### Statistics 6871 - Time Series

### Lab One

### Introduction to Splus and Time Series data.

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# Wine Data: We use the Wine Data to examine trends and seasonal patterns in time series data.

# First we plot the data.

par(mfcol=c(3,2)) # The par command lets us divide the graph sheet up into 3 rows and 2 columns.

# The rts command tells splus that what is inside the () is regular time series data.

# The scan command reads data from a file.

# The ts.plot command plots time series data.

Wine <- rts(scan("I:\\Courswrk\\Stat\\esuess\\Stat6871\\Data_bd\\Wine.txt"), start=1980, frequency=12, units="months")

ts.plot(Wine, main="The Austrailian Red Wine Sales", ylab="(thousands)")

# Plot the data again against the index.

Wine <- rts(scan("I:\\Courswrk\\Stat\\esuess\\Stat6871\\Data_bd\\Wine.txt"))

ts.plot(Wine, main="The Austrailian Red Wine Sales", ylab="(thousands)")

# To plot the autocorrelation function for the Wine data we use the acf function.

acf(Wine)

# Note that the Wine data seems to have increasing variance in time. We apply the log to

# the data to stabilize the variance. Note that the acf looks the same.

Wine.log <- rts(log(Wine))

ts.plot(Wine.log, main="Log Red Wine Sales", ylab="log(thousands)",ylim=c(6,8))

acf(Wine.log)

# Note that the Wine data has an increasing trend. To remove the trend we fit a line to

# the data using the lm (linear model) command.

# fit a line

y <- Wine.log

x <- 1:length(Wine.log)

fit <- lm(y ~ x)

# Plot the data and the line.

ts.plot(Wine.log, main="Log Red Wine Sales", ylab="log(thousands)", ylim=c(6,8))

par(new=T)

y.hat <- rts(fit$fitted)

ts.plot(y.hat, ylim=c(6,8))

# Next we plot the detrended data, which are the residuals of the line fit.

par(mfcol=c(3,2))

Wine.log.detrend <- rts(fit$resid)

ts.plot(Wine.log.detrend, main="Detrended Log Austrailian Red Wine Sales")

# Note that the acf shows a 12 month seasonal pattern.

acf(Wine.log.detrend, 40)

# To remove the seasonal pattern we difference the data with a lag of 12. Note that the seasonal

# pattern is gone and that there is not pattern in the acf now.

Wine.log.detrend.diff12 <- diff(Wine.log.detrend, 12)

ts.plot(Wine.log.detrend.diff12, main="Differenced 12 Detrended Log Austrailian Red Wine Sales")

acf(Wine.log.detrend.diff12,40)

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# Accidental Deaths: What patterns do you see in the Accidental Deaths data?

par(mfcol=c(3,2))

Deaths <- rts(scan("I:\\Courswrk\\Stat\\esuess\\Stat6871\\Data_bd\\Deaths.txt"),start=1973,frequency=12,units="months")

ts.plot(Deaths, main="Accidental Deaths USA", ylab="(thousands)")

Deaths <- rts(scan("I:\\Courswrk\\Stat\\esuess\\Stat6871\\Data_bd\\Deaths.txt"))

ts.plot(Deaths, main="Accidental Deaths USA", ylab="(thousands)")

acf(Deaths)

Deaths.diff <- diff(Deaths, 12)

tsplot(Deaths.diff)

acf(Deaths.diff)

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# Lake Huron: What patterns do you see in the Lake Huron data?

par(mfcol=c(3,2))

Lake <- rts(scan("I:\\Courswrk\\Stat\\esuess\\Stat6871\\Data_bd\\Lake.txt"),start=1975,frequency=12,units="months")

tspar(Lake)

ts.plot(Lake, main="Level of Lake Huron")

Lake <- rts(scan("I:\\Courswrk\\Stat\\esuess\\Stat6871\\Data_bd\\Lake.txt"))

tspar(Lake)

ts.plot(Lake, main="Level of Lake Huron")

# fit a line

y <- Lake

x <- 1:length(Lake)

fit <- lm(y ~ x)

ts.plot(Lake, main="Level of Lake Huron", ylim=c(6,12))

par(new=T)

y.hat <- rts(fit$fitted)

ts.plot(y.hat, ylim=c(6,12))

Lake.detrend <- rts(fit$resid)

ts.plot(Lake.detrend, main="Detrended Level of Lake Huron")

acf(Lake.detrend)