Slides_Econ140A_Serial_Correlation

Slides_Econ140A_Serial_Correlation - Goals Define serial...

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11/8/2011 1 Serial Correlation Copyright Dick Startz 1 Goals Define serial correlation What happens to OLS? How to do GLS? Testing for serial correlation Serial correlation and lagged dependent variables Higher order serial correlation Copyright Dick Startz 2 Assumptions 1. ? ? = 𝛽 1 ? ?1 + 𝛽 2 ? ?2 + ⋯ + 𝛽 ? ? ?? + 𝜀 ? , true model of DGP 2. ? nonrandom (or exogenous), ? not perfectly collinear 3. ? 𝜀 ? = 0 ∀? 4. Homoskedasticity ? 𝜀 ? 𝜀 ? = 𝜎 2 , ? = ? 0, ? ≠ ? 5. (sometimes) 𝜀~??𝑟?𝑎? Copyright Dick Startz 3 Word “correlation” pops up in two completely unrelated contexts Copyright Dick Startz 4 Terminology General: E 𝜀 𝑡 𝜀 𝑡+? = 𝜎 𝑡,𝑡+? ≠ 0 Specific: Autocorrelation Autoregressive AR(1) 𝜀 𝑡 = 𝜌𝜀 𝑡−1 + 𝜂 𝑡 , 𝜌 < 1 Copyright Dick Startz 5 What facts about OLS are still true? Still best fit Still unbiased Unless lagged dependent variable Which now fail, and is there a fix-up within OLS?
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