17 autocorrelation model e t ρ e t 1 v t v t s are

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17 Autocorrelation Model: e t = ρ e t 1 + v t v t ‘s are independent Figure 17.7: Specifying Rho As a benchmark, we begin by specifying rho to equal .0; consequently, no autocorrelation present. Click Start and then after many, many repetitions click Stop. As we observed before, both the estimation procedure for the coefficient value and the estimation procedure for the variance of coefficient estimate’s probability distribution are unbiased. When the ordinary least squares (OLS) standard regression premises are met all is well. But what happens when autocorrelation is present and the error term/error term independence premise is violated? To investigate this, we set rho to equal .6. Click Start and then after many, many repetitions click Stop. There is both good news and bad news: Good news: The ordinary least squares (OLS) estimation procedure for the coefficient value is still unbiased. The average of the estimated values equals the actual value, 2. Bad news: The ordinary least squares (OLS) estimation procedure for the variance of the coefficient estimate’s probability distribution is biased. The average the actual variance of the estimated coefficient values equals 1.11 while the average of the estimated variances equals .28. Just as we feared, when autocorrelation is present, the ordinary least squares (OLS) calculations to estimate the variance of the coefficient estimates are flawed. When the estimation procedure for the variance of the coefficient estimate’s probability distribution is biased, all calculations based on the estimate of the variance will be flawed also; that is, the standard errors, t -statistics, and tail probabilities appearing on the ordinary least squares (OLS) regression printout are unreliable. Consequently, we shall use an example to explore how we account for the presence of autocorrelation.
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18 Accounting for Autocorrelation: An Example We can account for autocorrelation by applying the following steps: Step 1: Apply the Ordinary Least Squares (OLS) Estimation Procedure o Estimate the model’s parameters with the ordinary least squares (OLS) estimation procedure. Step 2: Consider the Possibility of Autocorrelation o Ask whether there is reason to suspect that autocorrelation may be present. o Use the ordinary least squares (OLS) regression results to “get a sense” of whether autocorrelation is a problem by examining the residuals. o Use the Lagrange Multiplier approach by estimating an artificial regression to test for the presence of autocorrelation. o Estimate the value of the autocorrelation parameter, ρ . Step 3: Apply the Generalized Least Squares (GLS) Estimation Procedure o Apply the model of autocorrelation and algebraically manipulate the original model to derive a new, tweaked model in which the error terms do not suffer from autocorrelation.
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