On Market Timing And Investment Performance Part Ii Statistical Procedures for
On Market Timing And Investment Performance Part Ii Statistical Procedures for
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= x|N. , p) = p^'ci - p) "- ; i = 1, 2 . (5) Given the null hypothesis, we can use Bayes' Theorem to determine the probability that n = x given N, , N, and n, i. E. , PCn = x|N, ,N„, n). Denote the event that our market timer forecasts m times that Z„ < R (i. E. , n = m) as "A" and the event that of the M — times he forecasts that Z _< R, he is correct x times and incorrect m - X times (i. E. , n = x and n- = m - x) as "B. " P(n = x|N^, N„, m) = P(b|A), and by Bayes' Theorem, we have that p(BlA) = P(B_ + ^^ P(B). ^^^J^-* P(A) P(A) N- \ / N„ \ N -X N. -m-hc ' ' ' ' ' P"(l - P) ' P"-"(1 - P) ' X / \ m - X, (6) N', m, T, N-m ^ . P (1 - P) m ^1 ^2 \ X / \m - X Hence, under the null hypothesis, the probability distribution for n, the number of correct forecasts, given that Z < R, has the form of a hypergeometric distribution and is independent of both p and p„. Therefore to test the null hypothesis, it is unnecessary to -12- estiinate either of the conditional probabilities. So, provided that che forecasts are known, all the variables necessary for the test are directly observable.
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To quickly assess the difficulty of the text, read a short excerpt:
= x|N. , p) = p^'ci - p) "- ; i = 1, 2 . (5) Given the null hypothesis, we can use Bayes' Theorem to determine the probability that n = x given N, , N, and n, i. E. , PCn = x|N, ,N„, n). Denote the event that our market timer forecasts m times that Z„ < R (i. E. , n = m) as "A" and the event that of the M — times he forecasts that Z _< R, he is correct x times and incorrect m - X times (i. E. , n = x and n- = m - x) as "B. " P(n = x|N^, N„, m) = P(b|A), and by Bayes' Theorem, we have that p(BlA) = P(B_ + ^^ P(B). ^^^J^-* P(A) P(A) N- \ / N„ \ N -X N. -m-hc ' ' ' ' ' P"(l - P) ' P"-"(1 - P) ' X / \ m - X, (6) N', m, T, N-m ^ . P (1 - P) m ^1 ^2 \ X / \m - X Hence, under the null hypothesis, the probability distribution for n, the number of correct forecasts, given that Z < R, has the form of a hypergeometric distribution and is independent of both p and p„. Therefore to test the null hypothesis, it is unnecessary to -12- estiinate either of the conditional probabilities. So, provided that che forecasts are known, all the variables necessary for the test are directly observable.
What to read after On Market Timing And Investment Performance Part Ii Statistical Procedures for?
You can find similar books in the "Read Also" column, or choose other free books by Roy Henriksson to read online
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