time series model - Advanced Quantitative Research...

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Advanced Quantitative Research Methodology, Gov2001, Lecture Notes: Time Series Fundamentals 1 Gary King http://GKing.Harvard.Edu January 29, 2008 Reading: Gary King. Unifying Political Methodology: The Likelihood Theory of Statistical Inference . Ann Arbor: University of Michigan Press, 1998: Chapter 5. 1 c Copyright 2006 Gary King, All Rights Reserved. Gary King http://GKing.Harvard.Edu () Advanced Quantitative Research Methodology, Gov2001, Lecture Notes: January 29, 2008 1 / 1
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Time Series Models Reading: Gary King. Unifying Political Methodology: The Likelihood Theory of Statistical Inference . Ann Arbor: University of Michigan Press, 1998: Chapter 7. Here we will learn how to drop the assumption that Y i and Y j are conditionally independent. Gary King () Time Series Fundamentals 2 / 1
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Time Series Models Reading: Gary King. Unifying Political Methodology: The Likelihood Theory of Statistical Inference . Ann Arbor: University of Michigan Press, 1998: Chapter 7. Here we will learn how to drop the assumption that Y i and Y j are conditionally independent. A generic likelihood function: Gary King () Time Series Fundamentals 2 / 1
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Time Series Models Reading: Gary King. Unifying Political Methodology: The Likelihood Theory of Statistical Inference . Ann Arbor: University of Michigan Press, 1998: Chapter 7. Here we will learn how to drop the assumption that Y i and Y j are conditionally independent. A generic likelihood function: L ( θ | y ) = P ( y 1 | θ ) P ( y 2 | y 1 , θ ) P ( y 3 | y 2 , y 1 , θ ) · · · Gary King () Time Series Fundamentals 2 / 1
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Observations: Gary King () Time Series Fundamentals 3 / 1
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Observations: 1. If θ = g ( X , β ) and controlling for X wipes out the effects of the lagged y ’s, then you don’t need to change anything Gary King () Time Series Fundamentals 3 / 1
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Observations: 1. If θ = g ( X , β ) and controlling for X wipes out the effects of the lagged y ’s, then you don’t need to change anything 2. If lags have no effect (in any way — linear, nonlinear, variances, etc.), then you’re also ok. Gary King () Time Series Fundamentals 3 / 1
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Observations: 1. If θ = g ( X , β ) and controlling for X wipes out the effects of the lagged y ’s, then you don’t need to change anything 2. If lags have no effect (in any way — linear, nonlinear, variances, etc.), then you’re also ok. 3. If you include lags of y among your X ’s and this takes into account the entire time series process, you’re ok. Gary King () Time Series Fundamentals 3 / 1
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Observations: 1. If θ = g ( X , β ) and controlling for X wipes out the effects of the lagged y ’s, then you don’t need to change anything 2. If lags have no effect (in any way — linear, nonlinear, variances, etc.), then you’re also ok. 3. If you include lags of y among your X ’s and this takes into account the entire time series process, you’re ok. 4. Aside from fixing problems, time series data pose opportunities : e.g., If there is a rally around the flag effect, how long will it last?
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