Deck 18: Models for Time Series and Forecasting

Question 1

The larger the smoothing constant ( $\alpha$ ),the more importance is given to the actual y value for the most recent time period.

Answer 1

True

Question 2

True or False A trend component in a time series model must be expressed as a linear relationship over time using a linear trend equation.

Answer 2

False

Question 3

True or False Compared to the Mean Squared Error approach,the Mean Absolute Deviation places a greater penalty on estimates for which there is a large error.

Answer 3

False

Question 4

True or False When exponential smoothing is used for forecasting,the forecast will tend to be too high for time series that are increasing (positive trend)and too low for time series that are decreasing (negative trend).

Question 5

True or False In general,a moving average with a base equal to the duration of a strong cyclical or seasonal pattern will be highly useful in dampening fluctuations caused by the pattern.

Question 6

True or False In de-seasonalizing a time series,we remove the seasonal influences and generate a time series that is said to be seasonally adjusted.

Question 7

True or False A time series may consist of weekly production output,monthly sales,annual rainfall,or any other variable for which the value is observed or repeated at regular intervals.

Question 8

True or False By analyzing a time series,we can identify patterns and tendencies that help explain variation in past sales,shipments,rainfall,or any other variable of interest.

Question 9

True or False In general,the most important component of most time series is the irregular,which can be examined by using regression techniques.

Question 10

True or False The seasonal index is a factor that inflates or deflates a trend value to compensate for the effect of a pattern that repeats over a period of one year or less.

Question 11

True or False The smoothing techniques,such as moving average or exponential smoothing,function much like the shock absorbers of an automobile; damping the sudden upward and downward "jolts" that occur over the series.

Question 12

True or False The Consumer Price Index (CPI)describes the change in prices from one time period to another for a fixed "market basket" of goods and services.

Question 13

True or False A common method of testing for autocollinearity (serial correlation)is a Durbin-Watson test.

Question 14

True or False Analysis of a time series involves identifying the components that have led to the fluctuations in the data.

Question 15

True or False The Mean Absolute Deviation criterion is analogous to the least squares criterion used in determining the regression equation.

Question 16

True or False The trend component of a time series can be examined (1)by using regression techniques to fit a trend line to the data,or (2)by using smoothing techniques to moderate the peaks and valleys within the series.

Question 17

True or False A common method of testing for autocollinearity (serial correlation)is a Wilcoxon matched pairs signed rank test.

Question 18

True or False Exponential smoothing requires that we assume an initial forecast value in order to get things started.

Question 19

True or False Second-order autocorrelation is the correlation between e_t and e_t-2.

Question 20

True or False If you are not using a computer,it is desirable to select an even number of periods for a centered moving average unless there is some compelling reason to do otherwise.

Question 21

The time series component that reflects variability over short repetitive time periods and has duration of less than one year is called:

A) trend.
B) cyclical.
C) seasonal.
D) random variation.

Question 22

True or False The Durbin-Watson test can be used to determine whether the residuals in a regression model are independent.

Question 23

Which of the following components of a time series measures the overall general directional movement over a long period of time?

A) irregular
B) cycle
C) seasonal
D) trend
E) exponential

Question 24

The upsurge in school supply sales in the fall of each year is an example of the:

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

Question 25

True or False A common method of testing for autocollinearity (serial correlation)is a Wilcoxon signed rank test for one sample.

Question 26

In general,the most important component of most time series is the

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

Question 27

Of the four components of the multiplicative time series model,the ratio-to-moving average procedure isolates the:

A) irregular component.
B) trend component.
C) seasonal component.
D) cyclical component.
E) All of these.

Question 28

Which of the four time series components is more likely to exhibit the steady growth of the population of the United States from 1950 to 2000?

A) Trend
B) Cyclical
C) Seasonal
D) Random variation

Question 29

The component of a time series that has repeating patterns that have a period longer than one year is the:

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

Question 30

True or False The analysis of time series data is useful in identifying past patterns and tendencies as well as helping to forecast future values.

Question 31

The classical time series model combines the various components in which of the following ways?

A) $y = T \bullet C \cdot S \bullet I$
B) $y = T \bullet ( C + S + I )$
C) $y = T \bullet C \bullet ( S + I )$
D) $y = \frac { T \bullet C } { S \bullet I }$
E) None of these.

Question 32

The time series component that reflects a long-term,relatively smooth pattern or direction exhibited by a time series over a long time period (more than two years)is called:

A) trend.
B) cyclical.
C) seasonal.
D) random variation.

Question 33

Different values of the smoothing constant employed in exponential smoothing cause the smoothing procedure to react more or less rapidly to changes in the value of a series.Which of the following smoothing constants causes the least rapid reaction to a change in the current value of a series?

A) 0.30
B) 0.25
C) 0.15
D) 0.10
E) 0.40

Question 34

True or False All index numbers are unit-less.

Question 35

True or False In autoregressive forecasting,each independent variable represents the value of the dependent variable for a previous time period.

Question 36

The purpose of the moving average technique is to

A) take away the short-term trend and cyclical variation leaving behind seasonal and irregular movement.
B) take away the short-term trend and seasonal variation leaving behind cyclical and irregular movement.
C) take away the short-term trend and irregular variation leaving behind cyclical and seasonal movement.
D) take away the short-term seasonal and irregular variation leaving behind trend and cyclical movement.

Question 37

Selecting a large the number of periods (N)for a centered moving average

A) results in greater dampening.
B) is less responsive to directional changes.
C) results in a more accurate forecast.
D) both A and B.
E) All of the above.

Question 38

The effect that business recessions and prosperity have on time series values is an example of the:

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

Question 39

The time series component that reflects the irregular changes in a time series that are not caused by any other component,and tends to hide the existence of the other more predictable components,is called:

A) trend.
B) cyclical.
C) seasonal.
D) random variation.

Question 40

The time series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called:

A) trend.
B) cyclical.
C) seasonal.
D) random variation.

Question 41

The following trend line was calculated from quarterly data for 1995 - 1999: where t is 1 for the first quarter of 1995.Calculate the trend value for the second quarter of the year 2000.

Question 42

Which of the following statements is not true?

A) In forecasting based on time series information,data from the past are used in predicting the future value of the variable of interest.
B) Extrapolation of a trend equation fitted to time series is one approach to time series forecasting.
C) Exponential smoothing is one approach to time series forecasting.
D) All of these statements are true.
E) All of these statements are not true.

Question 43

The mean absolute deviation averages the absolute differences between the actual values of the time series at time t and the forecast values at time:

A) t + 1.
B) t.
C) t - 1.
D) t - 2.

Question 44

Which method would you recommend to your statistics professor in selecting the appropriate forecasting model if avoiding large errors is extremely important to him or her?

A) Mean absolute deviation (MAD)
B) Mean square error (MSE)
C) Either A or B
D) Neither A nor B

Question 45

In determining weekly seasonal indexes for gas consumption,the sum of the 52 means for gas consumption as a percentage of the moving average is 5050.To get the seasonal indexes,each weekly mean is to be multiplied by:

A) 5200/5050.
B) (5200 + 5050)/52.
C) (5050 + 52)/5200.
D) 5050/5200.

Question 46

NARRBEGIN: Susan Young
Susan Young is a college student who has just completed her junior year.The table below summarizes her Grade Point Average (GPA)for each of the last nine semesters.

What is the linear trend estimate for Susan's GPA for Spring semester Sophomore year?

Question 47

Selecting a large value for the smoothing constant ( $\alpha$ )in exponential smoothing

A) results in more importance being placed on the exponentially smoothed value from the previous period.
B) results in more importance being placed on the actual y value for the current time period.
C) more strongly dampens the fluctuations in the original series.
D) results in a less accurate forecast.

Question 48

We calculate the three-period moving average for a time series for all time periods except the:

A) first period.
B) last period.
C) first and last period.
D) first and last two periods.

Question 49

Which of the following statements is not true regarding the Consumer Price Index (CPI)?

A) The CPI describes the change in prices from one period to the next for a fixed "market basket" of goods and services.
B) The CPI is used as a measurement of inflation.
C) The CPI is used as a "cost of living" adjustment in labor contracts.
D) The CPI is used as a means of deflating current prices or wages to "real" prices wages.
E) All of these statements are true.

Question 50

A factor that inflates or deflates a trend value to compensate for the effect of a pattern that repeats over a period of one year or less is known as a

A) smoothing factor.
B) dampening factor.
C) seasonal index.
D) residual factor.

Question 51

Which of the following will not be present in a de-seasonalized time series?

A) Trend effects
B) Cyclical effects
C) Seasonal effects
D) Random variation

Question 52

The trend equation = 1300 + 25x has been fitted to a time series for auto industry worker days lost due to job-related injuries.If x = 1 for 1999,estimate the number of worker days lost during 2010.

Question 53

NARRBEGIN: Cell Phones
The number of peak cell-phones minutes used each month by a particular person is shown in the table below:

What is the linear trend estimate for Month 7?

Question 54

An auto parts supplier forecasted 1998 annual sales of $800,000.Seasonal indexes of sales for each quarter of the year were: I - 80,II - 112,III - 117,IV - 91.The sales forecast for quarter II was:

A) 300,000.
B) 200,000.
C) 224,000.
D) 228,000.
E) 284,000.

Question 55

One of the assumptions required by the regression model is that the residuals (errors)be independent of each other.When this assumption is not met:

A) multicollinearity exists.
B) heteroscedasticity exists.
C) homoscedasticity exists.
D) serial correlation exists.
E) a normal distribution exists.

Question 56

Selecting a small value for the smoothing constant ( $\alpha$ )in exponential smoothing results in

A) more importance being placed on the exponentially smoothed value from the previous period.
B) more importance being placed on the actual y value for the current time period.
C) a more accurate forecast.
D) a less accurate forecast.

Question 57

The results of a quadratic model fit to time series data were = 7.5 - 0.25t + 3.5t2, where t = 1 for 1995. The forecasted value for 2002 is:

A) -2.0.
B) 10.75.
C) 28.
D) 229.5.

Question 58

The trend equation for quarter sales data (in millions of dollars)for 1996-2000 is $\hat { \mathrm { y } } _ { t }$ = 6.8 + 1.2t,where t = 1 for the first quarter of 1996.If the seasonal index for the third quarter of 2001 is 1.25,then the forecasted sales for the third quarter of 2001 is:

A) 34.4.
B) 27.52.
C) 43.00.
D) 35.65.

Question 59

In determining monthly seasonal indexes for gas consumption,the sum of the 12 means for gas consumption as a percentage of the moving average is 1150.To get the seasonal indexes,each of the 12 monthly means is to be multiplied by:

A) 1150/1200.
B) (1200 + 1150)/12.
C) (1150 + 12)/1200.
D) 1200/1150.

Question 60

Which of the following equations de-seasonalize a time series?

A) $( \mathrm { T } \cdot \mathrm { C } \cdot \mathrm { S } \cdot \mathrm { I } ) / \mathrm { T } = \mathrm { C } \cdot \mathrm { S } \cdot \mathrm { I }$
B) $( \mathrm { T } \cdot \mathrm { C } \cdot \mathrm { S } \cdot \mathrm { I } ) / \mathrm { C } = \mathrm { T } \cdot \mathrm { S } \cdot \mathrm { I }$
C) $( \mathrm { T } \cdot \mathrm { C } \cdot \mathrm { S } \cdot \mathrm { I } ) / \mathrm { S } = \mathrm { T } \cdot \mathrm { C } \cdot \mathrm { I }$
D) $( \mathrm { T } \cdot \mathrm { C } \cdot \mathrm { S } \cdot \mathrm { I } ) / \mathrm { I } = \mathrm { T } \cdot \mathrm { C } \cdot \mathrm { S }$

Question 61

In forecasting,we use data from the ____________________ in predicting the ____________________ value of the variable of interest,such as automobile sales.

Question 62

The monthly seasonal index for August is 101.The de-seasonalized August output is 250,000 units.What is the annual output?
Remove all commas from your answer before submitting.

Question 63

NARRBEGIN: Inventory
The following values are the means for each month of the inventory as a percentage of the moving average for the twelve months of the year.
Compute the de-seasonalized value for February if the inventory in February is $48,000.

Question 64

The following trend line was calculated from quarterly data for 1996 - 2000: = 0.70 + 0.005t,where t = 1 for the first quarter of 1996.The seasonal indexes computed from the trend line for the four quarters of the year 2001 were 0.85,1.05,1.15,and 0.80,respectively.What is the seasonalized forecast for the third quarter of the year 2001?

Question 65

NARRBEGIN: Stock exchange
Membership on a stock exchange for five years is given below:
Use the exponential smoothing procedure to obtain estimates of the trend.Set the smoothed value for 1996 equal to the actual and use a smoothing constant, = 0.2.Compute the forecasted value for 2000.

Question 66

NARRBEGIN: Time periods
The following are the values of a time series for the first four time periods:
Suppose that we calculate the four-period moving average of the following time series What is the centered moving average for period 3?

Question 67

The trend equation for annual sales is = 32 + 3.1x where x = 0 in 1992.Sales (y)are in millions of dollars.The monthly seasonal index for July is 98.What is the July sales estimate for 2000?

Question 68

NARRBEGIN: Stock exchange
Membership on a stock exchange for five years is given below:
Use the exponential smoothing procedure to obtain estimates of the trend (this is not the logarithm approach here).Set the smoothed value for 1996 equal to the actual and use a smoothing constant, = 0.4.Compute the forecasted value for 2000.

Question 69

NARRBEGIN: Highland Automotvie
The table below summarizes the number of new cars Highland Automotive sold during each of the last five weeks along with a forecast that was generated for each of those weeks.

What is the mean absolute deviation for this forecast?

Question 70

NARRBEGIN: Highland Automotvie
The table below summarizes the number of new cars Highland Automotive sold during each of the last five weeks along with a forecast that was generated for each of those weeks.

What is the mean squared error for this forecast?

Question 71

NARRBEGIN: Time periods
The following are the values of a time series for the first four time periods:
Using exponential smoothing,with = 0.30,what is the forecasted value for time period 5?

Question 72

Five trend models for the same time series data are compared and the MSE values are 35,9,15,118,and 25.The worst fitting model to the data is the one whose MSE is ____________________.

Question 73

Daily sales volume from the Avalon Convenience Store is shown in the table below.
What is the linear trend estimate for Day 4?

Question 74

NARRBEGIN: Inventory
The following values are the means for each month of the inventory as a percentage of the moving average for the twelve months of the year.
Compute the seasonal index for February.

Question 75

NARRBEGIN: Time periods
The following are the values of a time series for the first four time periods:
Using a four-period moving average,what is the forecasted value for time period 5?

Question 76

Based on annual car rentals over years,a rental firm has developed the following quadratic trend equation: = 425 + 18x + 6.5x²,with x = 1 for 1998.Forecast y for 2005.

Question 77

The linear trend equation = 100 + 5.2x has been developed,where = estimated sales (thousands of dollars)and x = 1 for the year 1995.What level of sales would be forecast for 2012?
____________________ thousand

Question 78

NARRBEGIN: Table
What is the computed value of the Durbin-Watson statistic?

Question 79

If summer 2003 sales were $12,600 and the summer seasonal index was 1.20.What is the de-seasonalized 2003 summer sales value?
Remove all commas from your answer before submitting.

Question 80

The seasonal indexes for a convention center's bookings are 85,128,104,and 83 for quarters 1 through 4,respectively.What percentage of the center's annual bookings tend to occur during the second quarter?