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#### Business Forecasting 6th Edition by Wilson – Test Bank

**Chapter 6**

** **

**MULTIPLE CHOICE TEST BANK**

Note: The correct answer is denoted by **.

- The time-series decomposition model presented in Chapter Six is best described as a

- A) ratio-to-exponential smoothing technique.
- B) ratio-to-moving average technique. **
- C) multiplicative moving average technique.
- D) moving average factorization technique.
- E) None of the above.

- Which of the following is
__not__a reason why time-series decomposition has gained favor with forecasters and their managers?

- A) Forecast accuracy.
- B) Ease in understanding.
- C) Very little computation is required. **
- D) Time-series decomposition resembles the way many managers analyze the future.
- E) None of the above.

- Which of the following is
__not__a technique used to generate forecasts with time series decomposition?

- A) Moving averages.
- B) Trend projection.
- C) Multiplicative seasonality.
- D) Dummy variables. **
- E) All of the above.

- In time-series decomposition analysis, decomposition refers to:

- A) converting an annual trend line into a monthly trend line.
- B) deseasonalizing the data.
- C) separating a time series into component parts. **
- D) isolating the cyclical component of a time series.
- E) None of the above.

- Which of the following is
__not__a component in the time series decomposition model?

- A)
- B) Seasonal variation.
- C) Irregular variation.
- D) Business indicators. **
- E) Cyclical variation.

- Which forecasting model identifies and forecasts component factors that influence the level of a time series?

- A) Exponential smoothing.
- B) Time series decomposition. **
- C) Moving average smoothing.
- D) Exponential smoothing.
- E) Winter’s smoothing.

- Which of the following best describes the general approach to forecasting when applying classical time-series decomposition as described in the text?

- A) Y = T + S + C + I.
- B) Y = T * S * C * I. **
- C) Y = T * S * C.
- D) Y = (T + C) * S.
- E) None of the above.

- Classical time series decomposition, as described in the text, model seasonality

- A) using dummy variables.
- B) in an additive fashion.
- C) in an exponential manner.
- D) similar to Winter’s smoothing. **
- E) None of the above.

- Which of the following is
__not__correct about using moving averages to deseasonalize a time series?

- A) The number of periods in the average should reflect the number of seasons.
- B) The number of periods for annual data should be 12. **
- C) The number of periods for quarterly data should be 4.
- The moving average is interpreted as the typical level of a variable in a given year.
- E) All of the above.

- Deseasonalizing the data using moving averages

- A) removes the seasonal component of a time series.
- B) removes the irregular component of a time series.
- C) preserves the cyclical component of a time series.
- D) preserves the trend component of a time series.
- E) All of the above. **

- When calculating centered moving-averages in time-series decomposition, which of the following is
__not__true?

- A) If the number of periods in the average is odd, the moving averages will automatically be centered, and no further adjustment is usually made.
- B) If the number of periods in the average is four, the convention is to place the moving average in period 3.
- C) To center moving averages, a two-period moving average of the moving averages is calculated.
- D) The second smoothing for even numbers of period helps to further smooth out irregular components in the data.
- E) All of the above. **

- When calculating centered moving averages, how many data points are lost for a given time series, when a n-period moving average is used?

- A) n points at the beginning.
- B) n points at the end.
- C) n points on both ends.
- D) sample size minus n points at the beginning.
- E) None of the above. **

- When calculating centered moving-averages using a 4-period moving average, how many data points are lost at the beginning of the original series?

- A)
- B) **
- C)
- D)
- E) None of the above.

- When calculating centered moving-averages using a 4-period moving average, how many data points are lost at both ends of the original series?

- A)
- B) **
- C)
- D)
- E) None of the above.

- In time-series decomposition, seasonal factors are calculated by

- A) SFt = (Yt)*(CMAt).
- B) SFt = CMAt/Yt.
- C) SFt = Yt / CMAt. **
- D) SFt = Yt – CMAt.
- E) None of the above.

- A seasonal index number of .80 for quarter one of an automobile parts manufacturer suggests

- A) Quarter one sales are 80% above the norm.
- B) Quarter one sales are 1.80% below the norm.
- C) Quarter one sales are 20% below the norm. **
- D) Quarter one sales are 80% below the norm.
- E) None of the above.

- The sum of seasonal index numbers should equal

- A)
- B) sample size/2.
- C) number of seasons. **
- D)
- E) 4

- The sum of seasonal index numbers for monthly data should equal

- A)
- B) sample size/2.
- C)
- D) **
- E) None of the above.

- Quarter one sales for a tire manufacturer were $120,000,000. If the quarter one seasonal index was 1.20, what is an estimate of annual sales for this firm?

- A) $100,000,000.
- B) $144,000,000.
- C) $400,000,000. **
- D) $576,000,000.
- E) None of the above.

- Suppose Nike sales are expected to be 1.2 billion dollars for the year 2009. If the January seasonal index for Nike is .98, what is a reasonable estimate for January 2009 sales revenue?

- A) .098 billion. **
- B) .1 billion.
- C) 176 billion.
- D) 18 billion.

The following seasonal indexes are used to answer the next three questions.

Seasonal Indexes of sales revenue of People’s Bank are:

January | 1.20 |

February | .90 |

March | 1.00 |

April | 1.08 |

May | 1.02 |

June | 1.10 |

July | 1.05 |

August | .90 |

September | .85 |

October | 1.00 |

November | 1.10 |

December | .80 |

- Total revenue for People’s Bank in 2009 is forecasted to be $60,000. Based on the seasonal indexes above, sales in the first three months of 2009 should be:

- A) $4,800
- B) $15,500 **
- C) $14,723
- D) $13,500
- E) None of the above.

- If December 1999 revenue for People’s Bank amounted to $5,000, a reasonable estimate of revenue for January 2000, based on the seasonal indexes given above would be:

- A) $3,000
- B) $4,500
- C) $4,800
- D) $7,500 **
- E) None of the above.

- If revenue of People’s Bank amounted to $5,500 in November 2009; the November 2009 sales revenue, after adjustment for seasonal variation using the indexes given above, would be:

- A) $6,500
- B) $6,050
- C) $5,500
- D) $4,500

E None of the above. **

- A company has computed a seasonal index for its quarterly sales. Which of the following statements is
__not__correct?

- A) The sum of the four quarterly seasonal index numbers is 4.
- B) An index of .75 for quarter-one sales indicates that sales were 25 percent lower than average sales.
- C) An index of 1.10 indicates sales 10% above the norm.
- D) The index for any quarter must be between 0 and 2. **
- E) The average index is 1.

- In computing a seasonal index, specific seasonals were tabulated for each month. The averages over time for the twelve months were obtained and summed. If the mean seasonal factor for June was 96.9, and the sum for all twelve months is 1195; the adjusted seasonal index for June is:

- A) 7 **
- B) 9.
- C) 4.
- D) 7.
- E) None of the above.

- Assume the following specific seasonal factors for January based on the ratio-to-moving average method:

88.2 85.9 79.2 92.4 80.1 82.4

What is the seasonal index for January using the modified mean method?

- A) 1
- B) 5
- C) 3
- D) 2
- E) 7 **

- The following specific seasonal factors were estimated for the month of October:

65.4 76.8 66.9 72.6 70.0

If the adjustment is .98 and the modified mean is used, and if the expected trend for October is $800, which of the following is closest to the seasonally adjusted forecast?

- A) $570
- B) $561
- C) $551 **
- D) $1,169
- E) None of the above.

- The long-term trend of a time series in the decomposition model is estimated using

- A) the cycle factors.
- B) the actual unsmoothed data.
- C) the centered moving average data. **
- D) the series of seasonal factors.
- E) All of the above.

- Consider the following data:

Year |
Sales Revenue | Coded Time |

2006 |
800 | 0 |

2007 |
840 | 1 |

2008 |
900 | 2 |

Which linear trend model best fits this data?

- A) Y = 846.67 + 100X.
- B) Y = 840 + 100X.
- C) Y = 846.67 + 50X.
- D) Y = 796.67 + 50X. **
- E) None of the above.

- Which trend model would you choose if the variable you are seeking to forecast were increasing at a constant percentage rate?

- A) Y = a + bX.
- B) Y = abX. **
- C) Y = b + b1X + b2X2.
- D) Y = b(1/X).
- E) None of the above.

- The cyclical component of a time series is measured by

- A) Yt / CMAt.
- B) CMAt / CMATt. **
- C) Yt / SIt.
- D) CMAt / CMAt-1.
- E) None of the above.

- A cycle factor

- A) ranges between 0 and 1
- B) ranges between -1 and +1
- C) above 1 means a high period in the cycle **
- D) above 1 means a low period in the cycle
- E) is usually negative

- Which data series is
__not__used in the calculation of cycle factors?

- A)
- B)
- C)
- D) **
- E) All of the above.

- A researcher mistakenly uses deseasonalized data in calculating the seasonal factors. The calculated seasonal factors are likely to be:

- A) negative
- B) a mix of negative and positive values
- C) very close to one
- D) ver close to zero
- E) None of the above.

- The Sky-Is-Falling forecasting firm is predicting a deep recession next year. What would be the average forecasted cycle factor for next year if you believe such a forecast?

- A) Less than zero.
- B) Close to zero, but negative.
- C) Close to one, but greater than one.
- D) Substantially greater than one.
- E) Less than one. **

- Which of the following is
__not__a similarity between seasonal and cycle factors?

- A) They are both calculated as ratios.
- B) They both sum to the number of data points in the averaging process. **
- C) They both model variability in the dependent variable.
- D) They both may equal one.
- E) All of the above.

- Which of the following is
__not__helpful in generating forecasts of cycle factors?

- A) A time-series plot of the data.
- B) Length of previous cycles.
- C) Amplitude of previous cycles.
- D) The seasonal factors **.

- The range of economic activity from the beginning trough of an expansion to the peak of the expansion is called

- A) recession phase.
- B) contraction phase.
- C) **
- D)
- E) None of the above.

- If business cycles were pure cycles, they

- A) would have constant amplitude.
- B) would have constant periodicity.
- C) would be easy to forecast.
- D) all of the above. **

- Over a long period of time, if measured correctly, cycle factors should average

- A)
- B) **
- C)
- D)
- E)

- Which of the following is
__not__part of the index of leading economic indicators?

- A) Index of stock prices.
- B) Index of industrial production. **
- C) M2 Money Supply.
- D) Index of new private housing starts.

- Which of the following is
__not__a part of the index of lagging economic indicators?

- A) Average prime rate of interest.
- B) Index of unit labor costs.
- C) Outstanding commercial loans.
- D) Ratio of consumer installment credit to personal income.
- E) M2 money supply. **

- What is the major problem when using time-series smoothing techniques to forecast the cyclical component of a time series?

- A) It takes too much data.
- B) It takes too much computer time and effort.
- C) Trend reversals are difficult to forecast. **
- D) Holt’s smoothing estimates a linear trend.

- Which statement is
__not__correct?

- A) Time series decomposition tends to fit the data very well.
- B) Time series decomposition accuracy is usually overstated by model fit statistics.
- C) The better the forecast of the cycle factors, the better the out-of-sample accuracy of time-series decomposition.
- D) Time series decomposition tends to be well understood by forecast consumers.
- E) All of the above. **

- Which of the following statements regarding time series decomposition is
__not__correct?

- A) The fluctuating components of a time series are cyclical, seasonal, and irregular.
- B) Short-term forecasts are more accurate than long term.
- C) If the original data are valued in dollars, the values of the cycle factors must also be in dollars. **
- D) Seasonal index numbers for monthly data average 1 and total 12.
- E) All of the above.

# ESSAY/PROBLEM EXAM QUESTIONS

- The time-series decomposition model, it is argued, has the advantage in allowing analysts to forecast the cyclical components of a time series.

- a) Present a brief overview of time-series decomposition paying specific attention to how the business cycle is modeled.

ANSWER: The time-series decomposition model, which can be expressed by a simple multiplicative expression:

Y = T * S * C * I,

where T is the long-term trend component, S is a seasonal index number, C is a cycle factor representing the impact of the business cycle, and I is the irregular component. This model decomposes a time series into component parts, analyzes and generates forecasts of each subcomponent, and then recombines in a multiplicative fashion to generate forecasts.

Defined as wavelike movements about the long-term trend, the cyclical component of a time series represents variation in a time series explained by the business cycle. The cyclical component is measured by a series of cycle factors, which are simply the ratio of deseasonal value to centered moving-average trend value.

As shown in the text, when applied to forecasting domestic car sales, time-series decomposition produces excellent in sample fit as measured by RMSE, but poor out-of-sample accuracy. This lack of accuracy is critically tied to the forecast cycle factors, which are not easily obtained.

- b) Present a brief discussion on how analysts provide forecasts of the cyclical component of a time series.

ANSWER: While there are substantial rewards for correctly forecasting the cyclical component of a time series, it can be a rather difficult task. First of all, application of smoothing techniques may work fine for trends, but fare poorly when predicting turning points in the business cycle. Regression analysis maybe a better tool, but requires a substantial data history of many variables to generate reliable estimates of cycle factors. Finally, this is one application where subjective judgment (analysts’ forecasts) may play a particularly important role in creating forecasts.

- You are the sales manager for Tom Turkey Farms, which is a major producer of turkey food products. Discuss the reasons why you might prefer to use time-series decomposition to generate sales forecasts. In your answer address each aspect of the time-series decomposition procedure.

ANSWER: First of all, time series decomposition is capable of producing quite accurate forecasts. Second, the model is easy to understand and to present forecast results to upper-level management. Third, time-series decomposition helps manager’s focus on specific issues such as trend, seasonality, and the business cycle in preparing sales forecasts, which supports the business planning process. For instance, in forecasting the trend in sales, managers may look at trends in dietary needs and tastes, such as demand for low-fat products. Thanksgiving and other holidays lead to analysis of seasonality. In addition, the state of the economy may affect consumer purchasing power and the demand for low-cost turkey products. Finally, smoothing the data removes short-term random noise from the data so managers can focus on more important issues. The point is simple: Time series decomposition fits naturally into the business planning process.

- Consider the following sales data measured in millions of dollars:

Period |
Time Index | Actual Sales (millions) |

1999Q1 |
1 | 12 |

1999Q2 |
2 | 18 |

1999Q3 |
3 | 20 |

1999Q4 |
4 | 12 |

2000Q1 |
5 | 12 |

2000Q2 |
6 | 20 |

- a) Find a four-period moving average for each quarter.

ANSWER: Moving averages will not exist for Q1 and Q2 of 1999 and for Q2 of 2000 because of data limitations. For the other periods the moving averages were found as:

MA3 = (12 + 18 + 20 + 12)/4 = 15.5

MA4 = (18 + 20 + 12 + 12)/4 = 15.5

MA5 = (20 + 12 + 12 + 20)/4 = 16.0.

- b) Find the centered moving averages for the sample.

ANSWER: Since calculating the centered moving average is essentially another smoothing, we will not be able to calculate the centered moving average for the second first quarter of 2000. For Q3 and Q4 of 1999, the centered moving averages are found as follows:

CMA3 = (MA3 + MA4)/2 = (15.5 + 15.5)/2 = 15.5

CMA4 = (MA4 + MA5)/2 = (15.5 + 16.0)/2 = 15.75.

- c) Find the seasonal factors for Q3 and Q4 of 1999? Can you find the seasonal factor for 2000Q1?

ANSWER: To find seasonal factors we must have both the actual series value and the centered moving average value for a given period of time. Accordingly, we cannot calculate a seasonal factor for Q1 2000.

Seasonal factors of Q3 and Q4 of 1998 are found as follows:

SFt = Yt/CMAt.

Accordingly, our Q3 and Q4 seasonal factors are:

PERIOD |
SEASONAL FACTOR |

1999Q3 |
20/15.5 = 1.29 |

1999Q4 |
12/15.75 = 0.76 |

These factors suggest that sales are above the yearly average in Q3 and below the yearly average in Q4.

Note that since these factors are calculated based upon data for Q3 and Q4 of 1999, they must be smoothed with similar estimates from other periods to calculate the Q3 and Q4 seasonal index numbers.

- Quarter 3 seasonal factors for sales of Gerber baby foods were reported to be:

YEAR |
SEASONAL FACTOR |

1996 |
1.25 |

1997 |
1.13 |

1998 |
1.03 |

1999 |
1.32 |

2000 |
1.24 |

- a) What is the unadjusted seasonal index for Q3 sales?

ANSWER: SI(Q3) = (1.25 + 1.13 + 1.03 + 1.32 + 1.24)/5 = 1.194.

- b) If the sum of seasonal index numbers is 3.95, find the adjusted Q3 seasonal index.

ANSWER: Adjusted SI(Q3) = 1.194(4/3.95) = 1.209.

This adjustment ensures that the seasonal index numbers sum to four.

- You are the chief financial officer of a highly cyclical enterprise. Part of your job responsibility to generate quarterly sales revenue forecasts for the firm. Your Board of Directors prefers that you use time-series decomposition as one of methods used to generate forecasts.

Next board meeting, you are scheduled to present a detailed analysis of how forecasts of the cyclical component of sales were obtained. This is because in quarter four of last year, your staff under-predicted the health of the economy leading to a 5 percent error in forecasting the firm’s revenue for that quarter. What are you going to tell the Board?

ANSWER: First of all, a five percent forecast error is not all that bad, depending on the accuracy of competitors’ forecasts. In addition, the board probably wants to see why you failed to forecast the rapid growth last quarter, and that you are attempting to learn from such a mistake. In general, it is never a good idea to try a hide or explain away forecast errors. Accordingly, you should ask board members their input into the forecast process.

As for methods to forecast the cycle factor in a time series, there are three principal methods.

First, time series smoothing methods with the exception of Winter’s (which accounts for seasonality) may be employed. These methods require little data and are quite accurate in forecasting trends. They, however, are prone to serial correlation, which may generate artificial cycles, and they can never forecast data turning points since they are effectively based on past data observations.

If the researcher has lots of time and data, they can employ causal regression models to forecast the cycle factors. Here, forecasters can employ factors making up the leading, coincident, and lagging index of economic indicators, discussed in the chapter. This method is likely to give greater forecast accuracy relative to smoothing methods.

Finally, the forecasting of cycle factors may depend on the experience of the forecaster and this is one area of forecasting where subjective analyst’s opinions are especially valued.

**Chapter 7**

**Multiple Choice**

*Identify the choice that best completes the statement or answers the question.*

____ 1. Why are Box-Jenkins models often referred to as “black boxes?”

a. | They ignore causal variables. |

b. | They use regression analysis in non-standard ways. |

c. | They evaluate forecast accuracy different from regression models. |

d. | They are difficult to understand. |

e. | All of the above. |

____ 2. Which of the following is __not__ a potential advantage to using ARIMA models to generate forecasts?

a. | They are useful when a set of explanatory variables cannot be identified. |

b. | They are useful when the only data available are the variable to be forecast. |

c. | They determine a great deal of information about a time series. |

d. | They are especially useful for long-term forecasts. |

e. | All of the above are potential advantages. |

____ 3. What is a key difference between ARIMA-type models and multiple regression models?

a. | The dependent variable. |

b. | Attention to data trend and seasonality. |

c. | Attention to serial correlation. |

d. | Use of data of the explanatory variables. |

e. | None of the above. |

____ 4. In the model selection process for ARIMA-type models, the ultimate goal is to find an underlying model that

a. | explains the dependent variable. |

b. | leads to non-random errors. |

c. | produces white noise forecast errors. |

d. | models the nonlinear components in a time series. |

e. | None of the above. |

____ 5. If it is found that the forecast errors from an ARIMA-type model exhibit serial correlation, the model

a. | is not an adequate forecasting model. |

b. | is a candidate for adding another explanatory variable. |

c. | almost surely contains seasonality. |

d. | is a candidate for Cochrane-Orcutt regression. |

e. | All of the above. |

____ 6. “Black box” in the ARIMA model methodology does __not__ refer to

a. | autoregressive models. |

b. | moving average models. |

c. | causal models. |

d. | mixed autoregressive-moving-average models. |

e. | All of the above. |

____ 7. “White noise” refers to model forecast errors that are

a. | normally distributed. |

b. | non-normal. |

c. | serially independent. |

d. | heteroscedastic. |

e. | None of the above. |

____ 8. The ARIMA model selection process seeks to find that underlying model which removes

a. | all deterministic components from the data. |

b. | data trend. |

c. | data seasonality. |

d. | any serial correlation in the data. |

e. | All of the above. |

____ 9. Which of the following model is __not__ considered as a potential correct “black box” in Box-Jenkins modeling?

a. | MA(1) models. |

b. | Exponential smoothing models. |

c. | Time-trend regression models. |

d. | Autoregressive models. |

e. | None of the above are considered as a potential correct “black box.” |

____ 10. Which of the following is __not__ in the moving-average class of Box-Jenkins models?

a. | Yt = et + W1et-1 + W2et-2. |

b. | Yt = et + W1et-1. |

c. | Yt = Xt + et + et-1. |

d. | Yt = et + 0.7et-1. |

____ 11. Moving-average models are best described as

a. | simple averages. |

b. | non-weighted averages. |

c. | weighted averages of white noise series. |

d. | weighted averages of non-normal random variates. |

e. | None of the above. |

____ 12. Autocorrelation and partial autocorrelation functions differ in

a. | what series is being analyzed. |

b. | their length. |

c. | diagnostic ability to identify ARIMA models. |

d. | what is being held constant in the observed correlogram. |

e. | All of the above. |

____ 13. For a moving-average solution to a forecasting problem, the autocorrelation plot should _____ and the partial autocorrelation plot should _____.

a. | slowly approach zero; slowly approach zero. |

b. | dramatically approach zero; exponentially approach one. |

c. | slowly approach one; and cyclically approach zero. |

d. | dramatically cut off to zero; decline to zero wither monotonically or in a wavelike manner. |

e. | None of the above. |

____ 14. The autocorrelation function correlogram should show spikes close to ____ lags if a moving-average type model generates the true data.

a. | One. |

b. | Two. |

c. | Three. |

d. | Four. |

e. | All of the above. |

____ 15. Which of the following patterns of the partial autocorrelation function correlogram is inconsistent with an underlying moving-average data process?

a. | Exponentially declining to zero. |

b. | Cyclically declining to zero. |

c. | Positive at first, then negative and increasing to zero. |

d. | Negative at first, then positive and declining to zero. |

e. | None of the above. |

____ 16. The autocorrelation function of a time series shows coefficients significantly different from zero at lags 1 through 4. The partial autocorrelation function shows one spike and monotonically increases to zero as lag length increases. Such a series can be modeled as a _____ model.

a. | MA(1). |

b. | MA(2). |

c. | MA(3). |

d. | MA(4). |

e. | None of the above. |

____ 17. A time series that can be best represented as a MA(2) model has a partial autocorrelation function that

a. | exponentially declines to zero as lag length increases. |

b. | cyclically declines to zero as lag length increases. |

c. | has one large negative spike and then goes to zero. |

d. | has one large positive spike and then goes to zero. |

e. | All of the above. |

____ 18. The order of a moving-average (MA) process can best be determined by the

a. | Durbin-Watson statistic. |

b. | Box-Pierce chi-square statistic. |

c. | autocorrelation function. |

d. | partial autocorrelation function. |

e. | All of the above. |

____ 19. Which of the following is __not__ in the autoregressive class of Box-Jenkins models?

a. | Yt = A1Yt-1 + A2Yt-2 + et. |

b. | Yt = et + W1et-1. |

c. | Yt – Yt-1 = et. |

d. | Yt = 0.1Yt-1 + et. |

e. | All of the above. |

____ 20. Autoregressive models are best described as

a. | simple averages of lagged values of the series. |

b. | weighted averages of lagged series values plus white noise. |

c. | weighted average of white noise series. |

d. | weighted averages of normal random variates. |

e. | None of the above. |

____ 21. An autocorrelation and partial autocorrelation function for an AR-type process differs from that of a MA-type process in

a. | what series is being analyzed. |

b. | their length. |

c. | diagnostic ability to access a moving-average model. |

d. | that they are opposites. |

e. | All of the above. |

____ 22. For an autoregressive model solution to a forecasting problem, the autocorrelation plot should _____ and the partial autocorrelation plot should _____.

a. | gradually approach zero, dramatically cut off to zero. |

b. | dramatically approach zero, exponentially approach one. |

c. | slowly approach one, and cyclically approach zero. |

d. | dramatically cut off to zero, decline to zero either monotonically or in
a wavelike manner. |

e. | None of the above. |

____ 23. The autocorrelation function correlogram should show significant correlation (spikes) at lags of _____ if an autoregressive-type model generates the true data.

a. | One. |

b. | Two. |

c. | Three. |

d. | Four. |

e. | None of the above. |

____ 24. Which of the following patterns of the partial autocorrelation function correlogram is inconsistent with an underlying autoregressive data process?

a. | Exponentially declining to zero. |

b. | Cyclically declining to zero. |

c. | Positive at first, then negative and increasing to zero. |

d. | Negative at first, then positive and declining to zero. |

e. | All of the above. |

____ 25. The partial autocorrelation function shows one spike at lag length one. Such a series can be modeled as a _____ model.

a. | AR(1). |

b. | AR(2). |

c. | AR(3). |

d. | AR(4). |

e. | None of the above. |

____ 26. A time series that can be best represented as an AR(2) model has a partial autocorrelation function that

a. | exponentially declines to zero as lag length increases. |

b. | cyclically declines to zero as lag length increases. |

c. | has one large negative spike and then goes to zero. |

d. | has one large positive spike and then goes to zero. |

e. | None of the above. |

____ 27. The order “p” of an autoregressive (AR) process can best be determined by the

a. | Durbin-Watson statistic. |

b. | Box-Pierce chi-square statistic. |

c. | autocorrelation function. |

d. | partial autocorrelation function. |

e. | All of the above. |

____ 28. Which of the following is __not__ an ARMA(p, q) model?

a. | Yt = et + W1Yt-1 + W2Yt-2. |

b. | Yt = et + W1Yt-1. |

c. | Yt = Yt-1 + et + et-1. |

d. | Yt = Yt-1 + 0.7et-1. |

e. | None of the above. |

____ 29. Mixed moving-average models of order (1, 1) have spikes exhibited in

a. | the autocorrelation function. |

b. | the partial autocorrelation function. |

c. | both autocorrelation and partial-autocorrelation functions. |

d. | neither the autocorrelation and partial-autocorrelation functions. |

e. | None of the above. |

____ 30. ARMA(p, q) models have autocorrelation and partial autocorrelation functions that

a. | may both show spikes. |

b. | may both show monotonically declining estimates. |

c. | may look amazingly similar. |

d. | may look quite dissimilar in the nature of adjustment. |

e. | All of the above. |

____ 31. For an ARMA(1,2) solution to a forecasting problem, the autocorrelation plot should have _____ spike(s) and the partial autocorrelation plot should have _____. spike(s)?

a. | 1,2. |

b. | 2,1. |

c. | 1,1. |

d. | 2,2 |

e. | None of the above. |

____ 32. The autocorrelation function correlogram should show spikes close to ____ lags if an ARMA (2, 3) -type model generates the true data.

a. | One. |

b. | Two. |

c. | Three. |

d. | Four. |

e. | None of the above. |

____ 33. The partial-autocorrelation function correlogram should show spikes close to ____ lags if an ARMA (2, 3) -type model generates the true data.

a. | One. |

b. | Two. |

c. | Three. |

d. | Four. |

e. | None of the above. |

____ 34. Which of the following patterns of the partial autocorrelation function correlogram is inconsistent with an underlying ARMA data process?

a. | Exponentially declining to zero. |

b. | Cyclically declining to zero. |

c. | Positive at first, then negative and increasing to zero. |

d. | Negative at first, then positive and declining to zero. |

e. | None of the above. |

____ 35. The autocorrelation function of a time series shows coefficients significantly different from zero at lags 1 through 4. The partial autocorrelation function shows one spike and monotonically increases to zero as lags length increases. Such a series can be modeled as a _____ model.

a. | ARMA(1, 4). |

b. | ARMA(2, 4). |

c. | MA(3). |

d. | ARMA(4, 1). |

e. | None of the above. |

____ 36. A time series that can be best represented as an ARMA(2, 0) model has a partial autocorrelation function that

a. | have no significant lags. |

b. | slowly declines to zero as lag length increases. |

c. | has one large negative spike and then goes to zero. |

d. | has one large positive spike and then goes to zero. |

e. | None of the above. |

____ 37. The order of an ARMA(p, q) process can best be determined by the

a. | number of AR and MA terms that are significant. |

b. | Box-Pierce chi-square statistic. |

c. | autocorrelation function alone. |

d. | partial autocorrelation function alone. |

e. | None of the above. |

____ 38. Which of the following are incorrect?

a. | Spikes in the partial-autocorrelation function indicate moving-average terms. |

b. | Spikes in the autocorrelation function indicate autoregressive terms. |

c. | Most economic data can be modeled as a higher-order ARMA(p, q) model. |

d. | For an ARMA(p, q) model, both the autocorrelation and partial-autocorrelation functions show abrupt stops. |

e. | All of the above. |

____ 39. Which of the following is a stationary time series?

a. | A series in which consecutive values depend only on the interval of time between them. |

b. | A series whose mean is constant over time. |

c. | A series with no trend. |

d. | A series whose autocorrelation function shows no significant spikes. |

e. | All of the above. |

____ 40. Which of the following is __not__ a way to induce stationarity out of non-stationary data?

a. | First-difference the original series. |

b. | Second-difference the original series. |

c. | Transform the original series using logarithms. |

d. | Examine the data in percentage terms. |

e. | None of the above. |

____ 41. ARMA models applied to nonstationary data are called

a. | ARIMA(p, q) models. |

b. | ARMA(p, d, q) models. |

c. | ARIMA(p, d, q) models. |

d. | MA(p, q) models. |

e. | MA(d, q) models. |

____ 42. Integration refers to the

a. | moving-average order of a time series. |

b. | autoregressive order of a time series. |

c. | number of differences required to induce data stationarity. |

d. | fit of an ARIMA model. |

e. | None of the above. |

____ 43. Most economic time series are integrated of what order?

a. | Zero. |

b. | One. |

c. | Two. |

d. | Four. |

e. | None of the above. |

____ 44. What transformation will transform any trend in variance to a trend in the mean of a time series?

a. | First-differencing the data. |

b. | Squaring the data. |

c. | Taking natural logarithms of the data. |

d. | Second-differencing the data. |

e. | All of the above. |

____ 45. Which of the following models utilizes a transformed series to induce a stationary series?

a. | ARIMA(1, 0, 1). |

b. | ARIMA(1, 0, 0). |

c. | ARIMA(1, 1, 1). |

d. | ARIMA(0, 0, 1). |

e. | None of the above. |

____ 46. Which of the following is __not__ a way to generate stationarity data out of non-stationary data?

a. | First-difference the original series. |

b. | Second-difference the original series. |

c. | Transform the original series using logarithms. |

d. | Examine a non-linear form of the model. |

e. | All of the above. |

____ 47. Which of the following best describes the autocorrelation function (ACF) of a nonstationary time series?

a. | The ACF has several significant spikes. |

b. | The ACF has coefficients that very gradually go to zero. |

c. | The ACF has a spurious pattern of spikes as lags increase. |

d. | The null of zero autocorrelation is rejected for a significant amount of lags. |

e. | All of the above. |

____ 48. Which of the following is __not__ a characteristic of a time series best represented as an ARIMA(3,0,1) model?

a. | The original series is stationary. |

b. | The autocorrelation function has one dominant spike. |

c. | The partial autocorrelation function has one dominant spike. |

d. | The partial autocorrelation function has three spikes. |

e. | None of the above. |

____ 49. Which of the following is __not__ a first-step in the ARIMA model selection process?

a. | Examine the autocorrelation function of the raw series. |

b. | Examine the partial autocorrelation function of the raw series. |

c. | Test the data for stationarity. |

d. | Estimate an ARIMA(1,1,1) model for reference purposes. |

e. | All of the above. |

____ 50. Which of the following rules is __not__ a useful first-step in the ARIMA model selection process?

a. | If the autocorrelation function stops after q spikes, the appropriate model is a MA(q) type. |

b. | If the partial autocorrelation function stops after p spikes, then the appropriate model is an AR(p) type. |

c. | If the autocorrelation function does not rapidly approach zero, then first-difference the data. |

d. | If the partial autocorrelation function quickly approaches zero, then data first differencing may be recommended. |

e. | All of the above. |

____ 51. The third-step of the ARIMA model selection process is to diagnose whether the correct model has been chosen. Which of the following is __not__ used in this diagnostic process?

a. | The autocorrelation function of the forecast errors. |

b. | The partial autocorrelation function of the forecast errors. |

c. | The Ljung-Box Z statistic. |

d. | The chi-square distribution. |

e. | All of the above. |

____ 52. The Q-statistic

a. | is based on the estimated autocorrelation function. |

b. | is used to test whether a series is white noise or not. |

c. | follows the chi-square distribution. |

d. | tests whether the residual autocorrelations as a set are significantly different from zero. |

e. | All of the above. |

____ 53. Using the Ljung-Box statistic applied to a sample of 30 forecast errors, we cannot reject the null of a white noise process if the sample Q-value is less than ____ at the 10% level of significance.

a. | 10. |

b. | 20. |

c. | 30. |

d. | 40. |

e. | None of the above. |

____ 54. The Q-statistic follows which probability distribution?

a. | Normal. |

b. | Standard Normal. |

c. | t distribution. |

d. | F distribution. |

e. | None of the above. |

____ 55. The diagnostic step in the Box-Jenkins model selection process essentially examines the forecast errors for

a. | trend. |

b. | serial correlation. |

c. | independence. |

d. | white noise. |

e. | All of the above. |

____ 56. What is the null hypothesis being tested using the Ljung-Box statistic?

a. | The set of autocorrelations is jointly equal to zero. |

b. | The set of autocorrelations are jointly not equal to zero. |

c. | The set of autocorrelations are jointly equal to one. |

d. | What is the null hypothesis being tested using the Ljung-Box statistic? |

e. | All of the above. |

____ 57. What problem arises when applying ARIMA-type models to highly seasonal monthly data?

a. | Autocorrelation. |

b. | Heteroscedasticity. |

c. | Extremely high-order AR and MA processes. |

d. | Stationarity. |

e. | All of the above. |

____ 58. Besides using sophisticated ARIMA-type models capable of internally handling data seasonality, an alternative is to use

a. | seasonal dummy variables. |

b. | trend dummy variables. |

c. | deseasonalized data, and then reseasonalize to generate forecasts. |

d. | Holt’s smoothing. |

e. | All of the above. |

____ 59.

What ARIMA model is suggested by the above correlogram

‘

a. | ARIMA (2,0,2) |

b. | ARIMA (4,0,2) |

c. | ARIMA (2,0,4) |

d. | ARIMA (0,0,2) |

____ 60.

What ARIMA model is suggested by the correlogram above?

a. | ARIMA (0,1,0) |

b. | ARIMA (0,1,1) |

c. | ARIMA (1,1,0) |

d. | ARIMA (1,0,1) |

____ 61.

The correlogram above suggests what type of ARIMA model?

a. | ARIMA (1,0,1) |

b. | ARIMA (2,0,1) |

c. | ARIMA (1,0,2) |

d. | ARIMA (0,2,1) |

**Electricity Usage Data (144 monthly observations):**

**Correlogram of the original electricity usage data:**

**ARIMA Model:**

____ 62. In the electricity usage data above

a. | the chosen ARIMA model took into account seasonality. |

b. | the chosen ARIMA model does not include any adjustment for seasonality. |

c. | the chosen ARIMA model appears to suffer from autocorrelation. |

d. | the chosen ARIMA model appears to suffer from multicollinearity. |

____ 63. In the electricity usage model above

a. | the residuals do not appear to be white noise. |

b. | the “Q” statistic is not statistically significant. |

c. | there is one autoregressive term. |

d. | there are no seasonal terms. |

____ 64.

Consider the ARIMA model specified above.

a. | This is an MA1 model. |

b. | This is an AR1 model. |

c. | There is one degree of normal differencing used. |

d. | The model adjusts for seasonality. |

____ 65.

The ARIMA model above represents an analysis of data with 200 observations. Is the “Q” statistic acceptable?

a. | Yes, because the critical value is about 26. |

b. | Yes, because the critical value is about 32. |

c. | No, because the critical value is about 17. |

d. | No, because the critical value is about 6. |

____ 66.

The ARIMA model above was estimated from 200 observations of data. Twelve lags were used to calculate the “Q” statistic.

The ARIMA model above would require how many degrees of freedom in the test statistic to determine if the model is appropriate?

a. | 3 |

b. | 6 |

c. | 10 |

d. | 14 |

____ 67.

The ARIMA model above was estimated using 78 quarterly observations. Using the appropriate test, examine whether this is an appropriate model.

a. | The model is appropriate because the critical value is about 17. |

b. | The model is appropriate because the critical value is about 33. |

c. | The model is inappropriate because the critical value is about 8. |

d. | The model is inappropriate because the critical value is about 12. |

____ 68.

The correlogram above was calculated from the residuals to an ARIMA model that analyzed quarterly data.

a. | The model appears to have produced white noise. |

b. | The model does not seem to be an appropriate model. |

c. | The model appears to be seasonal. |

d. | The model could be an AR16. |

**Chapter 7**

**Answer Section**

**MULTIPLE CHOICE**

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