# sim_sv: Simulate log-returns from a stochastic volatility model In stochvolTMB: Likelihood Estimation of Stochastic Volatility Models

## 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

 ```1 2 3 4 5 6``` ```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).

stochvolTMB documentation built on Aug. 13, 2021, 5:07 p.m.