R/ForecastHMMCdf.R

In GenHMM1d: Goodness-of-Fit for Univariate Hidden Markov Models

#'@title Forecasted cumulative distribution function of a univariate HMM at times n+k1, n+k2,....
#'
#'@description This function computes the forecasted cumulative distribution function of a univariate HMM for multiple horizons, given observations up to time n
#'
#'@param y  points at which the cdf function is comptuted
#'@param family    distribution name; run the function distributions() for help
#'@param theta parameters; (r  x p)
#'@param Q    probability transition  matrix; (r  x r)
#'@param eta    vector of the estimated probability of each regime at time n; (1 x r)
#'@param k  times of prediction.
#'@param graph (0 or else) produce plots
#'
#'@return \item{cdf}{values of the cdf function}
#'
#'
#'@examples
#'family = "gaussian"
#'lb = -6
#'ub = 6
#'
#'
#'theta = matrix(c(-1.5, 1.7, 1, 1),2,2)
#'Q = matrix(c(0.8, 0.3, 0.2, 0.7), 2, 2)
#'eta = c(0.96091218, 0.03908782)
#'
#'forecastedhmmcdf = ForecastHMMCdf(y=seq(from=-6, to=6, by=0.1), family=family,
#' theta= theta, Q=Q, eta=eta, k=c(1,5,10,20), graph=1)
#'
#'
#'@export

ForecastHMMCdf<-function(y, family, theta, Q, eta, k=1, graph=0){

  if(is.null(dim(Q))){
    QQ0 = matrix(Q)
    r = dim(QQ0)[1]
  } else {
    r = dim(Q)[2]
  }

  cdf = matrix(0, nrow=length(y), ncol=length(k))

  for (d in 1:length(k)){
    Q_prime = matrixcalc::matrix.power(Q, as.integer(k[d]))
    for (l in 1:r){
      for (j in 1:r){
        cdf[,d] = cdf[,d] + eta[j] * Q_prime[j, l] * CDF(family, y, theta[l,])
      }
    }
  }


  if (graph != 0){
          df = data.frame(cdf)
          colnames(df) = as.character(k)
          df$index = y
          df = reshape2::melt(df ,  id.vars = 'index', variable.name = 'horizon')
          print(
          ggplot2::ggplot(df, ggplot2::aes(df$index,df$value)) + ggplot2::geom_line(ggplot2::aes(colour = df$horizon)) +
            ggplot2::theme(panel.grid = ggplot2::element_blank(),
                  panel.background = ggplot2::element_rect(fill = "white"),
                  panel.border = ggplot2::element_rect(colour = "black", fill = NA, size = 0.2),
                  legend.position = c(.02, .95),
                  legend.justification = c("left", "top"),
                  legend.margin = ggplot2::margin(6, 6, 6, 6),
                  legend.box.background = ggplot2::element_rect(color="black", size=1),
                  legend.box.margin = ggplot2::margin(1, 1, 1, 1),
                  plot.title = ggplot2::element_text(hjust = 0.5)) +
            ggplot2::labs(title="Forecasted cumulative density function", x="observations", y="densities" )
          )
  }


  return(cdf)


}