Exam 23: Time-Series Analysis and Forecasting

The term 'seasonal variation' may refer to the four traditional seasons, or to systematic patterns that occur during a quarter, a week, or even one day, but within 12 months.

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

Regression analysis with t = 1 to 80 was used to develop the following forecast equation: = 135 + 4.8t - 1.3Q₁ - 1.7Q₂ + 1.5Q₃ where: Q_i = 1, if quarter i (i = 1, 2, 3) = 0, otherwise. Forecast the next four values.

Which of the following statements is not correct?

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 time series for the years 1990-1995 is shown below. Year 1990 125 1991 115 1992 120 1993 126 1994 140 1995 122 a. Develop forecasts for the years 1996-1998, with the following smoothing constant values: w = 0.2, w = 0.5 and w = 0.6. b. Compare each of the three sets of forecasts above with the actual values for 1996-1998 given in the following table, and compute the MAD for each model. Which model is best? Year 1996 130 1997 125 1998 135

The following trend line and seasonal indexes were computed from four weeks of daily observations. $=145+1.66 t$ . Day S Sunday 1.403 Monday 0.517 Tuesday 0.515 Wednesday 0.621 Thursday 0.675 Friday 1.145 Saturday 2.124 Forecast the seven values for the next week.

The most commonly used measures of forecast accuracy are the:

The result of a quadratic model fit to time-series data was $= 8.5 - 0.25 t + 2.5 t ^ { 2 }$ , where t = 1 for 1994. The forecast value for 2001 is 129.25.

The actual and forecast values of a time series are shown below. Actual values Forecast values 135 140 162 165 155 150 182 191 174 168 194 190 233 220 280 240 a. Calculate the mean absolute deviation (MAD). b. Calculate the sum of squares for forecast error (SSE).

To calculate the random component of a time series, ignoring the cyclical component, it would be the difference between an actual observation and the predicted value using a regression model with indicator variables for the seasonal component and time as the trend component.

Regression analysis with t = 1 to 40 was used to develop the following equation: $= 1500 + 5 t + 1.5 Q _ { 1 } + 1.8 Q _ { 2 } - 3.0 Q _ { 3 }$ , where: $Q _ { i }$ = 1, if quarter i (i = 1, 2, 3) = 0, otherwise. Forecast the next four quarters.

One of the simplest ways to reduce random variation is to smooth the time series via moving averages and exponential smoothing.

The smoothing component is one of the four components of a time series.

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

The following are the values of a time series for the first four time periods: t 1 2 3 4 23 25 28 24 Using exponential smoothing, with w = 0.25, the forecast value for time period 5 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:

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?

Quarterly enrolments in a business statistics class for three years are shown below. Year Quarter Enrolment 1996 1 26 2 29 3 33 4 18 1997 1 27 2 25 3 36 4 21 1998 1 32 2 36 3 39 4 30 Compute the four-quarter centred moving averages.

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