B. Liu and D. Munson, "Generation of a random sequence having a jointly specified marginal distribution and autocovariance," IEEE Trans. on Acoustics, Speech, and Signal Proc., vol. 30, pp. 973--983, Dec. 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the latter are strong requirements, as they call for the simultaneous capture of first order and second order statistics of the empirical data, and can therefore be expected to yield better models than those obtained by capturing a weaker statistical signature. For similar modeling approaches, see [21, 23, 32, 3], and especially [3] which is capable of matching precisely the empirical autocorrelation function in addition to the empirical distribution. For a comprehensive survey of this topic, refer to [16] The rest of the paper is organized as follows. Section 2 contains some notational and technical ....

Liu, B. and Munson, D.C., "Generation of a Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance", IEEE Trans. on Acoustics, Speech and Signal Processing 30(6), 973--983, 1982.

.... similar sample paths can considerably enhance a practitioner s confidence in a proposed model. Furthermore, qualitative similarity is quite emphatically not a substitute for the two preceding quantitative criteria; rather, it is required in addition, not instead. A similar view is adopted in [23, 21, 32]. An excellent comprehensive survey of methods for constructing stochastic processes with prescribed marginals and autocorrelations may be found in [15] which defines a taxonomy of input analysis methods. In this taxonomy, TES methods, as well as those proposed in [23, 21, 32] would be ....

....view is adopted in [23, 21, 32] An excellent comprehensive survey of methods for constructing stochastic processes with prescribed marginals and autocorrelations may be found in [15] which defines a taxonomy of input analysis methods. In this taxonomy, TES methods, as well as those proposed in [23, 21, 32], would be classified as approximate correlation distortion methods. TES processes and the underlying TES methodology conform neatly to this paradigm. First, the TES modeling methodology guarantees an exact fit to arbitrary marginal distributions. In particular, it can match any empirical density ....

B. Liu and D.C. Munson. Generation of a Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance. IEEE Transactions on Acoustics, Speech and Signal Processing Vol. 30, No. 6, 973-983, 1982.

....the autocorrelation function (a second order statistic) of empirical data. Most importantly, TES aims to fit both marginals and autocorrelations simultaneously. This goal is not new; in fact, engineers have attempted such simultaneous fitting, mainly in the context of signal processing (see, e.g. [13] and references therein) The TES variation on this theme is to precisely fit the empirical marginal distribution (typically an empirical histogram) and at the same time capture temporal dependence proxied by the autocorrelation function (a measure of linear dependence) Being able to do this is ....

....or messy and vaguely right 1. 3 Goodness Criteria for Modeling Empirical Time Series The TES modeling approach stipulates a number of requirements precise requirements as well as heuristic ones for the goodness of a candidate time series model based on empirical sample paths (see also [13, 12, 20] for related views) Requirement 1: The marginal distribution of the model should match its empirical counterpart. Requirement 2: The autocorrelation function of the model should approximate its empirical counterpart. Because the empirical data is finite, the model need only approximate the ....

B. Liu and D.C. Munson. "Generation of a Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance". IEEE Transactions on Acoustics, Speech and Signal Processing Vol. 30, No. 6, 973--983, 1982.

....25, 12, 16, 22] A natural idea is to capture first order and second order properties of empirical time series (assumed to be from a stationary probability law) by fitting simultaneously both the empirical distribution (histogram) and empirical autocorrelation function. This approach was used in [14], and more recently in the theoretical work reported in [7, 8, 9, 17] and the applied work described in [20, 21, 23, 19] An extensive survey of modeling methods within this purview may be found in [11] TES (Transform Expand Sample) is a versatile class of stationary stochastic processes with ....

Liu, B. and Munson, D.C. "Generation of Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance", IEEE Transaction on Acoustics, Speech and Signal Processing, Vol. 30, No. 6, 973--983, 1982.

....to model and synthesize nonGaussian LRD processes. To create a nonGaussian process with a target LRD covariance, we simply pass a Gaussian process through an appropriate nonlinear transformation, with the transformation chosen to convert the Gaussian marginal to the desired nonGaussian marginal [18, 19]. Transformation in hand, we need only prewarp the covariance of the input Gaussian process to account for the effect of the transformation on the covariance of the nonGaussian output process. In theory, this approach can be used for any finite variance nonGaussian process and a wide class of ....

....distributions. For a fast, but approximate, synthesis of positive valued LRD data based on wavelets, see [35] 5. 1 Creating a nonGaussian process from one Gaussian process By definition, the random variable Phi(X[n] is distributed uniformly on [0; 1] and we can apply the inversion principle [18, 19, 41] to synthesize a random process Y [n] with distribution F Y . Let the value X[n] have a Gaussian first order marginal distribution N(X ; oe 2 X ) and let F Y (y) be a continuous distribution function on IR with inverse F Gamma1 Y defined by [41] F Gamma1 Y (u) inf fy : F (y) u; 0 ....

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B. Liu and D. Munson, "Generation of a random sequence having a jointly specified marginal distribution and autocovariance," IEEE Trans. on Acoustics, Speech, and Signal Proc., vol. 30, pp. 973--983, Dec. 1982.

....must be added to the ARMA. Its autocorrelation structure is a discrete version of (1) The design of the ARMA system with Gaussian output is straightforward. Yet, it is impractical to solve the analytical distribution form of ffl for the ARMA to match any non Gaussian distributions. The authors in [25] proposed an approximate technique for generating random variables with a jointly specified autocovariance function and marginal distribution. This method consists of passing the output of a digital linear filter through a Zero Memory Non linear (ZMNL) device so that it s distribution is changed ....

B. Liu and D. Munson, Jr., "Generation of a Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance," IEEE Trans. on Acoust., Speech, Signal Process. Vol. ASSP-30, no. 6, pp. 973-983, Dec. 1982.

....process fY t g with a desired spectral density function S Y ( Delta) and marginal distribution f Y ( Delta) For simplicity we suppose that the mean Y of fY t g is zero. The basic idea of the method appears to have been originally suggested in Gujar and Kavanagh (1968) and developed further by Liu and Munson (1982), and Sondhi (1983) and may be illustrated thus: ffl t Gamma U(f) Gamma X t Gamma Z( Delta) Gamma Y t The input is a zero mean unit variance white noise fffl t g which is passed through the linear filter with transfer function U(f ) to produce a linear Gaussian process fX t g with zero ....

....to fs X;k g is SX (f) say, and will be given by SX (f) jU(f)j 2 ; from which suitable filter coefficients with transfer function U(f) can be found. Distortion effects due to finite length sequences will be tiny for our simulation length (1024) and exponentially decaying autocovariances (see Liu and Munson, 1982; Sondhi, 1983) 4. ESTIMATION OF SPECTRUM AT ZERO We want to estimate the quantity SZ j (0) required in (6) from a sample fW 2 j;t g: We discuss two approaches, autoregressive parametric spectrum estimation, and multitaper nonparametric spectrum estimation. We assume in both cases that the ....

Liu, B. and Munson, D. C. (1982) Generation of a Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance. IEEE Trans. Acoustics, Speech and Signal Processing , 30, 973--83.

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B. Liu and D. Munson, "Generation of a random sequence having a jointly specified marginal distribution and autocovariance," IEEE Trans. on Acoustics, Speech, and Signal Proc., vol. 30, pp. 973--983, Dec. 1982.

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B. Liu and D. Munson, Jr., "Generation of a Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance," IEEE Trans. on Acoust., Speech, Signal Process. Vol. ASSP-30, no. 6, pp. 973-983, Dec. 1982. 13

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Liu, B. and Munson, D. C. (1982) "Generation of a Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance", IEEE Transactions on Acoustics, Speech and Signal Processing 30(6), 973-983.

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