(a) Name two advantages and two disadvantages of each of the common trend models (linear, exponential, quadratic). Explain!
(b) When would the exponential trend model be preferred to a linear trend model? Explain!
One of the methods that is used to moderate (smooth) the peaks and valleys within a time series, is known as the centered moving average method for smoothing a time series. This method smooth out the short-term fluctuations in the data, replacing the original times series with as new time series, where short-term seasonal and irregular variation are removed, leaving behind a combined trend and cyclical movement. The following is an exercise, where you are to perform the required calculations to develop typical seasonal pattern for a given time series data, using the centered to moving average method.
Problem Statement: The Appliance Center sells a variety of electronics equipments and home appliances. For last four years the following quarterly sales (in $ millions) were recorded.
Winter Spring Summer Fall
2001 5.3 4.1 6.8 6.7
2002 4.8 3.8 5.6 6.8
2003 4.3 3.8 5.7 6.0
2004 5.6 4.6 6.4 5.9
a) Using Excel, plot the data on a chart (Please code the years, starting with code = 1 for 2001). Describe the overall long term pattern ( upward or downward movement of the time series over time)
b) Develop the typical seasonal pattern for Appliance Center Company, using the ratio-to-moving-average method. Explain the typical index for each season.
The solution provides step by step method for the calculation of trend for a time series model The solution also provides advantages and disadvantages of common trend models. Formula for the calculation and Interpretations of the results are also included.