Product autoregression: a time-series characterization of the gamma distribution

1982 ◽  
Vol 19 (2) ◽  
pp. 463-468 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Gamma Distribution ◽  
Stationary Stochastic Process ◽  
Correlation Structure ◽  
First Order ◽  
Non Linear ◽  
Autoregressive Correlation

A non-linear stationary stochastic process {Xt} is derived and shown to have the property that both the processes {Xt} and {log Xt} have the same correlation structure, viz. the Markov or first-order autoregressive correlation structure. The generation of such processes is discussed briefly and a characterization of the gamma distribution is obtained.

Product autoregression: a time-series characterization of the gamma distribution

1982 ◽  
Vol 19 (02) ◽  
pp. 463-468 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Gamma Distribution ◽  
Stationary Stochastic Process ◽  
Correlation Structure ◽  
First Order ◽  
Non Linear ◽  
Autoregressive Correlation

A non-linear stationary stochastic process {Xt } is derived and shown to have the property that both the processes {Xt } and {log Xt } have the same correlation structure, viz. the Markov or first-order autoregressive correlation structure. The generation of such processes is discussed briefly and a characterization of the gamma distribution is obtained.

Detection and characterization of changes of the correlation structure in multivariate time series

2005 ◽  
Vol 71 (4) ◽  
Author(s):  
Markus Müller ◽  
Gerold Baier ◽  
Andreas Galka ◽  
Ulrich Stephani ◽  
Hiltrud Muhle
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Correlation Structure

Characterization of a class of second-order density functions

1967 ◽  
Vol 4 (1) ◽  
pp. 123-129 ◽  
Author(s):  
C. B. Mehr
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Gaussian Distribution ◽  
Random Variables ◽  
Second Order ◽  
Independent Random Variables ◽  
Density Functions ◽  
Linear Filtering ◽  
Non Linear

Distributions of some random variables have been characterized by independence of certain functions of these random variables. For example, let X and Y be two independent and identically distributed random variables having the gamma distribution. Laha showed that U = X + Y and V = X | Y are also independent random variables. Lukacs showed that U and V are independently distributed if, and only if, X and Y have the gamma distribution. Ferguson characterized the exponential distribution in terms of the independence of X – Y and min (X, Y). The best-known of these characterizations is that first proved by Kac which states that if random variables X and Y are independent, then X + Y and X – Y are independent if, and only if, X and Y are jointly Gaussian with the same variance. In this paper, Kac's hypotheses have been somewhat modified. In so doing, we obtain a larger class of distributions which we shall call class λ1. A subclass λ0 of λ1 enjoys many nice properties of the Gaussian distribution, in particular, in non-linear filtering.

scholarly journals ON SEQUENTIAL ESTIMATION AND PREDICTION FOR DISCRETE TIME SERIES

2007 ◽  
Vol 07 (04) ◽  
pp. 417-437 ◽  
Author(s):  
GUSZTÁV MORVAI ◽  
BENJAMIN WEISS
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Recent Work ◽  
Discrete Time ◽  
Sequential Estimation ◽  
Stationary Stochastic Process ◽  
Stopping Times ◽  
Estimation And Prediction ◽  
Discrete Time Series ◽  
Points Of View

The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process X0,X1,…,Xn has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for P(Xn+1|X0,X1,…,Xn) can be found which converges to the true estimator almost surely. Despite this result, for restricted classes of processes, or for sequences of estimators along stopping times, universal estimators can be found. We present here a survey of some of the recent work that has been done along these lines.

scholarly journals Integration of Attributes from Non-Linear Characterization of Cardiovascular Time-Series for Prediction of Defibrillation Outcomes

PLoS ONE ◽  
2016 ◽  
Vol 11 (1) ◽  
pp. e0141313 ◽  
Author(s):  
Sharad Shandilya ◽  
Michael C. Kurz ◽  
Kevin R. Ward ◽  
Kayvan Najarian
Keyword(s):  
Time Series ◽  
Non Linear

Uniformly distributed first-order autoregressive time series models and multiplicative congruential random number generators

1992 ◽  
Vol 29 (4) ◽  
pp. 896-903 ◽  
Author(s):  
A. J. Lawrance
Keyword(s):  
Time Series ◽  
Random Number ◽  
Autoregressive Process ◽  
Noise Component ◽  
Random Number Generators ◽  
Order Linear ◽  
First Order ◽  
Uniformly Distributed Sequence ◽  
Non Linear ◽  
Scatter Plots

The work is concerned with the first-order linear autoregressive process which has a rectangular stationary marginal distribution. A derivation is given of the result that the time-reversed version is deterministic, with a first-order recursion function of the type used in multiplicative congruential random number generators, scaled to the unit interval. The uniformly distributed sequence generated is chaotic, giving an instance of a chaotic process which when reversed has a linear causal and non-chaotic structure. An mk-valued discrete process is then introduced which resembles a first-order linear autoregressive model and uses k-adic arithmetic. It is a particular form of moving-average process, and when reversed approximates in m a non-linear discrete-valued process which has the congruential generator function as its deterministic part, plus a discrete-valued noise component. The process is illustrated by scatter plots of adjacent values, time series plots and directed scatter plots (phase diagrams). The behaviour very much depends on the adic number, with k = 2 being very distinctly non-linear and k = 10 being virtually indistinguishable from independence.

Characterization of the formation of base sheet paper using spectral moments determined from time-series models

1977 ◽  
Vol 82 (2) ◽  
pp. 261-272
Author(s):  
Warren R. Devries ◽  
S. M. Wu
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Continuous Time ◽  
Light Transmission ◽  
Time Series Models ◽  
Flock Size ◽  
Spectral Moments ◽  
Fibre Distribution ◽  
Moments Estimates

The fibre distribution in a sheet of paper, referred to as the formation, is largely the result of turbulence, a stochastic process. Continuous time-series models developed from discrete light-transmission profiles are used to characterize formation. The models are used to obtain explicit expressions for the spectral moments of the profiles. From the moments, estimates of two characteristic lengths of the fibre distribution can be obtained and are interpreted as the average and largest flock size. These lengths are used to develop an index for evaluating the formation of four samples of base sheet paper. The results of this characterization agree with other methods, but this technique has the advantage of providing a physical interpretation of the index.

RELIABILITY OF DETERIORATED MARINE STRUCTURES BASED ON MEASURED DATA

2021 ◽  
Vol 158 (A4) ◽  
Author(s):  
Y Garbatov ◽  
C Guedes Soares
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Initial Period ◽  
Linear Increase ◽  
General Corrosion ◽  
Marine Structures ◽  
Depth Data ◽  
Reliability Estimates ◽  
Non Linear ◽  
Spectral Density Functions

Reliability assessment of a corroded deck of a tanker ship subjected to non-linear general corrosion wastage is performed, accounting for an initial period without corrosion due to the presence of a corrosion protection system, and a non-linear increase in wastage up to a steady state value. The reliability model is based on the analysis of corrosion depth data. Two types of uncertainties are accounted for. The first one is related to the corrosion degradation trend as a function of time, which is identified by a sequence independent data analysis. The second uncertainty is related to the variation of the corrosion degradation around its trend, which is identified as a stochastic process, and is defined based on the time series analysis. The time series determines the autocorrelation and spectral density functions of the stochastic process applying the Fast Fourier transform. The reliability estimates with respect to a corroded deck of cargo tank of a tanker ship is analysed by a time variant formulation and the effect of inspections is also incorporated employing the Bayesian updating formulation.

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