simulateARL: Simulation for thresholds of the Lindley's recursion

In chindhanai/GSoC2017: Advancing factorAnalytics

Description

This function simulates thresholds of Lindley's recursion used in the function cusumActMgr.

Usage

simulateARL(mu, Threshold, delta, k = 3, EW_constant = 0.9,
  Fixed_Sigma = 1)

Arguments

mu	A numeric value that determines the information ratio we want to simulate thresholds for. No default value is set.
Threshold	A numeric value that determines the threshold for the Lindley's recursion to be updated in the recursion. No default value is set.
delta	A numeric value representing the simulation accuracy. In other words, we will simulate until k * sigma / mu < precision.
k	A numeric value that determines the level of cut-off. Default is 3.
EW_constant	A numeric value representing the ratio between the former sigma and the new sigma. The default is set to 0.9
Fixed_Sigma	The logical value representing if the sigma should be constant of not. 0 represents fixed sigma, 1 represents weighted sigma. The default is set to 1.

Value

simulateARL returns a vector of the following:

ARL	The average return length
s	The standard deviation of the ARLs

Author(s)

Thomas Philips, Chindhanai Uthaisaad.

References

Philips, T. K., Yashchin, E. and Stein, D. M. (2003). “Using Statistical Process Control to Monitor Active Managers”, Journal of Portfolio Management, Fall 2003, pp. 86-94.

Examples

Lower_Threshold = 1.00
Upper_Threshold = 11.0
#Monthly mu's for monthly sigma=1, annualized IR = +0.5, 0
mu = c(0.5, 0) / sqrt(12)
Seq_M = 20:70
Thresholds = Lower_Threshold + Seq_M * (Upper_Threshold - Lower_Threshold) / 100
Threshold_upper = sapply(Thresholds, FUN = simulateARL, mu = mu[1], delta = 0.01)
Threshold_lower = sapply(Thresholds, FUN = simulateARL, mu = mu[2], delta = 0.01)

chindhanai/GSoC2017 documentation built on May 3, 2019, 5:15 p.m.