Quantitative Investment Analysis by Richard A. DeFusco CFA & McLeavey Dennis W. & Pinto Jerald E. & Runkle David E. & Anson Mark J

Author:Richard A. DeFusco, CFA & McLeavey, Dennis W. & Pinto, Jerald E. & Runkle, David E. & Anson, Mark J.
Language: eng
Format: epub
Publisher: Wiley
Published: 2010-12-29T16:00:00+00:00

This test statistic has a t-distribution with n − 2 degrees of freedom if the null hypothesis is true. One practical observation concerning Equation 8-3 is that the magnitude of r needed to reject the null hypothesis H0: ρ = 0 decreases as sample size n increases, for two reasons. First, as n increases, the number of degrees of freedom increases and the absolute value of the critical value tc decreases. Second, the absolute value of the numerator increases with larger n, resulting in larger-magnitude t-values. For example, with sample size n = 12, r = 0.58 results in a t-statistic of 2.252 that is just significant at the 0.05 level (tc = 2.228). With a sample size n = 32, a smaller sample correlation r = 0.35 yields a t-statistic of 2.046 that is just significant at the 0.05 level (tc = 2.042); the r = 0.35 would not be significant with a sample size of 12 even at the 0.10 significance level. Another way to make this point is that sampling from the same population, a false null hypothesis H0: ρ = 0 is more likely to be rejected as we increase sample size, all else equal.

EXAMPLE 8-7 Testing the Correlation between Money Supply Growth and Inflation

Earlier in this chapter, we showed that the sample correlation between long-term money supply growth and long-term inflation in six industrialized countries was 0.8702 during the 1970-2001 period. Suppose we want to test the null hypothesis, H0, that the true correlation in the population is 0 (ρ = 0) against the alternative hypothesis, Ha, that the correlation in the population is different from 0 (ρ ≠ 0).

Recalling that this sample has six observations, we can compute the statistic for testing the null hypothesis as follows:

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.