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For a Gaussian time profile, the autocorrelation width is longer than the width of the intensity, and it is 1.54 longer in the case of a hyperbolic secant squared (sech 2) pulse. This numerical factor, which depends on the shape of the pulse, is sometimes called the deconvolution factor. If this factor is known, or assumed, the time duration ...
Calibration Factor-- the factor to convert real-time to pulse delay time when viewing the output of the autocorrelator.One example of this would be 30 ps/ms in the Coherent Model FR-103 scanning autocorrelator, which suggests that a 30 ps pulse autocorrelation width would produce a 1 ms FWHM trace when viewed on an oscilloscope.
The traditional test for the presence of first-order autocorrelation is the Durbin–Watson statistic or, if the explanatory variables include a lagged dependent variable, Durbin's h statistic. The Durbin-Watson can be linearly mapped however to the Pearson correlation between values and their lags. [ 12 ]
The product of two Gaussian functions is a Gaussian, and the convolution of two Gaussian functions is also a Gaussian, with variance being the sum of the original variances: = +. The product of two Gaussian probability density functions (PDFs), though, is not in general a Gaussian PDF.
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum ...
In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation function) or 1/f noise.
In EViews, this test is already done after a regression, at "View" → "Residual Diagnostics" → "Serial Correlation LM Test". In Julia, the BreuschGodfreyTest function is available in the HypothesisTests package. [10] In gretl, this test can be obtained via the modtest command, or under the "Test" → "Autocorrelation" menu entry in the GUI ...
Many stochastic processes can be completely characterized by their correlation functions; the most notable example is the class of Gaussian processes. Probability distributions defined on a finite number of points can always be normalized, but when these are defined over continuous spaces, then extra care is called for.