ARIMA Forecasting - Free Statistics and Forecasting Software (Calculators) v.1.2.1

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the extrapolation forecasts of a univariate ARIMA model for a time series Y[t] (for t = 1, 2, ..., T). The user may specify a cut-off period K which implies that the ARIMA model is estimated based on Y[t] for t = 1, 2, ..., T-K and such that the extrapolation forecast F[t] for t = T-K+1, ..., T is computed and compared with the actual values that were dropped: various extrapolation forecast statistics are computed (MPE, RMSE, MAPE, ...). In addition, the following probabilities are computed: P(F[t]>Y[t-1]), P(F[t]>Y[t-s]), and P(F[t]>Y[T-K]).

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Data [reset data]
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Sample Range: (leave blank to include all observations)
From:
To:

Testing Period (?)


Box-Cox lambda transformation parameter (lambda)


Degree of non-seasonal differencing (d)


Degree of seasonal differencing (D)


Seasonal period (s)


AR(p) order


MA(q) order


SAR(P) order


SMA(Q) order


Include mean?


Chart options
Width:
Height:

Source code of R module

par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == "TRUE") par10 <- TRUE
if (par10 == "FALSE") par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5*2
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method="ML"))
(forecast <- predict(arima.out,fx))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file="test1.png")
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type="n",xlim=c(first,lx))
usr <- par("usr")
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col="lemonchiffon")
rect(nx1,usr[3],usr[2],usr[4],border=NA,col="lavender")
abline(h= (-3:3)*2 , col ="gray", lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = "orange", lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ="white")
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.spe <- array(0, dim=fx)
perf.scalederr <- array(0, dim=fx)
perf.mase <- array(0, dim=fx)
perf.mase1 <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.smape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.smape1 <- array(0,dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
perf.scaleddenom <- 0
for (i in 2:fx) {
perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1])
}
perf.scaleddenom = perf.scaleddenom / (fx-1)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i]
perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+i] + forecast$pred[i])
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape[1] = abs(perf.pe[1])
perf.smape[1] = abs(perf.spe[1])
perf.mape1[1] = perf.mape[1]
perf.smape1[1] = perf.smape[1]
perf.mse[1] = perf.se[1]
perf.mase[1] = abs(perf.scalederr[1])
perf.mase1[1] = perf.mase[1]
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.smape[i] = perf.smape[i-1] + abs(perf.spe[i])
perf.smape1[i] = perf.smape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i])
perf.mase1[i] = perf.mase[i] / i
}
perf.rmse = sqrt(perf.mse1)
bitmap(file="test2.png")
plot(forecast$pred, pch=19, type="b",main="ARIMA Extrapolation Forecast", ylab="Forecast and 95% CI", xlab="time",ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:par1] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file="createtable")
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,"Univariate ARIMA Extrapolation Forecast",9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,"time",1,header=TRUE)
a<-table.element(a,"Y[t]",1,header=TRUE)
a<-table.element(a,"F[t]",1,header=TRUE)
a<-table.element(a,"95% LB",1,header=TRUE)
a<-table.element(a,"95% UB",1,header=TRUE)
a<-table.element(a,"p-value<br />(H0: Y[t] = F[t])",1,header=TRUE)
a<-table.element(a,"P(F[t]>Y[t-1])",1,header=TRUE)
a<-table.element(a,"P(F[t]>Y[t-s])",1,header=TRUE)
mylab <- paste("P(F[t]>Y[",nx,sep="")
mylab <- paste(mylab,"])",sep="")
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,"-")
a<-table.element(a,"-")
a<-table.element(a,"-")
a<-table.element(a,"-")
a<-table.element(a,"-")
a<-table.element(a,"-")
a<-table.element(a,"-")
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file="mytable.tab")
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,"Univariate ARIMA Extrapolation Forecast Performance",10,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,"time",1,header=TRUE)
a<-table.element(a,"% S.E.",1,header=TRUE)
a<-table.element(a,"PE",1,header=TRUE)
a<-table.element(a,"MAPE",1,header=TRUE)
a<-table.element(a,"sMAPE",1,header=TRUE)
a<-table.element(a,"Sq.E",1,header=TRUE)
a<-table.element(a,"MSE",1,header=TRUE)
a<-table.element(a,"RMSE",1,header=TRUE)
a<-table.element(a,"ScaledE",1,header=TRUE)
a<-table.element(a,"MASE",1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape1[i],4))
a<-table.element(a,round(perf.smape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[i],4))
a<-table.element(a,round(perf.rmse[i],4))
a<-table.element(a,round(perf.scalederr[i],4))
a<-table.element(a,round(perf.mase1[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file="mytable1.tab")

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:: ARIMA Forecasting - Free Statistics Software (Calculator) ::