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Data:
235.1 280.7 264.6 240.7 201.4 240.8 241.1 223.8 206.1 174.7 203.3 220.5 299.5 347.4 338.3 327.7 351.6 396.6 438.8 395.6 363.5 378.8 357.00 369.00 464.8 479.1 431.3 366.5 326.3 355.1 331.6 261.3 249.00 205.5 235.6 240.9 264.9 253.8 232.3 193.8 177.00 213.2 207.2 180.6 188.6 175.4 199.00 179.6 225.8 234.00 200.2 183.6 178.2 203.2 208.5 191.8 172.8 148.00 159.4 154.5 213.2 196.4 182.8 176.4 153.6 173.2 171.00 151.2 161.9 157.2 201.7 236.4 356.1 398.3 403.7 384.6 365.8 368.1 367.9 347.00 343.3 292.9 311.5 300.9 366.9 356.9 329.7 316.2 269.00 289.3 266.2 253.6 233.8 228.4 253.6 260.1 306.6 309.2 309.5 271.00 279.9 317.9 298.4 246.7 227.3 209.1 259.9 266.00 320.6 308.5 282.2 262.7 263.5 313.1 284.3 252.6 250.3 246.5 312.7 333.2 446.4 511.6 515.5 506.4 483.2 522.3 509.8 460.7 405.8 375.00 378.5 406.8 467.8 469.8 429.8 355.8 332.7 378.00 360.5 334.7 319.5 323.1 363.6 352.1 411.9 388.6 416.4 360.7 338.00 417.2 388.4 371.1 331.5 353.7 396.7 447.00 533.5 565.4 542.3 488.7 467.1 531.3 496.1 444.00 403.4 386.3 394.1 404.1 462.1 448.1 432.3 386.3 395.2 421.9 382.9 384.2 345.5 323.4 372.6 376.00 462.7 487.00 444.2 399.3 394.9 455.4 414.00 375.5 347.00 339.4 385.8 378.8 451.8 446.1 422.5 383.1 352.8 445.3 367.5 355.1 326.2 319.8 331.8 340.9 394.1 417.2 369.9 349.2 321.4 405.7 342.9 316.5 284.2 270.9 288.8 278.8 324.4 310.9 299.00 273.00 279.3 359.2 305.00 282.1 250.3 246.5 257.9 266.5 315.9 318.4 295.4 266.4 245.8 362.8 324.9 294.2 289.5 295.2 290.3 272.00 307.4 328.7 292.9 249.1 230.4 361.5 321.7 277.2 260.7 251.00 257.6 241.8 287.5 292.3 274.7 254.2 230.00 339.00 318.2 287.00 295.8 284.00 271.00 262.7 340.6 379.4 373.3 355.2 338.4 466.9 451.00 422.00 429.2 425.9 460.7 463.6 541.4 544.2 517.5 469.4 439.4 549.00 533.00 506.1 484.00 457.00 481.5 469.5 544.7 541.2 521.5 469.7 434.4 542.6 517.3 485.7 465.8 447.00 426.6 411.6 467.5 484.5 451.2 417.4 379.9 484.7 455.00 420.8 416.5 376.3 405.6 405.8 500.8 514.00 475.5 430.1 414.4 538.00 526.00 488.5 520.2 504.4 568.5 610.6 818.00 830.9 835.9 782.00 762.3 856.9 820.9 769.6 752.2 724.4 723.1 719.5 817.4 803.3 752.5 689.00 630.4 765.5 757.7 732.2 702.6 683.3 709.5 702.2 784.8 810.9 755.6 656.8 615.1 745.3 694.1 675.7 643.7 622.1 634.6 588.00 689.7 673.9 647.9 568.8 545.7 632.6 643.8 593.1 579.7 546.00 562.9 572.5
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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R Server
Big Analytics Cloud Computing Center
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