GarchDGP: Normal errors with stationary GARCH(1,1) variance

In kavehsn/PredictiveDGP: Predictive DGPs exhibiting various distributions

Description

The processes y and x are generated by a predictive regression of the form y_t=β x_{t-1}+\varepsilon_t for t=1,\cdots,T, in which the regressors follow an AR(1) process - i.e. x_t=θ x_{t-1}+u_t. The predictor's errors are distributed according to u_t\sim N(0,1), whereas the disturbances of the predictive regression, \varepsilon_t, are distributed \varepsilon_t\sim N(0,σ_t^2), where σ_t^2=0.00037+0.0888\varepsilon_{t-1}^2+0.9024σ_{t-1}^2. Examples of DGPs with Normal disturbances and stationary GARCH(1,1) variance can be found in \insertCitedufour2010exact;textualPredictiveDGP and \insertCitecoudin2009finite;textualPredictiveDGP. The initial value of the process x is generated by x_0=\frac{w_0}{√{1-θ^2}}, where w_t\sim N(0,1). Finally, the contemporaneous correlation between the disturbances \varepsilon_t and u_t is captured by ρ\varepsilon_t+w_t√{1-ρ^2}.

Usage

GarchDGP(n, beta, theta, rho)

Arguments

n	the number of observations
beta	the regressor coefficient of the predictive regression
theta	the autocorrelation coefficient of the predictor
rho	the contemporaneous correlation coefficient

References

\insertAllCited

Examples

GarchDGP(n=50, beta=0.5, theta=0.999, rho=0.9)

kavehsn/PredictiveDGP documentation built on Dec. 21, 2021, 5:21 a.m.