simulateARL: Simulation for thresholds of the Lindley's recursion
In sangeeuw/factorAnalytics_Avinash: Factor Analytics

Description Usage Arguments Details Value Author(s) References Examples

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

1 2	simulateARL(mu, Threshold, delta, k = 3, EW_constant = 0.9, Fixed_Sigma = 1)

`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.

Simulate the thresholds used in cusumActMgr

simulateARL returns a vector of the following:

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

Thomas Philips, Chindhanai Uthaisaad.

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.

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 = 30:40
Thresholds = Lower_Threshold + Seq_M * (Upper_Threshold - Lower_Threshold) / 100
Threshold_upper = sapply(Thresholds, FUN = simulateARL, mu = mu[1], delta = 0.05)
Threshold_lower = sapply(Thresholds, FUN = simulateARL, mu = mu[2], delta = 0.05)