Time Series Lab

Adapted from Time Series PrimerRH Shumway and DS Stoffer

Crawl before walking

# toy data set(mydata = c(1,2,3,2,1))

#convert to time series(mydata = as.ts(mydata))

#start the series in 1950(mydata = ts(mydata,start=1950))

#quarterly series starting in the 3rd quarter of 1950(mydata = ts(mydata,start=c(1950,3),frequency=4))

# disply the sampled timestime(mydata)

# use window() to get part of the series object(x=window(mydata,start=c(1951,1),end=c(1951,3)))

#create a new time seriesx=ts(1:5)

#now add two lagged columns: 2nd col shift time base back, 3rd col shift forwardcbind(x,lag(x),lag(x,-1))

# find the intersection covered by all series ts.intersect(x, lag(x,1), lag(x, -1))

#difference a time series, i.e.,diff(x)

#Note diff(x,2) is not 2nd order differencing#2nd order differencing is given by diff(diff(x))

#similarly for higher order differencing

#create a seriesx=-5:5

# and another seriesy=5*cos(x)

#set up the plotting window for 3 rows 2 colsop=par(mfrow=c(3,2))

#plot x by itself plot(x,main="plot(x)")

#plot x and y plot(x,y,main="plot(x,y)")

#plot time series component xplot.ts(x,main="plot.ts(x)")

#plot time series component x and y plot.ts(x,y,main="plot.ts(x,y)")

#time series plot function on x ts.plot(x,main="ts.plot(x)")

#time series plot function on x & y ts.plot(ts(x),ts(y),col=1:2,main="ts.plot(x,y)")

#reset the graphical paramters par(op)

#fix the seed so we all get the same resultsset.seed(1999)

#sample 10 points normally distributed w mu=0 and sd=1 x = rnorm(10,0,1)

#sample another 10 points & sum with x y=x+rnorm(10,0,1)

#get summary statistics summary(fit <- lm(y~x))

#display x and yplot(x,y)

#add a fitted line to the plot abline(fit)

#show the residualsresid(fit)

#show the fitted valuesfitted(fit)

#exclude the interceptlm(y~0 + x)

#load data sets cmort – cardiovascular mortaility and #part – particulate pollutiondata(cmort, part)

#find the time series intersection with cmort, part, and part lagged# 4 weeks gets rid of nonoverlaping sectons of part & part4ded = ts.intersect(cmort,part,part4=lag(part,-4), dframe=TRUE)

# perform regression on time series data fits part & part4fit = lm(cmort~part+part4, data=ded, na.action=NULL)

#display summary statisticssummary(fit)

#load Johnson&Johnson quarterly earningsdata(jj)

#create a line spanning the time of jj data trend = time(jj)-1970

#Create an array of factors corresponding to quarters Q = factor(rep(1:4,21))

# perform a regression without intercept reg = lm(log(jj)~0 + trend + Q, na.action=NULL)

#display the model matrix model.matrix(reg)

#view results summary(reg)

Examples of ARIMA simulations

#AR(1) with mean 50 x = arima.sim(list(order=c(1,0,0),ar=.9),n=100)+50 plot(x)

#AR(2) x = arima.sim(list(order=c(2,0,0),ar=c(1,-.9)),n=100) plot(x)

#ARIMA(1,1,1)x = arima.sim(list(order=c(1,1,1),ar=.9,ma=-.5),n=200)plot(x)

Example: fit ARMA(1,1)

#we want reproduceable resultsset.seed(666)

# run simulation for 200 points x = 50 + arima.sim(list(order=c(1,0,1),ar=.9, ma=-.5),n=200)

# display autocorrelation function & partial autocorrelation function acf(x); pacf(x)

#or use this function to plot both acf2(x)

#fit to model(x.fit = arima(x,order=c(1,0,1)))

#fit the ARIMA model assuming ARIMA(1,0,1)sarima(x,1,0,1)

# finally forecast using x and an ARIMA(1,0,1) modelsarima.for(x,10,1,0,1)