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Multiplicative Decomp Dissection

# Multiplicative Decomp Dissection - Multiplicative...

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Multiplicative Decomposition: Dissection (Using Average of All Data to Compute Seasonal Indexes) I have prepared this handout to help you understand Multiplicative Decomposition, all steps involved in it, and why it is important to account for seasons if time series has seasonality in it. I hope you find it worthwhile. Dr. J. _______________________________________________ The bolded data in table 1 show a time series. Table 1: 4-Year Time series data, and its seasonal indexes The following line graph shows the time series data with a linear trend line inserted in the line graph. Clearly there is positive trend and also recurring seasonal effects in this time series. Therefore, we must use a forecasting method that accounts for both. The number of seasons in this data is 4, which represents Q1, Q2, Q3, and Q4. These are the recurring seasons in each year. Figure 1: Line graph of actual time series data (16 quarters) 1 Quarter Year 1 Year 2 Year 3 Year 4 Total 1 218 225 234 250 1000 2 247 254 265 283 1033 3 243 255 264 289 1090 4 292 299 327 356 1178 Total 927 1049 1051 1274 4301 Qtr. Avg. 231.75 262.25 262.75 318.5 268.81 Seasonal Indexes 0.8621 0.9756 0.9775 1.1849 Average of all 16 quarters.

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To compute the seasonal indexes for the four quarters, since we have an even number of seasons (i.e., 4 is an even number), you could use CMA (centered moving averages). Essentially, if the number of seasons is even (like 12 months, or 4 quarters, etc.), then you could use CMA to compute seasonal indexes. You could use CMA b/c we have "even" numbered seasons. Since we have 4 quarters, and 4 is an even number, you would use CMA. But CMA is a time-consuming process for big data sets if using hand calculations . Instead, I suggest using AVERAGING ALL DATA. By the way, the QM software has options to perform both CMA and Average of All Data calculations when working with seasonal data. I have listed below the process for manual calculations when using Average of All Data. The steps below show you how to compute the seasonal indexes, how to deseasonalize the data, and how to create unadjusted and seasonally-adjusted forecasts. _________________________________________________________ The manual process to do seasonal analysis is summarized below. To understand, you will need the files that I have attached. The QM file uses Time Series, Multiplicative Decomposition, 4 seasons, AVERAGE of ALL DATA.
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