Question 1

The model that assumes the time-series value at time t is the sum of the four time-series components is referred to as the:
A)additive model.
B)multiplicative model.
C)moving averages model.
D)forecast model.

Accepted Answer

The additive model assumes that the time-series value at time t is the sum of its four components: the overall mean or intercept, the trend component, the seasonal component, and the residual component. This is the most commonly used forecasting model and is appropriate for time series where the magnitude of the seasonal fluctuations or noise is constant over time.

Question 2

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?
A)Trend.
B)Cyclical.
C)Seasonal.
D)Random variation.

Accepted Answer

The answer of The high level of airline ticket sales...

Question 3

A time series regression equation measuring the number of surfboards sold by a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q₁ + 0.5Q₃ + 8Q₄ + 3t With t in quarters and the origin is December 2010 and Q₁ is the indicator variable for March, Q₃ is the indicator variable for September and Q₄ is the indicator variable for December. Which of the following statements is correct? A)There is a mistake with this regression model because all the coefficients of the indicator variables are positive. B)There is no indicator variable for the June quarter in this model because there is no seasonal effect in June due to winter in Australia. C)There is a mistake with this model because the indicator variable for the June quarter has been left out. D)There is no indicator variable for the June quarter in this model because we need one less indicator variable than number of categories to use indicator variables with regression for a time series.

Accepted Answer

In regression analysis with categorical variables, one category is typically left out as the baseline, and indicator variables are created for the other categories. This approach, known as the "dummy variable trap," avoids multicollinearity by ensuring that the indicator variables are not perfectly multicollinear. In this case, with four quarters in a year, three indicator variables are used, one for each quarter except the baseline (June), to avoid perfect multicollinearity and allow the model to estimate the effect of the other quarters relative to the baseline.

Question 4

In determining weekly seasonal indexes for petrol consumption, the sum of the 52 means for petrol consumption as a percentage of the moving average is 5050. To get the seasonal indexes, each weekly mean is to be multiplied by:
A)5200 / 5050.
B)(5200 + 5050) / 52.
C)(5050 + 52) / 5200.
D)5050 / 5200.

Accepted Answer

To find the seasonal indexes, we need to divide the mean for each week by the overall mean (the sum of all 52 means divided by 52). We can express this as:
Seasonal index = Weekly mean / (Sum of all 52 means / 52)

We know that the sum of all 52 means is 5050, so we can substitute this in:
Seasonal index = Weekly mean / (5050 / 52)

Simplifying this expression, we get:
Seasonal index = Weekly mean * (52 / 5050)

Therefore, each weekly mean needs to be multiplied by 52 / 5050 to get the corresponding seasonal index. The only choice that matches this expression is A) 5200 / 5050. We can simplify this expression to get:
52 / 5050 = 4 / 385
So, each weekly mean needs to be multiplied by 4/385 to get the seasonal index for petrol consumption.

Question 5

In determining monthly seasonal indexes, the first step is to construct a centred moving average with a period of:
A)24 months.
B)12 months.
C)6 months.
D)3 months.

Accepted Answer

A centred moving average with a period of 12 months allows for the capture of seasonal patterns over a full year. This is commonly used in time series analysis for monthly data, where the seasonality is often annual. A period of 24 months would smooth out the seasonal pattern too much and a period of 6 or 3 months would not capture the full year's seasonal pattern.

Question 6

For which of the following values of the smoothing constant w will the smoothed series catch up most quickly whenever the original time series changes direction?
A)0.10.
B)0.50.
C)0.30.
D)0.70.

Accepted Answer

The smoothed series will catch up most quickly to changes in the original time series direction when the smoothing constant (w) is higher. A higher value of w gives more weight to the most recent observations, making the series more responsive to changes. Therefore, 0.70 will result in the quickest adjustment.

Question 7

The results of a quadratic model fit to time-series data were ŷt = 7.5-0.2t + 2.8t2, where t = 1 for 2002. The forecast value for 2011 is:
A)289.5.
B)285.5.
C)236.1.
D)232.5.

Accepted Answer

To find the forecast value for 2011, we substitute t = 10 (since t = 1 corresponds to 2002) into the model equation: 
ŷ10 = 7.5F1F1F1S1F1F1F10 0.2(10) + 2.8(10)2 = 285.5. Therefore, the forecast value for 2011 is 285.5.

Question 8

Which of the following is true?
A)In trend analysis, the independent variable is time only if the equation is linear.
B)The number of time periods in a centred moving average is always even.
C)If the seasonal index for December sales is 120, this means that December sales tend to be 120% higher than the 'average' month.
D)The cyclical component of a time series refers to repeating patterns that have a period of a year or less.

Accepted Answer

A seasonal index of 120 means that December sales are 20% higher than the "average" month, as the average is typically represented by an index of 100. The other options are incorrect. In trend analysis, time is always the independent variable regardless of linearity. The number of time periods in a centered moving average can be even or odd. The cyclical component refers to repeating patterns with a period of more than a year.

Question 9

Which of the following smoothing constants causes the most rapid reaction to a change in the current time-series value?
A)0.40.
B)0.48.
C)0.43.
D)0.37.

Accepted Answer

The higher the smoothing constant, the more rapidly the smoothing method reacts to changes in the time-series data. Among the given options, 0.48 is the highest, causing the most rapid reaction.

Question 10

The trend equation for annual sales data (in millions of dollars) is $\ddot{\mathbf{p}}_{t}= 65 + 2.5 t$ , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is:
A)90.0.
B)7.28.
C)7.50.
D)7.69.

Accepted Answer

The answer of The trend equation for annual sales data...

Question 11

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:
A)lowest MAD and highest SSE.
B)highest MAD and lowest SSE.
C)lowest MAD and SSE.
D)highest MAD and SSE.

Accepted Answer

The MAD measures the average absolute difference between the forecasted values and the actual values. A lower MAD indicates better accuracy.
The SSE measures the sum of the squared differences between the forecasted values and the actual values. A lower SSE indicates better accuracy.
Therefore, the best model will have the lowest MAD and the lowest SSE, which is option C.

Question 12

Which of the following models might be appropriate to describe a new product that has experienced a rapid early growth rate followed by the inevitable levelling-off?
A)The autoregressive model.
B)The linear model for long-term trend.
C)The quadratic model for long-term trend.
D)All of these choices are correct.

Accepted Answer

The quadratic model for long-term trend is appropriate to describe a new product that experiences rapid early growth followed by levelling-off. This model considers both a linear and a quadratic trend, capturing the initial fast growth with the quadratic term and the eventual slowing down with the linear term. The autoregressive model is more appropriate for time series data with autocorrelation, and the linear model for long-term trend assumes a constant growth rate which does not account for the initial rapid growth and levelling-off.

Question 13

Suppose that we calculate the four-period moving average of the following time series: $$\begin{array} { | c | c c c c c c | } 
\hline t & 1 & 2 & 3 & 4 & 5 & 6 \
\hline y _ { t } & 18 & 28 & 23 & 17 & 26 & 14 \
\hline
\end{array}$$ The centred moving average for period 4 is:
A)20.00.
B)22.50.
C)23.50.
D)21.75.

Accepted Answer

The answer of Suppose that we calculate the four-period moving...

Question 14

Of the four components of the multiplicative time-series model, the ratio of the time series to the moving average isolates the:
A)trend and cyclical components.
B)cyclical and seasonal components.
C)seasonal and random variation components.
D)four components.

Accepted Answer

The ratio of the time series to the moving average isolates the seasonal and random variation components by removing the trend component.

Question 15

Smoothing time-series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:
A)trend component.
B)cyclical component.
C)seasonal component.
D)random variation component.

Accepted Answer

Smoothing time-series data using methods like the moving average or exponential smoothing is primarily aimed at reducing the impact of the random variation component. These techniques help in filtering out the noise, making the underlying patterns (such as trends or seasonal variations) more visible for analysis.

Question 16

The regression trend line for annual energy consumption for 1985-2005 is given by ŷt = 70 + 0.53t, where t = 1 for 1985. If the annual energy consumption for 2000 was 82.5, then the percentage of trend for 2000 was:
A)105.122%.
B)95.127%.
C)104.321%.
D)98.462%.

Accepted Answer

To calculate the percentage of trend for 2000, first find the trend value for 2000 using the given equation. For 2000, $t = 2000 - 1984 = 16$, so $ŷ_{2000} = 70 + 0.53 \times 16 = 78.48$. The actual value for 2000 is 82.5. The percentage of trend is calculated as $\frac{Actual}{Trend} \times 100 = \frac{82.5}{78.48} \times 100 = 105.122%$.

Question 17

One measure of the accuracy of a forecasting model is the:
A)deseasonalised time series.
B)four-period moving average.
C)mean absolute deviation.
D)smoothing constant.

Accepted Answer

The mean absolute deviation (MAD) is a measure of the accuracy of a forecasting model. It is calculated as the average absolute difference between the forecasted values and the actual values. A lower MAD indicates a more accurate model. The other options mentioned are not directly related to measuring the accuracy of a forecasting model.

Question 18

The trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is $$\ddot{\mathbf{p}}_{t} = 6.8 + 1.2 t$$ , where t = 1 for the first quarter of 2001. The seasonal index for the third quarter of 2006 is 1.25. The forecast sales for the third quarter of 2006 is:
A)34.40.
B)27.52.
C)43.00.
D)35.65.

Accepted Answer

To forecast the sales for the third quarter of 2006, first calculate the trend value for that quarter. Since t = 1 for the first quarter of 2001, the third quarter of 2006 is t = 3 + (2006-2001)*4 = 23. Plug t = 23 into the trend equation: $\ddot{\mathbf{p}}_{23} = 6.8 + 1.2 \times 23 = 34.4$. Then, adjust for the seasonal index: $34.4 \times 1.25 = 43.00$.

Question 19

The model that assumes the time-series value at time t is the product of the four time-series components is referred to as the:
A)additive model.
B)forecast model.
C)moving averages model.
D)multiplicative model.

Accepted Answer

The statement describes the multiplicative model. The additive model assumes that the time-series value at time t is the sum of the four time-series components. The forecast model and moving averages model are not specific models, but rather general terms used in time series analysis.

Question 20

In determining monthly seasonal indexes for petrol consumption, the sum of the 12 means for petrol consumption as a percentage of the moving average is 1230. To get the seasonal indexes, each of the 12 monthly means is to be multiplied by:
A)1200 / 1230.
B)1230 / 1200.
C)(1230 + 1200) / 2.
D)(1230 + 1200) / 12.

Accepted Answer

To normalize the seasonal indexes so that their sum equals 1200 (100% for each month), each mean should be multiplied by 1200 / 1230 to adjust the total sum from 1230 to 1200.

Quiz 17: Time-Series Analysis and Forecasting

The model that assumes the time-series value at time t is the sum of the four time-series components is referred to as the:

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?

In determining weekly seasonal indexes for petrol consumption, the sum of the 52 means for petrol consumption as a percentage of the moving average is 5050. To get the seasonal indexes, each weekly mean is to be multiplied by:

In determining monthly seasonal indexes, the first step is to construct a centred moving average with a period of:

For which of the following values of the smoothing constant w will the smoothed series catch up most quickly whenever the original time series changes direction?

The results of a quadratic model fit to time-series data were ŷt = 7.5-0.2t + 2.8t2, where t = 1 for 2002. The forecast value for 2011 is:

Which of the following is true?

Which of the following smoothing constants causes the most rapid reaction to a change in the current time-series value?

The trend equation for annual sales data (in millions of dollars) is $\ddot{\mathbf{p}}_{t}= 65 + 2.5 t$ , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is:

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:

Which of the following models might be appropriate to describe a new product that has experienced a rapid early growth rate followed by the inevitable levelling-off?

Suppose that we calculate the four-period moving average of the following time series: $\begin{array} { | c | c c c c c c | } \hline t & 1 & 2 & 3 & 4 & 5 & 6 \\\hline y _ { t } & 18 & 28 & 23 & 17 & 26 & 14 \\\hline\end{array}$ The centred moving average for period 4 is:

Of the four components of the multiplicative time-series model, the ratio of the time series to the moving average isolates the:

Smoothing time-series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:

The regression trend line for annual energy consumption for 1985-2005 is given by ŷt = 70 + 0.53t, where t = 1 for 1985. If the annual energy consumption for 2000 was 82.5, then the percentage of trend for 2000 was:

One measure of the accuracy of a forecasting model is the:

The trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is $\ddot{\mathbf{p}}_{t} = 6.8 + 1.2 t$ , where t = 1 for the first quarter of 2001. The seasonal index for the third quarter of 2006 is 1.25. The forecast sales for the third quarter of 2006 is:

The model that assumes the time-series value at time t is the product of the four time-series components is referred to as the:

In determining monthly seasonal indexes for petrol consumption, the sum of the 12 means for petrol consumption as a percentage of the moving average is 1230. To get the seasonal indexes, each of the 12 monthly means is to be multiplied by: