Question 1

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 model that assumes the time-series value at time t is the product of four time-series components (trend, seasonality, cycle, and random) is referred to as a multiplicative model. This is because the components are multiplied together rather than added together in an additive model. Therefore, option D is the correct choice.

Question 2

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 3

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 is the best choice because it captures the seasonal pattern of a full year, which is typically the length of a seasonal cycle. A moving average with a shorter period may not capture the full seasonal pattern, and a longer period may oversmooth the data and obscure important variation.

Question 4

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 four components: level, trend, seasonality, and noise. This is typically represented as Yt = L + T + S + N, where Yt is the value at time t, L is the level component, T is the trend component, S is the seasonal component, and N is the noise component. The multiplicative model assumes that the components are multiplied together, rather than added, and is typically represented as Yt = L x T x S x N. While moving averages and forecast models can be used within the additive or multiplicative models, they do not define the overall model itself. Therefore, the best choice is A) additive model.

Question 5

The results of a quadratic model fit to time-series data were ?_t = 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 need to substitute t = 10 (2011-2002 = 9, and t = 1 corresponds to 2002) in the given quadratic model. Thus, ŷ_t = 7.5 F1F1F1S1F1F1F10 + 0.2(10) + 2.8(10)² ŷ_t = 285.5 Therefore, the forecast value for 2011 is 285.5.

Question 6

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

According to the method of computing seasonal indexes, each weekly mean is to be divided by the corresponding moving average, and the resulting ratios are averaged for each week of the year to obtain the seasonal indexes. The sum of the 52 means as a percentage of the moving average is 5050. This means that the sum of the seasonal indexes is 5200 (since the sum of the ratios should always be equal to the number of weeks). Therefore, the multiplier for each weekly mean should be 5200/5050, which is option A.

Question 7

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 the best choice as it fits the description of a product that experiences rapid initial growth followed by a levelling-off. This model allows for a curve to represent the long-term trend, which better represents a product's growth trajectory than a straight line (linear model) or a stationary process (autoregressive model).

Question 8

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 9

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.

Question 10

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 answer of Of the four components of the multiplicative...

Question 11

A time series regression equation for 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) The overall general movement of number of surfboards sold by this company is positive because the coefficients of the indicator variables are positive. B) The overall general movement of number of surfboards sold by this company is positive because the intercept is positive. C) The overall general movement of number of surfboards sold by this company is positive because the coefficient of time t is positive. D) None of these choices are correct.

Accepted Answer

The coefficient of time t is positive, which shows that the number of surfboards sold is increasing over time. The coefficients of the indicator variables only show the effect of specific months on the number of surfboards sold, but do not indicate the overall trend. The intercept being positive only means that there is a minimum level of number of surfboards sold even in the absence of any other explanatory variables.

Question 12

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, whether by moving average or exponential smoothing methods, is primarily aimed at reducing the impact of the random variation component. These techniques help in filtering out the noise to better identify the underlying pattern in the data.

Question 13

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

The seasonal index for December sales being 120 means that December sales tend to be 20% higher than the 'average' month, not 120% higher. A is false because time is always the independent variable in trend analysis. B is false because the number of time periods in a centred moving average can be either odd or even. D is false because the cyclical component of a time series refers to repeating patterns that have a period longer than a year.

Question 14

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 best model will have the lowest MAD and SSE. MAD measures the average magnitude of forecast errors, so a lower MAD indicates better accuracy. SSE measures the sum of the squared differences between actual and forecast values, so a lower SSE indicates better accuracy. Therefore, the combination of the lowest MAD and SSE is the best choice.

Question 15

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 16

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

The answer of A time series regression equation measuring the...

Question 17

The regression trend line for annual energy consumption for 1985-2005 is given by ŷ_t = 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

The trend value for 2000 (t = 16) is ŷ₁₆ = 70 + 0.53(16) = 78.48. The percentage of trend is (82.5 / 78.48) * 100 = 105.122%.

Question 18

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) measures the average magnitude of the errors in a set of forecasts, providing a good measure of the accuracy of the forecasting model. The other options listed are not direct measures of forecasting accuracy.

Question 19

The trend equation for annual sales data (in millions of dollars) is $=65+2.5 t$ , 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 20

The trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is $\ddot { y } _ { t } = 6.8 + 1.2 t$ , 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

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

Quiz 23: Time-Series Analysis and Forecasting

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:

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

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

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

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:

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?

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?

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:

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:

Which of the following is true?

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:

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

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 annual sales data (in millions of dollars) is =65+2.5t=65+2.5 t=65+2.5t , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is:

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

The regression trend line for annual energy consumption for 1985-2005 is given by ŷ_t = 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:

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