Deck 16: Time-Series Forecasting

Question 1

Given a data set with 15 yearly observations, there are only thirteen 3-year moving averages.

Answer 1

True

Question 2

Based on the following scatter plot, which of the time-series components is not present in this quarterly time series?

A) Trend
B) Seasonal
C) Cyclical
D) Irregular

Answer 2

Cyclical

Question 3

A model that can be used to make predictions about long-term future values of a time series is

A) linear trend.
B) quadratic trend.
C) exponential trend.
D) All of the above.

Answer 3

All of the above.

Question 4

The effect of an unpredictable, rare event will be contained in the ________ component.

A) trend
B) cyclical
C) irregular
D) seasonal

Question 5

If a time series does not exhibit a long-term trend, the method of exponential smoothing may be used to obtain short-term predictions about the future.

Question 6

The fairly regular fluctuations that occur within each year would be contained in the ________ component.

A) trend
B) cyclical
C) irregular
D) seasonal

Question 7

The method of moving averages is used

A) to plot a series.
B) to exponentiate a series.
C) to smooth a series.
D) in regression analysis.

Question 8

After estimating a trend model for annual time-series data, you obtain the following residual plot against time.
The problem with your model is that

A) the cyclical component has not been accounted for.
B) the seasonal component has not been accounted for.
C) the trend component has not been accounted for.
D) the irregular component has not been accounted for.

Question 9

When using the exponentially weighted moving average for purposes of forecasting rather than smoothing,

A) the previous smoothed value becomes the forecast.
B) the current smoothed value becomes the forecast.
C) the next smoothed value becomes the forecast.
D) None of the above.

Question 10

Which of the following methods should not be used for short-term forecasts into the future?

A) Exponential smoothing
B) Moving averages
C) Linear trend model
D) Autoregressive modeling

Question 11

When a time series appears to be increasing at an increasing rate, such that percentage difference from value to value is constant, the appropriate model to fit is the

A) linear trend.
B) quadratic trend.
C) exponential trend.
D) None of the above.

Question 12

Which of the following statements about moving averages is not true?

A) It can be used to smooth a series.
B) It gives equal weight to all values in the computation.
C) It is simpler than the method of exponential smoothing.
D) It gives greater weight to more recent data.

Question 13

Which of the following is not an advantage of exponential smoothing?

A) It enables you to perform one-period ahead forecasting.
B) It enables you to perform more than one-period ahead forecasting.
C) It enables you to smooth out seasonal components.
D) It enables you to smooth out cyclical components.

Question 14

A trend is a persistent pattern in annual time-series data that has to be followed for several years.

Question 15

You need to decide whether you should invest in a particular stock. You would like to invest if the price is likely to rise in the long run. You have data on the daily mean price of this stock over the past 12 months. Your best action is to

A) compute moving averages.
B) perform exponential smoothing.
C) estimate a least square trend model.
D) compute the MAD statistic.

Question 16

Given a data set with 15 yearly observations, a 3-year moving average will have fewer observations than a 5-year moving average.

Question 17

Which of the following statements about the method of exponential smoothing is not true?

A) It gives greater weight to more recent data.
B) It can be used for forecasting.
C) It uses all earlier observations in each smoothing calculation.
D) It gives greater weight to the earlier observations in the series.

Question 18

Given a data set with 15 yearly observations, there are only seven 9-year moving averages.

Question 19

The annual multiplicative time-series model does not possess ________ component.

A) a trend
B) a cyclical
C) an irregular
D) a seasonal

Question 20

The overall upward or downward pattern of the data in an annual time series will be contained in the ________ component.

A) trend
B) cyclical
C) irregular
D) seasonal

Question 21

In selecting a forecasting model, you should perform a residual analysis.

Question 22

The cyclical component of a time series

A) represents periodic fluctuations which reoccur within 1 year.
B) represents periodic fluctuations which usually occur in 2 or more years.
C) is obtained by adjusting for the seasonal variation.
D) is obtained by adjusting for calendar variation.

Question 23

The MAD is a measure of the mean of the absolute discrepancies between the actual and the fitted values in a given time series.

Question 24

A least squares linear trend line is just a simple regression line with the years recoded.

Question 25

Which of the following terms describes the overall long-term tendency of a time series?

A) Trend
B) Cyclical component
C) Irregular component
D) Seasonal component

Question 26

Each forecast using the method of exponential smoothing depends on all the previous observations in the time series.

Question 27

MAD is the summation of the residuals divided by the sample size.

Question 28

TABLE 16-1
The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows.
Referring to Table 16-1, set up a scatter diagram (i.e., a time-series plot)with year on the horizontal X-axis.

Question 29

The principle of parsimony indicates that the simplest model that gets the job done adequately should be used.

Question 30

In selecting an appropriate forecasting model, the following approach is suggested.

A) Perform a residual analysis.
B) Measure the size of the forecasting error.
C) Use the principle of parsimony.
D) All of the above.

Question 31

After estimating a trend model for annual time-series data, you obtain the following residual plot against time.
The problem with your model is that

A) the cyclical component has not been accounted for.
B) the seasonal component has not been accounted for.
C) the trend component has not been accounted for.
D) the irregular component has not been accounted for.

Question 32

A first-order autoregressive model for stock sales is:
Salesᵢ = 800 + 1.2(Sales)ᵢ₋₁.
If sales in 2010 is 6,000, the forecast of sales for 2011 is ________.

Question 33

Microsoft Excel was used to obtain the following quadratic trend equation:
Sales = 100 - 10X + 15X².
The data used was from 2001 through 2010 coded 0 to 9. The forecast for 2011 is ________.

Question 34

The method of least squares may be used to estimate both linear and curvilinear trends.

Question 35

The method of least squares is used on time-series data for

A) eliminating irregular movements.
B) deseasonalizing the data.
C) obtaining the trend equation.
D) exponentially smoothing a series.

Question 36

To assess the adequacy of a forecasting model, one measure that is often used is

A) quadratic trend analysis.
B) the MAD.
C) exponential smoothing.
D) moving averages.

Question 37

The manager of a company believed that her company's profits were following an exponential trend. She used Microsoft Excel to obtain a prediction equation for the logarithm (base 10)of profits:
log₁₀(Profits)= 2 + 0.3X
The data she used were from 2005 through 2010 coded 0 to 5. The forecast for 2011 profits is ________.

Question 38

A second-order autoregressive model for average mortgage rate is:
Rateᵢ = - 2.0 + 1.8(Rate)ᵢ₋₁ - 0.5 (Rate)ᵢ₋₂.
If the average mortgage rate in 2010 was 7.0, and in 2009 was 6.4, the forecast for 2011 is ________.

Question 39

A second-order autoregressive model for average mortgage rate is:
Rateᵢ = - 2.0 + 1.8(Rate)ᵢ₋₁ - 0.5 (Rate)ᵢ₋₂.
If the average mortgage rate in 2010 was 7.0, and in 2009 was 6.4, the forecast for 2012 is ________.

Question 40

TABLE 16-1
The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows.
Referring to Table 16-1, does there appear to be a relationship between year and the number of cases of wine sold?

A) No, there appears to be no relationship between the year and the number of cases of wine sold by the vintner.
B) Yes, there appears to be a slight negative linear relationship between the year and the number of cases of wine sold by the vintner.
C) Yes, there appears to be a slight positive relationship between the year and the number of cases of wine sold by the vintner.
D) Yes, there appears to be a negative nonlinear relationship between the year and the number of cases of wine sold by the vintner.

Question 41

Which of the following terms describes the up and down movements of a time series that vary both in length and intensity?

A) Trend
B) Cyclical component
C) Irregular component
D) Seasonal component

Question 42

TABLE 16-2
The monthly advertising expenditures of a department store chain (in $1,000,000s) were collected over the last decade. The last 14 months of this time series follows:

Referring to Table 16-2, set up a scatter plot (i.e., time-series plot)with months on the horizontal X-axis.

Question 43

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, if this series is smoothed using exponential smoothing with a smoothing constant of 1/3, how many values would it have?

A) 3
B) 4
C) 5
D) 6

Question 44

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, a centered 5-year moving average is to be constructed for the wine sales. The moving average for 2005 is ________.

Question 45

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, a centered 3-year moving average is to be constructed for the wine sales. The moving average for 2004 is ________.

Question 46

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, if a three-month moving average is used to smooth this series, how many values would it have?

A) 2
B) 3
C) 4
D) 5

Question 47

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

If you want to recover the trend using exponential smoothing, you will choose a weight (W)that falls in the range

A) [0, 0.2]
B) [0.2, 0.4]
C) [0.6, 0.8]
D) [0.8, 1.0]

Question 48

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, if this series is smoothed using exponential smoothing with a smoothing constant of 1/3, what would be the second value?

A) 39
B) 42
C) 45
D) 53

Question 49

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, if a three-month moving average is used to smooth this series, what would be the second calculated value?

A) 36
B) 40.5
C) 54
D) 72

Question 50

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, suppose the last two smoothed values are 81 and 96 (Note: they are not). What would you forecast as the value of the time series for July?

A) 81
B) 86
C) 91
D) 96

Question 51

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, a centered 5-year moving average is to be constructed for the wine sales. The number of moving averages that will be calculated is ________.

Question 52

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, if this series is smoothed using exponential smoothing with a smoothing constant of 1/3, what would be the third value?

A) 53
B) 65.33
C) 68
D) 81

Question 53

TABLE 16-2
The monthly advertising expenditures of a department store chain (in $1,000,000s) were collected over the last decade. The last 14 months of this time series follows:

Referring to Table 16-2, advertising expenditures appear to be increasing in a linear rather than curvilinear manner over time.

Question 54

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, a centered 3-year moving average is to be constructed for the wine sales. The moving average for 2007 is ________.

Question 55

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, suppose the last two smoothed values are 81 and 96 (Note: they are not). What would you forecast as the value of the time series for September?

A) 81
B) 86
C) 91
D) 96

Question 56

The following is the list of MAD statistics for each of the models you have estimated from time-series data:
Based on the MAD criterion, the most appropriate model is

A) linear trend.
B) quadratic trend.
C) exponential trend.
D) second-order autoregressive.

Question 57

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, construct a centered 3-year moving average for the wine sales.

Question 58

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, if a three-month moving average is used to smooth this series, what would be the last calculated value?

A) 72
B) 93
C) 114
D) 126

Question 59

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, a centered 3-year moving average is to be constructed for the wine sales. The result of this process will lead to a total of ________ moving averages.

Question 60

TABLE 16-3
The following table contains the number of complaints received in a department store for the first 6 months of last year.

Referring to Table 16-3, if this series is smoothed using exponential smoothing with a smoothing constant of 1/3, what would be the first value?

A) 36
B) 39
C) 42
D) 45

Question 61

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, the number of arrivals will be exponentially smoothed with a smoothing constant of 0.1. The smoothed value for the second Monday will be ________.

Question 62

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, the number of arrivals will be smoothed with a 5-term moving average. The last smoothed value will be ________.

Question 63

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, the number of arrivals will be exponentially smoothed with a smoothing constant of 0.25. The smoothed value for the second Monday will be ________.

Question 64

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, construct a centered 5-year moving average for the wine sales.

Question 65

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, exponential smoothing with a weight or smoothing constant of 0.4 will be used to smooth the wine sales. The value of E₅, the smoothed value for 2007 is ________.

Question 66

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, the number of arrivals will be smoothed with a 5-term moving average. The first smoothed value will be ________.

Question 67

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, exponential smoothing with a weight or smoothing constant of 0.4 will be used to smooth the wine sales. The value of E₂, the smoothed value for 2004 is ________.

Question 68

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, a centered 5-year moving average is to be constructed for the wine sales. The moving average for 2008 is ________.

Question 69

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, exponential smoothing with a weight or smoothing constant of 0.4 will be used to forecast wine sales. The forecast for 2011 is ________.

Question 70

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, exponentially smooth the number of arrivals using a smoothing constant of 0.1.

Question 71

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, the number of arrivals will be smoothed with a 3-term moving average. The last smoothed value will be ________.

Question 72

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, the number of arrivals will be exponentially smoothed with a smoothing constant of 0.1. Then the forecast for the seventh Monday will be ________.

Question 73

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, exponential smoothing with a weight or smoothing constant of 0.2 will be used to forecast wine sales. The forecast for 2011 is ________.

Question 74

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, exponentially smooth the wine sales with a weight or smoothing constant of 0.2.

Question 75

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, exponentially smooth the wine sales with a weight or smoothing constant of 0.4.

Question 76

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, the number of arrivals will be smoothed with a 3-term moving average. The first smoothed value will be ________.

Question 77

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, exponential smoothing with a weight or smoothing constant of 0.2 will be used to smooth the wine sales. The value of E₂, the smoothed value for 2004 is ________.

Question 78

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, the number of arrivals will be exponentially smoothed with a smoothing constant of 0.1. The smoothed value for the sixth Monday will be ________.

Question 79

TABLE 16-4
The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows.

Referring to Table 16-4, exponential smoothing with a weight or smoothing constant of 0.2 will be used to smooth the wine sales. The value of E₄, the smoothed value for 2006 is ________.

Question 80

TABLE 16-5
The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48.
Referring to Table 16-5, the number of arrivals will be smoothed with a 3-term moving average. There will be a total of ________ smoothed values.