Deck 12: Forecasting With Time Series Data

Question 1

Sydney is evaluating monthly sales for her Etsy account. Based on the given data y₁ = 4,370; y₂ = 3,769; y₃ = 4,119, what is her 3-period moving average?

A) 4,086
B) 4,119
C) 4,069
D) 4,244

Answer 1

4,086

Question 2

Sydney is evaluating monthly sales for her Etsy account. Based on the given data y₁= 4,321; y₂= 3876; y₃= 4,190, what is her 3-period moving average?

A) 4,129
B) 4,190
C) 4,098
D) 4,255

Answer 2

4,129

Question 3

Mark is using a 3-period moving average to forecast the number of filters needed for the fourth quarter. Using the following data, what is the forecasted amount?

A) 36 Filters
B) 37 Filters
C) 38 Filters
D) 40 Filters

Answer 3

38 Filters

Question 4

Mark is using a 3-period moving average to forecast the number of filters needed for the fourth quarter. Using the following data, what is the forecasted amount?

A) 37 Filters
B) 38 Filters
C) 39 Filters
D) 40 Filters

Question 5

Using only the residual in the following table, calculate the overall MSE.

A) 3,121.50
B) 2,954.25
C) 58,053.75
D) 219.83

Question 6

Using only the residual in the following table, calculate the overall MSE.

A) 2,946.50
B) 2,909.75
C) 11,112.75
D) 210.83

Question 7

Complete the simple exponentially smoothed series on the following table where ? = 0.20 and L₁ = y₁.

A) 2,916.80
B) 2,892.40
C) 2,875.60
D) 2,870.40

Question 8

Complete the simple exponentially smoothed series on the following table where ? = 0.40 and L₁ = y₁.

A) 3,027.20
B) 2,969.28
C) 2,971.52
D) 2,934.40

Question 9

Consider the following estimated linear trend model and make a forecast for t = 18 and y^ = 10.88 + 1.04t.

A) 0.68
B) 1.65
C) 28.88
D) 29.60

Question 10

Consider the following estimated linear trend model and make a forecast for t = 18 and y^= 11.23 + 1.04t.

A) 0.68
B) 1.67
C) 29.23
D) 29.95

Question 11

Consider the following quadratic trend model and make a forecast for t = 22 and $\hat{y}$ = 11.21 + 1.18t + 0.02t².

A) 38.05
B) 46.85
C) 36.29
D) 61.60

Question 12

Consider the following quadratic trend model and make a forecast for t = 20 and $\hat{y}$ = 15.84 + 0.98t + 0.02t².

A) 35.08
B) 43.44
C) 25.80
D) 45.10

Question 13

Consider the following exponential trend model and make a forecast for t = 21 and y^=exp 2.12+0.08t+ 0.0122 .

A) 44.70
B) 44.15
C) 44.61
D) 44.26

Question 14

Consider the following exponential trend model and make a forecast for t = 20 and $\hat{y}$ = exp (2.4 + 0.08t + $\frac{0.01^2}{2}$ ).

A) 54.60
B) 54.33
C) 54.50
D) 54.05

Question 15

Based on the following plotted series of linear and exponential trends with an overlay of observation points, which model is the best fit for the observed data?

A) the exponential trend model
B) the linear trend model
C) neither model
D) the quadratic model

Question 16

Which option is not a description of polynomial trend models?

A) Higher level polynomials run the risk of overfitting.
B) MSE, MAD, MAPE cannot be used to compare polynomial trend models.
C) Adjusted R² is used to compare polynomial models.
D) The coefficient $\beta$ ₂ determines the direction of the linear trend line.

Question 17

Using the following table of results, what is the estimated linear trend model for the sample?

A) $\hat{y}$ = 0.91881 + 0.5364t
B) $\hat{y}$ = 11.8846 + 0.5364t
C) $\hat{y}$ = 0.8471 + 0.83556t
D) $\hat{y}$ = 0.83556 + 11.8846t

Question 18

Using the following table of results, what is the estimated linear trend model for the sample?

A) $\hat{y}$ = 0.91881 + 0.3144 t
B) $\hat{y}$ = 11.7606 + 0.3144 t
C) $\hat{y}$ = 0.84421 + 0.83556 t
D) $\hat{y}$ = 0.83556 + 11.7606 t

Question 19

Using the following table of results, what is the estimated quadratic trend model for the sample?

A) $\hat{y}$ = 12.6476 + 0.8117t ? 6.3274t2
B) $\hat{y}$ = 12.6476 + 0.9563t + 0.0034t2
C) $\hat{y}$ = 12.6476 + 0.0034t + 0.0207t2
D) $\hat{y}$ = 12.6476 + 0.8117t? 0.0207t2

Question 20

Using the following table of results, what is the estimated quadratic trend model for the sample?

A) $\hat{y}$ = 10.0651 + 0.7768t ? 6.3274t²
B) $\hat{y}$ = 10.0651 + 0.9481t + 0.0034t²
C) $\hat{y}$ = 10.0651 + 0.0034t + 0.0220t²
D) $\hat{y}$ = 10.0651 + 0.7768t ? 0.0220t²

Question 21

Based on the following results, which model is the best fit for the data?

A) The adjusted R² for the quadratic model is higher, thus best fit for the data.
B) The adjusted R² for the linear model is lower, thus best fit for the data.
C) The R² for the quadratic model is higher, thus best fit for the data.
D) The R² for the linear model is lower, thus best fit for the data.

Question 22

Using the following table, estimate quadratic trend model with seasonal dummy variables.

A) = 0.9352 + 0.0174d₁ - 0.0734d₂ - 0.0636d₃ - 0.0040t + 0.0003t²
B) = 1.4155 + 0.0174d₁ - 0.0734d₂ - 0.0636d₃ - 0.0040t + 0.0003t²
C) = 0.8560 + 0.0174d₁ - 0.0734d₂ - 0.0636d₃ - 0.0549t + 0.0003t²
D) = 1.4155 + 0.9352d₁ - 0.8746d₂ - 0.8560d₃ - 0.0549t + 0.0003t²

Question 23

Using the following results, estimate linear trend model with seasonal dummy variables.

A) = 2.3036 + 0.0615d1 + 0.0667d2 + 0.0618d3 + 0.0128t
B) = 2.3036 - 0.0615d1 - 0.0667d2 - 0.0618d3 + 0.0128t
C) = 2.3036 + 0.0615d1 - 0.0667d2 - 0.0618d3 - 0.0128t
D) = 2.3036 - 0.0615d1 + 0.0667d2 + 0.0618d3 + 0.0128t

Question 24

Using the following results, estimate linear trend model with seasonal dummy variables.

A) 1.4702 + 0.0174d₁ + 0.0729d₂ + 0.0630d₃ + 0.0137t
B) 1.4702 - 0.0174d₁ - 0.0729d₂ - 0.0630d₃ + 0.0137t
C) 1.4702 + 0.0174d₁ - 0.0729d₂ ? 0.0630d₃ - 0.0137t
D) 1.4702 - 0.0174d₁ + 0.0729d₂ + 0.0630d₃ + 0.0137t

Question 25

Mary is determining the maximum quantity given the seasonality is constant. If the coefficients are 107t and -22.8190t² in a quadratic model, what is the maximum quantity that can be reached?

A) 4.69
B) 0.107
C) 7.86
D) 2.345

Question 26

Mary is determining the maximum quantity given the seasonality is constant. If the coefficients are 112t and -23.4502t² in a quadratic model, what is the maximum quantity that can be reached?

A) 4.78
B) 0.015
C) 9.10
D) 2

Question 27

Which one of the following is not a step in cross-validation with time series?

A) Use both the training and validation set to re-estimate the preferred model.
B) Split data series into early and later periods, representing both training and validation set.
C) Determine the proper forecast model based on R² results.
D) Explore suitable forecasting models to compute MSE, MAD, and MAPE.

Question 28

In the __________ model, to estimate, the response variable is measured in natural logs, ln (y_t), and then a run regression of ln (y_t) on t.

A) linear
B) exponential
C) cubed
D) quadratic

Question 29

The following model yt = $\beta$ ₀ + $\beta$ ₁t + $\beta$ 2t² + $\beta$ ₃t³ + $\varepsilon$ _t allows for what changes in a series?

A) allows for a curvature indicating the change of direction
B) allows for one change in the direction of a series
C) allows for two changes in the directions of a series
D) allows for the increase in the time period and standard error of the estimate

Question 30

Martin owns a foot truck that for the past five years has frequented local festivals selling fried cheese curds. He has experienced a variation in sales for no known reason and wants to develop a forecast using the exponential smoothing method. After loading data from the previous 20 days, the following summary table was calculated. What is the MSE?

A) 10.49
B) 4.07
C) 11.04
D) 2.711

Question 31

Martin owns a foot truck that for the past five years has frequented local festivals selling fried cheese curds. He has experienced a variation in sales for no known reason and wants to develop a forecast using the exponential smoothing method. After loading data from the previous 20 days, the following summary table was calculated. What is the MSE?

A) 10.85
B) 4.02
C) 10.30
D) 2.695

Question 32

Martin owns a foot truck that for the past five years has frequented local festivals selling fried cheese curds. He has experienced a variation in sales for no known reason and wants to develop a forecast using the exponential smoothing method. After loading data from the previous 20 days, the following summary table was calculated. What is the MAD?

A) 10.65
B) 4.09
C) 11.21
D) 2.739

Question 33

Martin owns a foot truck that for the past five years has frequented local festivals selling fried cheese curds. He has experienced a variation in sales for no known reason and wants to develop a forecast using the exponential smoothing method. After loading data from the previous 20 days, the following summary table was calculated. What is the MAD?

A) 10.30
B) 4.02
C) 10.85
D) 2.695

Question 34

Martin is handed quarterly sales data from a small subsidiary. Prior to creating a strategy, he wants to forecast the Q4 results to have an idea of the full year potential sales. What is the most popular technique Martin can use to compute the Q4 sales estimate?

A) quadratic trend model
B) 3-period moving average technique
C) polynomial trend model
D) exponential smoothing model

Question 35

Consider the following table of the derivations for the MSE, MSA, and MAPE in the validation set. Based on the results, which model is preferred and why?

A) Exponential, because the MSE, MAD, and MAPE are consistently lower.
B) Both Linear and Exponential are preferred models because the results are positive.
C) Linear, because the MSE, MAD, and MAPE are consistently higher.
D) Neither, because an adjusted R² is needed for determination.

Question 36

Which method would be the best fit for a sample containing seasonality, but no trend, and is further divided into structures depending on the type of seasonality exhibited by the series?

A) the exponential method
B) the Holt exponential smoothing method
C) the Holt-Winters exponential smoothing method
D) quadratic trend model

Question 37

When constructing a quick review table in Excel, knowing the formula is essential in populating the cells correctly. Using the Holt exponential smoothing method, complete the following table for Year 3 where $\alpha$ = 0.1 and $\beta$ = 0.2.

A) 6,600
B) 8,980
C) 7,180
D) 11,580

Question 38

When constructing a quick review table in Excel, knowing the formula is essential in populating the cells correctly. Using the Holt exponential smoothing method, complete the following table for Year 3 where $\alpha$ = 0.1 and $\beta$ = 0.2.

A) 6,680
B) 8,980
C) 8,680
D) 11,180

Question 39

When constructing a quick review table in Excel, knowing the formula is essential in populating the cells correctly. Using the Holts exponential smoothing method, complete the following table for Year 4 where $\alpha$ = 0.1 and $\beta$ = 0.2.

A) 104,624
B) 105,452
C) 103,260.8
D) 115,957.6

Question 40

When constructing a quick review table in Excel, knowing the formula is essential in populating the cells correctly. Using the Holts exponential smoothing method, complete the following table for Year 4 where $\alpha$ = 0.1 and $\beta$ = 0.2.

A) 103,864
B) 102,472
C) 104,510.8
D) 114,625.6

Question 41

When performing a cross-validation of regression model with R, in the forecast package, we use the _____ function to find the number of observations in the validation set.

A) length
B) forecast
C) tslm
D) accuracy

Question 42

When using R to perform the Holt-Winters exponential smoothing method, in forecast, we use ____ function with the model inputs of 'AAA' and 'AAM'.

A) ts
B) window
C) ets
D) fAdd

Question 43

Of the smoothing methods, which one does the level L_t, as well as the trend T_t, adapt over time and is a best fit when the time series expresses no seasonality?

A) simple exponentially smoothing technique
B) the moving average technique
C) the Holt exponential smoothing method
D) the Holt-Winters exponential smoothing method

Question 44

Aimee's bookstore had a 45% increase in profits on Wednesday, June 12^th, over the previous year's sales. Without the presence of a holiday, events in the area, or sale promotion, this business event is considered random.

Question 45

The use of quantitative forecast can be criticized because biases in optimism and overconfidence may skew the results.

Question 46

In a 3-period moving average, when a new observation becomes available, the highest numerical observation is dropped.

Question 47

When a time series is expected to grow by fixed amounts each time period, then the linear trend model should be used.

Question 48

When visually inspecting data to confirm the existence of a trend, a scatterplot of the data with a superimposed linear trend line is advisable to view the series over time.

Question 49

In reviewing stock growth in Amazon, the linear trend model would be best use for when an increase in the series happens over time.

Question 50

If a time series reverses direction, then a quadratic trend model will allow for the curvature to be graphed.

Question 51

By combining the validation and the training set, the sample is larger for estimation and includes the most recent validation set for predictions.

Question 52

When a time series exhibits seasonal variations, the Holt exponential smoothing method, or double exponential smoothing method, is appropriate to capture the upward and downward movement of the time series.

Question 53

The triple exponential smoothing method uses seasonality variations in the analysis of the data.