
Review of Short Phrases and Links 
This Review contains major "Autocorrelation" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 Autocorrelation is a mathematical tool used frequently in signal processing for analysing functions or series of values, such as time domain signals.
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 The autocorrelation is a Hermitian operator since .
 The autocorrelation is a function (of j) while the autocovariance is a number.
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 Autocorrelation is a method for identifying timerelated patterns within a data set.
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 Autocorrelation is an interesting concept and is very useful in attempting to observe patterns in timeseries data.
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 The spatial autocorrelation was calculated using Moran's I with contiguity as well as distance weighting.
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 In geographic applications there is usually positive spatial autocorrelation.
 In order to incorporate distance as a measure of spatial autocorrelation we use contiguity as well as distance to define the weighting function.
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 If the ordinary DurbinWatson test indicates no firstorder autocorrelation, you can use the secondorder test to check for secondorder autocorrelation.
 In this case, the firstorder DurbinWatson test is highly significant, with p < .0001 for the hypothesis of no firstorder autocorrelation.
 Small values of the DurbinWatson statistic indicate the presence of autocorrelation.
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 The autocorrelogram indicates that we removed too much of the lag 1 and lag 12 components, as they have now negative autocorrelation coefficients.
 Responses to autocorrelation include differencing of the data and the use of lag structures in estimation.
 Since autocorrelation is a specific type of crosscorrelation, it maintains all the properties of crosscorrelation.
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 CORR, a numeric variable containing the autocorrelation or crosscorrelation function values.
 These methods include autocorrelation and crosscorrelation of time series.
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 As the lag increases, the autocorrelation function of shortrange dependent processes decays quickly.
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 When a process is under minimum variance control, the autocorrelation function is zero for all lags greater than the process deadtime.
 Structure in the autocorrelation function may provide clues about what is causing the clusters of packet drops from an individual mailbox queue.
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 The only difference then is whether other methods like Fourier analysis might give you more information than the autocorrelation function.
 The autocorrelation of a periodic function is, itself, periodic with the very same period.
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 Negative autocorrelation means standard errors are too large.
 Scaling The type of scaling for the autocorrelation: None, Biased, Unbiased, or Unity at zerolag.
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 As such, interpolation was performed only where this was true for both autocorrelation statistics.
 Strong autocorrelation in the squared returns is also a symptom of changing unconditional or conditional 4 variance.
 When normalised by dividing by the variance  2 then the autocovariance becomes the autocorrelation R( k).
 It is common practice in many disciplines to drop the normalisation by  2 and use the term autocorrelation interchangeably with autocovariance.
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 Autocorrelation: Autocorrelation is the serial correlation of equally spaced time series between its members one or more lags apart.
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 In order to confirm this trend we are going to analyse the autocorrelation function of the series.
 Computes the sample autocorrelation function of a stationary time series.
 In addition, autocorrelation plots are used in the model identification stage for BoxJenkins autoregressive, moving average time series models.
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 AutoCorrelation.NonPosVariancesException  exception com.imsl.stat.
 AutoCorrelation(double[], int)  Constructor for class com.imsl.stat.
 In a sample, the kth autocorrelation is the OLS estimate that results from the regression of the data on the kth lags of the data.
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 There are relatively well known adjustments for the variance estimates in OLS that are robust to general forms of heteroskedasticity or autocorrelation.
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 Alternatively, signals that last forever can be treated by a shorttime autocorrelation function analysis, using finite time integrals.
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 Formally, the discrete autocorrelation R at lag j for signal xn is Figure3(3)(Wikipedia 2006) where m is the average value (expected value) of xn.
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 This test is based on the autocorrelation plot and is commonly used in the context of ARIMA modeling.
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 Autocorrelation plots are also used in the model identification stage for fitting ARIMA models.
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 Spatial autocorrelation can be analyzed using correlograms, covariance functions and variograms (=semivariograms).
 Kriging models use a semivariogram to depict the spatial autocorrelation between measured sample points.
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 Spatial autocorrelation statistics are used to describe the relationships between data observed at different geographic locations.
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 The table below summarizes the results of spatial autocorrelation tests, variogram fitting, and kriging cross validation.
 Both spatial error autocorrelation as well as heteroskedasticity are therefore incorporated in the SAR model.
 The Autocorrelation block does not accept a samplebased fulldimension matrix input.
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 The block computes the autocorrelation along each column of a framebased input, and computes along the vector dimension of a samplebased vector input.
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 The following diagram shows the data types used within the Autocorrelation block for fixedpoint signals.
 Maximum nonnegative lag (less than input length) Specify the maximum positive lag, l, for the autocorrelation.
 Compute all nonnegative lags Select to compute the autocorrelation over all nonnegative lags in the range [ 0, length(input)1].
 In statistics, the autocorrelation function (ACF) of a random process describes the correlation between the process at different points in time.
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 However, correlation is limited to autocorrelation in a single variable.
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 This patent does not employ autocorrelation or cross correlation and does not use a quality control chart.
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 The autocorrelation plot is an excellent way of checking for such randomness.
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 The plot consists of: Vertical axis = subsample autocorrelation; Horizontal axis = subsample index.
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 The autocorrelation function and cross correlation function are normalized versions of the autocovariance and cross covariance functions.
 However, the user also cannot inspect any time series functions such as the autocorrelation function, cross covariance function, power spectrum, etc.
 The continuous autocorrelation function reaches its peak at the origin, where it takes a real value, i.e.
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 The Autocorrelation block accepts both real and complex floatingpoint inputs.
 Spatial autocorrelation statistics can be calculated for polygon as well as point coverages.
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 Arc Attribute Tables and Polygon Attribute Tables), and these tables are very useful for calculating various autocorrelation statistics.
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Definition
 Different definitions of autocorrelation are in use depending on the field of study which is being considered and not all of them are equivalent.
 I have tried to reconcile the differing definitions of autocorrelation in different disciplines.
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 An appropriate test for residual autocorrelation is provided by the LM test in § 18.4.3 below.
 The LM tests for autocorrelation, heteroscedasticity and functional form require an auxiliary regression involving the original regressors x it.
 This output has the same form as the autocorrelation check for white noise that the IDENTIFY statement prints for the response series.
 Inaddition, PcGive prints the partial autocorrelation function (PACF) (see the OxMetrics book).
 An indication of ARCH is that the residuals will be uncorrelated but the squared residuals will show autocorrelation.
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 It is usually used to test for autocorrelation in regression residuals rather than for spurious correlation.
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 However, the sample autocorrelation function of the squared residuals tells a different story.
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 Nonetheless, the GARCH model presented is designed to account for any heteroskedasticity and serial autocorrelation within the residuals.
Autocorrelation
 At zero time the autocorrelation function is positive since it is the means square value of the flux at equilibrium.
 Independent observations (absence of autocorrelation) leading to uncorrelated error terms.
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 We model the system as an autoregressive one, and our proposal is based on the calculation of the poles of the autocorrelation function.
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 It makes use of information extra to that usually used in 'traditional' signal processing measures such as the power spectrum and autocorrelation function.
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