Deck 17: Time Series Analysis and Forecasting

Question 1

For the following time series, you are given the moving average forecast.


$\begin{array} { l l l } \text {Time Period } & \text {Time Series Value } & \text { Moving Average For ecast } \\1 & 23 & \\2 & 17 & \\3 & 17 & \\3 & 26 & 19 \\4 & 11 & 20 \\5 & 23 & 18 \\6 & 17 & 20\end{array}$ The mean squared error equals

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

Answer 1

41

Question 2

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

Answer 2

multiplicative decomposition model

Question 3

Below are the first four values of a time series.

$\begin{array} { l l } \text { Time Period } & \text { Time Series Value } \\1 & 18 \\ 2 & 20 \\ 3 & 25 \\ 4 & 17 \end{array}$ Using a four-period moving average, the forecasted value for period 5 is _____.

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

Answer 3

20

Question 4

A group of observations measured at successive time intervals is known as a(n) _____.

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

Question 5

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(n) _____.

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

Question 6

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 7

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

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

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 following information on the seasonal-irregular component values is for a quarterly time series: $\begin{array}{l} & \text { Seasonal-Irregular } \\ \text { Quarter } & \text { Comp onent Values (StIt) } \\1&1.23,1.15,1.16 \\2&.86, .89, .83 \\3&.77, .72, .79 \\4&1.20,1.13,1.17\end{array}$ The seasonal index for quarter 1 is ______.

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

Question 11

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 12

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) the qualitative forecasting method

Question 13

The trend pattern is easy to identify by using _____.

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

Question 14

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

Question 15

Below are the first two values of a time series and the first two values of the exponential smoothing forecast. $$\begin{array}{l}\begin{array} { l l l } &&\text { Exp onential Smoothing }\\\text { Time Period } ( t ) & \text { Time Series Value } \left( Y _ { \mathbf { t } } \right) & \text { Forecast } \left( F _ { \mathbf { t } } \right) \\1 & 18 & 18 \\2 & 22 & 18\end{array}\end{array}$$ If the smoothing constant equals .3, then the exponential smoothing forecast for time period 3 is _____.

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

Question 16

Given an actual demand of 61, forecast of 58, and α 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 17

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 18

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 19

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 20

Below are some values of a time series consisting of 26 time periods. $\begin{array}{ll}\text { Time Period } & \text { Time Series Value } \\1 & 37 \\2 & 48 \\3 & 50 \\4 & 63\\.\\.\\.\\23 & 105 \\24 & 107 \\25 & 112 \\26 & 114\end{array}$ The estimated regression equation for these data is Y_t = 16.23 + .52Yt_-1 + .37Yt-₂
The forecasted value for time period 27 is _____.

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

Question 21

All of the following are true about a cyclical pattern EXCEPT it is ______.

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

Question 22

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 23

A parameter of the exponential smoothing model that 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 the answers is correct.

Question 24

The forecasting model that makes use of the "least squares" method is ______.

A) weighted moving average
B) exponential smoothing
C) moving average
D) regression

Question 25

A qualitative forecasting method that obtains forecasts through "group consensus" is known as the ______.

A) autoregressive model
B) Delphi approach
C) mean absolute deviation
D) None of the answers is correct.

Question 26

The term "exponential smoothing" comes from ______.

A) its emphasis on minimizing mean squared error
B) the exponential nature of the weighting scheme used
C) its use in fitting exponential trend lines
D) the nonlinear noise it attempts to remove

Question 27

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 28

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) the qualitative forecasting methods

Question 29

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 30

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 31

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 32

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

A) exponential smoothing with α = .3
B) exponential smoothing with α = .2
C) moving average using the most recent four periods
D) moving average using the most recent three periods

Question 33

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) y-intercept

Question 34

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 35

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

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

Question 36

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 37

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) a cycle
C) regression
D) a trend

Question 38

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 39

One measure of the accuracy of a forecasting model is ______.

A) the smoothing constant
B) a deseasonalized time series
C) the mean squared error
D) None of the answers is correct.

Question 40

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 41

To calculate an exponential smoothing forecast of demand, what values are required?

A) alpha, number of periods, last actual demand
B) alpha, last forecast, number of periods
C) alpha, last forecast, last actual demand
D) last forecast, number of periods, averaging period

Question 42

The sales records of a major auto manufacturer over the past 10 years are shown below. ​
Develop a linear trend expression and project the sales (the number of cars sold) for time period t = 11.

Question 43

Regarding a regression model, all of the following can be negative EXCEPT the ______.

A) coefficient of determination
B) coefficient of correlation
C) coefficient of "x" in the regression equation
D) y-intercept in the regression equation

Question 44

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 45

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 46

Actual sales for January through April are shown below. Use exponential smoothing with α = .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 47

The number of new central air conditioning systems installed by CoolBreeze, Inc. in each of the last nine years is listed below.
​ ​
Assuming a linear trend function, forecast the number of system installations CoolBreeze will perform in 10using linear trend regression.