Speed up WMA (Weighted Moving Average) calculation

Question

I am trying to calculate exponential moving average on 15 day bars, but want to see \"evolution\" of the 15 day bar EMA on each (end of) day/bar. So, this means that I have 15 d

Answer 1

I have not find a satisfactory solution for my question using R. So I took the old tool, c language, and results are better than I would have ever expected. Thanks for "pushing" me using this great tools of Rcpp, inline etc. Amazing. I guess, whenever I have performance requirements in the future and can not be met using R I will add C to R and performance is there. So, please see below my code and resolution of the performance issues.

# How to speedup cumulative EMA calculation
# 
###############################################################################

library(quantmod)
library(Rcpp)
library(inline)
library(rbenchmark)

do.call.rbind <- function(lst) {
    while(length(lst) > 1) {
        idxlst <- seq(from=1, to=length(lst), by=2)

        lst <- lapply(idxlst, function(i) {
                    if(i==length(lst)) { return(lst[[i]]) }

                    return(rbind(lst[[i]], lst[[i+1]]))
                })
    }
    lst[[1]]
}

to.period.cumulative <- function(x, name=NULL, period="days", numPeriods=15) {
    if(is.null(name))
        name <- deparse(substitute(x))

    cnames <- c("Open", "High", "Low", "Close")
    if (has.Vo(x)) 
        cnames <- c(cnames, "Volume")

    cnames <- paste(name, cnames, sep=".") 

    if (quantmod:::is.OHLCV(x)) {
        x <- quantmod:::OHLCV(x)
        out <- do.call.rbind( 
                lapply(split(x, f=period, k=numPeriods), 
                        function(x) cbind(rep(first(x[,1]), NROW(x[,1])), 
                                cummax(x[,2]), cummin(x[,3]), x[,4], cumsum(x[,5]))))
    } else if (quantmod:::is.OHLC(x)) {
        x <- OHLC(x)
        out <- do.call.rbind( 
                lapply(split(x, f=period, k=numPeriods), 
                        function(x) cbind(rep(first(x[,1]), NROW(x[,1])), 
                                cummax(x[,2]), cummin(x[,3]), x[,4])))
    } else {
        stop("Object does not have OHLC(V).")
    }

    colnames(out) <- cnames

    return(out)
}

EMA.cumulative<-function(cumulativeBars, nEMA = 4, period="days", numPeriods=15) {
    barsEndptCl <- Cl(cumulativeBars[endpoints(cumulativeBars, on=period, k=numPeriods)])

    # TODO: This is sloooooooooooooooooow... 
    outEMA <- do.call.rbind(
            lapply(split(Cl(cumulativeBars), period), 
                    function(x) {
                        previousFullBars <- barsEndptCl[index(barsEndptCl) < last(index(x)), ]
                        if (NROW(previousFullBars) >= (nEMA - 1)) {
                                last(EMA(last(rbind(previousFullBars, x), n=(nEMA + 1)), n=nEMA))
                        } else {
                            xts(NA, order.by=index(x))
                        }
                    }))

    colnames(outEMA) <- paste("EMA", nEMA, sep="")

    return(outEMA)
}

EMA.c.c.code <- '
    /* Initalize loop and PROTECT counters */
    int i, P=0;

    /* ensure that cumbars and fullbarsrep is double */
    if(TYPEOF(cumbars) != REALSXP) {
      PROTECT(cumbars = coerceVector(cumbars, REALSXP)); P++;
    }

    /* Pointers to function arguments */
    double *d_cumbars = REAL(cumbars);
    int i_nper = asInteger(nperiod);
    int i_n = asInteger(n);
    double d_ratio = asReal(ratio);

    /* Input object length */
    int nr = nrows(cumbars);

    /* Initalize result R object */
    SEXP result;
    PROTECT(result = allocVector(REALSXP,nr)); P++;
    double *d_result = REAL(result);

    /* Find first non-NA input value */
    int beg = i_n*i_nper - 1;
    d_result[beg] = 0;
    for(i = 0; i <= beg; i++) {
        /* Account for leading NAs in input */
        if(ISNA(d_cumbars[i])) {
            d_result[i] = NA_REAL;
            beg++;
            d_result[beg] = 0;
            continue;
        }
        /* Set leading NAs in output */
        if(i < beg) {
            d_result[i] = NA_REAL;
        }
        /* Raw mean to start EMA - but only on full bars*/
        if ((i != 0) && (i%i_nper == (i_nper - 1))) {
            d_result[beg] += d_cumbars[i] / i_n;
        }
    }

    /* Loop over non-NA input values */
    int i_lookback = 0;
    for(i = beg+1; i < nr; i++) {
        i_lookback = i%i_nper;

        if (i_lookback == 0) {
            i_lookback = 1;
        } 
        /*Previous result should be based only on full bars*/
        d_result[i] = d_cumbars[i] * d_ratio + d_result[i-i_lookback] * (1-d_ratio);
    }

    /* UNPROTECT R objects and return result */
    UNPROTECT(P);
    return(result);
'

EMA.c.c <- cfunction(signature(cumbars="numeric", nperiod="numeric", n="numeric",     ratio="numeric"), EMA.c.c.code)

EMA.cumulative.c<-function(cumulativeBars, nEMA = 4, period="days", numPeriods=15) {
    ratio <- 2/(nEMA+1)

    outEMA <- EMA.c.c(cumbars=Cl(cumulativeBars), nperiod=numPeriods, n=nEMA, ratio=ratio)  

    outEMA <- reclass(outEMA, Cl(cumulativeBars))

    colnames(outEMA) <- paste("EMA", nEMA, sep="")

    return(outEMA)
}

getSymbols("SPY", from="2010-01-01")

SPY.cumulative <- to.period.cumulative(SPY, name="SPY")

system.time(
        SPY.EMA <- EMA.cumulative(SPY.cumulative)
)

system.time(
        SPY.EMA.c <- EMA.cumulative.c(SPY.cumulative)
)


res <- benchmark(EMA.cumulative(SPY.cumulative), EMA.cumulative.c(SPY.cumulative),
        columns=c("test", "replications", "elapsed", "relative", "user.self", "sys.self"),
        order="relative",
        replications=10)

print(res)

EDIT: To give an indication of performance improvement over my cumbersome (I am sure it can be made better, since in effect I have created double for loop) R here is a print out:

> print(res)
                              test replications elapsed relative user.self
2 EMA.cumulative.c(SPY.cumulative)           10   0.026    1.000     0.024
1   EMA.cumulative(SPY.cumulative)           10  57.732 2220.462    56.755

So, by my standards, a SF type of improvement...