Question

6.33 The data file named deere1 contains 82 consecutive values for the amount of deviation (in 0.000025 inch units) from a specified target value that an industrial machining process at Deere & Co. produced under certain specified operating conditions (a) Display the time series plot of this series and comment on any unusual points (b) Calculate the sample ACF for this series and comment on the results (c) Now replace the unusual value by a much more typical value and recalculate the sample ACF. Comment on the change from what you saw in part (b). (d) Calculate the sample PACF based on the revised series that you used in part (c). What model would you specify for the revised series? (Later we will investigate other ways to handle outliers in time series modeling.)

That is R code. The data is at library(TSA) from R.

Answer 1

ANSWER: Below is the R code. I have added the required comments in the code itself.

#################################

rm(list=ls(all=TRUE))

library(TSA)

data(deere1)
X=deere1

summary(X)

## A: Time Series Plot

ts.plot(X,main="Time Series Plot of the data")

d=which(X==max(X))
d
max(X)

# Comment: The data point at index 27 is an outlier. It value is 30
# which is very different from usual trend of the data.

## B: Sample ACF

acf(X,lag.max = length(X))

# Comment: All the acf's except the second one are inside the confidence
# bounds.

# C: NEW ACF

# WE replace the outlier observation with the median of the rest of
# the observations

X[d]=median(X[-d])

acf(X,lag.max = length(X)) # New ACF

# Comment: Now all the acf's are inside confidence bounds. This
# tells that observations are i.i.d.

## D: NEW PACF

pacf(X,lag.max = length(X)) # New PACF

# Comment: The PACF is also under the confidence bounds, so we cannot use
# AR models to model the data. Since ACF says it is i.i.d, it is better
# not to use any time series model.