Question 1

In selecting a forecasting model, you should perform a residual analysis.

Accepted Answer

Performing a residual analysis helps to evaluate the accuracy of a forecasting model by examining the difference between actual and predicted values. This can help in identifying any patterns or trends in the residuals and assess whether the model is underfitting or overfitting the data.

Question 2

The cyclical component of a time series
A) represents periodic fluctuations which reoccur within 1 year.
B) represents periodic fluctuations which usually occur in 2 or more years.
C) is obtained by adjusting for the seasonal variation.
D) is obtained by adjusting for calendar variation.

Accepted Answer

The cyclical component of a time series represents periodic fluctuations which usually occur in 2 or more years. It is different from the seasonal component, which represents fluctuations that occur within 1 year, and the calendar component, which represents fluctuations due to events such as holidays or weekdays. The cyclical component is often attributed to business cycles or other long-term economic patterns.

Question 3

The MAD is a measure of the mean of the absolute discrepancies between the actual and the fitted values in a given time series.

Accepted Answer

This is a correct definition of MAD (Mean Absolute Deviation).

Question 4

A least squares linear trend line is just a simple regression line with the years recoded.

Accepted Answer

A least squares linear trend line is a type of regression line that is used to model the relationship between two variables, typically a dependent variable and an independent variable such as time. The trend line is based on the principle of least squares, which is a statistical method used to find the best fit line through a set of data points. In the case of a linear trend line, the years would be recoded as a numerical variable to create the independent variable, and the dependent variable would be the variable of interest being measured over time.

Question 5

Which of the following terms describes the overall long-term tendency of a time series?
A) Trend
B) Cyclical component
C) Irregular component
D) Seasonal component

Accepted Answer

The overall long-term tendency of a time series is represented by its trend.

Question 6

Each forecast using the method of exponential smoothing depends on all the previous observations in the time series.

Accepted Answer

Exponential smoothing is a time series forecasting method that assigns exponentially decreasing weights to past observations, which means that the forecast for the next period depends on all the previous observations in the time series. So, each forecast using exponential smoothing is influenced by the entire history of the data.

Question 7

MAD is the summation of the residuals divided by the sample size.

Accepted Answer

MAD, or Mean Absolute Deviation, is the average of the absolute deviations from the mean, not simply the summation of residuals divided by the sample size.

Question 8

TABLE 16-1
The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows. $$\begin{array} { c c } 
\text { Year } & \text { Cases of Wine } \
\hline 2003 & 270 \
2004 & 356 \
2005 & 398 \
2006 & 456 \
2007 & 438 \
2008 & 478 \
2009 & 460 \
2010 & 480
\end{array}$$
-Referring to Table 16-1, set up a scatter diagram (i.e., a time-series plot)with year on the horizontal X-axis.

Accepted Answer

The answer of TABLE 16-1
The number of cases of chardonnay...

Question 9

The principle of parsimony indicates that the simplest model that gets the job done adequately should be used.

Accepted Answer

The principle of parsimony, also known as Occam's Razor, suggests that the simplest explanation or model that can explain the observed data or phenomenon should be preferred over complex or convoluted explanations/models.

Question 10

In selecting an appropriate forecasting model, the following approach is suggested.
A) Perform a residual analysis.
B) Measure the size of the forecasting error.
C) Use the principle of parsimony.
D) All of the above.

Accepted Answer

A residual analysis should be performed to check the adequacy of the chosen model. Measuring the size of the forecasting error helps in comparing different models and selecting the one with the lowest error. The principle of parsimony suggests choosing the simplest model that adequately fits the data. Therefore, all the choices are important in selecting an appropriate forecasting model.

Question 11

After estimating a trend model for annual time-series data, you obtain the following residual plot against time. 
The problem with your model is that
A) the cyclical component has not been accounted for.
B) the seasonal component has not been accounted for.
C) the trend component has not been accounted for.
D) the irregular component has not been accounted for.

Accepted Answer

The residual plot shows patterns in the form of a curved line, indicating that the trend component has not been fully accounted for. The residual plot does not show any significant cyclical or seasonal pattern. Although there may be some irregularity in the data, it does not explain the systematic pattern observed in the residual plot. Therefore, the problem with the model is that the trend component has not been accounted for.

Question 12

A first-order autoregressive model for stock sales is:
Salesᵢ = 800 + 1.2(Sales)ᵢ₋₁.
If sales in 2010 is 6,000, the forecast of sales for 2011 is ________.

Accepted Answer

The answer of A first-order autoregressive model for stock sales...

Question 13

Microsoft Excel was used to obtain the following quadratic trend equation:
Sales = 100 - 10X + 15X².
The data used was from 2001 through 2010 coded 0 to 9. The forecast for 2011 is ________.

Accepted Answer

The answer of Microsoft Excel was used to obtain the...

Question 14

The method of least squares may be used to estimate both linear and curvilinear trends.

Accepted Answer

The method of least squares is a statistical technique that can be used to find a line or curve of best fit through a set of data points. It can be used for linear and nonlinear models, including curvilinear trends.

Question 15

The method of least squares is used on time-series data for
A) eliminating irregular movements.
B) deseasonalizing the data.
C) obtaining the trend equation.
D) exponentially smoothing a series.

Accepted Answer

The method of least squares is primarily used for obtaining the trend equation in time-series analysis, allowing for the identification and modeling of the underlying trend in the data.

Question 16

To assess the adequacy of a forecasting model, one measure that is often used is
A) quadratic trend analysis.
B) the MAD.
C) exponential smoothing.
D) moving averages.

Accepted Answer

The MAD (mean absolute deviation) measures the accuracy of a forecasting model by calculating the average deviation between the actual values and the predicted values. A lower MAD indicates a more accurate forecasting model.

Question 17

The manager of a company believed that her company's profits were following an exponential trend. She used Microsoft Excel to obtain a prediction equation for the logarithm (base 10)of profits:
log₁₀(Profits)= 2 + 0.3X
The data she used were from 2005 through 2010 coded 0 to 5. The forecast for 2011 profits is ________.

Accepted Answer

The answer of The manager of a company believed that...

Question 18

A second-order autoregressive model for average mortgage rate is:
Rateᵢ = - 2.0 + 1.8(Rate)ᵢ₋₁ - 0.5 (Rate)ᵢ₋₂.
If the average mortgage rate in 2010 was 7.0, and in 2009 was 6.4, the forecast for 2011 is ________.

Accepted Answer

The answer of A second-order autoregressive model for average mortgage...

Question 19

A second-order autoregressive model for average mortgage rate is:
Rateᵢ = - 2.0 + 1.8(Rate)ᵢ₋₁ - 0.5 (Rate)ᵢ₋₂.
If the average mortgage rate in 2010 was 7.0, and in 2009 was 6.4, the forecast for 2012 is ________.

Accepted Answer

The answer of A second-order autoregressive model for average mortgage...

Question 20

TABLE 16-1
The number of cases of chardonnay wine sold by a Paso Robles winery in an 8-year period follows. $$\begin{array} { c c } 
\text { Year } & \text { Cases of Wine } \
\hline 2003 & 270 \
2004 & 356 \
2005 & 398 \
2006 & 456 \
2007 & 438 \
2008 & 478 \
2009 & 460 \
2010 & 480
\end{array}$$
-Referring to Table 16-1, does there appear to be a relationship between year and the number of cases of wine sold?
A) No, there appears to be no relationship between the year and the number of cases of wine sold by the vintner.
B) Yes, there appears to be a slight negative linear relationship between the year and the number of cases of wine sold by the vintner.
C) Yes, there appears to be a slight positive relationship between the year and the number of cases of wine sold by the vintner.
D) Yes, there appears to be a negative nonlinear relationship between the year and the number of cases of wine sold by the vintner.

Accepted Answer

There appears to be a slight positive relationship between the year and the number of cases of wine sold by the vintner. The number of cases sold increases from 270 in 2003 to 480 in 2010. This indicates a general upward trend in sales over the 8-year period.

Quiz 16: Time-Series Forecasting

In selecting a forecasting model, you should perform a residual analysis.

The cyclical component of a time series

The MAD is a measure of the mean of the absolute discrepancies between the actual and the fitted values in a given time series.

A least squares linear trend line is just a simple regression line with the years recoded.

Which of the following terms describes the overall long-term tendency of a time series?

Each forecast using the method of exponential smoothing depends on all the previous observations in the time series.

MAD is the summation of the residuals divided by the sample size.

The principle of parsimony indicates that the simplest model that gets the job done adequately should be used.

In selecting an appropriate forecasting model, the following approach is suggested.

After estimating a trend model for annual time-series data, you obtain the following residual plot against time. The problem with your model is that

A first-order autoregressive model for stock sales is: Salesᵢ = 800 + 1.2(Sales)ᵢ₋₁. If sales in 2010 is 6,000, the forecast of sales for 2011 is ________.

Microsoft Excel was used to obtain the following quadratic trend equation: Sales = 100 - 10X + 15X². The data used was from 2001 through 2010 coded 0 to 9. The forecast for 2011 is ________.

The method of least squares may be used to estimate both linear and curvilinear trends.

The method of least squares is used on time-series data for

To assess the adequacy of a forecasting model, one measure that is often used is

A second-order autoregressive model for average mortgage rate is: Rateᵢ = - 2.0 + 1.8(Rate)ᵢ₋₁ - 0.5 (Rate)ᵢ₋₂. If the average mortgage rate in 2010 was 7.0, and in 2009 was 6.4, the forecast for 2011 is ________.

A second-order autoregressive model for average mortgage rate is: Rateᵢ = - 2.0 + 1.8(Rate)ᵢ₋₁ - 0.5 (Rate)ᵢ₋₂. If the average mortgage rate in 2010 was 7.0, and in 2009 was 6.4, the forecast for 2012 is ________.