Deck 17: Time Series Analysis and Forecasting

Question 1

Given an actual demand of 50, its forecast of 53, and an α of .2, what would be the forecast for the next period using exponential smoothing?

A) 52.4
B) 58.9
C) 61.0
D) 50.6

Answer 1

52.4

Question 2

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) 1.2.
C) 4.
D) 3.

Answer 2

1.2.

Question 3

The trend component is easy to identify using the method of

A) moving averages.
B) exponential smoothing.
C) regression analysis.
D) naïve forecasting.

Answer 3

regression analysis.

Question 4

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) _____ component.

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

Question 5

Below you are given some values of a time series consisting of 27 time periods. ​ The estimated quadratic regression equation for these data is
T_t = 14.25 + .45t + .21t²
The forecasted value for time period 28 is

A) 32.73.
B) 100.7.
C) 109.5.
D) 191.49.

Question 6

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 .2, then the exponential smoothing forecast for time period 3 is

A) 18.
B) 18.8.
C) 21.2.
D) 40.

Question 7

The time series component which reflects gradual shifts or movements to relatively higher or lower values over a longer period of time is a(n) _____ component.

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

Question 8

Which of the following is not present in a time series?

A) seasonality
B) cross-sectional pattern
C) trend
D) cyclical pattern

Question 9

The following linear trend expression was estimated using a time series with 17 time periods. ​
T_t = 129.5 + 4.8t
​
The trend projection for time period 18 is

A) 68.4.
B) 211.1.
C) 215.9.
D) 134.3.

Question 10

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. ​ An estimate of the combined trend-cycle component (T₂Ct) for Quarter 3 of Year 1 (used for estimating the de-trended values), when a four-quarter moving average is used, is

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

Question 11

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

A) 42.5.
B) 20.25.
C) 170.
D) 0.

Question 12

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

A) 0
B) .1
C) .5
D) 1.0

Question 13

The component that reflects unexplained variability in the time series is called a(n) _____ component.

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

Question 14

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

A) 20.6.
B) 18.
C) 20.
D) 10.

Question 15

The time series component that reflects gradual variability over a long time period is called a(n) _____ component.

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

Question 16

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. ​ 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 17

The time series component that exhibits a repeating pattern over successive periods, often one-year intervals is called a(n) _____ component.

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

Question 18

If data for a time series analysis are collected on an annual basis only, which of the following components may be ignored?

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

Question 19

If the estimate of the trend component is 160.2, 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) 1.55.
B) 147.58.
C) 154.96.
D) 154,960,532.

Question 20

A sequence of observations on a variable measured at successive periods of time is known as a(n)

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

Question 21

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 4 periods
D) moving average using the most recent 3 periods

Question 22

All of the following are true about qualitative forecasting methods except they

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

Question 23

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 24

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

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

Question 25

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

A) a smoothing average.
B) a moving average.
C) additive approach.
D) exponential smoothing.

Question 26

A seasonal pattern

A) exists if the time series plot exhibits a repeating pattern over successive periods, often one-year intervals.
B) can take more than a year to repeat itself.
C) is a multiyear run of observations above and below the trend line.
D) reflects a shift in the time series over time.

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

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

Question 29

One measure of the accuracy of a forecasting model is

A) the smoothing constant.
B) a deseasonalized time series.
C) the mean absolute error.
D) a projected index value.

Question 30

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

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

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

All of the following are true about a cyclical pattern except​ it is

A) often due to multiyear 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 in length of time.

Question 33

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 34

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

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

Question 35

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

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

Question 36

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

A) seasonality.
B) a ​cycle.
C) ​indexing.
D) ​trend.

Question 37

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

A) forecast
B) multiplicative
C) additive
D) horizontal

Question 38

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 39

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

A) moving averages approach.
B) decomposition model.
C) ​simple linear regression.
D) ​qualitative forecasting method.

Question 40

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 squared error.
B) mean absolute error.
C) smoothing constant.
D) exponential estimate.

Question 41

The quarterly sales of a company (in millions of dollars) over the past three years are given in the following table. ​
a.
Compute the four seasonal indexes.
b.
The trend for these data is Trend = 20.82 + .336t (t represents time, where t = 1 for Quarter 1 of 2013 and t = 12 for Quarter 4 of 2015). Forecast sales for the first quarter of 2016 using the trend only.
c.
Forecast sales for the first quarter of 2016 using the trend and seasonal indexes and write your answer below.

Question 42

Which of the following exponential smoothing constant values puts the same weight on the most recent time series value as does a four-period moving average?

A) α = .2
B) α = .25
C) α = .75
D) α = .8

Question 43

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 the forecasts along with the answer.

Question 44

The quarterly sales of a company (in millions of dollars) over the past three years are given in the following table.
​ ​
a.
Compute the four seasonal indexes.
b.
The trend for these data is Trend = 185.86 + 5.25t (t represents time, where t = 1 for Quarter 1 of 2013 and t = 12 for Quarter 4 of 2015). Forecast sales for the first quarter of 2016 using the trend only.
c.
Forecast sales for the first quarter of 2016 using the trend and seasonal indexes and write your answer below.

Question 45

For the following time series data, using the naïve method (the most recent value as the forecast for the next period), answer the following questions. ​
a
Compute mean absolute error (MAE).
b.
Compute mean squared error (MSE).
c.
What is the forecast for period 7?

Question 46

Using a naive forecasting method, the forecast for next month's sales volume equals

A) the most recent month's forecast.
B) the most recent month's sales volume.
C) the average of the last four month's sales volumes.
D) next month's production volume.

Question 47

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

Question 48

Actual sales for January through April are shown below. ​
Use exponential smoothing with α = .3 to calculate smoothed values and forecast sales for May from the above data. Assume the forecast for the initial period (January) is 18. Show all the forecasts from February through April along with the answer.

Question 49

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, 4, and 3 (largest weight is for most recent data)? Show all the forecasts for April through June along with the answer.
​

Question 50

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: 6, 4, and 1(largest weight is for most recent data)? Show all the forecasts for April through June along with the answer.

Question 51

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 the forecasts for April through June along with the answer.