Deck 23: Time-Series Analysis and Forecasting

Question 1

Which of the following components of a time-series reflects the overall general movement of the data?

A) Random Variation
B) Trend
C) Cyclical component
D) Seasonal component

Answer 1

B

Question 2

The most commonly used measures of forecast accuracy are the:

A) mean absolute deviation and the sum of squares for forecast errors.
B) sum of squares for forecast error and seasonal indexes.
C) seasonal indexes and the percentage of trend.
D) All of these choices are correct.

Answer 2

A

Question 3

Which of the following is the time-series component that reflects the irregular changes in a time series?

A) Trend
B) Cyclical component
C) Random variation
D) Seasonal component

Answer 3

C

Question 4

We calculate the five-period moving average for a time series for all time periods except the:

A) first five periods.
B) last five periods.
C) first and last period.
D) first two and last two periods.

Question 5

In general, it is easy to identify the trend component of a time series by using:

A) exponential smoothing.
B) moving averages.
C) regression analysis.
D) seasonally adjusted time series.

Question 6

Which of the following best describes a time series?

A) A time series is a set of measurements on a variable collected at the same time.
B) A time series is a set of measurements on a variable taken over some time period in sequential order.
C) A time series is a model that attempts to analyze the relationship between a dependent variable and one or more independent variables.
D) A time series is a model that attempts to forecast the future value of a variable.

Question 7

We calculate the three-period moving averages for a time series for all time periods except the:

A) first and last period.
B) first two periods.
C) last two periods.
D) first and last two periods.

Question 8

The linear model for long-term trend is $y = \beta _ { 0 } + \beta _ { 1 } t + \varepsilon$ , where t is the time period. The trend is indicated by:

A) $\beta _ { 0 }$ .
B) $\beta _ { 1 }$ .
C) $y$ .
D) $t$ .

Question 9

Which of the four time-series components is most likely to exhibit the changes in a stock market crash?

A) Trend.
B) Cyclical.
C) Seasonal.
D) Random variation.

Question 10

Which of the following methods may be used to smooth a time series sufficiently to remove the random variation and to discover the existence of the other time-series components?

A) Moving averages and exponential smoothing.
B) Exponential smoothing and deseasonalising.
C) Deseasonalising and mean absolute deviation.
D) Mean absolute deviation and the percentage of trend.

Question 11

Which of the following represents the fluctuations up to a twelve month time period?

A) Seasonal component
B) Irregular component
C) Trend
D) Cyclical component

Question 12

In measuring the cyclical effect of a time series, cycles need to be isolated. The measure we use to identify cyclical variation is the:

A) mean absolute deviation.
B) trend value ŷ.
C) percentage of trend.
D) ratio of the time series divided by the moving average.

Question 13

If we wanted to measure the seasonal variations on stock market performance by quarter, we would need:

A) four indicator variables.
B) three indicator variables.
C) two indicator variables.
D) one indicator variable.

Question 14

Which of the following are examples of seasons when measuring the seasonal component of a time series?

A) Centuries
B) Decades
C) Quarters
D) None of these choices are correct.

Question 15

Which of the four time-series components is most likely to exhibit the steady growth of the population of Australia from 1945 to 1995?

A) Trend.
B) Cyclical.
C) Seasonal.
D) Random variation.

Question 16

The mean absolute deviation averages the absolute differences between the actual values of the time series at time t and the forecast values at time:

A) t + 1.
B) t.
C) t - 1.
D) t - 2.

Question 17

Which of the following best describes what may be used when measuring the seasonal and random variation of a time series with no cyclical effect?

A) The trend value ŷ.
B) The ratio of the time series divided by the predicted values.
C) The ratio of the time series divided by the moving average and the ratio of the time series divided by the predicted values.
D) The ratio of the time series divided by the moving average.

Question 18

The time-series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called:

A) trend.
B) cyclical.
C) seasonal.
D) random variation.

Question 19

Which of the following will not be present in a deseasonalised time series?

A) Trend effects.
B) Cyclical variation.
C) Seasonal variation.
D) Random variation.

Question 20

In an exponentially smoothed time series, the smoothing constant w is chosen on the basis of how much smoothing is required. In general:

A) a small value of w, such as w = 0.1, results in very little smoothing, while a large value, such as w = 0.8, results in too much smoothing.
B) a small value of w, such as w = 0.1, results in too much smoothing, while a large value such as w = 0.8, results in very little smoothing.
C) a small value of w, such as w = 0.1, and a large value, such as w = 0.8, may both result in very little smoothing.
D) a small value of w, such as w = 0.1, and a large value, such as w = 0.8, may both result in too much smoothing.

Question 21

If autumn 2013 sales were $20 500 and the summer seasonal index was 1.17, then the deseasonalised 2010 autumn sales value would be:

A) $19 422.
B) $13 675.
C) $14 188.
D) $18 720.

Question 22

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.

Question 23

Which of the following statements is not correct?

A) A moving average for a time period is the simple arithmetic average of the values in that time period and those close to it.
B) A value of the smoothing constant w close to 1 results in a very large smoothing, where as a value of w close to zero results in very little smoothing.
C) The accuracy of the forecast with exponential smoothing decreases rapidly for predictions of the time series more than one period into the future.
D) A moving average 'forgets' most of the previous time-series values, and is considered a relatively crude method of removing the random variation.

Question 24

Which of the following equations will deseasonalise a time series, where T, C, S and R are respectively the trend, cyclical, seasonal and random variation components of the time series?

A) (T $\times$ C $\times$ S $\times$ R) / T = C $\times$ S $\times$ R.
B) (T $\times$ C $\times$ S $\times$ R) / C = T $\times$ S $\times$ R.
C) (T $\times$ C $\times$ S $\times$ R) / S = T $\times$ C $\times$ R.
D) (T $\times$ C $\times$ S $\times$ R) / R = T $\times$ C $\times$ S.

Question 25

Which of the following will be reflected by a deseasonalised time series?

A) Trend effects.
B) Cyclical effects.
C) Random variation.
D) All of these choices are correct.

Question 26

Which of the following methods is appropriate for forecasting a time series when the trend, cyclical and seasonal components of the series are not significant?

A) Moving averages.
B) Exponential smoothing.
C) Mean absolute deviation.
D) Seasonal indexes.

Question 27

The stock market has a 5-day working week. If we wanted to measure the impact of the day of the week on stock market performance, we would need:

A) seven indicator variables.
B) six indicator variables.
C) five indicator variables.
D) four indicator variables.

Question 28

Time-series forecasting with exponential smoothing uses the following formula:` $S _ { t } = w y _ { t } + ( 1 - w ) S _ { t - 1 }$ . where $S _ { t }$ is the exponentially smoothed time series at time t, $y _ { t }$ is the value of the time series at time t, and w is the smoothing constant. The forecast value at time t + 1, where w = 0.3, is given by:

A) F_t+1 = 0.3y_t+1 + 0.7S_t+1.
B) F_t+1 = 0.3y_t + 0.7S_t-1.
C) F_t+1 = 0.3y_t + 0.7S_t.
D) F_t+1 = 0.3y_t-1 + 0.7S_t.

Question 29

The following trend line was calculated from quarterly data for 2006-2010: ŷ = 2.35 + 0.12t, where t = 1 for the first quarter of 2006. The trend value for the third quarter of the year 2011 is:

A) 5.110.
B) 4.990.
C) 5.230.
D) None of these choices are correct.

Question 30

If data for a time-series analysis are collected on a monthly basis only, which component of the time series may be ignored?

A) Long-term trend.
B) Cyclical variation.
C) Seasonal variation.
D) Random variation.

Question 31

Which method would you recommend in selecting the appropriate forecasting model if avoiding large errors is extremely important?

A) Mean absolute deviation (MAD).
B) Either Mean absolute deviation (MAD) or Sum of squares for forecast error (SSE).
C) Sum of squares for forecast error (SSE).
D) Neither Mean absolute deviation (MAD) or Sum of squares for forecast error (SSE)

Question 32

The following trend line was calculated from quarterly data for 2006-2010: ŷ = 2.35 + 0.12t, where t = 1 for the first quarter of 2006. The seasonal indexes computed from the trend line for the four quarters of the year 2011 are 0.88, 0.93, 1.04, and 1.17, respectively. The seasonalised forecast for the third quarter of the year 2011 is:

A) 5.314.
B) 6.119.
C) 4.286.
D) 4.641.

Question 33

The following are the values of a time series for the first four time periods: $$\begin{array} { | c | c c c c | } \hline t & 1 & 2 & 3 & 4 \\\hline y _ { t } & 23 & 25 & 28 & 24 \\\hline\end{array}$$ Using exponential smoothing, with w = 0.25, the forecast value for time period 5 is:

A) 18.352.
B) 23.500.
C) 24.469.
D) 23.000.

Question 34

Forecasts based on trend and seasonality are generated by:

A) identifying and removing the seasonal effect.
B) extrapolating the linear trend.
C) adjusting the forecasts to the seasonal effect.
D) All of these choices are correct.

Question 35

The term $b _ { 1 }$ in the equation $\ = b _ { 0 } + b _ { 1 } t + b _ { 2 } Q _ { 1 } + b _ { 3 } Q _ { 2 } + b _ { 4 } Q _ { 3 }$ , where ?_t represents the predicted value of y at time t, is:

A) the time trend.
B) the seasonal trend.
C) an indicator variable.
D) a value between 0 and 4.

Question 36

The time-series multiplicative model is used for forecasting, where $T _ { t } , C _ { t } , S _ { t }$ and $R _ { t }$ are respectively the trend, cyclical, seasonal and random variation components of the time series, and $y _ { t }$ is the value of the time series at time t. The following estimates are obtained: $\hat { T _ { 1 } }$ = 125, $\tilde { C } _ { t }$ = 1.03, $\hat { S } _ { t }$ = 1.02, $\hat { R } _ { t }$ = 0.97. The model will produce a forecast of:

A) 122.659.
B) 131.325.
C) 118.980.
D) 127.385.

Question 37

The following linear trend was estimated using a time series regression with the origin in the year 2000. ŷ = 76.80 + 3.14t.
Which of the following is the forecast for the year 2013?

A) 114.48
B) 120.76
C) 79.94
D) 117.62

Question 38

Which of the following is not true in regard to the weights used in exponential smoothing?

A) The last weight is always the smallest.
B) They are all positive.
C) They add up to 1.
D) They decrease exponentially into the past.

Question 39

If we wanted to measure the seasonal variations on stock market performance by month, we would need:

A) 50 indicator variables, since the stock market has a 5-day working week.
B) 12 indicator variables to represent the 12 months.
C) 11 indicator variables.
D) 55 indicator variables.

Question 40

The level of construction employment in Sydney is lowest during the winter. A model designed to forecast construction employment in Sydney should use:

A) a time trend.
B) a moving average.
C) a seasonal indicator variable.
D) an autoregressive model.

Question 41

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.

Question 42

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.

Question 43

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.

Question 44

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.

Question 45

The trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is $=6.8+1.2 t$ , 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.

Question 46

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.

Question 47

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.

Question 48

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.

Question 49

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.

Question 50

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.

Question 51

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.

Question 52

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.

Question 53

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.

Question 54

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.

Question 55

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.

Question 56

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%.

Question 57

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.

Question 58

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.

Question 59

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.

Question 60

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.

Question 61

The purpose of using the moving average is to take away the short-term seasonal and random variation, leaving behind a combined trend and cyclical movement.

Question 62

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 regarding the trend component?

A) There were 43 surfboards sold in December 2010, and this increases by 3 surfboards per quarter, irrespective of the season of the year.
B) There were 35 surfboard sold in December 2010, and this increases by 15.5 surfboards per quarter, irrespective of the season of the year.
C) There were 35 surfboard sold in December 2010, and this increases by 3 surfboards per quarter, irrespective of the season of the year.
D) None of these choices are correct.

Question 63

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, 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 is the correct value of the estimate for the number of surfboards sold by this manufacturing company in June 2013?

A) 68
B) 77.5
C) 65
D) None of these choices are correct

Question 64

The time-series component that reflects a long-term, relatively smooth pattern or direction exhibited by a time series over a long time period is called trend.

Question 65

We calculate the three-period moving average for a time series for all time periods except the first.

Question 66

The most commonly used measures of forecast accuracy are the mean absolute deviation (MAD) and the sum of squares for forecast error (SSE).

Question 67

Any variable that is measured over time in sequential order is called a time series.

Question 68

Cycle is one of the four different components of a time series. It has a wavelike pattern over short, repetitive calendar periods and, by definition, has duration of less than one year.

Question 69

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 regarding the coefficient of Q₄?

A) This company expects to sell 8 more surfboards in the December quarter than in the March quarter or the September quarter.
B) This company expects to sell 8 more surfboards in the December quarter than in the June quarter.
C) This company expects to sell 8 more surfboards in the June quarter than in the December quarter.
D) None of these choices are correct.

Question 70

A time series can consist of four different components: long-term trend, cyclical variation, seasonal variation, and random variation.

Question 71

To calculate the five-period moving average of a time series for a given time period, we average the value in that time period and the values in the four preceding periods.

Question 72

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) The coefficients of the indicator variables are all positive because the June Quarter has the lowest sales of surfboards.
B) The coefficients of the indicator variables are all positive because sales of surfboards in the March, September and December quarter are all above June.
C) The coefficients of the indicator variables are all positive indicating that the June quarter is seasonally disadvantaged for selling surfboards due to winter in Australia in this quarter.
D) All of these choices are correct.

Question 73

The cyclical variation component of a time series is a wave like movement, showing peaks and troughs.

Question 74

The equation F_t+1 = wy_t + (1-w)S_t-1 (for t $\ge$ 2) refers to a time series forecast prepared by exponential smoothing.

Question 75

The effect that business recessions and prosperity have on time-series values is an example of the disaster component of a time series.

Question 76

In forecasting, we use data from the past in predicting the future value of the variable of interest.

Question 77

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, 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 is the correct value of the estimate for the number of surfboards sold by this manufacturing company in March 2015?

A) 86
B) 90
C) 93
D) 51

Question 78

In determining monthly seasonal indexes for natural gas consumption, the sum of the 12 means for gas consumption as a percentage of the moving average is 1195. To get the seasonal indexes, each monthly mean is to be multiplied by (1195 / 1200).

Question 79

A trend is one of the four different components of a time series. It is a long-term, relatively smooth pattern or direction exhibited by a series, and its duration is more than one year.

Question 80

In determining weekly seasonal indexes for natural gas consumption, the sum of the 52 means for gas consumption as a percentage of the moving average is 5195. To get the seasonal indexes, each monthly mean is to be multiplied by (5200 / 5195).