Partial autocorrelation

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Topic: Partial autocorrelation

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	CHAPTER 7. AUTOCORRELATION IN TIME SERIES
		For example, the partial autocorrelation coefficient for order k=5 is computed in such a manner that the effects of the k=1, 2, 3, and 4 partial autocorrelations have been excluded.
		Autocorrelation order k=3 would be for the correlation between each entry and the third from it in the series, and so on.
		One means for identifying and assessing the strength of autocorrelation in a time series is to compute the coefficients of autocorrelation between pairs of entries within the series.
	facweb.furman.edu /~dstanford/forecast/h7.htm

	6.4.4.6.3. Partial Autocorrelation Plot
		The partial autocorrelation plot is demonstrated in the Negiz data case study.
		If the sample autocorrelation plot indicates that an AR model may be appropriate, then the sample partial autocorrelation plot is examined to help identify the order.
		Specifically, partial autocorrelations are useful in identifying the order of an autoregressive model.
	www.6sigma.us /handbook/pmc/section4/pmc4463.htm

	AutoCorrelation (JMSL Numerical Library)
		for k = 1,..., K is the sample partial autocorrelation function.
		One method (Bartlett 1946) is based on a general asymptotic expression for the variance of the sample autocorrelation coefficient of a stationary time series with independent, identically distributed normal errors.
		A second method (Moran 1947) utilizes an exact formula for the variance of the sample autocorrelation coefficient of a random process with independent, identically distributed normal errors.
	vni.com /products/imsl/jmsl/v30/api/com/imsl/stat/AutoCorrelation.html

	The Partial Autocorrelation Function
		The approximation for a standard error for the estimated partial autocorrelation function at lag k is based on a null hypothesis that a pure autoregressive Gaussian process of order k-1 generated the time series.
	www.asu.edu /sas/sasdoc/sashtml/ets/chap7/sect26.htm

	R: Autocovariance and Autocorrelation Function Estimation
		is the function used for the partial autocorrelations.
		computes (and by default plots) estimates of the autocovariance or autocorrelation function.
		function to be called to handle missing values.
	www.eco.utexas.edu /doc/R/library/ts/html/acf.html

	AutoCorrelation (JMSL Numerical Library)
		for k = 1,..., K is the sample partial autocorrelation function.
		One method (Bartlett 1946) is based on a general asymptotic expression for the variance of the sample autocorrelation coefficient of a stationary time series with independent, identically distributed normal errors.
		A second method (Moran 1947) utilizes an exact formula for the variance of the sample autocorrelation coefficient of a random process with independent, identically distributed normal errors.
	vni.com /products/imsl/jmsl/v30/api/com/imsl/stat/AutoCorrelation.html

	R: periodic partial autocorrelation function
		When the period, p=1, this reduces to the usual partial autocorrelation function as defined in Box and Jenkins (1976) and is equivalent then to the Splus function acf(type="partial").
		The periodic partial autocorrelation function of a periodic time series is calculated and plotted if the argument plot=TRUE.
		Note that our partial autocorrelation is the negative of that given in Sakai's paper.
	www.maths.lth.se /help/R/.R/library/pear/html/pepacf.html

	Estimating the Differencing Parameter Via the Partial Autocorrelation Function (ResearchIndex)
		We construct a new estimator for the di!erencing parameter based on the partial autocorrelation...
		This is because for all n strictly bigger than 1, the nth-order autocorrelation function does not depend uniquely on the di!erencing parameter.
		(1996, Journal of Econometrics 71, 249}264) that a substantial e$ciency loss occurs if low-order autocorrelations are omitted when estimating the di!erencing parameter, d.
	citeseer.lcs.mit.edu /chong00estimating.html

	6.4.4.6. Box-Jenkins Model Identification
		For higher-order autoregressive processes, the sample autocorrelation needs to be supplemented with a partial autocorrelation plot.
		The partial autocorrelation of an AR(p) process becomes zero at lag p+1 and greater, so we examine the sample partial autocorrelation function to see if there is evidence of a departure from zero.
		This is usually determined by placing a 95% confidence interval on the sample partial autocorrelation plot (most software programs that generate sample autocorrelation plots will also plot this confidence interval).
	www.itl.nist.gov /div898/handbook/pmc/section4/pmc446.htm

	lab3.rtw
		* * In this lab, we use RATS to estimate the autocorrelation * and partial autocorrelation functions of several * macroeconomic time series.
		* * As we have discussed in lecture, the sample autocorrelation * function (SACF) and the sample partial autocorrelation * function (SPACF) can be useful tools for deciding on an * appropriate ARMA(p,q) model of a macroeconomic time series.
		* In particular, we'd like to find an ARMA(p,q) model that whose * theoretical autocorrelation function (ACF) and theoretical * partial autocorrelation function (PACF) is similar to the * SACF and SPACF.
	www.uncg.edu /eco/pmbearse/eco648/lab3.rtw

	acf
		type: a character string: "covariance" to estimate the autocovariance function, "correlation" for the autocorrelation function, or "partial", if the partial autocorrelation function is desired.
		plot: If TRUE, the autocovariance or autocorrelation function between pairs of univariate series will be plotted in an array of at most 5 by 5 plots per page.
		For the autocorrelation function, all covariances are further divided by the geometric mean of the corresponding variances.
	dmawww.epfl.ch /~gauthier/cours/IMC/dir/acf

	Common Correlation and Reliability Analysis with SPSS for Windows
		A partial autocorrelation reveals the precise autocorrelation of a series with itself without the confounding effects of intervening lagged autocorrelation.
		As for the kinds of variables, the kinds are dependent on the level of measurement of the answer categories to the questions that form the variables in the analysis.
		The coefficient of determination is a measure of the strength of the relationship between the predicted variable and model of the predictors in a regression model.
	www.nyu.edu /its/socsci/Docs/correlate.html

	MATHEMATICS DEPARTMENT
		Classical techniques of Time Series Analysis, Different Smoothing Techniques, General linear process, Autoregressive Processes AR(P), Moving average Process Ma(q): Autocorrelation, Partial autocorrelation and Spectrum, Identification in time domain, Forecasting, Estimation of Parameters, Model diagnostic checks, Use of time series techniques in Engg.
		Testing general linear hypotheis - testing equality of means of several normal distributions with common covariance matrix, MANOVA, testing independence of a set of variates, testing hypotheses of equality of covariance matrices.
		Banach spaces; bounded linear functionals and bounded linear operators, dual spaces, Hahn-Banach theorem, uniform boundedness principle, open mapping and closed graph theorems., weak convergence, Hilbert spaces, orthonormal sets, Riesz representation theorem, bounded linear operators on Hilbert spaces.
	www.iitkgp.ernet.in /ugcurricula/syll/math/syll.htm

	Beth Sparks-Jackson
		Spatial autocorrelation, variogram analyses, and use of the Mantel’s test can provide measures that are explicit functions of spatial scale and capture long-neglected aspects of spatial heterogeneity in river assemblages.
		Positive spatial autocorrelation, loosely defined as "the property of random variables taking values at a certain distance apart that are more similar than expected for randomly associated pairs of observations" (Legendre 1993) is likely common in river systems but poorly studied and understood.
		Table 1: A partial list of studies with sufficient data available to complete spatial analysis.
	www-personal.umich.edu /~danbrown/nre543/sparksb.html (3361 words)

	Poisson's equation
		Figure 1 Deconvolution by a filter whose autocorrelation is the two-dimensional Laplacian operator.
		As a simple illustration of how helical boundary conditions can lead to recursive solutions to partial differential equations, we consider Poisson's equation, which relates potential, u, to source density, f, through the Laplacian operator:
		Poisson's equation crops up in many different branches of physics: for example, in electrostatics, gravity, fluid dynamics (where the fluids are incompressible and irrotational), and steady-state temperature studies.
	sepwww.stanford.edu /public/docs/sep97/james3/paper_html/node2.html (193 words)

	Prediction Of Epileptic Seizures With Linear And Nonlinear Analysis Of EEG (ResearchIndex)
		Abstract: A set of linear and nonlinear methods (autocorrelation, linear prediction, mutual information, false nearest neighbors, local linear prediction, estimation of the largest Lyapunov exponent and the correlation dimension) is applied to multichannel scalp EEG records from 7 epileptic patients for the prediction of epileptic seizures of generalized tonic-clonic and complex partial type.
		The data were sampled a couple of minutes prior to the seizure onset and in many cases also longer before...
		4 Nonlinear dynamics of epileptic seizures on basis of intracr..
	citeseer.ist.psu.edu /394574.html (511 words)

	Prediction Of Epileptic Seizures With Linear And Nonlinear Analysis Of EEG (ResearchIndex)
		Abstract: A set of linear and nonlinear methods (autocorrelation, linear prediction, mutual information, false nearest neighbors, local linear prediction, estimation of the largest Lyapunov exponent and the correlation dimension) is applied to multichannel scalp EEG records from 7 epileptic patients for the prediction of epileptic seizures of generalized tonic-clonic and complex partial type.
		The data were sampled a couple of minutes prior to the seizure onset and in many cases also longer before...
		4 Nonlinear dynamics of epileptic seizures on basis of intracr..
	citeseer.ist.psu.edu /394574.html (511 words)

	Phylogeographical autocorrelation of phenotypic evolution in honey bees (Apis mellifera L.)
		In general terms, the partial regression slopes indicated that the variation in the characters traditionally associated with adaptive processes, such as body and wing size, were better explained by geographical position.
		Data on 39 phenotypic traits, derived from 417 colonies grouped into 14 subspecies, were analysed using autocorrelation methods.
		For the analysis of each trait, the effects of the geographical co-ordinates (latitude and longitude of subspecies geographical range) and of the phylogenetic patterns (defined by eigenvectors of the genetic distance matrix) on phenotypic variation were simultaneously analysed using an extension of a recently developed model, called Phylogenetic Eigenvector Regression (PVR).
	www.nature.com /cgi-taf/DynaPage.taf?file=/hdy/journal/v83/n6/abs/6886080a.html (511 words)

	Jacobson, Alexander Donald (1964-01-01) On the theory of noise-like electromagnetic fields of arbitrary spectral width. http://resolver.caltech.edu/CaltechETD:etd-09132002-124223
		Moreover, to make it applicable to fields of arbitrary spectral width, the theory is formulated in terms of a spectral representation, rather than directly in terms of the autocorrelation function of the vector field.
		In particular, a statistical analysis of partial polarization is presented with the aim of providing a physical interpretation of the polarization of a quasi-monochromatic field.
		A mathematical theory of noise-like electromagnetic fields of arbitrary spectral width is formulated.
	etd.caltech.edu /etd/available/etd-09132002-124223 (290 words)

	New Page
		The Mantel test and Partial Mantel test allow one to distinguish among these three cases by assessing the extent of spatial autocorrelation among subjects.
		The test statistic is calculated by constructing a matrix of residuals, A’, of the regression between A and C, and a matrix of residuals, B’, of the regression between B and C.
		The Mantel test computes a correlation between two n by n distance matrices, where one matrix might represent spatial distances, for example, while the other represents differences between pairs of plants in some measure of plant status (e.g., mass).
	userwww.sfsu.edu /~efc/classes/biol710/spatial/spatial.htm (290 words)

	lpchlac.html
		The LPC technique is used to represent the image sequence as a collection of the partial correlation (PARCOR) coefficients for each pixel intensity change over time, forming the PARCOR images.
		In solving these LPC parameters, our lipreading system uses the autocorrelation method which is most commonly used along with the covariance method in speech recognition.
		In speech recognition, linear predictive analysis approximates the speech sample as a linear combination of past speech samples, and by minimizing the sum of the squared differences (over a finite interval) between the actual samples and the linear predictive ones, a unique set of predictor coefficients can be determined.
	www.csse.uwa.edu.au /~eunjung/LPCproj/lpchlac.html (750 words)

	Brief Biography
		Subspace methods for spectral analysis can be adapted to the case where state-covariance matrix replaces the traditional Toeplitz matrix formed out of a partial autocorrelation sequence of a time-series.
		We use scalp EEG recordings of subjects where they are asked to imagine left or right hand movement.
		The results confirm the hypothesis that source analysis methods may improve accuracy for classification of motor imagery tasks.
	www.ece.umn.edu /users/nasiri/Biography.htm (1188 words)

	upcomingseminar.html
		The Burg algorithm estimates the partial autocorrelation by minimizing a sum of squares of observed forward and backward prediction errors, while Yule-Walker algorithm calculates it recursively using the estimated autocovariances up to lag
		The Burg estimator can be considered as the least-squares estimator constrained by the Durbin-Levinson recursion.
		Using computer algebra the biases to O (1/n) of these three estimators in AR(1) and AR(2) models is derived.
	www.mathstat.dal.ca /~hgu/upcomingseminar.html (382 words)

	Regression with dummy variables (in MARION)
		Special topics in the use of dummy variables -- Dummy variables in logit models -- Testing for curvilinearity -- Piecewise linear regression -- Dummy variables in time-series data -- Dummy variables and autocorrelation -- 7.
		Creating dummy variables -- Choosing a reference group -- Descriptive statistics -- Distributional statistics -- Correlation -- Partial correlations -- 3.
		Using dummy variables as regressors -- Regression with one dummy variable -- Regression with multiple dummy variables -- Assessing differences between specified categories -- Adding a second qualitative measure -- Predicted values -- Adding quantitative variables to the specification -- 4.
	library.tnstate.edu /MARION/ACO-2639 (382 words)

	Autoregressive and Distributed Lag Models
		Not to mention the estimation problem associated with the possible autocorrelation, the interpretation is quite different with the adaptive expectations model.
		Substitute the desired consumption equation into the partial adjustment, we have
		In appearance, this autoregressive model is not different from the adaptive expectations model.
	www.hkbu.edu.hk /%7Ebillhung/econ3600/application/app07/app07A_2.html (443 words)

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