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)

t-test of the coefficients and residual lag Chi-square values. constant term p-test and residual SSE Lag Chi-square value of the coefficients and standard error of the residuals None of the above determine reliability.

Question 2. 2. The "I" in the ARIMA Box-Jenkinstechnique represents (Points : 3)

the minimum error that is generated by the Moving Average process. the individual correlations for each lag period differencing to create a stationary data series. 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)

only through the 12th lag. at least through the 24th lag. after the 24th lag. 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)

Adequate time series data. Data that is stationary relative to trend and seasonality. Data that is non-linear. Data that has been transformed to improve linearity with other variables. 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)

standard deviation and variance data mean and residual variance autocorrelation and partial autocorrelation correlation coefficient and F value

Question 6. 6. A second order MA model implies that (Points : 3)

the autocorrelation function of the data has two significant early lags. there are two coefficients in the ARIMA model excluding the constant term. the partial autocorrelation function of the data has two significant lags. 1. and 2. above 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)

24 5 27 25 30

Question 8. 8. Natural log data transformation is useful because it (Points : 3)

enables ARIMA to be run with fewer observations. reduces the number of data differences required. can make concave from above curvilinear time series have linear characteristics. reduces the chance of type 1 error.

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)

(1,0, 1)(2,2,0) (2,2,0)(0,1,1) (2,2,1)(2,1,0) (1,2,0)(2,1,0)

Question 10. 10. The major disadvantages of differencing to make data stationary include (Points : 3)

Observations (degrees of freedom) will be lost to make the data series stationary relative to seasonality and trend/cycle. Lost observations haveinfluence on the significance of the ARIMA model. Too many differences are taken the differenced data series becomes more autoregressively unstable. Differencing may leave too few observations to calculate the OLS coefficient values for the ARIMA model. All of the above.

Question 11. 11. What is the rule of parsimony in ARIMA forecasting? (Points : 3)

Better forecast results can be obtained from more complex ARIMA models Simpler models are preferred due to fewer data differences. The less complex the model given the same results the better.. Everything being equal, ARIMA forecast accuracy is enhanced by adding more significant coefficients.

Question 12. 12. You have differenced a data series for trend and found the Trend Analysis slope term to be .064. You decide to difference it for trendagain an the slope term in now .083. Whatcan youconclude from this? (Points : 3)

You have differenced it one too many times. You should use the first differenced data for the ARIMA model. You need to difference it again to remove all of the trend to determine the best ARIMA model. The slope is much too low to have a good ARIMA model result with the data. Try a seasonal difference even though the data does not show any seasonality. You do not need a constant term in the ARIMA model.

Question 13. 13. Given the ARIMA standard formmenus below which will result in 4 model coefficients excluding a constant term? (Points : 3)

(1,1,2)(2,1,0) (0,1,2)(1,2,1) (0,2,1)(1,2,0) (1,2,0)(1,2,0)

Question 14. 14. 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)

3 coefficients and 5 observations lost 2 coefficients and 12 observations lost 4 coefficients and 13 observations lost 3 coefficients and 14 observations lost

Question 15. 15. Significant residuals from an ARIMA model indicate that the model did not explain the trend, cycle and seasonality of the data series and the model is unreliable in forecasting. (Points : 3)

True False

Question 16. 16. 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)

a moving average model a second order moving average model an ARMA model an autoregressive model

Question 17. 17. The Chi-Square values in ARIMA results determine the (Points : 3.5)

need for additional differencing. strength of the ARIMA model. autoregressiveness of the ARIMA residuals. normality of the residual distribution.

Question 18. 18. Autocorrelations differ from partial autocorrelations in that (Points : 3.5)

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. in autocorrelation other lag effects are allowed to vary while in partial autocorrelation the other lagged effects are held constant. 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. partial autocorrelation is closer to true correlation since the significance can be measured by t values while autocorrelation cannot. only 1 and 2 above.

Question 19. 19. 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)

trend and cycle trend and seasonality only cycle only seasonality non linearity

Question 20. 20. In the standard ARIMA menu notation what does P stand for? (Points : 3.5)

The measure of the probability of residuals equal to zero For the observed non seasonal moving average (MA) tendencies For the observed seasonal autoregressive (AR) tendencies For the observed non seasonal autoregressive (AR) tendencies For the MA significant ACF spikes

Question 21. 21. 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)

3.5 446 2.24 1.56

Question 22. 22. Some ARIMA models do not require a constant term. What determines the need for it? (Points : 3.5)

The t-value of the coefficients. The LBQ values. The mean value of the residuals. The mean or intercept value of the last differenced data series.

Question 23. 23. Given the data found in DocSharing under Exam 2 Data Problem23 what is the first differenced value of the second seasonal difference of the sales data? (Take 2 seasonal differences) (Points : 3.5)

110 -15 -143 25 21

Question 24. 24. Given the data for quarterly Silver Streak Bus Lines revenue found in Doc Sharing Exam 2 Data, Problem 24 tab..Do not take a hold out from this data. 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 an ARIMA model with non-significant residuals at the 95% confidence level for all lag periods. Also apply the law of parsimony. (Points : 4.5)

(0,1,0)(1,1,1) an Seasonal ARMA model with one seasonal difference and a MA1 model with one non seasonal difference (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 (0,1,1)(0,0,0) anMA 1 model with one non seasonal difference (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 (1, 1, 1) (0,0,0) A non-seasonal ARMA model with one non-seasonal difference.

Question 25. 25. What are the significant coefficient(s) of the best ARIMA model found in the question above excluding the constant term? (Points : 4.5)

-.3924 .7375 and .0394 .9432 -.4321, and .2839 -.2836, .7280 and .8890

Question 26. 26. What is the fit period MAPE of the best ARIMA model? (Points : 4.5)

2.50% 9.73% 14.04% 4.32% 7.34%

Question 27. 27. What is the fit periodRMSE of the best ARIMA model? (Points : 3.5)

25.3 114.3 64.4 46.7 90.7

Question 28. 28. What is the forecast value for the 8^thfuture quarter from the best ARIMA model? (Points : 3.5)

353.23 632.36 843.33 735.14 786.46

Question 29. 29. What do you note about the forecast? (Points : 3.5)

The forecast is growing at a rapid rate representing a strong trend. The forecast decreases at a rapid rate reflecting a strong negative trend. The forecast has constant values similar to a single exponential smoothing forecast. The forecast has seasonality similar to a Winter's method forecast result.

Question 30.30. You examine the forecast and compare it to actual future Silver Streak Bus Linequarterly revenue data that is shown below.

2014 Q1 $702.29

2014 Q2 $822.58

2014 Q3 $945.43

2014 Q4 $1104.84

What should you do as a result of this 2014 actual data? (Points : 3.5)

Since the track record of the forecast has been good through the quarters you stay with the forecast for at least the next quarter (forecast quarter 5). You accept the high actual Q4 value and raise the remaining forecast quarters to this level. When you note the Q4 actual data your include all of the new actual data in a new revised ARIMA model to forecast the remaining quarters. As soon as you get the first actual data (2014 Q1) observation you derive a new ARIMA model. Discard the ARIMA forecast after the second quarter of the forecast and reforecast the data using the same ARIMA model but with new data from Q1 and Q2.