Happy New Year! This post is going to continue on from my last post on the K-nearest algo http://gekkoquant.com/2013/12/02/k-nearest-neighbour-algo-fail/.

In the last post I speculated that the poor performance of the algo was potentially down to trying to compare the current day and find the most similar days in history, rather we should try to take the last N days and find the most similar period in history.

The code below does exactly that use windowSize to control how big the periods are that we compare.

**Sharpe ratio: -0.591864**

The performance is still poor, perhaps the similarity measure i’m using is rubbish. Maybe using implied vol would be good for identifying market regimes and should be used in the similarity measure.

Unfortunately this algo is very very slow (and gets worse over time since we have more history to look back over), this makes it difficult / time consuming to optimise variables.

Onto the code:

^{?}View Code RSPLUS

library("quantmod") library("PerformanceAnalytics") library("zoo") #INPUTS marketSymbol <- "^GSPC" nFastLookback <- 30 #The fast signal lookback used in linear regression curve nSlowLookback <- 50 #The slow signal lookback used in linear regression curve nFastVolLookback <- 30 #The fast signal lookback used to calculate the stdev nSlowVolLookback <- 50 #The slow signal lookback used calculate the stdev nFastRSILookback <- 30 #The fast signal lookback used to calculate the stdev nSlowRSILookback <- 50 #The slow signal lookback used calculate the stdev kNearestGroupSize <- 30 #How many neighbours to use normalisedStrengthVolWeight <- 2 #Make some signals more important than others in the MSE normalisedStrengthRegressionWeight <- 1 fastRSICurveWeight <- 2 slowRSICurveWeight <- 0.8 windowSize <- 10 #Compare the last 10 days with the most similar 10 day period in history #Specify dates for downloading data, training models and running simulation startDate = as.Date("2006-08-01") #Specify what date to get the prices from symbolData <- new.env() #Make a new environment for quantmod to store data in stockCleanNameFunc <- function(name){ return(sub("^","",name,fixed=TRUE)) } getSymbols(marketSymbol, env = symbolData, src = "yahoo", from = startDate) cleanName <- stockCleanNameFunc(marketSymbol) mktData <- get(cleanName,symbolData) linearRegressionCurve <- function(data,n){ regression <- function(dataBlock){ fit <-lm(dataBlock~seq(1,length(dataBlock),1)) return(last(fit$fitted.values)) } return (rollapply(data,width=n,regression,align="right",by.column=FALSE,na.pad=TRUE)) } volCurve <- function(data,n){ stdev <- function(dataBlock){ sd(dataBlock) } return (rollapply(data,width=n,stdev,align="right",by.column=FALSE,na.pad=TRUE))^2 } fastRegression <- linearRegressionCurve(Cl(mktData),nFastLookback) slowRegression <- linearRegressionCurve(Cl(mktData),nSlowLookback) normalisedStrengthRegression <- slowRegression / (slowRegression+fastRegression) fastVolCurve <- volCurve(Cl(mktData),nFastVolLookback) slowVolCurve <- volCurve(Cl(mktData),nSlowVolLookback) normalisedStrengthVol <- slowVolCurve / (slowVolCurve+fastVolCurve) fastRSICurve <-RSI(Cl(mktData),nFastRSILookback)/100 #rescale it to be in the same range as the other indicators slowRSICurve <-RSI(Cl(mktData),nSlowRSILookback)/100 #Lets plot the signals just to see what they look like dev.new() par(mfrow=c(2,2)) plot(normalisedStrengthVol,type="l") plot(normalisedStrengthRegression,type="l") plot(fastRSICurve,type="l") plot(slowRSICurve,type="l") #DataMeasure will be used to determine how similar other days are to today #It is used later on for calculate the days which are most similar to today according to MSE measure dataMeasure <- cbind(normalisedStrengthVol*normalisedStrengthVolWeight,normalisedStrengthRegression*normalisedStrengthRegression,fastRSICurve*fastRSICurveWeight,slowRSICurve*slowRSICurveWeight) colnames(dataMeasure) <- c("normalisedStrengthVol","normalisedStrengthRegression","fastRSICurve","slowRSICurve") #Finds the nearest neighbour and calculates the trade signal calculateNearestNeighbourTradeSignal <- function(dataMeasure,K,mktReturns,windowSize){ findKNearestNeighbours <- function(dataMeasure,K,windowSize){ calculateMSE <- function(dataA,dataB){ if(length(dataA) != length(dataB)){ return (Inf) } se <- ((as.vector(as.matrix(dataA)) - as.vector(as.matrix(dataB)))^2) res <- mean(se) if(is.na(res)){ res <- Inf } return (res) } mseScores <- as.data.frame(dataMeasure[,1]) mseScores[,1] <- Inf #Default all the mse scores to inf (we've not calculated them yet) colnames(mseScores) <- c("MSE") indexOfTheMostRecentWindowSizeDays <- seq(max(1,length(dataMeasure[,1])-windowSize),length(dataMeasure[,1])) mostRecentWindowDataMeasure <- dataMeasure[indexOfTheMostRecentWindowSizeDays,] for(i in seq(1,length(dataMeasure[,1]))){ indexHistoricalWindowDataMeasure <- seq(max(1,i-windowSize),i) historicalWindowDataMeasure <- dataMeasure[indexHistoricalWindowDataMeasure,] mseScores[i,1] <- calculateMSE(mostRecentWindowDataMeasure,historicalWindowDataMeasure) # print(paste("MSE is",mseScores[i,1])) } rowNum <- seq(1,length(dataMeasure[,1]),1) tmp <- c("MSE", colnames(dataMeasure)) dataMeasureWithMse <- as.data.frame(cbind(mseScores[,1],dataMeasure)) colnames(dataMeasureWithMse) <- tmp #print(head(mseScores)) #print(head(dataMeasureWithMse)) tmp <- c("rowNum", colnames(dataMeasureWithMse)) dataMeasureWithMse <- cbind(rowNum,dataMeasureWithMse) colnames(dataMeasureWithMse) <- tmp dataMeasureWithMse <- dataMeasureWithMse[order(dataMeasureWithMse[,"MSE"]),] #Starting from the 2nd item as the 1st is the current day (MSE will be 0) want to drop it return (dataMeasureWithMse[seq(2,min(K,length(dataMeasureWithMse[,1]))),]) } calculateTradeSignalFromKNeighbours <- function(mktReturns,kNearestNeighbours){ rowNums <- kNearestNeighbours[,"rowNum"] rowNums <- na.omit(rowNums) if(length(rowNums) <= 1) { return (0) } print("The kNearestNeighbours are:") print(rowNums) #So lets see what happened on the day AFTER our nearest match mktRet <- mktReturns[rowNums+1] # return (sign(sum(mktRet))) return (SharpeRatio.annualized(mktRet)) } kNearestNeighbours <- findKNearestNeighbours(dataMeasure,K,windowSize) tradeSignal <- calculateTradeSignalFromKNeighbours(mktReturns,kNearestNeighbours) return(tradeSignal) } ret <- (Cl(mktData)/Op(mktData))-1 signalLog <- as.data.frame(ret) signalLog[,1] <- 0 colnames(signalLog) <- c("TradeSignal") #Loop through all the days we have data for, and calculate a signal for them using nearest neighbour for(i in seq(1,length(ret))){ print (paste("Simulating trading for day",i,"out of",length(ret),"@",100*i/length(ret),"%")) index <- seq(1,i) signal <- calculateNearestNeighbourTradeSignal(dataMeasure[index,],kNearestGroupSize,ret,windowSize) signalLog[i,1] <- signal } dev.new() tradeRet <- Lag(signalLog[,1])*ret[,1] #Combine todays signal with tomorrows return (no lookforward issues) totalRet <- cbind(tradeRet,ret) colnames(totalRet) <- c("Algo",paste(marketSymbol," Long OpCl Returns")) charts.PerformanceSummary(totalRet,main=paste("K nearest trading algo for",marketSymbol,"kNearestGroupSize=",kNearestGroupSize,"windowSize=",windowSize),geometric=FALSE) print(SharpeRatio.annualized(tradeRet)) |