Question 1

In the final step, using the ratio-to-moving-average method, the total of the 12 modified means should theoretically be equal to 1,200 because the average of the 12 months is designated as 100.

Accepted Answer

The ratio-to-moving-average method ensures that the final total of the 12 modified means equals the starting total, which is 1,200 in this case. Therefore, the statement is true.

Question 2

Data that increases by equal percentages over a period of time appears as a ____________ on an arithmetic scaled graph.

Accepted Answer

curvilinear trend

Question 3

If the past data approximates a straight line, the equation used is Ŷ = a + bt, where a is the Y-intercept and b is the slope of the line.

Accepted Answer

This statement is true. The equation for a straight line is typically written in the form Ŷ = mx + b, where m is the slope and b is the Y-intercept. However, depending on the context, different variables may be used for the same concepts. Therefore, the equation Ŷ = a + bt is also a valid representation for a straight line if a represents the Y-intercept and b represents the slope.

Question 4

Episodic and residual variations can be projected into the future.

Accepted Answer

Episodic variations are irregular and unpredictable, and residual variations are the unexplained fluctuations after all other components have been accounted for, making them both difficult to project accurately into the future.

Question 5

A _____________ transformation should be used for a time series that increases by equal percentages over time.

Accepted Answer

The answer of A _____________ transformation should be used for...

Question 6

The moving average method smoothes out the fluctuations in the data.

Accepted Answer

The moving average method involves taking an average of a certain number of consecutive data points, which effectively smooths out the fluctuations in the data.

Question 7

In a linear trend equation, t is a coded value that corresponds with a time period in a time series.

Accepted Answer

The coded value in a linear trend equation typically represents the order or position of the time period in the time series data. So, t could be a simple integer value that indicates the first, second, third, etc. observation in the series.

Question 8

Autocorrelation is measured by the trend component of a time series.

Accepted Answer

Autocorrelation measures the correlation between a time series and its lagged values, not the trend component. The trend component of a time series is measured by its slope or long-term direction.

Question 9

An analysis of past seasonal fluctuations can be helpful in planning production for items such as toys, dolls, Easter eggs, and other holiday-oriented goods.

Accepted Answer

Analyzing past seasonal fluctuations can provide insights into the demand patterns for holiday-oriented goods, allowing for better production planning and inventory management.

Question 10

If the time series trend is non-linear, a transformation of the data is required.

Accepted Answer

Non-linear trends require transformation to make the data linear and suitable for further analysis. Common transformations include taking logarithms or square roots of the data.

Question 11

The two types of irregular variations that are unpredictable are ______________________ and _____________________.

Accepted Answer

The answer of The two types of irregular variations that...

Question 12

In the linear trend equation, the letter "b" is the average change in Ŷ for each change of one unit (either increase or decrease) in t.

Accepted Answer

This is correct as "b" is the slope or coefficient of the independent variable "t" in the linear trend equation Ŷ = a + bt.

Question 13

A typical seasonal index of 103.7 for January indicates that sales for January are below the annual average.

Accepted Answer

A seasonal index of 100 indicates that sales for a particular month or period are exactly at the annual average. A seasonal index above 100 indicates higher sales than the average, while a seasonal index below 100 indicates lower sales than the average. Therefore, a seasonal index of 103.7 for January indicates that sales for January are above the annual average, not below it.

Question 14

When estimating the specific seasonals for a monthly time series, the sum of the 12 modified means should theoretically be equal to 1,200 because the average of the 12 specific seasonals is designated as 100.

Accepted Answer

This statement is correct. The modified means are adjusted so that the sum of the 12 specific seasonals is equal to 1,200 (12*100).

Question 15

For a straight trend line, ______________ represents the amount of change in Ŷ for each increase of one unit in t.

Accepted Answer

The answer of For a straight trend line, ______________ represents...

Question 16

Knowing the seasonal pattern in the form of indexes allows the retailer to deseasonalize sales. This is accomplished by dividing the actual sales for a month by the typical index for that month.

Accepted Answer

Deseasonalizing sales involves dividing the actual sales for a month by the index for that month, which reflects the typical seasonal pattern. This removes the seasonal fluctuations and provides a more accurate picture of the underlying sales trend.

Question 17

The Durbin-Watson statistic is used to test for correlated residuals.

Accepted Answer

The Durbin-Watson statistic is a test for autocorrelation in the residuals of a regression model. It measures the extent to which the residuals are correlated with one another over time. A value of 2 indicates no autocorrelation, while values significantly less than 2 indicate positive autocorrelation and values significantly greater than 2 indicate negative autocorrelation.

Question 18

One component of a time series is cyclical variation. An example of cyclical variation is the business cycle that consists of periods of prosperity followed by periods of recession, depression, and recovery.

Accepted Answer

Cyclical variation refers to a pattern of ups and downs over a period of time, which is seen in the business cycle where periods of economic growth and decline alternate.

Question 19

If the trend equation is Ŷ = 10 + 100t, the forecasted value increases 100 units for the next time period, t.

Accepted Answer

Since the trend equation is Ŷ = 10 + 100t, the forecasted value (Ŷ) increases by 100 units for each unit increase in t. Therefore, if the next time period is t+1, then the forecasted value will increase by 100 units, making the answer A, true.

Question 20

The _____________ method is useful in smoothing out a time series.

Accepted Answer

The answer of The _____________ method is useful in smoothing...

Quiz 18: Time Series and Forecasting