sim_sv {stochvolTMB}

Simulate log-returns from a stochastic volatility model

Description

This function draws the initial log-volatility (h_t) from its stationary distribution, meaning that h_0 is drawn from a gaussian distribution with mean zero and standard deviation sigma_h / sqrt(1 - phi^2). h_{t+1} is then simulated from its conditional distribution given h_t, which is N(phi*h_t, sigma_h). Log-returns (y_t) is simulated from its conditional distribution given the latent process h. If model = "gaussian", then y_t given h_t is gaussian with mean zero and standard deviation equal to sigma_y*exp(h_t / 2). Heavy tail returns can be obtained by simulating from the t-distribution by setting model = "t". How heavy of a tail is specified by the degree of freedom parameter df. Note that the observations are scaled by sqrt((df-2)/2) so that the error term has variance equal to one. Asymmetric returns are obtained from the "skew_gaussian" model. How asymmetric is governed by the skewness parameter alpha. The so called leverage model, where we allow for correlation between log-returns and volatility can be simulated by setting model to "leverage" and specifying the correlation parameter rho.

Usage

sim_sv(
  param = list(phi = 0.9, sigma_y = 0.4, sigma_h = 0.2, df = 4, alpha = -2, rho = -0.7),
  nobs = 1000L,
  seed = NULL,
  model = "gaussian"
)

Arguments

param

List of parameters. This includes the standard deviation of the observations, sigma_y, the standard deviation of the latent volatility process, sigma_h, the persistence parameter phi. If model = "t", the degree of freedom df must be specified. If model = "skew_gaussian", the skewness parameter alpha must be specified and if model = "leverage", the correlation rho between the latent error term and the observational error has to be specified.

nobs

Length of time series.

seed

Seed to reproduce simulation.

model

Distribution of error term.

Value

data.table with columns y (observations) and h (latent log-volatility).