Carls_Time_Series.Rmd

---
title: "Carl's Time Series Analysis"
author: "Carl"
date: "April 10, 2016"
output: html_document
---

```{r}
library('xts')
library('forecast')
library('rgl')
library('TSclust')
library('corrplot')

oil = read.csv("oil.csv")
colnames(oil) = c("date","oil")
oil$date = as.Date(oil$date, format = "%d/%m/%Y")
oil$date = as.POSIXct(oil$date)
oil$oil = as.numeric(as.character(oil$oil))
oil = xts(oil$oil,oil$date)


unemp = read.csv("unemp.csv")
unemp$AgeGroup == "15 years and over"
colnames(unemp)

unemp.f = unemp[unemp$AgeGroup == "15 years and over" ,]
unemp.f= unemp.f[unemp.f$Sex == "Both sexes",]

colnames(unemp)
provinces = colnames(unemp)[c(4:14)]
unemp = unemp.f[,c("When",provinces)]

colnames(unemp) = c("date",provinces)
class(unemp$date)

unemp$date = as.Date(unemp$date, format = "%m/%d/%Y")
unemp$date = as.POSIXct(unemp$date)
unemp[,provinces] = apply(unemp[,provinces],2,function(x) as.numeric(as.character(x)))
unemp = xts(unemp[,provinces],unemp$date)
colnames(unemp) = provinces


for(i in 1:length(provinces)){
  
  if(i == 1){
    data = merge.xts(to.monthly(oil)[,4],to.monthly(unemp[,provinces[i]])[,4])
  }
  if(i > 1){
    data = merge.xts(data,to.monthly(unemp[,provinces[i]])[,4])
  }
}
colnames(data) = c("oil", provinces)

data = na.omit(data)
plot(data[,"Alberta"])

cor(data[,"Alberta"],data[,"Ontario"])
M = cor(data[,provinces])
corrplot(M)

cor(data[130:193,"Alberta"],data[130:193,"Ontario"])
M = cor(data[,provinces])
corrplot(M)



tsdist = diss(t(data[,provinces]) , "ACF", p=0.05)
hc <- hclust(tsdist)
plot(hc)

fit4 = stl(data[,"Alberta"], s.window= "periodic")
plot(fit4$time.series[,"trend"], ylim=c(0,10), col = "red", main = "Comparison", xlab = c("time"), ylab = c("Unemployment"))

fit5 = stl(data[,"Ontario"], s.window= "periodic")
lines(fit5$time.series[,"trend"], col = "blue")

legend("bottomright",c("Ontario","Alberta"),lty=c(1,1),lwd=c(2.5,2.5),col=c("blue","red")) 


library('vars')

model = VAR(data[,c("oil","Alberta")])
plot(model)
pred = predict(model, n.ahead =20)
plot(pred)


library('gam')
library('nlme')
library('mgcv')
gam.object = gam(Alberta ~ oil, data=data[,c("oil","Alberta")], na=na.gam.replace)
summary(gam.object)
plot(gam.object)

```