ch14-3 - Chapter 14 Introduction to Time Series Regression...

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Chapter 14 Introduction to Time Series Regression and Forecasting (Part 3)
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Problems Caused by Stochastic Trends If a regressor has a stochastic trend, the OLS t-statistic can have nonnormal distribution even in large samples. I The estimator of the autoregressive coefficient in an AR(1) is biased toward 0 if its true value is 1 I t-statistics on regressors with a stochastic trends can have a nonnormal distribution, even in large samples I An extreme example of the risks posed by stochastic trends is that two series that are independent will misleadingly appear to be related if they both have stochastic trends (spurious regression)
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Problem #1: Autoregressive coefficients that are biased toward zero Suppose that Y t follows the random walk but this is unknown, and you estimate the AR(1) model. In this case, OLS b β 1 is consistent but the asymptotic distribution of b β 1 is shifted toward zero (biased estimator) If Y t follows a random walk, the forecast based on AR(1) can perform substantially worse.
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This note was uploaded on 11/20/2011 for the course ECONOMICS 220:322 taught by Professor Otusbo during the Fall '10 term at Rutgers.

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ch14-3 - Chapter 14 Introduction to Time Series Regression...

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