# HSMM pseudo-residuals Pseudo-residuals based on the one-step ahead forecast distributions under the HSMM which was estimated using `pmleHSMM`. This function can only be used for HSMMs with state-dependent normal or gamma distributions. ```r pseudoResHSMM(y, mod) ``` ## Arguments - `y`: vector containing the observations. - `mod`: model object as returned by `pmleHSMM`. ## Returns Returns a vector containing the forecast pseudo-residuals. ## Details A good model fit is indicated by standard normally distributed pseudo-residuals. ## References For more details about pseudo-residuals in the context of HMMs, see: Zucchini, W., MacDonald, I.L. and Langrock, R. (2016): **Hidden Markov models for time series: An introduction using R**. 2nd edition. Chapman & Hall/CRC, Boca Raton. ## Examples ```r # running this example might take a few minutes # # 1.) 2-state gamma-HSMM for hourly muskox step length # with an unstructured start of length of 10 # # initial values p_list0<-list() p_list0[[1]]<-c(dgeom(0:9,0.2),1-pgeom(9,0.2)) p_list0[[2]]<-c(dgeom(0:9,0.2),1-pgeom(9,0.2)) mu0<-c(5,150) sigma0<-c(3,180) # # fit 2-state gamma-HSMM with lambda=c(100,100) # and difference order 3 # estimation might take a few minutes PHSMM<-pmleHSMM(y=muskox$step,N=2,p_list=p_list0,mu=mu0, sigma=sigma0,lambda=c(100,100),order_diff=3, y_dist='gamma') # # pseudo-residuals pseudoRes<-pseudoResHSMM(y=muskox$step,PHSMM) hist(pseudoRes,probability=TRUE) z<-seq(-3,3,0.01) lines(z,dnorm(z),col='blue') # running this example might take a few minutes # # 2.) 3-state gamma-HSMM for hourly muskox step length # with an unstructured start of length of 10 # # initial values p_list0<-list() p_list0[[1]]<-c(dgeom(0:9,0.2),1-pgeom(9,0.2)) p_list0[[2]]<-c(dgeom(0:9,0.2),1-pgeom(9,0.2)) p_list0[[3]]<-c(dgeom(0:9,0.2),1-pgeom(9,0.2)) omega0<-matrix(0.5,3,3) diag(omega0)<-0 mu0<-c(5,100,350) sigma0<-c(3,90,300) # # fit 3-state gamma-HSMM with lambda=c(1000,1000,1000) # and difference order 3 # estimation might take some minutes PHSMM<-pmleHSMM(y=muskox$step,N=3,p_list=p_list0,mu=mu0, sigma=sigma0,omega=omega0, lambda=c(1000,1000,1000), order_diff=3,y_dist='gamma') # # pseudo-residuals pseudoRes<-pseudoResHSMM(y=muskox$step,PHSMM) hist(pseudoRes,probability=TRUE) z<-seq(-3,3,0.01) lines(z,dnorm(z),col='blue') ```

pseudoResHSMM function