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Data:
876 80 2492 529 606 164 138 601 789 146 218 939 980 610 583 432 558 281 139 778 517 609 344 809 188 318 201 608 43 622 746 285 757 861 35 267 815 501 977 740 950 616 848 770 887 808 326 932 649 916 857 894 418 464 477 340 327 776 192 819 323 39 207 614 520 801 92 747 412 570
Seasonal period
12
12
1
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12
Number of Forecasts
18
12
1
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4
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12
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16
17
18
Algorithm
BFGS
BFGS
L-BFGS-B
Chart options
R Code
require('stsm') require('stsm.class') require('KFKSDS') par1 <- as.numeric(par1) par2 <- as.numeric(par2) nx <- length(x) x <- ts(x,frequency=par1) m <- StructTS(x,type='BSM') print(m$coef) print(m$fitted) print(m$resid) mylevel <- as.numeric(m$fitted[,'level']) myslope <- as.numeric(m$fitted[,'slope']) myseas <- as.numeric(m$fitted[,'sea']) myresid <- as.numeric(m$resid) myfit <- mylevel+myseas mm <- stsm.model(model = 'BSM', y = x, transPars = 'StructTS') fit2 <- stsmFit(mm, stsm.method = 'maxlik.td.optim', method = par3, KF.args = list(P0cov = TRUE)) (fit2.comps <- tsSmooth(fit2, P0cov = FALSE)$states) m2 <- set.pars(mm, pmax(fit2$par, .Machine$double.eps)) (ss <- char2numeric(m2)) (pred <- predict(ss, x, n.ahead = par2)) mylagmax <- nx/2 bitmap(file='test2.png') op <- par(mfrow = c(2,2)) acf(as.numeric(x),lag.max = mylagmax,main='Observed') acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level') acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal') acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals') par(op) dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) spectrum(as.numeric(x),main='Observed') spectrum(mylevel,main='Level') spectrum(myseas,main='Seasonal') spectrum(myresid,main='Standardized Residals') par(op) dev.off() bitmap(file='test4.png') op <- par(mfrow = c(2,2)) cpgram(as.numeric(x),main='Observed') cpgram(mylevel,main='Level') cpgram(myseas,main='Seasonal') cpgram(myresid,main='Standardized Residals') par(op) dev.off() bitmap(file='test1.png') plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b') grid() dev.off() bitmap(file='test5.png') op <- par(mfrow = c(2,2)) hist(m$resid,main='Residual Histogram') plot(density(m$resid),main='Residual Kernel Density') qqnorm(m$resid,main='Residual Normal QQ Plot') qqline(m$resid) plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit') par(op) dev.off() bitmap(file='test6.png') par(mfrow = c(3,1), mar = c(3,3,3,3)) plot(cbind(x, pred$pred), type = 'n', plot.type = 'single', ylab = '') lines(x) polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred + 2 * pred$se, rev(pred$pred)), col = 'gray85', border = NA) polygon(c(time(pred$pred), rev(time(pred$pred))), c(pred$pred - 2 * pred$se, rev(pred$pred)), col = ' gray85', border = NA) lines(pred$pred, col = 'blue', lwd = 1.5) mtext(text = 'forecasts of the observed series', side = 3, adj = 0) plot(cbind(x, pred$a[,1]), type = 'n', plot.type = 'single', ylab = '') lines(x) polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] + 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = 'gray85', border = NA) polygon(c(time(pred$a[,1]), rev(time(pred$a[,1]))), c(pred$a[,1] - 2 * sqrt(pred$P[,1]), rev(pred$a[,1])), col = ' gray85', border = NA) lines(pred$a[,1], col = 'blue', lwd = 1.5) mtext(text = 'forecasts of the level component', side = 3, adj = 0) plot(cbind(fit2.comps[,3], pred$a[,3]), type = 'n', plot.type = 'single', ylab = '') lines(fit2.comps[,3]) polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] + 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = 'gray85', border = NA) polygon(c(time(pred$a[,3]), rev(time(pred$a[,3]))), c(pred$a[,3] - 2 * sqrt(pred$P[,3]), rev(pred$a[,3])), col = ' gray85', border = NA) lines(pred$a[,3], col = 'blue', lwd = 1.5) mtext(text = 'forecasts of the seasonal component', side = 3, adj = 0) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Structural Time Series Model -- Interpolation',6,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,'Level',header=TRUE) a<-table.element(a,'Slope',header=TRUE) a<-table.element(a,'Seasonal',header=TRUE) a<-table.element(a,'Stand. Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nx) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,x[i]) a<-table.element(a,mylevel[i]) a<-table.element(a,myslope[i]) a<-table.element(a,myseas[i]) a<-table.element(a,myresid[i]) 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,'Structural Time Series Model -- Extrapolation',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,'Level',header=TRUE) a<-table.element(a,'Seasonal',header=TRUE) a<-table.row.end(a) for (i in 1:par2) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,pred$pred[i]) a<-table.element(a,pred$a[i,1]) a<-table.element(a,pred$a[i,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab')
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