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Data:
3650 3700 3750 3850 3950 3900 3700 3700 4000 4350 4350 4200 4050 4100 4150 4350 4350 4350 4000 4050 4350 4750 4750 4700 4300 4400 4450 4600 4500 4500 4200 4150 4500 4850 4900 4850 4500 4650 4600 4700 4750 4800 4400 4450 4750 5100 5200 4850 4600 4650 4850 5000 5050 5150 4650 4700 5100 5450 5550 5300 5200 5400 5500 5500 5650 5500 4850 5050 5550 6050 6050 5850 5600 5700 5700 5750 5950 5850 5150 5250 5900 6350 6400 6200 5850 5950 6150 6250 6250 6200 5200 5750 6200 6650 6700 6550 6100 6250 6300 6500 6250 6500 5400 6100 6550 6950 7150 7150 6700 6950 7050 7050 7100 7250
Seasonal period
12
12
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Number of Forecasts
12
12
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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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Big Analytics Cloud Computing Center
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