Extreme positive serial correlation d 0 2 extreme

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Unformatted text preview: urbin-Watson d statistic (for T observations): T d= (et − et−1 )2 t=2 T t=1 ≈ 2(1 − ρ) e2 t Values: 1. Extreme positive serial correlation: d ≈ 0 2. Extreme negative serial correlation: d ≈ 4 3. No serial correlation: d ≈ 2 11 / 30 U SING THE D URBIN -WATSON TEST 1. Obtain the OLS residuals from the equation to be tested 2. Calculate the d statistic 3. Determine the sample size T and the number of explanatory variables (excluding the intercept) k 4. Find the upper critical value dU and the lower critical value dL for T and k in statistical tables 5. Evaluate the test as one-sided or two-sided (see next slides) 12 / 30 O NE - SIDED D URBIN -WATSON TEST For cases when we consider only positive serial correlation as an option Hypothesis: H0 : ρ ≤ 0 (no positive serial correlation) HA : ρ > 0 (positive serial correlation) Decision rule: if d < dL reject H0 if d > dU do not reject H0 if dL ≤ d ≤ dU inconclusive 13 / 30 T WO - SIDED D URBIN -WATSON TEST For cases when we consider both signs of serial correlation Hypothesis: H0 : ρ = 0 (no serial correlation) HA : ρ = 0 (serial correlation) Decision rule: if d < dL reject H0 if d > 4 − dL reject H0 if 4 − dU > d > dU do not reject H0 otherwise inconclusive 14 / 30 E XAMPLE Estimating housing prices in the UK Quarterly time series data on prices of a representative hou...
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This document was uploaded on 02/26/2014.

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