## Chapter 8 Software

Available here are the MATLAB scripts (programs) used to fit the VCZAR model to the irregularly observed example series of Extinctions and Originations, together with the MATLAB functions used in these scripts. The scripts and function files can be downloaded from the two zipped files listed at the foot of this page. The text files of the example series are included with the scripts. A third zip file contains a number of further test scripts, for testing or checking some of the functions. Links to the pdf files of documentation for the scripts and functions are included in this page.

The main function for fitting the model is VCZARestimate.m. This is used in three scripts, firstly ExtOrigOrdersAIC.m to select the model order, then ExtOrigKappasDEV.m to select the time scale parameter kappa, and finally ExtOrigBookModelFit.m to fit and refine the model. A further script ExtOrigBookModelProperties.m computes and displays the model properties graphically. The document BookExampleCh8 explains these steps. The script ExtOrigBookModelInterp.m constructs and displays the filtered and smoothed model states which are estimated at intermediate time points using the function VCZstateFilterSmooth.m.Â The document SmoothingInterpolation explains the usage of this function and its application in the script, and also explains how the test script VCZARsmoothtest.m checks these computations.

The document VCZARestimation describes the usage of the function VCZARestimate.m for maximum likelihood estimation of the VCZAR model, and most of the subsidiary functions called by VCZARestimate.m. It further documents a variation VCZARestimate_reml.m on this function, used for residual maximum likelihood estimation, and similar variations on some of the subsidiary functions.

There are further functions described as utilities which are more widely used than the subsidiary functions; several of them compute model properties. Their usage is described in the document VCZARutilities which also describes two test scripts for some of these functions: VCZARMapTest.m and VCZARCovSpecTest.m.

Finally, there are five functions used to compute the integral of the continuous time state transition equation over a discrete time step. These are described in the document TransitionIntegration. There is a test script TransitionTest.m which checks the accuracy and comparative timings of these functions. There is a document CSSTransitionAlgorithmÂ provided also on the pages of the Algorithms and Technical material for Chapter 8, which explains their computations and presents the results of the test script. A further document also on these pages is GaussianEstimation, which explains the methodology used in the non-linear estimation of the VCZAR model.