Exam 17: Time-Series Analysis and Forecasting

The trend line ŷt = 14.13  0.54t was calculated from quarterly data for 2006-2010, where t = 1 for the first quarter of 2006. The trend value for the fourth quarter of the year 2011 is 1.170.

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

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.

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

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

Which of the following best describes a time series?

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

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:

The table below shows the number of pizzas sold daily during a four-week period at King Pizza in Melbourne. nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; Week Day 1 2 3 4 Sunday 253 234 248 232 Monday 98 93 99 104 Tuesday 106 88 87 115 Wednesday 119 134 113 102 Thursday 138 123 130 118 Friday 201 215 218 205 Saturday 327 399 415 390 a. Calculate the seasonal (daily) indexes, using a seven-day moving average. b. Use regression analysis to find the linear trend line. c. Calculate the seasonal (daily) indexes, using the trend line developed in (b).

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

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:

If summer 2010 sales were $26 800 and the summer seasonal index was 1.15, the deseasonalised 2010 summer sales value is $30 820.

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.

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:

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

The following trend line and seasonal indexes were computed from five years of quarterly observations: ŷt = 1800 + 75t - 2 t2 Quarter S 1 0.575 2 0.825 3 1.225 4 1.375 Forecast the four quarterly values for next year.

A 5 period moving average will show less fluctuation than a 3 period moving average, for the same time series.

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