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Data:
5483.5 5386.2 5781.8 5137.4 5001.7 5123.8 5340 5696.4 5544.7 5747.6 5487.4 5590.1 5571.9 5363.1 6014.1 5480.4 5907.5 5772.2 5620 6614.7 6294.7 5938.3 5722.6 5595.6 5569.5 5753.7 5838.8 5401.1 6013.9 5461.1 5176.3 5916.5 5519.5 5873.9 5663.8 5339 5671.2 5741 5881.3 5531.2 5811.2 5391.4 5461.2 6091.3 5951 6511.7 6371.4 5601.2 6001.2 5920.7 5455.2 5703.8 5863 5762.9 5997.8 6542.7 6594.5 6915.1 6584.6 6412.2 5930.1 6022.3 6268.6 6179.9 6608.6 6424 6230.8 6628.2 6576.2 6947 6672.8 6249.9 5964.2 5840.1 6115.2 5800.5 6566.6 6377.3 6355.2 6999.3 6603.7 6998.3 6966.2 6383.3 5960 5682.1 5640.2 5694.1 6392.4 5835.3 6075.6 7387.1 6632.6 7048.1 6792.1 6094 6408.3 6492.1 6596.8 6078.2 6297.3 5960.8 6125.1 7253.4 6505.8 7419.5 7308.2 6373.1 6667.4 6518.6 6324.8 6764.1 6985 6091.5 6526 7116.9 6770.3 7221.9 7344.5 6565.6 6577.3 6597.8 6560.6 6729.2 6703.2 6716.1
Seasonal period
12
12
1
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4
5
6
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8
9
10
11
12
Number of Forecasts
12
12
1
2
3
4
5
6
7
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9
10
11
12
13
14
15
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')
Compute
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Raw Input
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Raw Output
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Computing time
1 seconds
R Server
Big Analytics Cloud Computing Center
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