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node7 Smoothing STAT 510 - Applied Time Series Analysis

# node7 Smoothing STAT 510 - Applied Time Series Analysis -...

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This is Google's cache of http://onlinecourses.science.psu.edu/stat510/node/7 . It is a snapshot of the page as it appeared on 20 Jul 2010 18:28:13 GMT. The current page could have changed in the meantime. Learn more Text-only version STAT 510 - Applied Time Series Analysis ANGEL Department of Statistics Eberly College of Science Home // Section 1: Introduction and Basics Smoothing Submitted by gfj100 on Mon, 03/22/2010 - 14:06 Here is our model yet again : x t = μ t + y t we have worked on the following cases: , or But what if μ t doesn't fit into either category very well? What if we don't know anything about μ t ? In this section we will look at a general procedure called smoothing. We want to fit μ t which is changing in time, and now we will make another assumption which is that this change is gradual or continuous. Perhaps the trend looks something like: We have no idea what it is, however we are assuming it is smooth. We want to find some ways to fit this case. One of the ways is using the moving average technique. Now this can be a bit confusing because the term

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moving average is used in two contexts. The first context is the moving average model where you take a window of white noise terms and sum them with weights. We saw that this model was an example of a stationary process. The other context for moving average is to take the time series itself, the x t 's, and sum them with weights. Doing this you get: In other words, we take the k observations in front of you and k observations behind you, and the current observation then sum this weighted average. Think about this in a very simple situation, perhaps the simplest of moving averages. In this case, k = 1 and a j is 1/3. In general, we want the a j 's to sum to 1, and
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node7 Smoothing STAT 510 - Applied Time Series Analysis -...

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