Tasks
- Direct download task:
- Download data from
quantmod or Quandl data on the FTSE 100 share price index. Plot your resulting data.
- Create at least two models (e.g. ARIMA, exponential smoothing, time series decomposition). Which models appear best and why?
- Select an appropriate training period and select the best forecast model for each variable.
- Create forecasts for the FTSE closing price for the remaining Fridays this term (weeks 8–11) and submit at http://goo.gl/forms/ovduCxfyo6 (or see below).
#part (a)
library(Quandl)
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
##
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(forecast)
## Loading required package: timeDate
## This is forecast 5.8
Quandl.auth("y8y3ezt48WZeqUqq1yQd")
ftse <- Quandl("YAHOO/INDEX_FTSE")
ftse <- ftse[order(ftse$Date),]
ftse.0 <- ftse[ftse$Date<as.Date("2015-03-04"),]
plot(ftse$Date,ftse$Close,type="l",main="FTSE 100 Share Index Closing Price since 1984",xlab="Date",ylab="Index")
#part(b)
#ARIMA: first look at data using tsdisplay (having turned it into a ts object)
ftse.t <- ts(ftse$Close,start=1,freq=1)
tsdisplay(log(ftse.t))
tsdisplay(diff(log(ftse.t),differences=1))
ftse.ar.0 <- Arima(log(ftse.t),order=c(5,1,0))
tsdisplay(ftse.ar.0$residuals)
ftse.auto <- auto.arima(log(ftse.t))
#ETS
ftse.ets <- ets(ftse.t)
#decomposition - need to set some frequency that is annual, but for working days
table(format(ftse$Date,"%Y"))
##
## 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998
## 260 261 261 261 261 260 261 261 262 261 260 260 262 261 261
## 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
## 261 260 261 261 261 262 260 260 261 262 261 261 260 261 261
## 2014 2015
## 254 47
#on average, just over 260 working days per year
ftse.t2 <- ts(ftse$Close,start=c(1984,1),freq=260.6452)
ftse.stl <- stl(ftse.t2,s.window=10)
ftse.auto <- auto.arima(ftse$Close)
ftse.forc <- forecast(ftse.auto,h=50)
plot(ftse.forc,include=100)
ftse.forc$mean[seq(1,45,5)]
## [1] 6878.631 6887.958 6891.599 6895.230 6898.861 6902.492 6906.123 6909.754
## [9] 6913.385
ftse[ftse$Date==as.Date("2015-02-06"),]
## Date Open High Low Close Volume Adjusted Close
## 22 2015-02-06 6865.9 6886.2 6835.5 6853.4 0 6853.4
#part(c) - need to select training period. Got thousands of observations, no need to worry about it.
ftse.t0 <- window(ftse.t2,end=c(2015,1))
ftse.t1 <- window(ftse.t2,start=c(2015,1))
#checking via a plot that these are what I think they are
plot(window(ftse.t2,start=c(2014,200)),type="o")
lines(ftse.t0,col=2,type="o")
lines(ftse.t1,col=3,type="o")
#now run models and create forecasts
ftse.ar.0 <- Arima(ftse.t0,order=c(5,1,2))
ftse.ar.0.f <- forecast(ftse.ar.0,h=NROW(ftse.t1))
ftse.ets.0 <- ets(ftse.t0)
## Warning in ets(ftse.t0): I can't handle data with frequency greater than
## 24. Seasonality will be ignored. Try stlf() if you need seasonal
## forecasts.
ftse.ets.0.f <- forecast(ftse.ets.0,h=NROW(ftse.t1))
accuracy(ftse.ar.0.f,ftse.t1)
## ME RMSE MAE MPE MAPE
## Training set 0.7820675 49.12542 32.02523 0.01982392 0.7565775
## Test set 217.0436885 278.41455 251.42378 3.13971061 3.6753375
## MASE ACF1 Theil's U
## Training set 0.05835347 -0.0006394131 NA
## Test set 0.45691937 0.9072448017 5.115993
accuracy(ftse.ets.0.f,ftse.t1)
## ME RMSE MAE MPE MAPE
## Training set -0.2818733 49.33622 31.95011 -0.0135487 0.7546679
## Test set 202.9945407 261.59816 237.23762 2.9357335 3.4691964
## MASE ACF1 Theil's U
## Training set 0.05821659 -0.00647942 NA
## Test set 0.43113849 0.90277063 4.80837
plot(window(ftse.t2,start=c(2014,200)))
lines(ftse.ar.0.f$mean,col=2)
lines(ftse.ets.0.f$mean,col=3)
legend("topleft",lty=1,col=c(1,2,3),legend=c("Original","ARIMA","ETS"))
#based on all measures, ETS beats AR.
#part (d) construct forecast for Fridays until end of term
days <- seq(as.Date("2015-03-04"),as.Date("2015-03-27"),by="days")
fridays <- days[weekdays(days)=="Friday"]
#got this method by Googling "day of week R"
#now need to forecast forward from end of time series
ftse.ets.f <- forecast(ets(ftse.t2),h=NROW(days))
## Warning in ets(ftse.t2): I can't handle data with frequency greater than
## 24. Seasonality will be ignored. Try stlf() if you need seasonal
## forecasts.
ftse.ets.f$mean[days %in% fridays]
## [1] 6879.200 6885.083 6890.965 6896.848
#these are our forecasts for the remaining Fridays
- Indirect data collection task:
- Collect data on the popularity of David Cameron from Google Trends, and the Halifax House Price Index (3m/YoY) from http://www.fxstreet.com/economic-calendar/, import the data into R and plot the series (note you need a Google account to download the Google Trends data).
- Use the
isat function from the gets package to carry out both outlier and break detection on each variable, and implement these variables into an autoregressive model.
- Run at one alternative type of model for each variable and comment on each.
- Determine the best forecast model for David Cameron’s popularity, and generate forecasts for David Cameron’s popularity this week (week beginning 2nd March) and the remaining weeks of term at http://goo.gl/forms/ovduCxfyo6 (or see below).
- Determine the best forecast model for the Halifax House Price Index for February, and submit also at http://goo.gl/forms/ovduCxfyo6 (or see below).
dave <- read.csv("/home/readejj/Dropbox/Teaching/Reading/ec313/Examinations/2015/Midterm II/dave_090315.csv",
stringsAsFactors=F)
dave$date <- as.Date(substr(dave$Week,1,10))
#fix as only downloaded data after release was made
dave <- dave[dave$date<max(dave$date),]
plot(dave$date,dave$david.cameron,type="l",main="Popularity of David Cameron on Google Trends",
ylab="Relative Search Frequency",xlab="Date")
house <- read.csv("/home/readejj/Dropbox/Teaching/Reading/ec313/Examinations/2015/Midterm II/halifax_090315.csv",
stringsAsFactors=F)
#fix as only downloaded data after release was made
house$date <- as.Date(substr(house$DateTime,1,8),"%Y%m%d")
house <- house[house$date<max(house$date),]
house <- house[order(house$date),]
plot(house$date,house$Actual,type="l",main="Halifax House Price Index",ylab="% Change",xlab="Date")
#part (b)
library(gets)
dave.isat <- isat(dave$david.cameron,sis=T) #do isat
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##
## IIS block 18 of 20...
##
## Searching path no. 1 out of 29
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##
## IIS block 19 of 20...
##
## Searching path no. 1 out of 29
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## Searching path no. 29 out of 29
##
## IIS block 20 of 20...
##
## Searching path no. 1 out of 31
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## Searching path no. 30 out of 31
## Searching path no. 31 out of 31
##
## GETS of union of retained IIS indicators...
##
##
## SIS block 1 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
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## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 2 of 20...
##
## Searching path no. 1 out of 29
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## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
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## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 3 of 20...
##
## Searching path no. 1 out of 29
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## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
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## Searching path no. 26 out of 29
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## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 4 of 20...
##
## Searching path no. 1 out of 29
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## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 5 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
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## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
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## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 6 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
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## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
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## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
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## Searching path no. 15 out of 29
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## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 7 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
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## Searching path no. 9 out of 29
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## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
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## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 8 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
## Searching path no. 17 out of 29
## Searching path no. 18 out of 29
## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 9 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
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## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 10 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
## Searching path no. 17 out of 29
## Searching path no. 18 out of 29
## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 11 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
## Searching path no. 17 out of 29
## Searching path no. 18 out of 29
## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 12 of 20...
##
## Searching path no. 1 out of 25
## Searching path no. 2 out of 25
## Searching path no. 3 out of 25
## Searching path no. 4 out of 25
## Searching path no. 5 out of 25
## Searching path no. 6 out of 25
## Searching path no. 7 out of 25
## Searching path no. 8 out of 25
## Searching path no. 9 out of 25
## Searching path no. 10 out of 25
## Searching path no. 11 out of 25
## Searching path no. 12 out of 25
## Searching path no. 13 out of 25
## Searching path no. 14 out of 25
## Searching path no. 15 out of 25
## Searching path no. 16 out of 25
## Searching path no. 17 out of 25
## Searching path no. 18 out of 25
## Searching path no. 19 out of 25
## Searching path no. 20 out of 25
## Searching path no. 21 out of 25
## Searching path no. 22 out of 25
## Searching path no. 23 out of 25
## Searching path no. 24 out of 25
## Searching path no. 25 out of 25
##
## SIS block 13 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
## Searching path no. 17 out of 29
## Searching path no. 18 out of 29
## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 14 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
## Searching path no. 17 out of 29
## Searching path no. 18 out of 29
## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 15 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
## Searching path no. 17 out of 29
## Searching path no. 18 out of 29
## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 16 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
## Searching path no. 17 out of 29
## Searching path no. 18 out of 29
## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 17 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
## Searching path no. 17 out of 29
## Searching path no. 18 out of 29
## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 18 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
## Searching path no. 15 out of 29
## Searching path no. 16 out of 29
## Searching path no. 17 out of 29
## Searching path no. 18 out of 29
## Searching path no. 19 out of 29
## Searching path no. 20 out of 29
## Searching path no. 21 out of 29
## Searching path no. 22 out of 29
## Searching path no. 23 out of 29
## Searching path no. 24 out of 29
## Searching path no. 25 out of 29
## Searching path no. 26 out of 29
## Searching path no. 27 out of 29
## Searching path no. 28 out of 29
## Searching path no. 29 out of 29
##
## SIS block 19 of 20...
##
## Searching path no. 1 out of 29
## Searching path no. 2 out of 29
## Searching path no. 3 out of 29
## Searching path no. 4 out of 29
## Searching path no. 5 out of 29
## Searching path no. 6 out of 29
## Searching path no. 7 out of 29
## Searching path no. 8 out of 29
## Searching path no. 9 out of 29
## Searching path no. 10 out of 29
## Searching path no. 11 out of 29
## Searching path no. 12 out of 29
## Searching path no. 13 out of 29
## Searching path no. 14 out of 29
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##
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##
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## GETS of union of ALL retained indicators...
##
## regressor-matrix is column rank deficient, so dropping 4 regressors
##
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dave.t <- ts(dave$david.cameron,start=c(2004,1),freq=52.18182) #create ts object for Dave
dave.ar <- Arima(dave.t,order=c(1,0,0), xreg = ts(dave.isat$aux$mX[,-1],start=c(2004,1),freq=52.18182)) #ar model
house.isat <- isat(house$Actual,sis=T) #do isat
##
## IIS block 1 of 3...
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##
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##
## GETS of union of retained SIS indicators...
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## GETS of union of ALL retained indicators...
house.t <- ts(house$Actual,start=c(2007,10),freq=12) #ts for house index
house.ar <- Arima(house.t,order=c(1,0,0), xreg = ts(house.isat$aux$mX[,-1],start=c(2007,10),freq=12)) #ar model
#part (c) one alternative model: ETS
dave.ets <- ets(dave.t)
## Warning in ets(dave.t): I can't handle data with frequency greater than
## 24. Seasonality will be ignored. Try stlf() if you need seasonal
## forecasts.
plot(dave.ets)
plot(dave.ets$residuals)
#comment: unable to cope with variation around GE2010
house.ets <- ets(house.t)
plot(house.ets)
plot(house.ets$residuals)
#comment: residuals appear reasonably normal, no seasonality detected.
#part(d) submit dave forecast - could just be those from part (c).
dave.f <- forecast(dave.ets,h=4)
plot(dave.f,include=50)
dave.ar.f <- forecast(dave.ar,h=4,xreg = dave.isat$aux$mX[579:582,-1])
plot(dave.ar.f,include=50)
dave.ar.f$mean
## Time Series:
## Start = 2015.15330971591
## End = 2015.21080100311
## Frequency = 52.18182
## [1] 4.680330 4.833569 4.868084 4.875859
#part(e) submit house forecast
house.f <- forecast(house.ets,h=1)
plot(house.f,include=50)
house.f$mean
## Feb
## 2015 8.839019