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Data:
196.9 192.1 201.8 186.9 218.0 214.4 227.5 204.1 225.8 223.7 244.7 243.9 257.3 234.5 251.4 243.8 247.4 245.3 262.5 270.0 259.9 262.2 244.9 249.3 268.2 231.2 264.3 252.7 275.5 261.5 275.5 272.3 268.6 270.4 267.7 275.0 272.6 248.6 279.4 270.5 292.8 297.8 296.8 290.9 282.8 312.8 303.2 301.4 289.8 279.6 302.2 299.1 319.7 310.9 315.2 338.5 315.6 321.2 318.5 342.7 261.4 287.0 331.5 326.9 338.6 337.0 358.4 344.5 345.7 344.1 317.4 354.5 345.2 314.1 352.5 361.2 365.9 332.5 364.0 359.1 345.6 366.9 370.2 359.9 366.6 336.3 368.5 374.2 384.3 358.9 407.7 433.3 404.7 392.7 409.7 416.5 414.3 404.3 421.4 372.6 404.7 420.2 438.4 449.1 445.8 413.8 420.5 442.3 438.9 394.5 416.8 402.9 424.5 432.3 484.1 492.7 496.3 471.9 491.2 512.9 482.4 407.9 448.5 431.1 498.8 497.1 517.1 487.7 512.5 550.1 532.5 524.1 515.7 461.0 529.3 467.4 559.8 536.5 531.9 546.5 547.4 536.1 482.8 551.0 532.9 484.1 554.8 537.0 558.0 511.4 502.9 558.6 545.1 574.3 542.2 600.0 588.6 524.4 618.5 580.9 557.2 571.2 597.5 601.7 558.9 600.9 601.0 615.7 578.1 495.9 526.8 522.1 605.1 574.4 609.7 580.7 565.1 590.7 571.5 601.3 567.3 467.9 588.9 579.4 502.6 568.7 616.0 586.2 575.5 599.9 568.2 516.0 493.4 496.8 529.9 491.7 543.2 490.8 554.7 625.7 605.0 645.2 645.2 611.8 600.3 549.8 635.5 617.7 643.5 485.7 689.5 692.0 677.3 704.7 668.6 717.8 689.8 640.4 675.2 528.1 538.0 527.2 655.6 650.6 623.7 748.4 727.4 750.5 678.9 659.5 691.9 639.8 663.8 572.9 592.5 734.8 696.1 589.2 662.9 661.2 672.1 583.7 705.5 631.0 733.3 674.9 695.5 634.1 630.6 635.2 554.1 623.9 679.3 565.6 564.1 637.2 650.8 602.7 587.5 619.2 616.5 637.9 557.9 594.0 668.7 603.3 674.5 573.4 706.0 693.7 627.5 550.7 592.3 660.2 597.3 641.0 663.6 595.9 638.4 665.4 671.4 637.0 685.7 705.8 704.8 734.4 674.2 748.6 763.4 658.0 627.5 528.9 488.3 575.5 735.6 685.3 613.6 629.5 634.7 652.6 728.3 634.3 690.7 676.3 675.4 595.6 712.4 735.8 544.4 567.0 510.0 564.0 630.7 496.7 660.9 601.2 655.2 591.6 606.1 560.7 368.3 371.6 413.9 413.9 389.0 399.2 429.8 395.6 472.0 486.0 525.0 396.0 511.0 525.0 492.0 517.0 525.0 474.0 539.0 468.0 543.0 532.0 565.0 535.0 534.0 546.0 494.0 552.0 511.0 451.0 537.0 494.0 549.0 544.0 598.0 583.0 582.0 589.0 578.0 561.0 592.0 504.0 545.0 547.0 585.0 562.0 520.0 581.0 590.0 562.0 548.0 567.0 542.0 473.0 531.0 462.0 479.0 533.0 552.0 547.0 562.0 524.0 479.0 445.0 406.0 475.0 589.0 495.0 484.0 536.0 555.0 565.0 564.0 573.0 569.0 588.0 546.0 508.0 560.0 558.0 516.0 549.0 595.0 586.0 597.0 592.0 538.0 590.0 576.0 451.0 538.0 555.0 532.0 530.0 553.0 626.0 601.0 573.0 569.0 562.0 468.0 483.0 460.0 411.0 458.0 455.0 600.0 605.0 545.0 549.0 415.0 568.0 577.0 517.0 558.0 518.0 489.0 502.0 569.0 540.0 550.0 557.0 542.0 542.0 582.0 525.0 584.0 562.0 639.0 613.0 604.0 613.0 625.0 654.0 638.0
Seasonal period
12
12
1
2
3
4
5
6
7
8
9
10
11
12
Type of Exponential Smoothing
(?)
Triple
Single
Double
Triple
Type of seasonality
(?)
additive
additive
multiplicative
Number of Forecasts
12
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Chart options
R Code
par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) 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,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')
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Computing time
0 seconds
R Server
Big Analytics Cloud Computing Center
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