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Data:
358.59 362.96 362.42 364.97 364.04 361.06 358.48 352.96 359.59 360.39 357.40 362.93 364.55 365.73 364.70 364.65 359.43 362.14 356.97 354.82 353.17 357.06 356.18 355.01 355.65 357.31 357.07 357.91 358.48 358.97 351.77 352.16 359.08 360.35 359.53 359.30 358.41 359.68 355.31 357.08 349.71 354.13 345.49 341.69 344.25 340.17 342.47 344.43 333.23 339.72 342.61 346.36 339.09 339.73 341.12 335.94 333.46 335.66 341.12 342.21 342.62 346.06 344.43 346.65 343.74 335.67 342.75 341.77 345.84 346.52 350.79 345.44 345.87 338.48 337.21 340.81 339.86 342.86 343.33 341.73 351.38 351.13 345.99 347.55 346.02 345.29 347.03 348.01 345.48 349.40 351.05 349.70 350.86 354.45 355.30 357.48 355.24 351.79 355.22 351.02 350.28 350.17 348.16 340.30 343.75 344.71 344.13 342.14 345.04 346.02 346.43 347.07 339.33 339.10 337.19 339.58 327.85 326.81 321.73 320.45 327.69 323.95 320.47 322.13 316.34 314.78 308.90 308.62 314.41 306.88 310.60 321.60 321.50 325.68 324.35 320.01 326.88 332.39 331.48 332.62 324.79 327.12 328.91 328.37 324.83 325.90 326.18 328.94 333.78 328.06 325.87 325.41 318.86 319.13 310.16 311.73 306.54 311.16 311.98 306.72 308.05 300.76 301.90 293.09 292.76 294.58 289.90 296.69 297.21 293.31 296.25 298.60 296.87 301.02 304.73 301.92 295.72 293.18 298.35 297.99 299.85 299.85 304.45 299.45 298.14 298.78 297.02 301.33 294.96 296.69 300.73 301.96 297.38 293.87 285.96 285.41 283.70 284.76 277.11 274.73 274.73 274.73 274.73 274.69 275.42 264.15 276.24 268.88 277.97 280.49 281.09 276.16 272.58 270.94 284.31 283.94 284.18 282.83 283.84 282.71 279.29 280.70 274.47 273.44 275.49 279.46 280.19 288.21 284.80 281.41 283.39 287.97 290.77 290.60 289.67 289.84 298.55 296.07 297.14 295.34 296.25 294.30 296.15 296.49 298.05 301.03 300.52 301.50 296.93 289.84 291.44 286.88 286.74 288.93 292.19 295.39 295.86 293.36 292.86 292.73 296.73 285.02 285.24 288.62 283.36 285.84 291.48 291.41 287.77 284.97 286.05 278.19 281.21 277.92 280.08 269.24 268.48 268.83 269.54 262.37 265.12 265.34 263.32 267.18 260.75 261.78 257.27 255.63 251.39 259.49 261.18 261.65 262.01 265.23 268.10 262.27 263.59 257.85 265.69 271.15 266.69 265.77 262.32 270.48 273.03 269.13 280.65 282.75 281.44 281.99 282.86 287.21 283.11 280.66 282.39 280.83 284.71 279.99 283.50 284.88 288.60 284.80 287.20 286.22 286.54 279.58 283.08 288.88 280.18 284.16 290.57 286.82 273.00 278.69 264.54 271.92 283.60 269.25 263.58 264.16 268.85 269.67 249.41 268.99 268.65 260.16 256.55 251.47 234.93 232.96 215.49 213.68 236.07 235.41 214.77 225.85 224.64 238.26 232.44 222.50 225.28 220.49 216.86 234.70 230.06 238.27 238.56 242.70 249.14 234.89 227.78 234.04 230.70 230.17 218.23 232.20 220.76 215.60 217.69 204.35 191.44 203.84 211.86 210.57 219.57 219.98 226.01 207.04 212.52 217.92 210.45 218.53 223.32 218.76 217.63
Sample Range:
(leave blank to include all observations)
From:
To:
Testing Period
(?)
20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Box-Cox lambda transformation parameter (lambda)
1
1
-2.0
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Degree of non-seasonal differencing (d)
1
0
1
2
Degree of seasonal differencing (D)
0
0
1
Seasonal period (s)
1
1
2
3
4
6
12
AR(p) order
1
0
1
2
3
MA(q) order
0
0
1
2
SAR(P) order
2
0
1
2
SMA(Q) order
0
0
1
Include mean?
FALSE
FALSE
TRUE
Chart options
R Code
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 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.mape <- array(0, dim=fx) perf.se <- array(0, dim=fx) perf.mse <- array(0, dim=fx) perf.rmse <- array(0, dim=fx) for (i in 1:fx) { locSD <- (ub[i] - forecast$pred[i]) / 1.96 perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i] perf.mape[i] = perf.mape[i] + abs(perf.pe[i]) perf.se[i] = (x[nx+i] - forecast$pred[i])^2 perf.mse[i] = perf.mse[i] + perf.se[i] 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 = perf.mape / fx perf.mse = perf.mse / fx perf.rmse = sqrt(perf.mse) 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[1:12] <- 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',7,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,'Sq.E',1,header=TRUE) a<-table.element(a,'MSE',1,header=TRUE) a<-table.element(a,'RMSE',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.mape[i],4)) a<-table.element(a,round(perf.se[i],4)) a<-table.element(a,round(perf.mse[i],4)) a<-table.element(a,round(perf.rmse[i],4)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab')
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Computing time
1 seconds
R Server
Big Analytics Cloud Computing Center
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