Solved – Transforming a time series with a negative number

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I have been given data to forecast however it has a negative figure within the data which then, when doing a log transformation to make the series stationary, the ARIMA script i have written won't work.

datan<-c(144627.7451,575166.2487,854245.7137,1230639.153,1160052.421,479928.7072,-261427.4238,1181746.229,168251.621,556741.5149,1840484.518,1704679.404,1878380.278,1865288.502,1849340.253,1965974.112,2093192.242,1912399.391,2633179.421,2134618.008,2070856.492,1238565.331)  freqdata<-4 startdata<-c(9,2) horiz<-4 datats<-ts(datan,frequency=freqdata,start=startdata) force.log<-"log" datadates<-as.character(c("9q2","9q3","9q4","10q1","10q2","10q3","10q4","11q1","11q2","11q3","11q4","12q1","12q2","12q3","12q4","13q1","13q2","13q3","13q4","14q1","14q2","14q3")) dataMAT<-matrix(0,ncol=freqdata,nrow=(length(datats)+freqdata),byrow=TRUE) for (i in 1:freqdata)   {dataMAT[,i]<-c(rep(0,length=i-1),lag(datats,k=-i+1),rep(0,length=freqdata-i+1))} dataind<-dataMAT[c(-1:(-freqdata+1),-(length(dataMAT[,1])-freqdata+1):-(length(dataMAT[,1]))),] dataind2<-data.frame(dataind) lm1<-lm(X1~.,data=dataind2) lm2<-lm(X1~X2+dataind2[,length(dataind2[1,])],data=dataind2) library(lmtest) library(car) bptest1<-bptest(lm1) bptest2<-bptest(lm2) gqtest1<-gqtest(lm1) ncvtest1<-ncvTest(lm1) ncvtest2<-ncvTest(lm2) if(force.log=="level")    {aslog<-"n"}else     {{if(force.log=="log")        {aslog<-"y"}else          {if(bptest1$p.value<0.1|bptest2$p.value<0.1|gqtest1$p.value<0.1|ncvtest1$p<0.1|ncvtest2$p<0.1)            {aslog<-"y"}else               {aslog<-"n"}}}} if(aslog=="y")   {dataa<-log(datats)}else     {dataa<-datats} startLa<-startdata[1]+trunc((1/freqdata)*(length(dataa)-horiz)) startLb<-1+((1/freqdata)*(length(dataa)-horiz)-trunc((1/freqdata)*(length(dataa)-horiz)))*freqdata startL<-c(startLa,startLb) K<-ts(rep(dataa,length=length(dataa)-horiz),frequency=freqdata,start=startdata) L<-ts(dataa[-1:-(length(dataa)-horiz)],frequency=freqdata,start=startL) library(strucchange) efp1rc<-efp(lm1,data=dataind2,type="Rec-CUSUM") efp2rc<-efp(lm2,data=dataind2,type="Rec-CUSUM") efp1rm<-efp(lm1,data=dataind2,type="Rec-MOSUM") efp2rm<-efp(lm2,data=dataind2,type="Rec-MOSUM") plot(efp2rc) lines(efp1rc$process,col ="darkblue") plot(efp2rm) lines(efp1rm$process,col="darkblue") gefp2<-gefp(lm2,data=dataind2) plot(gefp2) plot(dataa) pacf(dataa) sctest(efp2rc) cat("log series,y/n?:",aslog)

then i want to run arima to get the forecasts

library(tseries) library(forecast) max.sdiff<-3 arima.force.seasonality<-"n" kpssW<-kpss.test(dataa,null="Level") ppW<-tryCatch({ppW<-pp.test(dataa,alternative="stationary")},error=function(ppW){ppW<-list(error="TRUE",p.value=0.99)}) adfW<-adf.test(dataa,alternative="stationary",k=trunc((length(dataa)-1)^(1/3))) if(kpssW$p.value<0.05|ppW$p.value>0.05|adfW$p.value>0.05)   {ndiffsW=1}else     {ndiffsW=0} aaW<-auto.arima(dataa,max.D=max.sdiff,d=ndiffsW,seasonal=TRUE,allowdrift=FALSE,stepwise=FALSE,trace=TRUE,seasonal.test="ch") orderWA<-c(aaW$arma[1],aaW$arma[6],aaW$arma[2]) orderWS<-c(aaW$arma[3],aaW$arma[7],aaW$arma[4]) if(sum(aaW$arma[1:2])==0)   {orderWA[1]<-1}else     {NULL} if(arima.force.seasonality=="y")   {if(sum(aaW$arma[3:4])==0)     {orderWS[1]<-1}else       {NULL}}else         {NULL} Arimab<-Arima(dataa,order=orderWA,seasonal=list(order=orderWS),method="ML") fArimab<-forecast(Arimab,h=8,simulate=TRUE,fan=TRUE) if(aslog=="y")   {fArimabF<-exp(fArimab$mean[1:horiz])}else     {fArimabF<-fArimab$mean[1:horiz]} plot(fArimab,main="ARIMA Forecast",sub="blue=fitted,red=actual")  lines(dataa,col="red",lwd=2) #changes colour and size of dataa lines(ts(append(fitted(Arimab),fArimab$mean[1]),frequency=freqdata,start=startdata),col="blue",lwd=2) if(aslog=="y")   {Arimab2f<-exp(fArimab$mean[1:horiz])}else     {Arimab2f<-fArimab$mean[1:horiz]}  start(fArimab$mean)->startARIMA ArimaALTf<-ts(prettyNum(Arimab2f,big.interval=3L,big.mark=","),frequency=freqdata,start=startARIMA) View(ArimaALTf,title="ARIMA2 final forecast") #brings up table of the forecasts summary(Arimab)

If anyone can help me figure out how to forecast this data with the negative i will be really grateful!!

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Best Answer

You could shift the data by adding a constat, e.g. datats <- datats + 500000, so that all the values are positive and logs can be taken. Remember to undo this shift and recover the original level when obtaining forecasts (as you already did undoing the logarithmic transformation by taking the exponential).

Why do you take logarithms? The data do not seem to show an increasing variance. I would rather say that there is a level shift around observation $11$.

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