monoRelation {monotonicity}

Testing the monotonic relationship in asset returns

Description

monoRelation implements the 'monotonic relationship' tests from Patton & Timmermann (2010, JFE). We define \Delta_i = E[r_(i,t)] - E[r_(i-1,t)] and test

H0: \Delta <= 0

vs.

H1: min_(i = 1..N){\Delta_i} > 0

Usage

monoRelation(data, bootstrapRep = 1000, increasing = TRUE,
  difference = FALSE, block_length)

Arguments

data

an object of class "matrix" (or one that can be coerced to that class): asset returns or differences in asset returns which are sorted in a maximum of 15 portfolios. Each column of the matrix 'data' represents a single portfolio. data is therefore limited to a 15 columns.

bootstrapRep

A numeric scalar: the number of used bootstrap samples.

increasing

An object of class "logical": Assume an increasing or a decreasing pattern in monotonicity for the returns of the sorted portfolios.

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

block_length

A numeric scalar: The average length of the block to usefor the stationary bootstrap. This parameter is related to how much serial correlation is in your data. Use 10/6/3/2 as the block length if data is measured in daily/monthly/quarterly/annual returns.

Value

monoRelation returns an object of class "matrix".

The returning matrix consists of the following components:

matrix

a 4x2 matrix. The values of the first column are non-studentised, the values of the second column are studentised. Row (1): the t-statistic associated with a t-test that \Delta_i <= 0 Row (2): the p-value associated with a t-test that \Delta_i <= 0 Row (3): the MR test p-value from the proposed test, based on adjacent portfolios Row (4): the MR test p-value from the proposed test, on all pair-wise portfolio comparisons

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.

Examples

## load non-difference return data and apply test with daily returns.
data(demo_returns)
monoRelation(demo_returns, block_length = 10)