#Get data for the Microsoft stock price GOOG/NASDAQ_MSFT and construct the log return yt = ∆logMSFTt.
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("tseries")
msp<-Quandl("GOOG/NASDAQ_MSFT", type="zoo")
mspt<-msp$Close
lmspt<-log(mspt)
dlmspt <- diff(lmspt,1)
par(mfrow=c(1,2))
plot(lmspt,xlab="Time", ylab="lmspt")
plot(dlmspt,xlab="Time", ylab="dlmspt")
#a) Estimate an ARMA model: use ACF, PACF, Ljung-Box statistics, to #identify and then estimate an appropriate model for log return
Quandl.auth(" 3HQPzReHC1WfzuSG41gy")
## Warning: 'Quandl.auth' is deprecated.
## Use 'Quandl.api_key' instead.
## See help("Deprecated")
plot(acf(coredata(dlmspt), type='correlation', lag=24, plot=FALSE), ylab="", main=expression(paste("ACF for dlmspt")))
acf(coredata(dlmspt),type="partial",lag=24,ylab="",main="PACF-dlmspt")
# estimate model -
m1 <- arima(dlmspt,order=c(2,0,2))
m1
##
## Call:
## arima(x = dlmspt, order = c(2, 0, 2))
##
## Coefficients:
## ar1 ar2 ma1 ma2 intercept
## -0.5344 -0.2307 0.4640 0.1463 9e-04
## s.e. 0.1690 0.1444 0.1717 0.1494 2e-04
##
## sigma^2 estimated as 0.0005335: log likelihood = 17803.19, aic = -35594.37
#Check model m1 for adequacy
tsdiag(m1,gof.lag=24)
BIC(m1)
## [1] -35552.77
AIC(m1)
## [1] -35594.37
# try another model
m2 <- arima(dlmspt,order=c(4,0,4))
## Warning in arima(dlmspt, order = c(4, 0, 4)): possible convergence problem:
## optim gave code = 1
m2
##
## Call:
## arima(x = dlmspt, order = c(4, 0, 4))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1 ma2 ma3 ma4
## 0.6334 -0.4169 -0.0674 0.2443 -0.7075 0.4161 0.0978 -0.3218
## s.e. 0.2263 0.2177 0.2020 0.1604 0.2246 0.2281 0.2080 0.1559
## intercept
## 8e-04
## s.e. 2e-04
##
## sigma^2 estimated as 0.0005307: log likelihood = 17815.3, aic = -35610.6
#Check model m1 for adequacy
tsdiag(m2,gof.lag=24)
BIC(m2)
## [1] -35541.27
AIC(m2)
## [1] -35610.6