Simulate Data from the CSPA Paper DGP

Generates data from the data generating process in Section 3.1 of Li, Liao, and Quaedvlieg (2022). The conditioning variable \(X_t\) follows a Gaussian AR(1) with coefficient 0.5, and the loss differentials are \(Y_{j,t} = 1 - a \exp(-(X_t - c)^2) + u_{j,t}\), where \(u_{j,t}\) follows an AR(1) with coefficient rho_u.

Usage

do_sim(J, n, a, c, rho_u)

Arguments

J

Integer; number of competing forecast methods.

n

Integer; sample size.

a

Numeric; controls the shape of the conditional mean function. a = 1 gives the null hypothesis (\(h_j(c) = 0\)).

c

Numeric; location parameter for the minimum of \(h_j(x)\).

rho_u

Numeric in \([0, 1)\); AR(1) coefficient of the error process. Higher values induce more serial dependence.

Value

A list with components:

Y

An n x J matrix of loss differentials.

X

A numeric vector of length n.

Examples

sim <- do_sim(J = 3, n = 250, a = 1, c = 0, rho_u = 0.4)
str(sim)
#> List of 2
#>  $ Y: num [1:250, 1:3] -1.763 -1.506 -0.567 -2.614 0.294 ...
#>  $ X: num [1:250] -1.446 1.041 0.614 0.234 0.546 ...