ARIMA Models INSTRUCTIONS: Use MINITAB 17 to complete the following questions. You are to work independently on this assignment. All data sets for this assignment have been provided. Please submit...

ARIMA Models
INSTRUCTIONS: Use MINITAB 17 to complete the following questions. You are to work
independently on this assignment. All data sets for this assignment have been provided.
Please submit your completed assignment that includes relevant MINITAB output and
comments (make sure to comment on your results when asked) as ONE WORD document .
1. Use the data set WeeklyRestaurantSales.MTW. These data
are weekly sales at a small restaurant.
(a) Prepare a time series plot, ACF and PACF for these data. Is there
evidence to suggest that the data should be differenced? Explain.
Time Series Plot


Going through the time series plot, it is observed that there exists irregular variation in the
weekly sales at a small restaurant
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Index
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Time Series Plot of Sales
ACF

PACF


Going through the PACF plot it is found that the first lag value is statistically significant,
while all other lags are not statistically significant. This provides a clear indication of promoting
AR(1) model for these data
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1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Lag
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Autocorrelation Function for Sales
(with 5% significance limits for the autocorrelations)
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1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Lag
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Partial Autocorrelation Function for Sales
(with 5% significance limits for the partial autocorrelations)
(b) Prepare the ACF and PACF for the first differenced data. Identify one
plausible ARIMA model based on these plots. Justify your selection.
(c) Fit an ARIMA (1, 1, 0) to these data and show the ACF and PACF for the
residuals. Is this model adequate based on the sampling statistics?
Explain.




2624222018161412108642
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Lag
A
u
to
c
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rr
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la
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ACF of Residuals for Sales
(with 5% significance limits for the autocorrelations)


The normal probability plot indicates that there exists outlier in the dataset. Going
through the PACF, it is found that all the lags are statistically insignificant. This indicates that
the process is not stationary
(d) Fit an ARIMA (0, 1, 1) to these data and show the ACF and PACF for the residuals. Is this
model adequate based on the sampling statistics? Explain.
2624222018161412108642
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Lag
P
a
rt
ia
l
A
u
to
c
o
rr
e
la
ti
o
n
PACF of Residuals for Sales
(with 5% significance limits for the partial autocorrelations)




The normal probability plot indicates that there exists outlier in the dataset. Going through the
PACF, it is found that all the lags are statistically insignificant. This indicates that the process is
not...