Deck 15: Time Series Analysis and Forecastng

Question 1

Which of the following smoothing constants would make an exponential smoothing forecast equivalent to a naive forecast?

A)0
B)1 divided by the number of periods
C)0.5
D)1.0

Answer 1

1.0

Question 2

A group of observations measured at successive time intervals is known as

A)a trend component
B)a time series
C)a forecast
D)an additive time series model

Answer 2

a time series

Question 3

Below you are given some values of a time series consisting of 26 time periods. The estimated regression equation for these data is
Y_t = 16.23 + .52Y_t-1 + .37Y_t-2
The forecasted value for time period 27 is

A)53.23
B)109.5
C)116.65
D)116.95

Answer 3

116.95

Question 4

Below you are given the first four values of a time series. Using a 4-period moving average, the forecasted value for period 5 is

A)2.5
B)17
C)20
D)10

Question 5

For the following time series, you are given the moving average forecast. The mean squared error equals

A)0
B)6
C)41
D)164

Question 6

If data for a time series analysis is collected on an annual basis only, which pattern can be ignored?

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

Question 7

The model that assumes that the actual time series value is the product of its components is the

A)linear trend regression model
B)multiplicative decomposition model
C)additive time series model
D)weighted moving average model

Question 8

Common types of data patterns that can be identified when examining a time series plot include all of the following except

A)horizontal
B)vertical
C)seasonal
D)cyclical

Question 9

If the estimate of the trend component is 158.2, the estimate of the seasonal component is 94%, the estimate of the cyclical component is 105%, and the estimate of the irregular component is 98%, then the multiplicative model will produce a forecast of

A)1.53
B)1.53%
C)153.02
D)153,020,532

Question 10

The time series pattern that reflects repeating variability within a single year is called the

A)trend pattern
B)seasonal pattern
C)trend and seasonal pattern
D)cyclical pattern

Question 11

The trend pattern is easy to identify by using

A)moving averages
B)exponential smoothing
C)regression analysis
D)the Delphi approach

Question 12

The following linear trend expression was estimated using a time series with 17 time periods. T_t = 129.2 + 3.8t
The trend projection for time period 18 is

A)68.4
B)193.8
C)197.6
D)6.84

Question 13

Given an actual demand of 61, forecast of 58, and an $\alpha$ of .3, what would the forecast for the next period be using simple exponential smoothing?

A)57.1
B)58.9
C)61.0
D)65.5

Question 14

The time series pattern that reflects a gradual shift or movement to a relatively higher or lower level over a longer time period is called the

A)trend pattern
B)seasonal pattern
C)cyclical pattern
D)trend and seasonal pattern

Question 15

You are given the following information on the seasonal-irregular component values for a quarterly time series: The seasonal index for Quarter 1 is

A).997
B)1.18
C)4
D)3

Question 16

The time series pattern that exists when the data fluctuate around a constant mean is the

A)horizontal pattern
B)trend pattern
C)seasonal pattern
D)cyclical pattern

Question 17

The time series pattern showing an alternating sequence of points below and above the trend line lasting more than one year is the

A)trend pattern
B)seasonal pattern
C)trend and seasonal pattern
D)cyclical pattern

Question 18

A component of the time series model that results in the multi-period above-trend and below-trend behavior of a time series is

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

Question 19

Below you are given the first two values of a time series. You are also given the first two values of the exponential smoothing forecast. If the smoothing constant equals .3, then the exponential smoothing forecast for time period three is

A)18
B)19.2
C)20
D)40

Question 20

The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal effect is

A)moving averages
B)mean squared error
C)mean average deviation
D)qualitative forecasting methods

Question 21

Gradual shifting or movement of a time series to relatively higher or lower values over a longer period of time is called

A)periodicity.
B)cycle.
C)regression.
D)trend.

Question 22

In the linear trend equation, T = b₀ + b_1t, b₀ represents the

A)time
B)slope of the trend line
C)trend value in period 1
D)the Y intercept

Question 23

All of the following are true about qualitative forecasting methods except

A)they generally involve the use of expert judgment to develop forecasts
B)they assume the pattern of the past will continue into the future
C)they are appropriate when past data on the variable being forecast are not applicable
D)they are appropriate when past data on the variable being forecast are not available

Question 24

All of the following are true about a cyclical pattern except

A)it is often due to multi-year business cycles
B)it is often combined with long-term trend patterns and called trend-cycle patterns
C)it is an alternating sequence of data points above and below the trend line
D)it is usually easier to forecast than a seasonal pattern due to less variability

Question 25

Holt's linear exponential smoothing is often called

A)nonlinear trend regression
B)time series decomposition
C)double exponential smoothing
D)time series deseasonalization

Question 26

In the linear trend equation, T_t = b₀ + b₁t b₁ represents the

A)trend value in period t
B)intercept of the trend line
C)slope of the trend line
D)point in time

Question 27

A method of smoothing a time series that can be used to identify the combined trend/cyclical component is

A)the moving average
B)the percent of trend
C)exponential smoothing
D)the trend/cyclical index

Question 28

A parameter of the exponential smoothing model which provides the weight given to the most recent time series value in the calculation of the forecast value is known as the

A)mean square error
B)mean absolute deviation
C)smoothing constant
D)None of these alternatives is correct.

Question 29

Using exponential smoothing, the demand forecast for time period 10 equals the demand forecast for time period 9 plus

A) $\alpha$ times (the demand forecast for time period 8)
B) $\alpha$ times (the error in the demand forecast for time period 9)
C) $\alpha$ times (the observed demand in time period 9)
D) $\alpha$ times (the demand forecast for time period 9)

Question 30

Which of the following forecasting methods puts the least weight on the most recent time series value?

A)exponential smoothing with $\alpha$ = .3
B)exponential smoothing with $\alpha$ = .2
C)moving average using the most recent 4 periods
D)moving average using the most recent 3 periods

Question 31

All of the following are true about time series methods except

A)they discover a pattern in historical data and project it into the future
B)they identify a set of related independent, or explanatory, variables
C)they assume that the pattern of the past will continue into the future
D)their forecasts are based solely on past values of the variable or past forecast errors

Question 32

The objective of smoothing methods is to smooth out

A)long range forecasts
B)wide seasonal variations
C)significant trend effects
D)random fluctuations

Question 33

In situations where you need to compare forecasting methods for different time periods, the most appropriate accuracy measure is

A)mean error
B)mean absolute error
C)mean squared error
D)mean absolute percentage error

Question 34

One measure of the accuracy of a forecasting model is the

A)smoothing constant
B)trend pattern
C)mean absolute error
D)seasonal index

Question 35

All of the following are true about a stationary time series except

A)its statistical properties are independent of time
B)a plot of the time series will always exhibit a horizontal pattern
C)the process generating the data has a constant mean
D)there is no variability in the time series over time

Question 36

Exhibit 15-1
Below you are given the first five values of a quarterly time series. The multiplicative model is appropriate and a four-quarter moving average will be used.

Refer to Exhibit 15-1. An estimate of the trend component times the cyclical component (T₂C_t) for Quarter 3 of Year 1, when a four-quarter moving average is used, is

A)24
B)25
C)26
D)28

Question 37

Exhibit 15-1
Below you are given the first five values of a quarterly time series. The multiplicative model is appropriate and a four-quarter moving average will be used.

Refer to Exhibit 15-1. An estimate of the seasonal-irregular component for Quarter 3 of Year 1 is

A).64
B)1.5625
C)5.333
D)30

Question 38

The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal effect is

A)moving averages
B)mean squared error
C)mean average deviation
D)qualitative forecasting methods

Question 39

A seasonal pattern

A)can occur within a day
B)can take more than a year to repeat itself
C)is a multi-year run of observations above and below the trend line
D)reflects a shift in the time series over time

Question 40

A method that uses a weighted average of past values for arriving at smoothed time series values is known as

A)regression analysis
B)deseasonalization
C)decomposition
D)exponential smoothing

Question 41

Exhibit 15-2
Consider the following time series.

Refer to Exhibit 15-2. The intercept, b₀, is

A)2.5
B)2.0
C)1.0
D)1.25

Question 42

What is the forecast for July based on a three-month weighted moving average applied to the following past demand data and using the weights: 5, 3,and 2 (largest weight is for most recent data)? Show all of your computations for April through July.

Question 43

The sales records of a major auto manufacturer over the past ten years are shown below.
Develop a linear trend expression and project the sales (the number of cars sold) for time period t = 11

Question 44

Exhibit 15-2
Consider the following time series.

Refer to Exhibit 15-2. The forecast for period 10 is

A)10.0
B)25.0
C)30.0
D)22.5

Question 45

John has collected the following information on the amount of tips he has collected from parking cars the last seven nights.

a.Compute the 3-day moving averages for the time series.
b.Compute the mean square error for the forecasts.
c.Compute the mean absolute deviation for the forecasts.
d.Forecast John's tips for day 7.

Question 46

The following data show the quarterly sales of Amazing Graphics, Inc. for the years 6 through 8.

a.Compute the four-quarter moving average values for the above time series.
b.Compute the seasonal factors for the four quarters.
c.Use the seasonal factors developed in Part b to adjust the forecast for the effect of season for year 6.

Question 47

The following time series shows the number of units of a particular product sold over the past six months.

a.Compute a 3-month moving average (centered) for the above time series.
b.Compute the mean square error (MSE) for the 3-month moving average.
c.Use $\alpha$ = 0.2 to compute the exponential smoothing values for the time series.
d.Forecast the sales volume for month 7.

Question 48

Exhibit 15-3
Consider the following time series.

Refer to Exhibit 15-3. The forecast for period 10 is

A)6.7
B)-6.7
C)23.3
D)15

Question 49

The sales volumes of CMM, Inc., a computer firm, for the past 8 years is given below.

a.Develop a linear trend expression for the above time series.
b.Forecast sales for period 9.

Question 50

The sales records of a company over a period of seven years are shown below.

a.Develop a linear trend expression for the above time series.
b.Forecast sales for period 10.

Question 51

The actual demand for a product and the forecast for the product are shown below. Calculate MAD and MSE. Show all of your computations.

Question 52

Student enrollment at a university over the past six years is given below.

a.Develop a linear trend expression for the above time series.
b.Forecast enrollment for year 10.

Question 53

Exhibit 15-2
Consider the following time series.

Refer to Exhibit 15-2. The forecast for period 5 is

A)10.0
B)2.5
C)12.5
D)4.5

Question 54

Exhibit 15-2
Consider the following time series.

Refer to Exhibit 15-2. The slope of linear trend equation, b₁, is

A)2.5
B)2.0
C)1.0
D)1.25

Question 55

Exhibit 15-3
Consider the following time series.

Refer to Exhibit 15-3. In which time period does the value of Y_i reach zero?

A)0.000
B)0.181
C)5.53
D)4.21

Question 56

Exhibit 15-3
Consider the following time series.

Refer to Exhibit 15-3. The slope of linear trend equation, b₁, is

A)-1.5
B)+1.5
C)8.3
D)-8.3

Question 57

The following time series shows the sales of a clothing store over a 10-week period.

a.Compute a 4-week moving average for the above time series.
b.Compute the mean square error (MSE) for the 4-week moving average forecast.
c.Use $\alpha$ = 0.3 to compute the exponential smoothing values for the time series.
d.Forecast sales for week 11.

Question 58

The quarterly sales (in thousands of copies) for a specific educational software over the past three years are given in the following table.

a.Compute the four seasonal factors (Seasonal Indexes). Show all of your computations.
b.The trend for these data is Trend = 174 + 4 t (t represents time, where t=1 for Quarter 1 of 2003 and t=12 for Quarter 4 of 2005). Forecast sales for the first quarter of 2006 using the trend and seasonal indexes. Show all of your computations.

Question 59

Actual sales for January through April are shown below.
Use exponential smoothing with $\alpha$ = 0.2 to calculate smoothed averages and forecast sales for May from the above data. Assume the forecast for the initial period (January) is 18. Show all of your computations.

Question 60

Exhibit 15-3
Consider the following time series.

Refer to Exhibit 15-3. The intercept, b₀, is

A)-1.5
B)+1.5
C)8.3
D)-8.3

Question 61

You are given the following information on the quarterly profits for Ajax Corporation.

a.Find the four-quarter centered moving averages.
b.Compute the seasonal-irregular component.
c.Compute the seasonal factors for all four quarters.
d.Represent the deseasonalized series.

Question 62

Weekly sales of the Weber Dicamatic food processor for the past ten weeks have been:

a. Determine, on the basis of minimizing the mean square error, whether a three period or four period simple moving average model gives a better forecast for this problem.
b. For each model, forecast sales for week 11.

Question 63

Four months ago, the Bank Drug Company introduced Jeffrey William brand designer bandages. Advertised using the slogan, "What the best dressed cuts are wearing", weekly sales for this period (in 1000's) have been as follows:
a) Plot a graph of sales vs. weeks. Does linear trend appear reasonable?
b) Assuming linear trend, forecast sales for weeks 17, 18, 19, and 20.

Question 64

Connie Harris, in charge of office supplies at First Capital Mortgage Corp., would like to predict the quantity of paper used in the office photocopying machines per month. She believes that the number of loans originated in a month influence the volume of photocopying performed. She has compiled the following recent monthly data:

a. Develop the least-squares estimated regression equation that relates sheets of photocopy paper used to loans originated.b). Use the regression equation developed in part (a) to forecast the amount of paper used in a month when 65 loan originations are expected.

Question 65

Below you are given information on crime statistics for Middletown.
The seasonal factors for these data are

a.Deseasonalize the series.
b.Obtain an estimate of the linear trend for this series.
c.Use the seasonal and trend components to forecast the number of crimes for each quarter of Year 5.

Question 66

Below you are given the seasonal factors and the estimated trend equation for a time series. These values were computed on the basis of 5 years of quarterly data. T = 126.23 - 1.6t
Produce forecasts for all four quarters of year 6 by using the seasonal and trend components.

Question 67

The number of new central air conditioning systems installed by CoolBreeze, Inc. in each of the last nine years are listed below.
Assuming a linear trend function, forecast the number of system installations CoolBreeze will perform in 2011 using linear trend regression.

Question 68

Delta Corp's plant in Austin has been experiencing imbalances in its inventory of components used in the production of a line of computer printers. Both stock shortages and overstock conditions are occurring.
The production analysis group is studying the pattern of demand for component PS2400, a power supply used in many of Delta's products. The group believes that the most recent 12 weeks of demand for the PS2400 is representative of the future weekly demand:

a. Use a four-week moving average to develop a forecast of the demand for the PS2400 component in week 13.
b. Use a four-week weighted moving average with weights of .4 (for the most recent datum), .3, .2, and .1 to forecast the demand for the PS2400 component in week 13.

Question 69

The following information has been collected on the sales of greeting cards for the past 6 weeks.

a.Produce exponential smoothing forecasts for the series using a smoothing constant of .2.
b.Compute the mean square error for the forecasts produced with a smoothing constant of .2.
c.What is the forecast of sales for week 7?
d.Is a smoothing constant of .2 or .3 better for the sales data? Explain.

Question 70

Below you are given information on John's income for the past 7 years.

a.Use regression analysis to obtain an expression for the linear trend component.
b.Forecast John's income for the next 5 years.

Question 71

Consider the following annual series on the number of people assisted by a county human resources department.

a.Prepare 3-year moving average values to be used as forecasts for periods 4 through 11. Calculate the mean squared error (MSE) measure of forecast accuracy for periods 4 through 11.
b.
b.Use a smoothing constant of .4 to compute exponential smoothing values to be used as forecasts for periods 2 through 11. Calculate the MSE.
c.Compare the results in Parts a and b.

Question 72

The following data show the quarterly sales of a major auto manufacturer (introduced in exercise 4) for the years 8 through 10.

a.Compute the four-quarter moving average values for the above time series.
b.Compute the seasonal factors for the four quarters.
c.Use the seasonal factors developed in Part b to adjust the forecast for the effect of season for year 9.

Question 73

The temperature in Chicago has been recorded for the past seven days. You are given the information below.

a.Produce exponential smoothing forecasts for the series using a smoothing constant of .2.
b.Compute the mean square error for the forecasts produced with a smoothing constant of .2.
c.What is the forecasted temperature for day 8?
d.Is a smoothing constant of .2 or .3 better for the temperature data? Explain.

Question 74

The number of haircuts performed each day at KwikKuts in the last four weeks are listed below.

a. Plot the sales data. Do you see both trend and seasonality components in the data?
b. Forecast the number of haircuts to be performed in each workday of week 6.

Question 75

The yearly series below exhibits a long-term trend. Use the appropriate forecasting technique to produce forecasts for years 11 and 12.