Question 1. 1.  What are at lest two diagnostic checks you should apply to a Box-Jenkins model to determine its reliability (excluding error measures such as MSE, RMSE, etc.)? (Points : 3.5)       [removed] t-test of the coefficients and residual lag Chi-square values.       [removed] constant term p-test and residual SSE       [removed] Lag Chi-square value of the coefficients and standard error of the residuals       [removed] None of the above determine reliability. Question 2. 2.  The "I" in the ARIMA technique represents (Points : 3.5)       [removed] the minimum error that is generated by the Moving Average process.       [removed] the individual correlations for each lag period       [removed] differencing to create a stationary data series.       [removed] autoregressiveness of the appropriate model Question 3. 3.  Given the following Chi-Square statistics from and ARIMA model at 95% confidence the residuals are not significantly autoregressive Lag             12        24       36       48 Chi-Square 13.0     28.8    60.5     68.5 DF              10        22       34       46 P-Value   0.222     0.152   0.003   0.017 (Points : 3.5)       [removed] only through the 12th lag.       [removed] at least through the 24th lag.       [removed] after the 24th lag.       [removed] in none of the lags. Question 4. 4.  The AR and MA and ARMA model forms can be applied to data with what major requirements? (Points : 3.5)       [removed] Adequate time series data.       [removed] Data that is stationary relative to trend and seasonality.       [removed] Data that is non-linear.       [removed] Data that has been deseasonalized (seasonal effects removed).       [removed] Only 1 and 2 above. Question 5. 5.  What two autoregressive statistics are used to determine the type of ARIMA model that may be appropriate? (Points : 3.5)       [removed] standard deviation and variance       [removed] data mean and residual variance       [removed] autocorrelation and partial autocorrelation       [removed] correlation coefficient and F value Question 6. 6.  A second order MA model implies that (Points : 3.5)       [removed] the autocorrelation function of the data has two significant early lags.       [removed] there are two coefficients in the ARIMA model excluding the constant term.       [removed] the partial autocorrelation function of the data has two significant lags.       [removed] 1. and 2. above       [removed] none of the above. Question 7. 7.  Given an ARIMA model of monthly data described by the menu (1,3,0)(2,2,0) how many data observations will be lost due to differencing to make the series stationary?  (Points : 3.5)       [removed] 24       [removed] 5       [removed] 27       [removed] 25       [removed] 30 Question 8. 8.  Natural log data transformation is useful because it (Points : 3.5)       [removed] enables ARIMA to be run with fewer observations.       [removed] reduces the number of da.

1. Question 1.
1.
What are at lest two diagnostic checks you should apply to a
Box-Jenkins model to determine its reliability (excluding error
measures such as MSE, RMSE, etc.)? (Points : 3.5)
[removed] t-test of the coefficients and residual lag Chi-
square values.
[removed] constant term p-test and residual SSE
[removed] Lag Chi-square value of the coefficients and
standard error of the residuals
[removed] None of the above determine reliability.
Question 2.
2.
The "I" in the ARIMA technique represents (Points : 3.5)
[removed] the minimum error that is generated by the
Moving Average process.
[removed] the individual correlations for each lag period
[removed] differencing to create a stationary data series.
[removed] autoregressiveness of the appropriate model
Question 3.
3.
Given the following Chi-Square statistics from and ARIMA
model at 95% confidence the residuals are not significantly
autoregressive
Lag 12 24 36 48
Chi-Square 13.0 28.8 60.5 68.5
DF 10 22 34 46
P-Value 0.222 0.152 0.003 0.017 (Points : 3.5)

2. [removed] only through the 12th lag.
[removed] at least through the 24th lag.
[removed] after the 24th lag.
[removed] in none of the lags.
Question 4.
4.
The AR and MA and ARMA model forms can be applied to data
with what major requirements? (Points : 3.5)
[removed] Adequate time series data.
[removed] Data that is stationary relative to trend and
seasonality.
[removed] Data that is non-linear.
[removed] Data that has been deseasonalized (seasonal
effects removed).
[removed] Only 1 and 2 above.
Question 5.
5.
What two autoregressive statistics are used to determine the
type of ARIMA model that may be appropriate? (Points : 3.5)
[removed] standard deviation and variance
[removed] data mean and residual variance
[removed] autocorrelation and partial autocorrelation
[removed] correlation coefficient and F value
Question 6.
6.
A second order MA model implies that (Points : 3.5)
[removed] the autocorrelation function of the data has two

3. significant early lags.
[removed] there are two coefficients in the ARIMA model
excluding the constant term.
[removed] the partial autocorrelation function of the data
has two significant lags.
[removed] 1. and 2. above
[removed] none of the above.
Question 7.
7.
Given an ARIMA model of monthly data described by the menu
(1,3,0)(2,2,0) how many data observations will be lost due to
differencing to make the series stationary?
(Points : 3.5)
[removed] 24
[removed] 5
[removed] 27
[removed] 25
[removed] 30
Question 8.
8.
Natural log data transformation is useful because it (Points :
3.5)
[removed] enables ARIMA to be run with fewer
observations.
[removed] reduces the number of data differences required.
[removed] can make curvilinear time series have linear
characteristics.
[removed] reduces the chance of type 1 error.

4. Question 9.
9.
A data series required one seasonal difference and two non
seasonal differences to make it stationary. You have found two
early spikes in the partial autocorrelation function after the non
seasonal differences with converging autocorrelations. In
addition you found one early lag spike in the autocorrelation
function for the seasonal differenced data along with
converging partial autocorrelations. Which is the appropriate
ARIMA menu for the model? (Points : 3.5)
[removed] (1,0, 1)(2,2,0)
[removed] (2,2,0)(0,1,1)
[removed] (2,2,1)(2,1,0)
[removed] (1,2,0)(2,1,0)
Question 10.
10.
The major disadvantages of differencing to make data stationary
include (Points : 3.5)
[removed] Observations (degrees of freedom) will be lost
and it requires a large amount of data.
[removed] Lost observations have influence on the
significance of the ARIMA model.
[removed] Too many differences are taken the differenced
data series becomes more autoregressively unstable.
[removed] All of the above.
[removed] None of the above since differencing does not
influence the data characteristics or the model outcome.
Question 11.
11.

5. What is the rule of parsimony in ARIMA forecasting? (Points :
3.5)
[removed] Better forecast results can be obtained from more
complex ARIMA models
[removed] Simpler models are preferred due to fewer data
differences.
[removed] The less complex the model given the same
results the better..
[removed] Everything being equal, ARIMA forecast
accuracy is enhanced by adding more significant coefficients.
Question 12.
12.
Given the ARIMA menus below which will result in 4 model
coefficients excluding a constant term? (Points : 3.5)
[removed] (1,1,2)(2,1,0)
[removed] (0,1,2)(1,2,1)
[removed] (0,2,1)(1,2,0)
[removed] (1,2,0)(1,2,0)
Question 13.
13.
In an ARIMA model with monthly data how many coefficients
(excluding the constant term) are in the ARIMA model specified
as (1,1,2)(0,1,1) and how many observations are
lost due to differencing? (Points : 3.5)
[removed] 3 coefficients and 5 observations lost
[removed] 2 coefficients and 12 observations lost
[removed] 4 coefficients and 13 observations lost
[removed] 3 coefficients and 14 observations lost

6. Question 14.
14.
Which ARIMA model type is used to derive forecasts of a
variable based only on a linear function of its past data values?
(Points : 3.5)
[removed] a moving average model
[removed] a second order moving average model
[removed] an ARMA model
[removed] an autoregressive model
Question 15.
15.
The Chi-Square values in ARIMA results determine the (Points
: 3.5)
[removed] need for additional differencing.
[removed] strength of the ARIMA model.
[removed] autoregressiveness of the ARIMA residuals.
[removed] normality of the residual distribution.
Question 16.
16.
Autocorrelations differ from partial autocorrelations in that
(Points : 3.5)
[removed] autocorrelation is the total effect correlation
between lag values of a time series that could include previous
lag autoregressive effects while partial autocorrelation is the
direct correlation only between the specific lag value and the
data observation.
[removed] in autocorrelation other lag effects are allowed
to vary while in partial autocorrelation the other lagged effects
are held constant.

7. [removed] partial autocorrelation is the indirect correlation
only between the specific lag value of the variable and the
variable observation while autocorrelation is the direct effect be
observations and the lagged observations.
[removed] partial autocorrelation is closer to true
correlation since the significance can be measured by t values
while autocorrelation cannot.
[removed] only 1 and 2 above.
Question 17.
17.
You have a quarterly data series ACFs and the first four
autocorrelation are significantly different from zero while the
subsequent autocorrelations decreases slowly toward zero. In
addition the autocorrelations for lag 8, 12 and 16 are
significantly different from zero. What are your data
autoregressive characteristics? (Points : 3.5)
[removed] trend and cycle
[removed] trend and seasonality
[removed] only cycle
[removed] only seasonality
[removed] non linearity
Question 18.
18.
In the standard ARIMA menu notation what does P stand for?
(Points : 3.5)
[removed]
The measure of the probability of residuals equal to zero
[removed]
For the observed non seasonal moving average (MA) tendencies
[removed]

8. For the observed seasonal autoregressive (AR) tendencies
[removed]
For the observed non seasonal autoregressive (AR) tendencies
[removed] For the MA significant ACF spikes
Question 19.
19.
What is the value of the coefficient if the standard error of the
coefficient is 1.25 and the t-value is 2.80? (Points : 3.5)
[removed] 3.5
[removed] 446
[removed] 2.24
[removed] 1.56
Question 20.
20.
Some ARIMA models do not require a constant term. What
determines the need for it? (Points : 3.5)
[removed] The t-value of the coefficients.
[removed] The LBQ values.
[removed] The mean value of the residuals.
[removed] The mean value of the last differenced data
series.
Question 21.
21.
Given the data found in DocSharing under Exam 2 Data
Problem 21 what is the first differenced value of the second
seasonal difference of the sales data? (Take 2 seasonal
differences) (Points : 6)

9. [removed] 110
[removed] -15
[removed] -143
[removed] 25
[removed] 21
Question 22.
22.
Given the following data for monthly pickup truck sales for a
large Texas dealership. Determine the best ARIMA model to
apply and select the menu for the model in (0,0,0)
(0,0,0)
form. (Remember that I will only accept this ARIMA model
with non-significant residuals.)
Note that you must obtain the monthly truck data from Exam 2
Data, Problem 22 tab found in DocSharing.
Do not
take a hold out from this data.
(Points : 6)
[removed]
(0,1,0)(1,1,1) an Seasonal ARMA model with one seasonal
difference and a MA1 model with one non seasonal difference
[removed] (0,1,1) (1,1,1) a seasonal ARMA model with one
seasonal difference and an MA1 non seasonal model with one
non seasonal difference
[removed]
(1,1,0)(0,0,0) an AR 1 model with one non seasonal difference
[removed]
(1,1,1)(1,1,0) a seasonal AR model with one seasonal difference
and a non seasonal ARMA model with one non seasonal
difference
[removed] (1, 2, 0) (1,1,0) A seasonal AR model with one
seasonal difference and a non seasonal AR model with two non

10. seasonal differences.
Question 23.
23.
What are the significant coefficient(s) of the best ARIMA
model found in the question above excluding the constant term?
(Points : 6)
[removed] .3833, .2930 and -.3209
[removed] .7375 and .0394
[removed] .9432
[removed] -.4321, and .2839
[removed] -.2836, .7280 and .8890
Question 24.
24.
What is the fit period MAPE of the best ARIMA model? (Points
: 6)
[removed] 2.503
[removed] 4.320
[removed] 1.404
[removed] -.3234
Question 25.
25.
What is the forecast value for the 6
th
month from the end of the data series? Develop a forecast with
the best ARIMA model—then choose the value for the 6the
month.
(Points : 6)

11. [removed]
353.234
[removed]
432.365
[removed]
143.334
[removed]
135.147
[removed] 134.595