Deck 14: Time Series Analysis

Question 1

An exponential trend can have a turning point (peak or trough).

Answer 1

False

Question 2

Multiplicative models are avoided in business because they are too complicated.

Answer 2

False

Question 3

Multiplicative models are most appropriate over longer periods of time or when the data magnitude is growing rapidly over time.

Answer 3

True

Question 4

Additive models are most appropriate over longer periods of time or when the data magnitude is growing rapidly over time.

Question 5

The shape of the fitted quadratic model y_t = 544 + 62t - 3.2t² is declining, then rising.

Question 6

Over the short run, exponential and linear trends may look alike.

Question 7

The shape of the fitted quadratic model y_t = 823 + 72t - 5.1t² is rising, then declining.

Question 8

The shape of the fitted quadratic model y_t = 324 - 42t - 1.3t² is declining, then rising.

Question 9

Exponential smoothing and moving averages are especially useful for data with a clear trend.

Question 10

The linear model's R² may exceed the quadratic model's R² fitted to the same data.

Question 11

An exponential trend allows growth but cannot be used if the time series is declining.

Question 12

Moving average models are causal models (as opposed to time-series models).

Question 13

A firm's balance sheet contains data measured over a period of time, as opposed to being measured at a point in time.

Question 14

The shape of the fitted exponential model y_t = 256e^-.07t is always declining.

Question 15

A firm's income statement contains data measured over a period of time, as opposed to being measured at a point in time.

Question 16

The quadratic model can never have more than one turning point (peaks or troughs).

Question 17

The quadratic model's R² is always at least as high as the linear model fitted to the same data.

Question 18

Cycles are usually ignored because there is no general theory to describe them.

Question 19

A multiplicative time-series model Y = T × C × S × I becomes an additive model if we take the logarithm of each side of the equation.

Question 20

Seasonality is usually ignored because there is no statistical way to describe it.

Question 21

Moving averages are most useful for irregular data with no clear trend.

Question 22

Increasing the smoothing constant α increases the weight assigned to the most recent observation.

Question 23

The smoothing constant α indicates the weight assigned to the most recent forecast.

Question 24

Over long periods of time, multiplicative time-series models may be favored over additive time-series models, because the data magnitude often changes over time.

Question 25

Averaging the first six data values is a way of initializing the forecasts in an exponential smoothing process.

Question 26

The shape of the fitted exponential model y_t = 256e^-.07t is rising at first, then declining.

Question 27

Occam's Razor says always to choose the simplest model.

Question 28

Moving averages are often used for making long-term forecasts (e.g., five periods ahead).

Question 29

The exponential model would be attractive for analyzing a growing company's revenues over time.

Question 30

A higher value of the smoothing constant α makes the forecast less responsive to recent data.

Question 31

Regression analysis can be used for forecasting monthly time-series data using a trend variable and 11 binary predictors (one for each month except omitting one month).

Question 32

In exponential smoothing, using α = .20 will give a smoother series than using α = .05.

Question 33

An attraction of MAPE as a measure of fit is its simple interpretation.

Question 34

Monthly seasonal factors should be adjusted so they sum to 12.

Question 35

A centered moving average provides good forecasts when there is a strong upward trend in the data.

Question 36

The MAD measures the average absolute size of the forecast error.

Question 37

Using the first observed data value is a common way of initializing the forecasts in the exponential smoothing model.

Question 38

Quarterly seasonal factors will sum to 4.

Question 39

The shape of the fitted quadratic model y_t = 248 - 84t + 2.4t² is declining, then rising.

Question 40

In exponential smoothing, using α = .20 will provide less smoothing than using α = .10.

Question 41

Suppose the estimated quadratic model y_t = 500 + 20t - t² is the best-fitting trend of sales of XYZ Inc. using data for the past 20 years (t = 1, 2, …, 20). Which statement is incorrect?

A)Sales are increasing by about 20 units per year.
B)The turning point would be in period 10.
C)Latest year sales are no better than in year zero.
D)The trend was higher in year 10 than in year 20.

Question 42

Which statement is most defensible regarding the time series shown below?

A)There appears to be strong seasonality.
B)There appears to be a six-month seasonal cycle.
C)The trend appears to be exponential.
D)The quadratic trend would be required.

Question 43

In the model y_t = 516 - 42t + 3t² the turning point:

A)is a peak.
B)is a trough.
C)could be either a peak or a trough.
D)is neither a peak nor a trough.

Question 44

The time-series model Y = T × C × S × I:

A)is an additive model.
B)is a multiplicative model.
C)is an exponential model.
D)is a polynomial model.

Question 45

If the trend model y_t = a + bt + ct² is fitted to a time series, we would get:

A)R² that could be lower than the linear model.
B)R² that could be either higher or lower than the linear model.
C)R² that is at least as high as the linear model.
D)no R² for this type of model because it is nonlinear.

Question 46

If a fitted trend equation is y_t = 120 - 40t + 2.5t², then the turning point will be:

A)a peak in period 40.
B)a trough in period 5.
C)a peak in period 4.
D)a trough in period 8.

Question 47

The implied turning point (peak or trough) of y_t = 516 - 42t + 3t² would be in which period? Hint: Use calculus to solve for the value of t that would maximize or minimize y_t.

A)t = 7
B)t = -7
C)t = 6
D)t = -42

Question 48

Might it be OK to use exponential smoothing to forecast 2010 for Bob's data?

A)No, under no circumstances
B)Yes, if you use only the most recent 10 years
C)Yes, if you need a long-term forecast
D)No, since the data appear to be erratic

Question 49

Which trend would you choose to forecast the number of tractors sold in 2010?

A)Linear model.
B)Polynomial model.
C)The forecasts are equivalent.

Question 50

Which trend would you choose to forecast the 2013 value of Bob's beer can collection?

A)Linear model.
B)Exponential model.
C)They are equivalent.

Question 51

Which trend would you choose to forecast the number of water damage claims in 2010?

A)Exponential model.
B)Polynomial model.
C)They are equivalent.

Question 52

If the fitted annual trend for a stock price is y_t = 27e^0.213t, then:

A)the slow growth rate is not very attractive.
B)the stock price seems to be approaching an asymptote.
C)the stock is probably undervalued in today's markets.
D)the stock would more than double every four years.

Question 53

A quadratic trend equation y_t = 900 + 80t - 5t² was fitted to a company's sales. This result implies that the sales trend:

A)hit a peak in period 8.
B)hit a peak in period 5.
C)hit a trough in period 8.
D)hit a trough in period 5.

Question 54

The fitted annual sales trend is y_t = 187e^-.047t. The sales forecast for year 5 would be:

A)236.9.
B)178.7.
C)175.3.
D)147.8.

Question 55

If we fit a linear trend to 10 observations on time-series data that are growing exponentially, then it is most likely that:

A)the fitted trend will be too high at t = 1 and t = 10.
B)the fitted trend will be too low in the middle.
C)the forecasts (if extrapolated) will be too low.
D)the residuals will show a pattern like - - - + + + + - - -.

Question 56

If Y₁ = 216 and Y₅ = 332, then the simple index number for period 5 is I₅ = 153.7.

Question 57

The fitted annual sales trend is y_t = 227e^.037t. The values of y_t are:

A)rising by an increasing amount each period.
B)rising by a declining amount each period.
C)declining by a declining amount each period.
D)declining by an increasing amount each period.

Question 58

A computer analysis reveals that the best-fitting trend model is y_t = 4.12e^0.987t. The trend was fitted using year-end common stock prices for Melodic Kortholt Outlet for the last six years. The R² is 0.8571. Which conclusion is not supportable?

A)The absolute annual growth (in dollars per share) is increasing.
B)Few investments could match the astounding growth rate.
C)At the end of year 3 the stock price would be nearly $80.
D)The exponential model is inappropriate for financial data.

Question 59

What is the approximate slope of a linear trend for the value of Bob's beer can collection?

A)-25
B)-50
C)-15
D)-10

Question 60

Which trend would you choose to forecast the 2013 value of Bob's beer can collection?

A)Exponential model.
B)Quadratic model.
C)They are equivalent.

Question 61

Which data would be measured over an interval of time as opposed to at a point in time?

A)Toyota's total revenue for fiscal 2010
B)Toyota's salaried employee head count at the end of June 2010
C)Toyota's short-term indebtedness at the end of fiscal 2010
D)Toyota's inventory of unsold vehicles on December 31, 2010

Question 62

In a multiplicative model, if the seasonal factor is 1.15 for a particular season, then we expect that the time series in that season would be (other things being equal):

A)115% above the trend.
B)115% below the trend.
C)15% above the trend.
D)15% below the trend.

Question 63

MegaStat's seasonal factor of 1.073 applied to a monthly trend forecast of 125.820 yields:

A)135.005.
B)126.893.
C)137.044.
D)124.228.

Question 64

If y_t = 256e^-0.07t, then the forecast for period 6 is approximately:

A)390.
B)203.
C)179.
D)168.

Question 65

Which of the following best describes the decomposition modeling approach to forecasting?

A)The values of certain variables are used to predict the values of others.
B)Series are separated into trend, seasonal, irregular, and cyclical components.
C)Forecasts are based on an average of recent values.
D)Sophisticated models such as regression with binaries are preferred.

Question 66

A quadratic trend equation was estimated from monthly sales of trucks in the United States from July 2006 to July 2011. The estimated trend is y_t = 106 + 1.03t + 0.048t², where y_t units are in thousands. From this trend, how many trucks would be sold in July 2012?

A)About 308,419
B)About 524,889
C)About 436,982
D)About 223,831

Question 67

For the fitted time-series trend model y_t = 9.23e^-0.0867t, it is correct to say that:

A)the series is growing by 9.23 percent.
B)the series is growing by 8.67 percent.
C)the model probably shows a low R².
D)the time series would be declining.

Question 68

If y_t = 50e^0.07t, then the forecast for period 10 is approximately:

A)100.7.
B)90.7.
C)80.7.
D)70.7.

Question 69

If we fit a linear trend to data that are growing exponentially, which is least likely?

A)The fitted trend will be too low at the beginning and end.
B)The fitted trend will be too high in the middle.
C)The forecasts (if extrapolated) will be too low.
D)The fit will be poor to the most recent data.

Question 70

Which of the following is the least useful time-series forecasting model when there is a strong upward trend in the data?

A)Estimated exponential trend model
B)A five-period centered moving average
C)Exponential smoothing with a high α
D)Regression model with trend and seasonal binaries

Question 71

A trend line has been fitted to a company's annual sales. The trend is given by y_t = 50 + 5t, where t is the time index (t = 1, 2, …, n) and y_t is annual sales (in millions of dollars). The implication of this trend line is:

A)sales will increase by $5 million every year.
B)sales increase exactly 5 percent every year.
C)sales increase on the average 5 percent per year.
D)sales increase on the average $5 million per year.

Question 72

Which data would be measured over an interval of time as opposed to at a point in time?

A)Toyota's accounts receivable on December 31, 2011
B)Costco's sales for fiscal year 2010
C)The Canadian unemployment rate on December 1, 2010
D)The closing price of Wal-Mart's stock last Friday

Question 73

If y_t = 544e^0.07t, then the forecast for period 7 is approximately:

A)989.
B)888.
C)678.
D)589.

Question 74

The fitted sales trend over the last 12 years is y_t = 14.7e^0.063t. We can say that:

A)sales grew (on average) at 63 percent per annum.
B)sales in year 10 would be about 39.
C)a continuously compounded model was used.
D)sales in year 1 were 14.7.

Question 75

Which is a characteristic of an additive (as opposed to multiplicative) time-series model?

A)Appropriate for financial data over a longer time period
B)Appropriate for rapidly growing financial data
C)Appropriate for data that vary by an order of magnitude
D)Appropriate for short-term data with a steady dollar growth

Question 76

Which statement is correct regarding forecasting using an exponential smoothing model?

A)A model with low α is more responsive to new data than a model with high α.
B)Increasing α will typically increase the forecast accuracy.
C)As α increases, more weight is put on recent data.
D)When data have an upward trend, the forecasts will have an upward bias.

Question 77

Consider the following linear trend equation of an industry's sales: y_t = 120 + 12t, where t is measured in years and sales are measured in millions of dollars. Which is the most reasonable conclusion?

A)We would forecast that sales will increase $12 million in the next year.
B)We would forecast that sales will increase 12 percent in the next year.
C)On the average, sales will increase 12/(120 + 12 × 10) = 0.05, or 5 percent next year.
D)The year-to-year change will depend on the value of t.

Question 78

Suppose you fit a (linear or nonlinear) trend regression to a monthly time series and discover that the R² is only 18 percent. The best conclusion is that:

A)adding seasonal factors might make things worse.
B)fitting a seasonal component could raise the R².
C)there is no seasonality in the time series.
D)the overall trend is probably negative.

Question 79

If a trend is given by y_t = ae^bt, then:

A)the fitted trend value in period 0 is b.
B)the trend is exponentially increasing.
C)the trend is exponentially decreasing.
D)the trend is increasing if b > 0 and decreasing if b < 0.

Question 80

A quadratic trend equation y_t = 900 + 30t - 2.5t² was fitted to a company's sales. This result implies that the sales trend:

A)hit a maximum in period t = 30.
B)hit a maximum in period t = 6.
C)hit a minimum in period t = 5.
D)hit a minimum in period t = 6.