Deck 18: Time Series and Forecasting

Question 1

The cyclical component of a time series typically represents repetitions within a one-year period.

Answer 1

False

Question 2

The exponential smoothing method weighs all available observations in a time series equally.

Answer 2

False

Question 3

Noncausal forecasting models are purely time series models in the sense that the forecasts are made based only on historical data concerning the variable of interest.

Answer 3

True

Question 4

Causal forecasting models are based on a regression model framework, where the variable of interest depends on one or more explanatory variables.

Question 5

When the exponential trend model is used to make forecasts, the forecasts are given by = exp(b₀ + b₁t + /2).

Question 6

The moving average method is one of the most complex smoothing techniques used for processing time series.

Question 7

In forecasting methods, the mean square error (MSE) is computed by dividing the sum of squared residuals (errors) by the number of observations n for which the residuals are available.

Question 8

The centered moving average (CMA), applied in the decomposition analysis of a time series with trend and seasonality, is the average of two consecutive moving averages.

Question 9

Smoothing techniques are suitable for use when forecasts need to be updated frequently due to new observations that become available.

Question 10

Although we use the MSE to compare the linear and the exponential trend models, we cannot use it to compare the linear, quadratic, and cubic trend models.

Question 11

Ideally, the chosen model is best in terms of its in-sample predictability and its ________ forecasting ability.

Question 12

When the forecasting method of seasonal dummy variables is applied on a quarterly time series, four dummy variables are needed.

Question 13

________ patterns are caused by the presence of a random error term.

Question 14

The optimal value of the speed of decline in the exponential smoothing procedure is determined by a(n) ________ method.

Question 15

Quantitative forecasting procedures are based on the judgment of the forecaster, who uses prior experience and expertise to make forecasts.

Question 16

The exponential trend model is attractive when the increase in the series gets larger over time.

Question 17

When a time series has both trend and seasonality, it is necessary to model seasonality along with trend.

Question 18

When the decomposition model, y_t = T_t × S_t × I_t, is applied, forecasts are made as = + , where represents the estimated trend for seasonally adjusted time series for period t, and is the seasonal index for period t.

Question 19

A linear trend can be estimated using ________ technique.

Question 20

The mean of the absolute residuals defines the ________.

Question 21

The ________ of the adjusted seasonal indices equals one.

Question 22

To extract the trend from a time series, we first eliminate seasonal ________ by dividing the original series y, by its corresponding adjusted seasonal index.

Question 23

Which of the following factors refers to quantitative forecasting methods?

A) Judgment of the forecaster.
B) A formal model for analyzing historical data.
C) Prior experience of the forecaster.
D) Expertise of the forecaster.

Question 24

Which of the following is not based on a regression model?

A) Moving average methods
B) Exponential trend models
C) Polynomial trend models
D) Autoregressive models

Question 25

Which of the following is an example of a time series?

A) The number of daily visitors to the Niagara Falls during the month of April.
B) The recorded exam scores of students in a class.
C) The sales prices of single family homes sold last month in Florida.
D) The current average prices of regular gasoline in different states of the U.S.

Question 26

After we have estimated the trend and the seasonal components, we ________ them to make a forecast.

Question 27

A time series with observed long-term upward movements in its values is said to have ________.

A) a cyclical component
B) an increasing trend component
C) a seasonally increasing component
D) a decreasing trend component

Question 28

In the model y_t = β₀ + β₁y_t-1 + ε_t, the parameter β₁ represents the ________ of the lagged response variable y.

Question 29

When comparing polynomial trend models, we use adjusted R², which imposes a penalty for ________.

Question 30

Which of the following is a causal forecasting method?

A) Moving average methods
B) Exponential trend models
C) Polynomial trend models
D) Autoregressive models

Question 31

With the method of seasonal dummy variables, we estimate a trend forecasting model that includes ________ variables to capture seasonal variations.

Question 32

Which of the following is not an example of a time series?

A) Hourly volume of stocks traded on the New York Stock Exchange (NYSE) on the five last trading days.
B) The number of daily visitors that frequent the Statue of Liberty during the month of July.
C) The monthly sales for a retailer over a five-year period.
D) The current temperature in the 49 state capitals.

Question 33

Which of the following is a smoothing technique?

A) Moving average methods
B) Exponential trend models
C) Polynomial trend models
D) Autoregressive models

Question 34

The seasonal component typically represents repetitions over a ________ period.

Question 35

The regression y_t = β₀ + β₁y_t-1 + ε_t is referred to as a(n) ________ model of order one.

Question 36

A time series is ________.

A) any set of data recorded at the same point in time
B) a set of sequential observations of a variable over time
C) a set of randomly measured data points of multiple variables at the same point in time
D) any set of data collected without regard to differences in time

Question 37

Under which of the following conditions is qualitative forecasting considered attractive?

A) When the forecasts have to be documented.
B) When the forecasts have to be independent of the forecaster's judgment.
C) When past data are either unavailable or are misleading.
D) When the forecasts can be based on reliable data.

Question 38

In which of the following situations is the use of qualitative forecasts most appropriate?

A) A marketing manager has to forecast monthly sales for the coming financial year based on the past monthly sales figures.
B) A TV network executive has to forecast viewership figures for a daily talk show based on historical data from the past on a similar show on a rival network.
C) An economist has to forecast credit flow resulting from a newly introduced stimulus package by the federal government.
D) A country's annual rate of growth for the upcoming year has to be estimated based on the annual GDP data from the last 20 years.

Question 39

Which of the following is a criticism made of qualitative forecasts?

A) They become the only possible forecast when past data are either not available or are misleading.
B) They provide no guidance on the likely effects of changes in explanatory variables.
C) They are prone to biases such as optimism and overconfidence.
D) They are difficult to document.

Question 40

When the increase in the series gets larger over time, it is attractive to use a(an) ________ trend model.

Question 41

Which of the following is not true of a time series with a cyclical component?

A) It has wavelike fluctuations lasting from several months to several years.
B) It is difficult to analyze because cycles vary in length and amplitude.
C) It typically coincides with business cycles in the economy.
D) It has wavelike fluctuations always lasting less than a year.

Question 42

The following table includes the information about a monthly time series. When a forecast is made by the three-month moving average method, all three monthly observations used to make this forecast are treated equally in the sense that each of them has the same weight of 1/3. What is the forecast for May when the three-month weighted moving average method is applied with the weights: 1/6, 2/6, and 3/6? Assign the smallest weight to the oldest data and the largest weight to the most recent data.

A) 19.00
B) 24.00
C) 18.67
D) 21.17

Question 43

The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.1 is applied, what is the MSE?

A) 20.796
B) 31.2336
C) 12.6736
D) 10.41

Question 44

The ________ method is a smoothing technique based on computing the average from a fixed number of the most recent observations.

A) exponential smoothing
B) moving average
C) linear regression
D) causal regression

Question 45

The past monthly demands are shown below. The naïve method, that is, the one-period moving average method, is applied to make forecasts. What is the mean absolute deviation (MAD) of the forecasts?

A) −1.67
B) 25.00
C) 91.67
D) 8.33

Question 46

In the exponential smoothing formula for updating the level of the series, , what does α represent?

A) The weighted average of the exponentially declining weights.
B) The speed of decline in the weights of older observations.
C) The initial value of the time series.
D) The last value of the time series.

Question 47

In a moving average method, when a new observation becomes available, the new average is computed by including the new observation and ________.

A) dropping the oldest observation
B) keeping the previous m observations
C) dropping the youngest previous observation
D) keeping any previous m - 1 observations

Question 48

The following table includes the information about a monthly time series. What is the forecast for May using the exponential smoothing method with α = 0.5?

A) 21
B) 21.5
C) 19
D) 19.5

Question 49

Which of the following is true of the linear trend model?

A) It assigns exponentially decreasing weights to older observations.
B) It is a causal forecasting model.
C) It can extract a long-term upward or downward steady movement in a series.
D) It is used when a series involves only random fluctuations.

Question 50

The following table includes the information about a monthly time series. What is the forecast for May when the three-month moving average method is applied?

A) 19
B) 5
C) 20
D) 21

Question 51

The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.5 is applied, what is the MSE?

A) 21.5
B) 25
C) 41
D) 13.67

Question 52

The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.1 and α = 0.5 is applied, what is the speed of decline for which the mean square error is better? What is this mean?

A) α = 0.5 and MSE = 13.67.
B) α = 0.1 and MSE = 13.67.
C) α = 0.5 and MSE = 10.41.
D) α = 0.1 and MSE = 10.41.

Question 53

The past monthly demands are shown below. The naïve method, that is, the one-period moving average method, is applied to make forecasts. If the demand in May appears to be 35, what is the residual (error) for May?

A) 35
B) 0
C) 68.75
D) 6.25

Question 54

The following table includes the information about a monthly time series. What is the forecast for May using the exponential smoothing method with α = 0.1?

A) 20.796
B) 21.000
C) 20.600
D) 20.440

Question 55

The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.1 is applied, what is the MAD?

A) 21.5
B) 3.00
C) 5.00
D) 9.00

Question 56

The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.1 is applied, what is the MAD?

A) 20.796
B) 9.16
C) 3.05
D) 3.56

Question 57

The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.1 and α = 0.5 is applied, what is the speed of decline for which the mean absolute deviation is better? What is this mean?

A) α = 0.1 and MAD = 3.05.
B) α = 0.1 and MAD = 3.00.
C) α = 0.5 and MAD = 3.00.
D) α = 0.5 and MAD = 3.05.

Question 58

Which of the following is a similarity between the exponential smoothing method and the moving average method?

A) Both methods give different weights to most recent observations.
B) Both methods assign weights to all available observations.
C) Both methods give equal weight to every observation.
D) Both methods continually revise a forecast when a new observation becomes available.

Question 59

The past monthly demands are shown below. The naïve method, that is, the one-period moving average method, is applied to make forecasts. What is the mean square error of the forecasts?

A) −1.67
B) 275.00
C) 91.67
D) 8.33

Question 60

Which of the following is true of the exponential smoothing method?

A) It does not incorporate new observations into existing forecasts.
B) It weighs all recent observations equally.
C) It assigns weights that decrease exponentially as observations gets older.
D) It does not use all available observations in making a forecast.

Question 61

Which of the following is a centered moving average?

A) The average of all moving averages in a series.
B) The average of all observations of a series.
C) The average of alternative moving averages in a series.
D) The average of two consecutive moving averages in a series.

Question 62

A polynomial trend model that only allows one change in the direction of a series is known as a(n) ________.

A) exponential trend model
B) linear trend model
C) cubic trend model
D) quadratic trend model

Question 63

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. Which of the following is a revenue forecast for 2012 found by the polynomial trend equation with the best fit?

A) About 2 billion and 149 million dollars
B) About 2 billion and 189 million dollars
C) About 2 billion and 337 million dollars
D) About 2 billion and 34 million dollars

Question 64

When comparing which of the following trend models is the adjusted R² not used?

A) Linear versus quadratic
B) Linear versus cubic
C) Quadratic versus cubic
D) Linear versus exponential

Question 65

Which of the following types of trend models will best suit a series where the value of the series changes by a fixed amount for each period?

A) Cubic trend
B) Linear trend
C) Exponential trend
D) Quadratic trend

Question 66

Which of the following types of trend models will best suit a series where the increase in value of the series gets larger over time?

A) Exponential trend
B) Linear trend
C) Quadratic trend
D) Polynomial trend

Question 67

The ________ is a trend model that allows for one change in the direction of a series.

A) linear trend model
B) exponential trend model
C) quadratic trend model
D) cubic trend model

Question 68

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. When all four trend regression equations are compared, which of them provides the best fit?

A) Linear
B) Exponential
C) Quadratic
D) Cubic

Question 69

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. Using the linear trend equation, one can say that the predicted revenue increases by ________.

A) $642,792,000 a year
B) $604,960,000 a year
C) $60,496,000 a year
D) $6,049,600 a year

Question 70

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. Which of the following is an exponential trend equation?

A) _t = exp(6.632 + 0.045t + (0.069)²⁄2)
B) _t = 6.632 + 0.045t + 0.069 ⁄ 2
C) _t = exp(6.632 + 0.045t + 0.069 ⁄ 2)
D) _t = 6.632 + 0.045t + (0.069)²⁄2

Question 71

Which of the following formulas is used to make forecasts using the exponential trend model?

A) A_t = αy_t + (1 - α)A_{t-1
B) t} = exp(b₀ + b₁t + /2)
C) _t = b₀ + b₁t
D) _t = b₀ + b₁t + b₁t ²

Question 72

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. Which of the following is a linear trend equation?

A) _t = 642.7t + 60.496
B) _t = 642.7 + 60.496t
C) _t = 642.7 + 60.496t^{2 D) y}_t = 642.7 + 60.496t + ε

Question 73

When a time series is analyzed by the model y_t = T_t × S_t × I_t and the trend component T_t is set to be the centered moving average _t, which of the following remains to be estimated?

A) S_t × I_t
B) T_t × S_t
C) T_t × I_t
D) S_t / I_t

Question 74

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. Which of the following is the revenue forecast for 2012 found by the linear trend equation?

A) About 2 billion 149 million dollars
B) About 2 billion and 189 million dollars
C) About 2 billion and 334 million dollars
D) About 2 billion and 34 million dollars

Question 75

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. Which of the following is the revenue forecast for 2013 found by the trend regression equation with the best fit?

A) About 2 billion and 337 million dollars
B) About 2 billion and 95 million dollars
C) About 2 billion and 248 million dollars
D) About 2 billion and 290 million dollars

Question 76

In comparison with the linear trend model, which of the following is not true of the cubic trend model?

A) It always has better MSE.
B) Two additional variables, t² and t³, are defined in the cubic model.
C) Only one change in the direction of a series can be modeled.
D) It may have better or worse adjusted R².

Question 77

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. When three polynomial trend equations are compared, which of them provides the best fit?

A) Linear
B) Exponential
C) Quadratic
D) Cubic

Question 78

If the model y_t = T_t × S_t × I_t is applied, which of the following indicates no seasonality?

A) The sum of the adjusted seasonal indices equals the number of seasons.
B) The average of the adjusted seasonal indices equals 1.
C) Every adjusted seasonal index is practically 1.
D) The product of the adjusted seasonal indices equals 1.

Question 79

In the quadratic trend model, y_t = β₀ + β₁t ² + ε_t, which coefficient determines if the trend is going to be U-shaped or inverted U-shaped?

A) β_0
B) β_1
C) β_2
D) ε_t

Question 80

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. Which of the following is a revenue forecast for 2012 found by the exponential trend equation?

A) About 2 billion and 334 million dollars
B) About 2 billion and 189 million dollars
C) About 2 billion and 141 million dollars
D) About 2 billion and 34 million dollars