By Douglas M. Patterson
The complicated dynamic habit exhibited through many nonlinear structures - chaos, episodic volatility bursts, stochastic regimes switching - has attracted a great deal of realization lately. A Nonlinear Time sequence Workshop offers the reader with either the statistical heritage and the software program instruments helpful for detecting nonlinear habit in time sequence facts. the main worthy present detection thoughts are defined, together with Engle's LaGrange Multiplier try out for conditional hetero-skedasticity and checks in keeping with the correlation size and at the predicted bispectrum. those suggestions are illustrated utilizing real information from fields comparable to economics, finance, engineering, and geophysics.
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Additional info for A Nonlinear Time Series Workshop: A Toolkit for Detecting and Identifying Nonlinear Serial Dependence
The taper parameter is expressed as a whole percentage also, and it represents the percentage of data points at the beginning and end of the series that are tapered with one-haifa cosine bell. We recommend that, if tapering is used, the percentage be kept relatively small, about 10 - 15%. Both the clipping and tapering parameters were set to zero in the calculations reported here. The smoothing width, m, is the width of the square used to smooth the bispectrum in the frequency domain ; the program sets m equal to the integer nearest to NI-e.
438 SIG. 530 SIG. 266 SIG. 156 SIG. cnl, contains the information the program needs to run the tests as desired by the user. All parameters and input data are read in free format; the user need not worry about what column each number starts or ends in - just separate each number by at least one space . All values are to be entered as integers (no decimal point) unless otherwise noted . cnl file in the distribution package. Looking at this file (or the example in Figure 3-1) you can see that comments can be added to each line after the data; similarly, an informative label can be added to the input data file after the last datum .
TSAYTEST The Tsay (1986) test is a generalization of the Keenan (1985) test; it explicitly looks 42 A Nonlinear Time Series Workshop for quadratic serial dependence in the data . Let the K = k(k-l )/2 column vectors V •... , Xl_j, where i E [1, k] andj E [i, k]. Thus, Vt,1 = X~_I; Vt,2 XI. _. , ... , Xt_k' The parameters Y•... ) since it is prewhitened using an AR(p) model" . The Tsay test statistic is then just the usual F statistic for testing the null hypothesis that YI ... YK are all zero. } is a realization from a third-order stationary stochastic process and tests for serial independence using the sample bicovariances of the data.
A Nonlinear Time Series Workshop: A Toolkit for Detecting and Identifying Nonlinear Serial Dependence by Douglas M. Patterson