Package HMMcopula. December 1, 2018
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1 Type Package Package HMMcopula December 1, 2018 Title Markov Regime Switching Copula Models Estimation and Goodness of Fit Version Author Mamadou Yamar Thioub Bouchra Nasri Romanic Pieugueu and Bruno Remillard Maintainer Mamadou Yamar Thioub R functions to estimate and perform goodness of fit test for several Markov regime switching and mixture bivariate copula models. The goodness of fit test is based on a Cramer von Mises statistic and uses the Rosenblatt transform and parametric bootstrap to estimate the p-value. The estimation of the copula parameters are based on the pseudo-maximum likelihood method using pseudo-observations defined as normalized ranks. License GPL (>= 2) Encoding UTF-8 LazyData true Depends matrixcalc, mvtnorm, foreach, doparallel, copula RoxygenNote NeedsCompilation no Repository CRAN Date/Publication :30:04 UTC R topics documented: dilog EstHMMCop EstKendallTau EstMixtureCop GofHMMCop
2 2 dilog GofMixtureCop KendallTau ParamCop ParamTau RosenblattClayton RosenblattFrank RosenblattGaussian RosenblattGumbel RosenblattStudent SimHMMCop SimMarkovChain SimMixtureCop SnB Tau2Rho Index 14 dilog Dilogarithm function This function computes the dilogarithm of a number. dilog(x) x a real number out dilogarithm
3 EstHMMCop 3 EstHMMCop Estimation of bivariate Markov regime switching bivariate copula model This function estimates parameters from a bivariate Markov regime switching bivariate copula model EstHMMCop(y, reg,, max_iter, eps) y reg max_iter (nx2) data matrix (observations or residuals) that will be transformed to pseudoobservations number of regimes maximum number of iterations of the EM algorithm eps precision (stopping criteria); suggestion dof Q eta tau U cvm W (1 x reg) estimated parameter of the copula according to CRAN copula package (except for Frank copula, where = log(_r_package)) for each regime (except for degrees of freedom) estimated degree of freedom, only for the Student copula (reg x reg) estimated transition matrix (n x reg) conditional probabilities of being in regime k at time t given observations up to time t estimated Kendall tau for each regime (n x 2) matrix of Rosenblatt transforms Cramer-von-Mises statistic for goodness-of-fit regime probabilities for the conditional distribution given the past Kendall s tau Examples Q <- matrix(c(0.8, 0.3, 0.2, 0.7),2,2) ; kendalltau <- c(0.3,0.7) ; data <- SimHMMCop(Q, 'clayton', kendalltau, 10)$SimData; estimations <- EstHMMCop(data,2,'clayton',10000,0.0001)
4 4 EstMixtureCop EstKendallTau Sample Kendall s tau Estimation This function estimates the sample Kendall s tau of a bivariate data matrix EstKendallTau(X) X (n x 2) matrix KendallTau estimated sample Kendall s tau of the data EstMixtureCop Estimation of bivariate mixture bivariate copula model This function estimates parameters from a mixture bivariate copula model EstMixtureCop(y, reg,, max_iter, eps) y reg max_iter (nx2) data matrix (observations or residuals) that will be transformed to pseudoobservations number of regimes maximum number of iterations of the EM algorithm eps precision (stopping criteria); suggestion
5 GofHMMCop 5 dof Q eta tau U cvm (1 x reg) estimated parameter of the copula according to CRAN copula package (except for Frank copula, where = log(_r_package)) for each component (except for degrees of freedom) estimated degree of freedom, only for the Student copula (1 x reg) estimated weights vector (n x reg) conditional probabilities of being in regime k at time t given observations up to time t estimated Kendall tau for each regime (n x 2) matrix of Rosenblatt transforms Cramer-von-Mises statistic for goodness-of-fit GofHMMCop Goodness-of-fit of Markov regime switching bivariate copula model This function performs goodness-of-fit test of a Markov regime switching bivariate copula model GofHMMCop(R, reg,, max_iter, eps, n_sample, n_cores) R reg max_iter (n x 2) data matrix that will be transformed to pseudo-observations number of regimes maxmimum number of iterations of the EM algorithm eps precision (stopping criteria); suggestion n_sample number of bootstrap; suggestion 1000 n_cores number of cores to use in the parallel computing pvalue pvalue (significant when the result is greater than 5) dof Q (1 x reg) estimated parameter of the copula according to CRAN copula package (except for Frank copula, where = log(_r_package)) for each regime (except for degrees of freedom) estimated degree of freedom, only for the Student copula (reg x reg) estimated transition matrix
6 6 GofMixtureCop eta tau U cvm W (n x reg) conditional probabilities of being in regime k at time t given observations up to time t estimated Kendall tau for each regime (n x 2) matrix of Rosenblatt transforms Cramer-von-Mises statistic for goodness-of-fit regime probabilities for the conditional distribution given the past Kendall s tau GofMixtureCop Goodness-of-fit of mixture bivariate copula model This function performs goodness-of-fit test of a mixture bivariate copula model GofMixtureCop(R, reg,, max_iter, eps, n_sample, n_cores) R reg max_iter (nx2) data matrix (observations or residuals) that will be transformed to pseudoobservations number of regimes maxmimum number of iterations of the EM algorithm eps precision (stopping criteria); suggestion n_sample number of bootstrap; suggestion 1000 n_cores number of cores to use in the parallel computing pvalue pvalue (significant when the result is greater than 5) dof Q eta tau U cvm (1 x reg) estimated parameter of the copula according to CRAN copula package (except for Frank copula, where = log(_r_package)) for each component (except for degrees of freedom) estimated degree of freedom, only for the Student copula (1 x reg) estimated weights vector (n x reg) conditional probabilities of being in regime k at time t given observations up to time t estimated Kendall tau for each regime (n x 2) matrix of Rosenblatt transforms Cramer-von-Mises statistic for goodness-of-fit
7 KendallTau 7 KendallTau Kendall s tau of a copula This function computes the Kendall s tau of a copula with a unconstrainted parameter alpha. KendallTau(, alpha) alpha "gaussian", "t", "clayton", "frank", "gumbel" unconstrainted parameters of the copula tau estimated Kendall s tau ParamCop Theta estimation This function computes the parameter of the copula according to CRAN copula package (except for Frank copula, where = log(_r_package)), corresponding to the unconstrainted parameters alpha. ParamCop(, alpha) alpha "gaussian", "t", "clayton", "frank", "gumbel" unconstrainted parameters of the copula matlab parameters
8 8 RosenblattClayton ParamTau Alpha estimation This function computes the unconstrainted parameter alpha for given Kendall s tau value ParamTau(, tau) tau Kendall s tau of the copula alpha estimated unconstrainted parameter RosenblattClayton Rosenblatt transform for Clayton copula This function computes the Rosenblatt transform fot the Clayton copula RosenblattClayton(u, ) u (n x d) matrix of pseudos-observations (normalized ranks) parameter of the Clayton copula R Rosenblatt transform
9 RosenblattFrank 9 RosenblattFrank Rosenblatt transform for Frank copula This function computes the Rosenblatt transform fot the Frank copula RosenblattFrank(U, ) U (n x d) matrix of pseudos-observations (normalized ranks) parameter of the Frank copula R Rosenblatt transform RosenblattGaussian Rosenblatt transform for Gaussian copula This function computes the Rosenblatt transform fot the Gaussian copula RosenblattGaussian(u, rho) u (n x d) matrix of pseudos-observations (normalized ranks) rho (d x d) correlation matrix, or the correlation coefficient (if, d = 2) R Rosenblatt transform
10 10 RosenblattStudent RosenblattGumbel Rosenblatt transform for Gumbel copula This function computes the Rosenblatt transform fot the Gumbel copula RosenblattGumbel(U, ) U (n x d) matrix of pseudos-observations (normalized ranks) parameter of the Gumbel copula R Rosenblatt transform RosenblattStudent Rosenblatt transform for Student copula This function computes the Rosenblatt transform fot the Student copula RosenblattStudent(u, rho, nu) u rho nu (n x d) matrix of pseudos-observations (normalized ranks) (d x d) correlation matrix degrees of freedom R Rosenblatt transform
11 SimHMMCop 11 SimHMMCop Simulation of bivariate Markov regime switching copula model This function simulates observation from a bivariate Markov regime switching copula model SimHMMCop(Q,, KendallTau, n, DoF) Q KendallTau n DoF Transition probality matrix (d x d); Kendall s rank correlation number of simulated vectors degree of freedom only for the Student copula SimData MC alpha Simulated Data Markov chain regimes parameters alpha Examples Q <- matrix(c(0.8, 0.3, 0.2, 0.7),2,2) ; kendalltau <- c(0.3,0.7) ; simulations <- SimHMMCop(Q, 'gumbel', kendalltau, 300) SimMarkovChain Markov chain simulation This function generates a Markov chain X(1),..., X(n) with transition matrix Q, starting from a state eta0 or the uniform distribution on 1,..., r SimMarkovChain(Q, n, eta0)
12 12 SimMixtureCop Q Transition probality matrix (d x d) n number of simulated vectors eta0 variable eta SimMixtureCop Simulation of bivariate mixture copula model This function simulates observation from a bivariate mixture copula model SimMixtureCop(Q,, KendallTau, n, DoF) Q KendallTau n DoF Weights vector (1 x component); Kendall s rank correlation number of simulated vectors vector of degree of freedom only for the Student copula SimData MC alpha Simulated Data Markov chain regimes parameters alpha Examples Q <- matrix(c(0.8, 0.2),1,2) ; kendalltau <- c(0.3,0.7) ; simulations <- SimMixtureCop(Q, 'gaussian', kendalltau, 300)
13 SnB 13 SnB Cramer-von Mises statistic SnB for GOF based on the Rosenblatt transform This function computes the Cramer-von Mises statistic SnB for GOF based on the Rosenblatt transform SnB(E) E (n x d) matrix of pseudos-observations (normalized ranks) Sn Cramer-von Mises statistic Tau2Rho Spearman s rho This function estimates the Spearman s rho corresponding to a constrainted (matlab) parameter for a copula. Tau2Rho(, ) parameter of the copula according to CRAN copula package (except for Frank copula, where = log(_r_package)) rho estimated Spearman s rho
14 Index dilog, 2 EstHMMCop, 3 EstKendallTau, 4 EstMixtureCop, 4 GofHMMCop, 5 GofMixtureCop, 6 KendallTau, 7 ParamCop, 7 ParamTau, 8 RosenblattClayton, 8 RosenblattFrank, 9 RosenblattGaussian, 9 RosenblattGumbel, 10 RosenblattStudent, 10 SimHMMCop, 11 SimMarkovChain, 11 SimMixtureCop, 12 SnB, 13 Tau2Rho, 13 14
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Type Package Package spatial.gev.bma February 20, 2015 Title Hierarchical spatial generalized extreme value (GEV) modeling with Bayesian Model Averaging (BMA) Version 1.0 Date 2014-03-11 Author Alex Lenkoski
1 Introduction. Amir T. Payandeh Najafabadi 1, Mohammad R. Farid-Rohani 1, Marjan Qazvini 2
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On the Systemic Nature of Weather Risk
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