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112.7
122
134.7
109.8
130.8
118.7
104.4
87.8
134.2
143.9
140.4
111
126.3
124.4
136.1
118.4
127.4
127.9
115
90.2
131
143.3
131.5
98.5
124.9
122.4
128.8
125.9
120.2
120
116
89.2
135.9
148.7
128.1
100.9
125.5
119.8
120.7
125
109
114.2
105.6
80.1
131.1
136.6
119.7
102.4
114.5
112.9
131.8
118.7
107.1
127
104.6
85.9
134
127.6
121.5
104.5
107.3
111.9
120.7
116.9
106.1
122.3
97.8
82.7
128.2
119
127.4
106
108.7
113.5
131.4
111.3
119
130.7
104.5
88.9
135.4
140.6
138.8
107.4
120.8
124.1
139.2
119.9
121
133.7
115.2
96.7
131
147.6
132.9
97.4
123.6
124.9
118.6
127.6
110.2
115.4
106.6
75.5
116.7
118
98.7
81.5
87
86.8
96.8
92.7
82.1
94.1
89.7
67.5
102
103.2
95.6
83
87.2
94
107.7
103.3
94.8
112.7
96.8
75.9
116.7
111.4
108.6
90.9
92.6
95.7
116.7
95.4
105.1
99.7
89.8
74
108
102.1
100.2
83.2
87.9
93.3
98.5
84.5
89.3
94.2
83.5
67.5
89.4
102.4
92
65.9
85.3
87
91.8
88.5
89.1
89.8
88.9
64
93.2
100.1
89.3
68.1
94.3
93.3
98.1
96.8
87.8
95.6
95.7
64.4
108.1
109.6
90.9
75.6
93.5
98.1
104.5
102.7
89.6
108.8
95.4
70.1
104.6
105.5
96.8
79.4
92.3
96.8
103
99.5
91
103.4
82
70.1
98.1
95.7
98
77.3
89.8
91.6
106.5
87.5
99.5
104.4
84.5
68.3

library(lattice)
if (par1 == 'TRUE') par1 <- TRUE
if (par1 == 'FALSE') par1 <- FALSE
par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial
par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial
par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial
armaGR <- function(arima.out, names, n){
try1 <- arima.out$coef
try2 <- sqrt(diag(arima.out$var.coef))
try.data.frame  <- data.frame(matrix(NA,ncol=4,nrow=length(names)))
dimnames(try.data.frame) <- list(names,c('coef','std','tstat','pv'))
try.data.frame[,1] <- try1
for(i in 1:length(try2)) try.data.frame[which(rownames(try.data.frame)==names(try2)[i]),2] <- try2[i]
try.data.frame[,3] <- try.data.frame[,1] / try.data.frame[,2]
try.data.frame[,4] <- round((1-pt(abs(try.data.frame[,3]),df=n-(length(try2)+1)))*2,5)
vector <- rep(NA,length(names))
vector[is.na(try.data.frame[,4])] <- 0
maxi <- which.max(try.data.frame[,4])
continue <- max(try.data.frame[,4],na.rm=TRUE) > .05
vector[maxi] <- 0
list(summary=try.data.frame,next.vector=vector,continue=continue)
}
arimaSelect <- function(series, order=c(13,0,0), seasonal=list(order=c(2,0,0),period=12), include.mean=F){
nrc <- order[1]+order[3]+seasonal$order[1]+seasonal$order[3]
coeff <- matrix(NA, nrow=nrc*2, ncol=nrc)
pval <- matrix(NA, nrow=nrc*2, ncol=nrc)
mylist <- rep(list(NULL), nrc)
names  <- NULL
if(order[1] > 0) names <- paste('ar',1:order[1],sep='')
if(order[3] > 0) names <- c( names , paste('ma',1:order[3],sep='') )
if(seasonal$order[1] > 0) names <- c(names, paste('sar',1:seasonal$order[1],sep=''))
if(seasonal$order[3] > 0) names <- c(names, paste('sma',1:seasonal$order[3],sep=''))
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML')
mylist[[1]] <- arima.out
last.arma <- armaGR(arima.out, names, length(series))
mystop <- FALSE
i <- 1
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- 2
aic <- arima.out$aic
while(!mystop){
mylist[[i]] <- arima.out
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML', fixed=last.arma$next.vector)
aic <- c(aic, arima.out$aic)
last.arma <- armaGR(arima.out, names, length(series))
mystop <- !last.arma$continue
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- i+1
}
list(coeff, pval, mylist, aic=aic)
}
arimaSelectplot <- function(arimaSelect.out,noms,choix){
noms <- names(arimaSelect.out[[3]][[1]]$coef)
coeff <- arimaSelect.out[[1]]
k <- min(which(is.na(coeff[,1])))-1
coeff <- coeff[1:k,]
pval  <- arimaSelect.out[[2]][1:k,]
aic   <- arimaSelect.out$aic[1:k]
coeff[coeff==0] <- NA
n <- ncol(coeff)
if(missing(choix)) choix <- k
layout(matrix(c(1,1,1,2,
3,3,3,2,
3,3,3,4,
5,6,7,7),nr=4),
widths=c(10,35,45,15),
heights=c(30,30,15,15))
couleurs <- rainbow(75)[1:50]#(50)
ticks <- pretty(coeff)
par(mar=c(1,1,3,1))
plot(aic,k:1-.5,type='o',pch=21,bg='blue',cex=2,axes=F,lty=2,xpd=NA)
points(aic[choix],k-choix+.5,pch=21,cex=4,bg=2,xpd=NA)
title('aic',line=2)
par(mar=c(3,0,0,0))
plot(0,axes=F,xlab='',ylab='',xlim=range(ticks),ylim=c(.1,1))
rect(xleft  = min(ticks) + (0:49)/50*(max(ticks)-min(ticks)),
xright = min(ticks) + (1:50)/50*(max(ticks)-min(ticks)),
ytop   = rep(1,50),
ybottom= rep(0,50),col=couleurs,border=NA)
axis(1,ticks)
rect(xleft=min(ticks),xright=max(ticks),ytop=1,ybottom=0)
text(mean(coeff,na.rm=T),.5,'coefficients',cex=2,font=2)
par(mar=c(1,1,3,1))
image(1:n,1:k,t(coeff[k:1,]),axes=F,col=couleurs,zlim=range(ticks))
for(i in 1:n) for(j in 1:k) if(!is.na(coeff[j,i])) {
if(pval[j,i]<.01)                            symb = 'green'
else if( (pval[j,i]<.05) & (pval[j,i]>=.01)) symb = 'orange'
else if( (pval[j,i]<.1)  & (pval[j,i]>=.05)) symb = 'red'
else                                         symb = 'black'
polygon(c(i+.5   ,i+.2   ,i+.5   ,i+.5),
c(k-j+0.5,k-j+0.5,k-j+0.8,k-j+0.5),
col=symb)
if(j==choix)  {
rect(xleft=i-.5,
xright=i+.5,
ybottom=k-j+1.5,
ytop=k-j+.5,
lwd=4)
text(i,
k-j+1,
round(coeff[j,i],2),
cex=1.2,
font=2)
}
else{
rect(xleft=i-.5,xright=i+.5,ybottom=k-j+1.5,ytop=k-j+.5)
text(i,k-j+1,round(coeff[j,i],2),cex=1.2,font=1)
}
}
axis(3,1:n,noms)
par(mar=c(0.5,0,0,0.5))
plot(0,axes=F,xlab='',ylab='',type='n',xlim=c(0,8),ylim=c(-.2,.8))
cols <- c('green','orange','red','black')
niv  <- c('0','0.01','0.05','0.1')
for(i in 0:3){
polygon(c(1+2*i   ,1+2*i   ,1+2*i-.5   ,1+2*i),
c(.4      ,.7      , .4        , .4),
col=cols[i+1])
text(2*i,0.5,niv[i+1],cex=1.5)
}
text(8,.5,1,cex=1.5)
text(4,0,'p-value',cex=2)
box()
residus <- arimaSelect.out[[3]][[choix]]$res
par(mar=c(1,2,4,1))
acf(residus,main='')
title('acf',line=.5)
par(mar=c(1,2,4,1))
pacf(residus,main='')
title('pacf',line=.5)
par(mar=c(2,2,4,1))
qqnorm(residus,main='')
title('qq-norm',line=.5)
qqline(residus)
residus
}
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
(selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5)))
bitmap(file='test1.png')
resid <- arimaSelectplot(selection)
dev.off()
resid
bitmap(file='test2.png')
acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test3.png')
pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
dev.off()
bitmap(file='test4.png')
cpgram(resid, main='Residual Cumulative Periodogram')
dev.off()
bitmap(file='test5.png')
hist(resid, main='Residual Histogram', xlab='values of Residuals')
dev.off()
bitmap(file='test6.png')
densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test7.png')
qqnorm(resid, main='Residual Normal Q-Q Plot')
qqline(resid)
dev.off()
ncols <- length(selection[[1]][1,])
nrows <- length(selection[[2]][,1])-1
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Iteration', header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,names(selection[[3]][[1]]$coef)[i],header=TRUE)
}
a<-table.row.end(a)
for (j in 1:nrows) {
a<-table.row.start(a)
mydum <- 'Estimates ('
mydum <- paste(mydum,j)
mydum <- paste(mydum,')')
a<-table.element(a,mydum, header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,round(selection[[1]][j,i],4))
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'(p-val)', header=TRUE)
for (i in 1:ncols) {
mydum <- '('
mydum <- paste(mydum,round(selection[[2]][j,i],4),sep='')
mydum <- paste(mydum,')')
a<-table.element(a,mydum)
}
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,'Menu of Residual Diagnostics',2,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Description',1,TRUE)
a <- table.element(a,'Link',1,TRUE)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Histogram',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_histogram.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_centraltendency.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'QQ Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_fitdistrnorm.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Kernel Density Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_density.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness/Kurtosis Test',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Skewness-Kurtosis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_skewness_kurtosis_plot.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Harrell-Davis Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_harrell_davis.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot1.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Blocked Bootstrap Plot -- Central Tendency',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_bootstrapplot.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'(Partial) Autocorrelation Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_autocorrelation.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Spectral Analysis',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_spectrum.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Tukey lambda PPCC Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_tukeylambda.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <-table.element(a,'Box-Cox Normality Plot',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_boxcoxnorm.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a <- table.row.start(a)
a <- table.element(a,'Summary Statistics',1,header=TRUE)
a <- table.element(a,hyperlink( paste('https://supernova.wessa.net/rwasp_summary1.wasp?convertgetintopost=1&data=',paste(as.character(resid),sep='',collapse=' '),sep='') ,'Compute','Click here to examine the Residuals.'),1)
a <- table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable7.tab')