Deck 8: Time Series Analysis and Forecasting

Question 1

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

A)seasonality
B)operational variations
C)trend
D)cycles

Answer 1

operational variations

Question 2

A time series plot of a period of time (in years) verses sales (in thousands of dollars) is shown below Which of the following data patterns best describes the scenario shown?

A)Linear trend pattern
B)Nonlinear trend pattern
C)Seasonal pattern
D)Cyclical pattern

Answer 2

Linear trend pattern

Question 3

____________________ is the amount by which the predicted value differs from the observed value of the time series variable.

A)Mean forecast error
B)Mean absolute error
C)Smoothing constant
D)Forecast error

Answer 3

Forecast error

Question 4

If a time series plot exhibits a horizontal pattern, then

A)it is evident that the time series is stationary.
B)the data fluctuates around the variable mean.
C)there is no relationship between time and the time series variable.
D)there is still not enough evidence to conclude that the time series is stationary.

Question 5

Which of the following states the objective of time series analysis?

A)To predict the values of a time series based on one or more other variables.
B)To analyze the cause-and-effect relationship of a dependent variable with a time series and one or more other variables.
C)To use present variable values to study what should have been the ideal past values.
D)To uncover a pattern in a time series and then extrapolate the pattern into the future.

Question 6

Which of the following is not true of a stationary time series?

A)The process generating the data has a constant mean.
B)The time series plot is a straight line.
C)The statistical properties are independent of time.
D)The variability is constant over time.

Question 7

A time series plot of a period of time period (quarterly) verses quarterly sales (in $1,000s) is shown below. Which of the following data patterns best describes the scenario shown?

A)Linear trend and cyclical pattern
B)Linear trend and horizontal pattern
C)Seasonal and cyclical patterns
D)Seasonal pattern and linear trend

Question 8

A time series plot of a period of time (in months) verses sales (in number of units) is shown below. Which of the following data patterns best describes the scenario shown?

A)Linear trend pattern
B)Logarithmic trend
C)Exponential trend
D)Seasonal pattern

Question 9

The mean absolute error, mean squared error, and mean absolute percentage error are all methods to measure the accuracy of a forecast.These methods measure forecast accuracy by

A)determining how well a particular forecasting method is able to reproduce the time series data that are already available.
B)using the current value to estimate how well the model generates previous values correctly.
C)predicting the future values and wait for a pre-defined time period to examine how accurate the predictions were.
D)adjusting the scale of the data.

Question 10

Trend refers to

A)the long-run shift or movement in the time series observable over several periods of time.
B)the outcome of a random experiment.
C)the recurring patterns observed over successive periods of time.
D)the short-run shift or movement in the time series observable for some specific period of time.

Question 11

If the forecasted value of the time series variable for period 2 is 22.5 and the actual value observed for period 2 is 25, what is the forecast error in period 2?

A)3
B)2
C)2.5
D)-2.5

Question 12

Which is not true regarding trend patterns?

A)Can result when business conditions shift to a new level at some point in time.
B)Exist when there are gradual shifts of values over long periods of time.
C)Can result from factors such as improving technology or changes in consumer preferences.
D)Can represent non-linear relationships.

Question 13

A time series plot of a period of time (in years) verses revenue (in millions of dollars) is shown below .Which of the following data patterns best describes the scenario shown?

A)Linear trend pattern
B)Nonlinear trend pattern
C)Seasonal pattern
D)Cyclical pattern

Question 14

A set of observations on a variable measured at successive points in time or over successive periods of time constitute a

A)geometric series.
B)time invariant set.
C)time series.
D)logarithmic series.

Question 15

A time series that shows a recurring pattern over one year or less is said to follow a

A)horizontal pattern.
B)stationary pattern.
C)cyclical pattern.
D)seasonal pattern.

Question 16

A time series plot of a period of time (in weeks) verses sales (in 1,000's of gallons) is shown below. Which of the following data patterns best describes the scenario shown?

A)Time series with a linear trend pattern
B)Time series with a nonlinear trend pattern
C)Time series with no pattern
D)Time series with a horizontal pattern

Question 17

An exponential trend pattern occurs when

A)the amount of increase between periods in the value of the variable is constant.
B)the percentage change between periods in the value of the variable is relatively constant.
C)there is a no relationship between the time series variable and time.
D)there are random fluctuations in the variable value with time.

Question 18

A forecast is defined as a(n)

A)prediction of future values of a time series.
B)quantitative method used when historical data on the variable of interest are either unavailable or not applicable.
C)set of observations on a variable measured at successive points in time.
D)outcome of a random experiment.

Question 19

With reference to time series data patterns, a cyclical pattern is the component of the time series that

A)shows a periodic pattern lasting one year or less.
B)does not vary with respect to time.
C)shows a periodic pattern lasting more than one year.
D)is characterized by a linear variation of the dependent variable with respect to time.

Question 20

Forecast error

A)takes a positive value when the forecast is too high.
B)cannot be negative.
C)cannot be zero.
D)is associated with measuring forecast accuracy.

Question 21

Suppose for a particular week, the forecasted sales were $4,000. The actual sales were $3,000. What is the value of the mean absolute percentage error?

A)-33.3%
B)-25%
C)25%
D)33.3%

Question 22

Demand for a product and the forecasting department's forecast (naïve model) for a product are shown below. Compute the mean squared error. ?
? $$\begin{array} { | c | c | c | } \hline \text { Period } & \text { Actual Demand } & \text { Forecasted Demand } \\\hline 1 & 12 & - \\\hline 2 & 15 & 12 \\\hline 3 & 14 & 15 \\\hline 4 & 18 & 16 \\\hline\end{array}$$

A)3.33
B)4.67
C)5.33
D)6.67

Question 23

Using a large value for order k in the moving averages method is effective in

A)tracking changes in a time series more quickly.
B)smoothing out random fluctuations.
C)providing a forecast when only the most recent time series are relevant.
D)eliminating the effect of seasonal variations in the time series.

Question 24

Demand for a product and the forecasting department's forecast (naïve model) for a product are shown below. Compute the mean absolute error. ?
? $$\begin{array} { | c | c | c | } \hline \text { Period } & \text { Actual Demand } & \text { Forecasted Demand } \\\hline 1 & 12 & - \\\hline 2 & 15 & 12 \\\hline 3 & 14 & 15 \\\hline 4 & 18 & 16 \\\hline\end{array}$$

A)1
B)1.5
C)2
D)2.5

Question 25

Autoregressive models

A)use the average of the most recent data values in the time series as the forecast for the next period.
B)are used to smooth out random fluctuations in time series.
C)relate a time series to other variables that are believed to explain or cause its behavior.
D)occur whenever all the independent variables are previous values of the time series.

Question 26

______________________ uses a weighted average of past time series values as the forecast.

A)The qualitative method
B)Exponential smoothing
C)Correlation analysis
D)The causal model

Question 27

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

A)It is a randomly generated value between -1 and +1.
B)It is small for a time series that has relatively little random variability.
C)It is chosen as the value that minimizes a selected measure of forecast accuracy such as the mean squared error.
D)It is computed in relation with the order value, k, for the moving averages.

Question 28

The process of ____________ might be used to determine the value of smoothing constant that minimizes the mean squared error.

A)quantization
B)nonlinear optimization
C)clustering
D)curve fitting

Question 29

Which of the following measures of forecast accuracy is susceptible to the problem of positive and negative forecast errors offsetting one another?

A)Mean absolute error
B)Mean forecast error
C)Mean squared error
D)Mean absolute percentage error

Question 30

In the moving averages method, the order k determines the

A)error tolerance.
B)compensation for forecasting error.
C)number of time series values under consideration.
D)number of samples in each unit time period.

Question 31

The moving averages and exponential smoothing methods are appropriate for a time series exhibiting

A)a horizontal pattern.
B)a cyclical pattern.
C)trends.
D)seasonal effects.

Question 32

A time series with a seasonal pattern can be modeled by treating the season as a

A)predictor variable.
B)dependent variable.
C)dummy variable.
D)quantitative variable.

Question 33

The moving averages method refers to a forecasting method that

A)is used when considerable trend, cyclical, or seasonal effects are present.
B)uses regression relationship based on past time series values to predict the future time series values.
C)relates a time series to other variables that are believed to explain or cause its behavior.
D)uses the average of the most recent data values in the time series as the forecast for the next period.

Question 34

Which of the following statements is the objective of the moving averages and exponential smoothing methods?

A)To maximize forecast accuracy measures
B)To smooth out random fluctuations in the time series
C)To characterize the variable fluctuations by an exponential equation
D)To transform a nonstationary time series into a stationary series

Question 35

The exponential smoothing forecast for period t + 1 is a weighted average of the

A)forecast value in period t with weight α and the actual value for period t with weight 1 - α.
B)actual value in period t + 1 with weight α and the forecast for period t with weight 1 - α.
C)forecast value in period t - 1 with weight α and the forecast for period t with weight 1 - α.
D)actual value in period t with weight α and the forecast for period t with weight 1 - α.

Question 36

The value of an independent variable from the prior period is referred to as a

A)lagged variable.
B)dummy variable.
C)predictor variable.
D)categorical variable.

Question 37

A causal model provides evidence of ______________ between an independent variable and the variable to be forecast.

A)a causal relationship
B)an association
C)no relationship
D)a seasonal relationship

Question 38

A positive forecast error indicates that the forecasting method ________ the dependent variable.

A)overestimated
B)underestimated
C)accurately estimated
D)closely approximated

Question 39

With reference to exponential forecasting models, a parameter that provides the weight given to the most recent time series value in the calculation of the forecast value is known as the

A)moving average.
B)regression coefficient.
C)smoothing constant.
D)mean forecast error.

Question 40

Causal models

A)provide evidence of a causal relationship between an independent variable and the variable to be forecast.
B)use the average of the most recent data values in the time series as the forecast for the next period.
C)occur whenever all the independent variables are previous values of the same time series.
D)relate a time series to other variables that are believed to explain or cause its behavior.

Question 41

Consider the following time series data. Using the naïve method (most recent value) as the forecast for the next year, compute the following measures of forecast accuracy.
a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for year 11?

Question 42

Consider the following time series.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. What is the forecast for t = 9?

Question 43

The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years.
a. Use α = 0.3 to compute the exponential smoothing values for the time series. Compute MSE and the forecast of profit (in $1000s) for the next quarter.
b. Compare the three-period moving average forecast with the exponential smoothing forecast using α = 0.3. Which appears to provide the better forecast based on MSE?

Question 44

Consider the following time series data. Using the average of all the historical data as a forecast for the next year, compute the following measures of forecast accuracy.
a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for year 11?

Question 45

The below time series gives the indices of Industrial Production in U.S for 10 consecutive years.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. What is the forecast for t = 11?

Question 46

The monthly market shares of General Electric Company for 12 consecutive months follow. Develop three-month and four-month moving averages for this time series. Does the three-month or the four-month moving average provide the better forecasts based on MSE? Explain your reasoning.
​​ ​
​

Question 47

For causal modeling, _______________ are used to detect linear or nonlinear relationships between the independent and dependent variables.

A)descriptive statistics on the data
B)scatter charts
C)contingency tables
D)pie charts

Question 48

Consider the following time series data.
a. Construct a time series plot. What type of pattern exists in the data?
b. Develop a three-year moving average for this time series. Compute MSE and a forecast for the year 11.

Question 49

The following times series shows the demand for a particular product over the past 10 months.
a. Construct a time series plot. What type of pattern exists in the data?
b. Develop a three-month moving average for this time series. Compute MSE and a forecast for month 11.

Question 50

Consider the following time series data:
a. Construct a time series plot. What type of pattern exists in the data?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. What is the forecast for t = 11?

Question 51

The monthly sales (in hundreds of dollars) of a company are listed below.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. What is the sales forecast (in hundreds of dollars) for next month?

Question 52

Consider the following time series data.
a. Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for year 11.
b. Use trial and error to find a value of the exponential smoothing coefficient α (rounded to 2 decimal places) that results in a smaller MSE than what you calculated for α = 0.2.
c. Compute the forecast for year 11 using the smoothing coefficient α selected using trial error.

Question 53

The following times series shows the demand for a particular product over the past 10 months.
a. Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 11.
b. Compare the three-month moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE?

Question 54

The yearly sales (in millions of dollars) of an automobile manufacturing company during the period 2000-2011 are given below.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. What is the sales forecast (in millions of dollars) for the year 2012?

Question 55

The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years.
a. Construct a time series plot. What type of pattern exists in the data?
b. Develop a three-period moving average for this time series. Compute MSE and a forecast of profit (in $1000s) for the next quarter.

Question 56

The monthly sales revenue (in hundreds of dollars) of a company for one year is listed below.
a. Compute MSE using the most recent value as the forecast for the next period. What is the forecast for the next month?
b. Compute MSE using the average of all the data available as the forecast for the next period. What is the forecast for the next month?
c. Which method appears to provide the better forecast?

Question 57

The following time series shows the sales of a particular commodity over the past 15 weeks.
a. Construct a time series plot. What type of pattern exists in the data?
b. Use α = 0.3 to develop the exponential smoothing values for the time series and compute the forecast of demand for the next week.
c. Use trial and error to find a value of the exponential smoothing coefficient α that results in a relatively small MSE.

Question 58

The monthly market shares of General Electric Company for 12 consecutive months follow. Construct a time series plot. What type of pattern exists in the data?
​​ ​
​