R/poissonJumps.R

In shill1729/trader: Mathematical finance analysis package

#' Count the number of jumps per period above a threshold
#'
#' @param prices the time-series of close prices
#' @param jump_thresh the jump-threshold (positive)
#' @param return_type the return type "log" or "arithmetic
#' @param side the side of the jump: "up", "down" or "both"
#' @param period the period, "daily", "weekly", "monthly", "quarterly", "yearly"
#'
#' @description {Counts the number of jumps \eqn{X_n >= a} (and the other respective events) for some jump-threshold \eqn{a} for different periods}
#' @return time-series of counts per period
#' @import xts
#' @export countJumps
countJumps <- function(prices, jump_thresh = 0.01, return_type = "arithmetic", side = "down", period = "weekly")
{
  jt <- jump_thresh
  if(return_type == "log")
  {
    jt <- log(1+jump_thresh)
  }
  x <- dailyReturns(prices)[, return_type]
  indicator_up <- ifelse(x >= jt, 1, 0)
  indicator_down <- ifelse(x <= -jt, 1, 0)
  indicator_both <- ifelse(abs(x) >= jt, 1, 0)
  indicator <- eval(as.name(paste("indicator_", side, sep = "")))
  apply_period <- paste("apply.", period, sep = "")
  apply_period <- get(apply_period, envir = environment(xts))
  jump_counts <- apply_period(indicator, sum)
  return(jump_counts)
}


#' Ad-hoc Poisson jump model
#'
#' @param symbol ticker symbol; can be stock ticker or a cryptocurrency
#' @param jump_thresh threshold of jump size
#' @param side direction of jump: up or down
#' @param envir environment to load stock data into
#'
#' @description {An ad-hoc model fitting a Poisson distribution to the number of
#' jumps excess a threshold per week.}
#' @details{ A chi-square test is run against the expected Poisson counts of jumps over the
#' observed number of events. Log-returns are used so that this can be used in an ad-hoc way to assess
#' fits for a Merton jump diffusion.}
#'
#' @return numeric
#' @importFrom graphics par
#' @importFrom stats Box.test acf dpois pexp
#' @importFrom utils tail
#' @export poissonJumps
poissonJumps <- function(symbol, jump_thresh = 0.03, side = "up", envir = parent.frame())
{
  num_weekdays <- 5
  symbol_data <- paste(symbol, "_", "daily", "_data", sep = "")
  if(exists(symbol_data))
  {
    print("Data already loaded")
    dat <- eval(as.symbol(symbol_data))
  } else
  {
    dat <- ravapi::getAssets(symbol)
  }
  if(symbol %in% c("DOGE", "BTC", "ETH", "LTC"))
  {
    num_weekdays <- 7
    adj_prices <- dat$close
  } else
  {
    adj_prices <- dat$adj_close
  }
  assign(x = symbol_data, value = dat, envir = envir)
  # Count number of jumps beyond threshold per week
  jc <- countJumps(adj_prices, jump_thresh = jump_thresh, return_type = "log", side = side, period = "weekly")
  # Testing for independence
  print(Box.test(x = jc))
  par(mfrow = c(1, 1))
  acf(as.numeric(jc), main = paste(symbol, "ACF"))

  # Poisson fit + evaluating goodness of fit
  z <- poissonFits::poissonFit(countsData = jc)
  print("Date range:")
  print(time(adj_prices)[c(1, length(adj_prices))])
  print("Number of samples in time-series")
  print(length(adj_prices))
  print("Time between jumps")
  print(c(weeks = 1/z$poisFit$estimate, days = num_weekdays/z$poisFit$estimate))
  print(paste("At least one jump", 1-dpois(x = 0, lambda = z$poisFit$estimate)))

  xtable::xtable(x = z$chiTest$table)
  xtable::xtable(x = z$chiTest$chisq_test)

  # Days since last jump
  jc_daily <- countJumps(adj_prices, jump_thresh = jump_thresh, side = side, period = "daily")
  last_jump_date <- as.Date(time(jc_daily[tail(which(jc_daily == 1), 1)]))
  date_yte(last_jump_date) # To initialize trading calendar
  if(!symbol %in% c("BTC", "ETH", "ETC", "LTC", "DOGE"))
  {
    days_since_last <- bizdays::bizdays(from = last_jump_date, to = Sys.Date(), cal = "trading")
  } else{
    days_since_last <- as.numeric(difftime(Sys.Date(), last_jump_date, units = "d"))
  }


  print(paste("Days since last jump:", days_since_last, "date:", last_jump_date))
  print(paste("Chance = ", 1-pexp(days_since_last/num_weekdays, rate = z$poisFit$estimate)))

}