monoBonferroni {monotonicity}

Test of weak monotonicity using Bonferroni bounds

Description

monoBonferroni implements the test of weak monotonicity using Bonferroni bounds described in Patton & Timmermann (2010, JFE): Test 1: H0*: d1 >= 0, d2 >= 0, ..., dK >= 0 vs. H1*: dj < 0 for some j=1,2,..,K

Test 2: H0**: d1 <= 0, d2 <= 0, ..., dK <= 0 vs. H1**: dj > 0 for some j=1,2,..,K.

Usage

monoBonferroni(data, difference = FALSE)

Arguments

data

an object of class "matrix" (or one that can be coerced to that class): asset returns or differences in asset returns for the sorting application.

difference

An object of class "logical": If data is already differences in asset returns, use TRUE. Otherwise data will be transformed to difference returns r_p(n+1) - r_p(n) between portfolio n+1 and portfolio n

Value

monoBonferroni returns an object of class "list"

The returning list contains p-values (see Note) using Bonferroni-bounds for the two statistical tests described above:

TestOnePvalBonferroni:

p-value for H0* of Test 1.

TestTwoPvalBonferroni:

p-value for H0** of Test 2.

Note

The "Bonferroni p-values" are in the sense that we reject the null hypothesis if they are less than the size of the test. NOTE of course that unlike usual p-valuess these won't be uniformly distributed between 0 and 1 under the null hypothesis. In fact, they do not even have to lie in [0,1] - they could be lesser than 0 or greater than 1. In such a case, monoBonferroni returns min(pvalBonferroni, 1) if pvalBonferroni > 1 and max(pvalBonferroni, 0) if pvalBonferroni < 1.

References

Patton, A. and Timmermann, A. (2010): Monotonicity in asset returns: New testes with applications to the term structure, the CAPM, and portfolio sorts. Journal of Financial Economics, 98, No. 3, p. 605–625. doi: 10.1016/j.jfineco.2010.06.006.

Bonferroni, Carlo E. (1936): Teoria statistica delle classi e calcolo delle probabillita. [Statistical Class Theory and Calculation of Probability]Pubbl. d. R. Ist. Super. di Sci. Econom. e Commerciali di Firenze, 8, p. 1–62.

Examples

## load non-difference return data and calculate the p-value for H0* of Test 1.
data(demo_returns)
tmp <- monoBonferroni(demo_returns, difference = FALSE)
tmp$TestOnePvalBonferroni