Exam 23: Time-Series Analysis and Forecasting

Petrol sales in Newcastle have been recorded over the past 10 months as shown below. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Sales 75 72 81 92 90 105 112 107 110 93 a. Compute the five-month moving average. b. Calculate the four-month moving average, and four-month centred moving average. c. Compute the exponentially smoothed sales with w = 0.4 and w = 0.8. d. Draw the time series and the two sets of exponentially smoothed values. Does there appear to be a trend component in the time series?

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

Forecasts based on trend and seasonality are generated by:

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

Suppose that we calculate the four-period moving average of the following time series: t 1 2 3 4 5 6 18 28 23 17 26 14 The centred moving average for period 4 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:

One application of seasonal indexes is to remove the seasonal variation in a time series. The process is called deseasonalising, and the result is called a seasonally adjusted time series.

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?

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

a. Plot the following time series. Would the linear or quadratic model fit better? Time period Time period 1 5 5 50 2 8 6 85 3 14 7 135 4 25 8 190 b. Use the regression technique to calculate the linear trend line and the quadratic trend line. c. Which line fits better?

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

A time series is shown in the table below: Period t 1 40 2 45 3 44 4 47 5 48 6 50 7 52 8 51 9 48 10 47 a. Apply exponential smoothing with w = 0.1 and w = 0.8 to help detect the components of the time series. b. Draw the time series and the two sets of exponentially smoothed values. Does there appear to be a trend component in the time series?

The agricultural exports (in millions of dollars) from a Latin American country for 10 years are shown below. Year t Exports 1988 1 96 1989 2 110 1990 3 125 1991 4 141 1992 5 132 1993 6 126 1994 7 118 1995 8 125 1996 9 133 1997 10 148 a. Use the regression technique to calculate the linear trend line. b. Calculate the percentage of trend. c. Plot the percentage of trend. d. Describe the cyclical effect (if there is one).

A time series regression model using quarterly time periods will only use three quarters as the indicator variables.

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 local newspaper that appears six days per week wanted to forecast two-day revenues from its business services classified ads section. The revenues (in $1000s) were recorded for the past 52 weeks. From these data, the following regression equation was computed: $=2000+0.6 t-150 D_{1}-40 D_{2}$ , t = 1, 2, 3,…156, where: $D _ { 1 }$ = 1, if Monday or Tuesday = 0, otherwise. $D _ { 2 }$ = 1, if Wednesday or Thursday = 0, otherwise. Forecast the two-day revenues for the next week.

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

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?

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?

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