 | :: ARIMA Forecasting - Free Statistics Software (Calculator) :: | |
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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]).
Click here to edit the underlying code of this R Module.Enter (or paste) your data delimited by hard returns. Click here to edit the underlying code of this R Module.
| Cite this software as: | | Wessa P., (2008), ARIMA Forecasting (v1.0.4) in Free Statistics Software (v1.1.22-r6), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/ | | | The R code is based on : | | | Borghers, E, and P. Wessa, Statistics - Econometrics - Forecasting, Office for Research Development and Education, http://www.xycoon.com/ | | | | | | | | | | | | | |
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| Source code of R module | | 1 | par1 <- as.numeric(par1) #cut off periods | | 2 | par2 <- as.numeric(par2) #lambda | | 3 | par3 <- as.numeric(par3) #degree of non-seasonal differencing | | 4 | par4 <- as.numeric(par4) #degree of seasonal differencing | | 5 | par5 <- as.numeric(par5) #seasonal period | | 6 | par6 <- as.numeric(par6) #p | | 7 | par7 <- as.numeric(par7) #q | | 8 | par8 <- as.numeric(par8) #P | | 9 | par9 <- as.numeric(par9) #Q | | 10 | if (par10 == "TRUE") par10 <- TRUE | | 11 | if (par10 == "FALSE") par10 <- FALSE | | 12 | if (par2 == 0) x <- log(x) | | 13 | if (par2 != 0) x <- x^par2 | | 14 | lx <- length(x) | | 15 | first <- lx - 2*par1 | | 16 | nx <- lx - par1 | | 17 | nx1 <- nx + 1 | | 18 | fx <- lx - nx | | 19 | if (fx < 1) { | | 20 | fx <- par5 | | 21 | nx1 <- lx + fx - 1 | | 22 | first <- lx - 2*fx | | 23 | } | | 24 | first <- 1 | | 25 | if (fx < 3) fx <- round(lx/10,0) | | 26 | (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")) | | 27 | (forecast <- predict(arima.out,fx)) | | 28 | (lb <- forecast$pred - 1.96 * forecast$se) | | 29 | (ub <- forecast$pred + 1.96 * forecast$se) | | 30 | if (par2 == 0) { | | 31 | x <- exp(x) | | 32 | forecast$pred <- exp(forecast$pred) | | 33 | lb <- exp(lb) | | 34 | ub <- exp(ub) | | 35 | } | | 36 | if (par2 != 0) { | | 37 | x <- x^(1/par2) | | 38 | forecast$pred <- forecast$pred^(1/par2) | | 39 | lb <- lb^(1/par2) | | 40 | ub <- ub^(1/par2) | | 41 | } | | 42 | if (par2 < 0) { | | 43 | olb <- lb | | 44 | lb <- ub | | 45 | ub <- olb | | 46 | } | | 47 | (actandfor <- c(x[1:nx], forecast$pred)) | | 48 | (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) | | 49 | bitmap(file="test1.png") | | 50 | opar <- par(mar=c(4,4,2,2),las=1) | | 51 | ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub)) | | 52 | plot(x,ylim=ylim,type="n",xlim=c(first,lx)) | | 53 | usr <- par("usr") | | 54 | rect(usr[1],usr[3],nx+1,usr[4],border=NA,col="lemonchiffon") | | 55 | rect(nx1,usr[3],usr[2],usr[4],border=NA,col="lavender") | | 56 | abline(h= (-3:3)*2 , col ="gray", lty =3) | | 57 | polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = "orange", lty=2,border=NA) | | 58 | lines(nx1:lx, lb , lty=2) | | 59 | lines(nx1:lx, ub , lty=2) | | 60 | lines(x, lwd=2) | | 61 | lines(nx1:lx, forecast$pred , lwd=2 , col ="white") | | 62 | box() | | 63 | par(opar) | | 64 | dev.off() | | 65 | prob.dec <- array(NA, dim=fx) | | 66 | prob.sdec <- array(NA, dim=fx) | | 67 | prob.ldec <- array(NA, dim=fx) | | 68 | prob.pval <- array(NA, dim=fx) | | 69 | perf.pe <- array(0, dim=fx) | | 70 | perf.mape <- array(0, dim=fx) | | 71 | perf.se <- array(0, dim=fx) | | 72 | perf.mse <- array(0, dim=fx) | | 73 | perf.rmse <- array(0, dim=fx) | | 74 | for (i in 1:fx) { | | 75 | locSD <- (ub[i] - forecast$pred[i]) / 1.96 | | 76 | perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i] | | 77 | perf.mape[i] = perf.mape[i] + abs(perf.pe[i]) | | 78 | perf.se[i] = (x[nx+i] - forecast$pred[i])^2 | | 79 | perf.mse[i] = perf.mse[i] + perf.se[i] | | 80 | prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD) | | 81 | prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD) | | 82 | prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD) | | 83 | prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD) | | 84 | } | | 85 | perf.mape = perf.mape / fx | | 86 | perf.mse = perf.mse / fx | | 87 | perf.rmse = sqrt(perf.mse) | | 88 | bitmap(file="test2.png") | | 89 | plot(forecast$pred, pch=19, type="b",main="ARIMA Extrapolation Forecast", ylab="Forecast and 95% CI", xlab="time",ylim=c(min(lb),max(ub))) | | 90 | dum <- forecast$pred | | 91 | dum[1:12] <- x[(nx+1):lx] | | 92 | lines(dum, lty=1) | | 93 | lines(ub,lty=3) | | 94 | lines(lb,lty=3) | | 95 | dev.off() | | 96 | load(file="createtable") | | 97 | a<-table.start() | | 98 | a<-table.row.start(a) | | 99 | a<-table.element(a,"Univariate ARIMA Extrapolation Forecast",9,TRUE) | | 100 | a<-table.row.end(a) | | 101 | a<-table.row.start(a) | | 102 | a<-table.element(a,"time",1,header=TRUE) | | 103 | a<-table.element(a,"Y[t]",1,header=TRUE) | | 104 | a<-table.element(a,"F[t]",1,header=TRUE) | | 105 | a<-table.element(a,"95% LB",1,header=TRUE) | | 106 | a<-table.element(a,"95% UB",1,header=TRUE) | | 107 | a<-table.element(a,"p-value
(H0: Y[t] = F[t])",1,header=TRUE) | | 108 | a<-table.element(a,"P(F[t]>Y[t-1])",1,header=TRUE) | | 109 | a<-table.element(a,"P(F[t]>Y[t-s])",1,header=TRUE) | | 110 | mylab <- paste("P(F[t]>Y[",nx,sep="") | | 111 | mylab <- paste(mylab,"])",sep="") | | 112 | a<-table.element(a,mylab,1,header=TRUE) | | 113 | a<-table.row.end(a) | | 114 | for (i in (nx-par5):nx) { | | 115 | a<-table.row.start(a) | | 116 | a<-table.element(a,i,header=TRUE) | | 117 | a<-table.element(a,x[i]) | | 118 | a<-table.element(a,"-") | | 119 | a<-table.element(a,"-") | | 120 | a<-table.element(a,"-") | | 121 | a<-table.element(a,"-") | | 122 | a<-table.element(a,"-") | | 123 | a<-table.element(a,"-") | | 124 | a<-table.element(a,"-") | | 125 | a<-table.row.end(a) | | 126 | } | | 127 | for (i in 1:fx) { | | 128 | a<-table.row.start(a) | | 129 | a<-table.element(a,nx+i,header=TRUE) | | 130 | a<-table.element(a,round(x[nx+i],4)) | | 131 | a<-table.element(a,round(forecast$pred[i],4)) | | 132 | a<-table.element(a,round(lb[i],4)) | | 133 | a<-table.element(a,round(ub[i],4)) | | 134 | a<-table.element(a,round((1-prob.pval[i]),4)) | | 135 | a<-table.element(a,round((1-prob.dec[i]),4)) | | 136 | a<-table.element(a,round((1-prob.sdec[i]),4)) | | 137 | a<-table.element(a,round((1-prob.ldec[i]),4)) | | 138 | a<-table.row.end(a) | | 139 | } | | 140 | a<-table.end(a) | | 141 | table.save(a,file="mytable.tab") | | 142 | a<-table.start() | | 143 | a<-table.row.start(a) | | 144 | a<-table.element(a,"Univariate ARIMA Extrapolation Forecast Performance",7,TRUE) | | 145 | a<-table.row.end(a) | | 146 | a<-table.row.start(a) | | 147 | a<-table.element(a,"time",1,header=TRUE) | | 148 | a<-table.element(a,"% S.E.",1,header=TRUE) | | 149 | a<-table.element(a,"PE",1,header=TRUE) | | 150 | a<-table.element(a,"MAPE",1,header=TRUE) | | 151 | a<-table.element(a,"Sq.E",1,header=TRUE) | | 152 | a<-table.element(a,"MSE",1,header=TRUE) | | 153 | a<-table.element(a,"RMSE",1,header=TRUE) | | 154 | a<-table.row.end(a) | | 155 | for (i in 1:fx) { | | 156 | a<-table.row.start(a) | | 157 | a<-table.element(a,nx+i,header=TRUE) | | 158 | a<-table.element(a,round(perc.se[i],4)) | | 159 | a<-table.element(a,round(perf.pe[i],4)) | | 160 | a<-table.element(a,round(perf.mape[i],4)) | | 161 | a<-table.element(a,round(perf.se[i],4)) | | 162 | a<-table.element(a,round(perf.mse[i],4)) | | 163 | a<-table.element(a,round(perf.rmse[i],4)) | | 164 | a<-table.row.end(a) | | 165 | } | | 166 | a<-table.end(a) | | 167 | table.save(a,file="mytable1.tab") |
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To cite Wessa.net in publications use:
Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
version 1.1.22-r6, URL http://www.wessa.net/
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