Exam 16: Time Series and Forecasting

i. One component of a time series is the secular trend that is the smooth movement of a series over a short period of time, such as a few months or quarters. ii. Many business and economic time series have a recurring seasonal pattern. iii. One component of a time series is cyclical variation. An example of cyclical variation is the business cycle that consists of periods of prosperity followed by periods of recession, depression, and recovery.

i. A typical monthly seasonal index of 107.0 indicates that sales (or whatever the variable is) are 107 percent above the annual average. ii. Each typical seasonal index is a percent with the average for the year equal to 100. iii. The ratio-to-moving-average method eliminates the seasonal, cyclical and irregular components from the original data (y).

i. The ratio-to-moving average method removes the time series trend component, resulting in 12 numbers that are called specific seasonals. ii. For a quarterly time series, the initial step, using the ratio-to-moving average method, is to remove the seasonal components from the time series using a 3-month centered moving average. iii. In the ratio-to-moving-average procedure, using the median or modified mean eliminates trend.

What is the forecast for year 9?

The table below shows the sales for a plastics manufacturer recorded over the past year. The seasonal indexes for each quarter are also provided. To track the trend for these four quarters, use the indexes to deseasonalize the sales data. What are deseasonalized sales for quarter 1?

For an annual time series extending from 1993 through 2001, how many years would be lost in a five-year moving average?

Given the trend equation ŷ = 25 + 0.6t (t = 0 in 2010), what would be the forecast value for 2014?

i. In the final step, using the ratio-to-moving-average method on quarterly data, the total of the modified means should theoretically be equal to 400 because the average of should be 100. ii. Seasonal variation is quite common in the retail and wholesale industries. iii. A typical seasonal index of 103.7 for January indicates that sales for January are below the annual average.

For a three-year moving average, how many values will be lost at the beginning and end of the time series?

The table below shows the sales for a plastics manufacturer recorded over the past year. The seasonal indexes for each quarter are also provided. To track the trend for these four quarters, use the indexes to deseasonalize the sales data. What are deseasonalized sales for quarter 3?

Listed below is the net sales in $ million for Home Depot Inc., and its subsidiaries from 1994 to 2003. Using the printout below, what are the estimated sales for 2010?

i. In the ratio-to-moving-average procedure, using the median or modified mean eliminates trend. ii. In the final step, using the ratio-to-moving-average method on quarterly data, the total of the modified means should theoretically be equal to 400 because the average of should be 100. iii. Seasonal variation is quite common in the retail and wholesale industries.

i. Long-term forecasts are usually from one year to more than 10 years into the future. ii. A forecast is considered necessary in order to have the raw materials, production facilities, and staff available to meet estimated future demands. iii. Many business and economic time series have a recurring seasonal pattern.

If the least squares equation for sales data is ŷ = 10 + 1.3t ($ millions),with t = 0 in 1995, what is the value of t and the forecast for 2002?

i. In a time series analysis, the letter "a" in the linear trend equation, is the value of when t = 0. ii. In the linear trend equation, the letter "b" is the average change each change of one unit (either increase or decrease) in y. iii. In the linear trend equation, t is any value that corresponds with a time period, (i.e. month or quarter.

If you have annual data for 1991 to 2002 and want to code the years for the calculation of the trend, what should you code the year 1991?

i. Each typical seasonal index is a percent with the average for the year equal to 100. ii. The ratio-to-moving-average method eliminates the seasonal, cyclical and irregular components from the original data (y). iii. The trend component of a time series is obtained my minimizing the sum of the squares of the errors.

Which of the following is true for the exponential equation?

i. The moving average method merely smooths out the fluctuations in the data. ii. To apply the moving average method to a time series, the data should follow a linear trend and have a definite rhythmic pattern of fluctuations that repeat (say, every three years). iii. Sales, production and other economic and business series usually have periods of oscillation that are of equal length or identical amplitudes.

i. A time series is a collection of data recorded over a period of time, usually monthly, quarterly, or yearly. ii. Episodic and residual variations can be projected into the future. iii. A forecast is considered necessary in order to have the raw materials, production facilities, and staff available to meet estimated future demands.