation systems which includes the effects of clutter, background receiver noise, and self-noise. Experimental studies con- ducted with both m-sequences and random signals, to verify the theo- retical analysis, indicate that in normal operation the correlation system performance is essentially equivalent in resolution and signal-toaoise ratio for these two types of transmit signals. Comparison of the signal- to-noise ratio formulas for pulse-echo and a correlation system suggests that under high input SNR conditions and where high-speed operation is also required, the pulse-echo system provides higher dynamic range and better output signal-tenoise ratio than a correlation system using either of the two types of signals studied. Under all other operating conditions, except when detection is clutter limited, the correlation system is shown to provide superior performance when compared to a conventional pulse-echo system, and can detect echo signals, buried in receiver noise and surrounded by clutter, which a conventional pulse- echo system would be unable to detect.

Real time pitch detection by stream processing

Abstract: Continuous stream processing of an input signal to find the autocorrelation function and pitch period is simplied. The input speech signal is sampled at 8 khz, from which the autocorrelation function is formed by multiplying each sample by a stored-delay reduced sequence of up to 30 past samples. The reduced sequence is formed by every fourth sample of input signal gated to storage. Autocorrelation values are sequentially compared by a peak-peaker for maxima, thus further minimizing storage requirements to find the pitch period.

Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory

Abstract: We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.

Group-complementary code sets for implementing pulse-compression processing with optimum aperiodic autocorrelation and optimum cross-correlation properties

Abstract: A group-complementary codes provide sets of binary word groups which have the combined properties of optimized aperiodic autocorrelation and optimized cross-correlation between word sets. The optimized aperiodic autocorrelation property allows the implementation of pulse compression processing in sensor systems to achieve zero value temporal or range sidelobes within the principal interpulse period without resorting to weighting techniques for sidelobe reduction. The orthogonal nature of group-complementary codes, apparent from their absence of cross-correlation between sets, allows sensors to be deployed in close proximity, using the same carrier frequency without direct path mutual interference when synchronized.

Calculating Digital FM Spectra by Means of Autocorrelation

Abstract: In sharp contrast to the task of calculating the power spectrum for a general digital FM scheme, the autocorrelation can easily be obtained. By considering a class of FM schemes having a time-limited autocorrelation function, truncation is avoided and, applying a Fourier transformation, power spectral densities are easily obtained. A method is applied taking these properties into account. Thus, a powerful tool is available for investigation of different parameters within the considered digital FM modulation format.

Computer simulation of the generalized brownian motion

Abstract: We introduce a new method, based on the theory of stationary stochastic processes, to represent by an analytical reference model a large class of autocorrelation functions known numerically. The analytical reference model is then used to give a very accurate representation of the velocity autocorrelation function of argon near the triple point by a Mori continued fraction truncated at very high order (up to 25 Mori coefficients). Under some restrictive hypothesis, the results of this analysis together with an appropriate numerical algorithm, permit the simulation of generalized brownian dynamics of an argon particle in argon fluid in a realistic way.

Autocorrelation apparatus and method for approximating the occurrence of a generally periodic but unknown signal

Abstract: A method and an apparatus for indicating in real time the occurrence of and measuring the frequency or period of the basic oscillation of a generally periodic unknown signal with statistically distributed spectral components is disclosed. Using an autocorrelation technique, the time interval from the initial peak value to the next successive peak value of the autocorrelation curve is measured and the unknown frequency or period is determined therefrom. A periodically occurring maximum of the next successive peak value is determined, and, on its appearance, a signal is produced, said signal approximating the occurrence in real time of the generally periodic signal.

Stochastic theory of scattering from idealized spinodal structures, I: Structure and autocorrelation function

Abstract: In the early stage (ES) of spinodal decomposition, composition fluctuations in a nominally homogeneous glass are selectively amplified over a narrow range of wavelengths. As their amplitude increases, nonlinear coupling slows further amplitude growth, coarsens the structure, sharpens the interfaces, and adjusts the phase compositions and volume fractions toward their equilibrium values; but the morphology of the late stage (LS) structure is dominated by the ES morphology. It is widely believed that the LS morphology can be modelled as the positive and negative composition deviations from the average, that are obtained from a superposition of waves of fixed wavelength Λ but of random orientation and phase. Here, Λ is not identified with the dominant ES wavelength. This LS model, and modifications of it, are analysed using stochastic theory. The autocorrelation function of the model is determined using methods developed for the analysis of electrical random noise signals that have passed through a nonlinear amplifier.

Dynamic statistical properties of laser speckle produced by a moving diffuse object under illumination of a Gaussian beam

Abstract: The dynamic statistical properties of laser speckle produced in the far-field diffraction region by a diffuse object moving in an arbitrary direction of three-dimensional space under illumination of a Gaussian beam are investigated theoretically and experimentally. It is found that the time-varying speckle intensity detected at the center of the far-field diffraction plane is a stationary random process with respect to time. The dependence of the autocorrelation function of the time-varying speckle-intensity fluctuation on both lateral and longitudinal components of the object velocity is studied in some detail by evaluating numerically the resultant equation of the time-varying speckle-intensity correlation. To confirm the theoretical results, an experiment has been performed. Good agreement between the theoretical and experimental results is obtained for the autocorrelation function of the time-varying speckle-intensity fluctuation that is due to three-dimensional translation of the diffuse object.