R/FRAMA.R

In IlyaKipnis/DSTrading: Digital Signal Trading

#'FRactal Adaptive Moving Average
#'@param HLC an HLC price series
#'@param n a lookback period
#'@param FC a fast constant--aka lowest n for an EMA
#'@param SC a slow constant--aka lowest n for an EMA
#'@param triggerLag a number of days by which to lag the original computation
#'@return an xts containing the FRAMA and the trigger
#'@references 
#'\cr\url{http://www.mesasoftware.com/Papers/FRAMA.pdf}
#'\cr\url{http://etfhq.com/blog/2010/09/30/fractal-adaptive-moving-average-frama/}
#'@export
"FRAMA" <- function(HLC, n=20, FC=1, SC=200, triggerLag=1, ...) {
  price <- ehlersPriceMethod(HLC, ...)
  if (n%%2==1) n=n-1 #n must be even
  N3 <- (runMax(Hi(HLC), n)-runMin(Lo(HLC), n))/n
  N1 <- (runMax(Hi(HLC), n/2)-runMin(Lo(HLC), n/2))/(n/2)
  lagSeries <- lag(HLC, n/2)
  N2 <- (runMax(Hi(lagSeries), n/2)-runMin(Lo(lagSeries), n/2))/(n/2)
  dimen <- (log(N1+N2)-log(N3))/log(2)
  w <- log(2/(SC+1))
  oldAlpha <- exp(w*(dimen-1))
  oldN <- (2-oldAlpha)/oldAlpha
  newN <- ((SC-FC)*(oldN-1)/(SC-1))+FC
  alpha <- 2/(newN+1)
  alpha[which(alpha > 1)] <- 1
  alpha[which(alpha < w)] <- w
  alphaComplement <- 1-alpha
  initializationIndex <- index(alpha[is.na(alpha)])
  alpha[is.na(alpha)] <- 1; alphaComplement[is.na(alphaComplement)] <- 0
  FRAMA <- rep(0, length(price))
  FRAMA[1] <- price[1]
  FRAMA <- computeFRAMA(alpha, alphaComplement, FRAMA, price)
  FRAMA <- xts(FRAMA, order.by=index(price))
  FRAMA[initializationIndex] <- alpha[initializationIndex] <- NA
  trigger <- lag(FRAMA, triggerLag)
  out <- cbind(FRAMA=FRAMA, trigger=trigger)
  return(out)
}