node6 Exploratory Data Analysis STAT 510 - Applied Time Series Analysis

Node6 Exploratory Data Analysis STAT 510 - Applied Time Series Analysis

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This is Google's cache of http://onlinecourses.science.psu.edu/stat510/node/6 . It is a snapshot of the page as it appeared on 20 Jul 2010 18:00:11 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 Exploratory Data Analysis Submitted by gfj100 on Mon, 03/22/2010 - 14:06 The Regression section introduces us to what this section will address more generally, i.e., things we can do when we first get a dataset. We want to understand what is going on by asking a few questions. Presumably we know we are working with a time series. Is it stationary? Is it something like a random walk where the mean is zero, but it is not stationary? Is there a trend (a mean that changes through time)? Is this trend a line or a quadratic or something else? Suppose that the data is generated from a model like: We discussed that if μ t is a polynomial, then we have two options. We would want to 'de-trend' the series to examine the stationary processes. What are your two options if μ t is a polynomial? First, we talked about regression. Let's say that y t is a line like :
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And, we perform least squares regression and return the β 0 and the β 1 . Do we trust these values? Do we think that these will be reasonable estimates? We will probably get decent estimates, but as we discussed earlier the standard errors or the p -values can not be trusted. The other option we have is differencing. If we difference the time series once and the trend in linear then it will be a stationary process, y t - y t-1 , which in some circumstances will be okay; however in other circumstances it might create confusion about what is going on. The important thing to note is the result with is not y t . This is not necessarily bad, but it is good to know. What if μ t is periodic? First we assume that μ t is: where ω is the frequency, (the number of periods per time), φ is the shift or offset and A is the amplitude. In other words, if we were dealing with temperature data A would tell us how strongly the seasons are and φ would tell you when your seasons are and ω would tell us how often they occur, (typically 1/12 for monthly data). We want to fit one sinusoidal curve but in many cases we don't know where it starts. This kind of thing comes up often in economic data. Unemployment has this kind of seasonal oscillation and we will see both of these kinds of examples later. We will take the model above and write it like this:
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Node6 Exploratory Data Analysis STAT 510 - Applied Time Series Analysis

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