Run shiny demo

Description

Run shiny demo

Usage

demo()

Estimate parameters for the stochastic volatility model

Description

Estimate parameters of a stochastic volatility model with a latent log-volatility following an autoregressive process of order one with normally distributed noise. The following distributions are implemented for the observed process:

• Gaussian distribution

• t-distribution

• Leverage: Gaussian distribution with leverage where the noise of the latent process is correlated with the observational distribution

• Skew gaussian distribution

The parameters is estimated by minimizing the negative log-likelihood (nll) and the latent log-volatility is integrated out by applying the Laplace approximation.

Usage

estimate_parameters(data, model = "gaussian", opt.control = NULL, ...)

Arguments

Value

Object of class stochvolTMB

Examples

# load data
data("spy")

# estimate parameters 
opt <- estimate_parameters(spy$log_return, model = "gaussian")

# get parameter estimates with standard error
estimates <- summary(opt)

# plot estimated volatility with 95 % confidence interval
plot(opt, include_ci = TRUE)

Construct objective function with derivatives using MakeADFun

Description

Construct objective function with derivatives using MakeADFun

Usage

get_nll(data, model = "gaussian", ...)

Arguments

Value

List of components returned from MakeADFun.

Logit transformation from the real line to (-1, 1).

Description

Logit transformation from the real line to (-1, 1).

Usage

logit(x)

Arguments

Value

double

Plot the estimated latent volatility process

Description

Displays the estimated latent volatility process over time.

Usage

## S3 method for class 'stochvolTMB'
plot(x, ..., include_ci = TRUE, plot_log = TRUE, dates = NULL, forecast = NULL)

Arguments

Value

ggplot object with plot of estimated estimated volatility.

Add predicted volatility.

Description

Adds predicted volatility to the volatility plot.

Usage

plot_forecast(p, forecast, include_ci = TRUE)

Arguments

Predict future returns and future volatilities

Description

Takes a stochvolTMB object and produces draws from the predictive distribution of the latent volatility and future log-returns.

Usage

## S3 method for class 'stochvolTMB'
predict(object, steps = 1L, nsim = 10000, include_parameters = TRUE, ...)

Arguments

Value

List of simulated values from the predictive distribution of the latent volatilities and log-returns.

Calculate one-step-ahead (OSA) residuals for stochastic volatility model.

Description

This function is very time consuming and by default computes the one-step-ahead residual for the last 100 observations. See the function oneStepPredict and the paper in the references for more details.

Usage

residuals(object, conditional = 1:(object$nobs - 100), ...)

Arguments

Value

Vector of one-step-ahead residuals. If the model is correctly specified, these should be standard normal.

References

https://www.researchgate.net/publication/316581864_Validation_of_ecological_state_space_models_using_the_Laplace_approximation

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

Value

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

Simulate from the asymptotic distribution of the parameter estimates

Description

Sampling is done on the scale the parameters were estimated. The standard deviations are simulated on log-scale and the persistence is simulated on logit scale. The same is true for the correlation parameter in the leverage model.

Usage

simulate_parameters(object, nsim = 1000)

Arguments

Value

matrix of simulated values.

Daily closing prices for the S&P500 from 2005 to 2018.

Description

A dataset containing the prices and log-returns of the S&P500 from 2005 to 2018

Usage

spy

Format

A data frame with 3522 rows and 3 variables:

date

date

price

price, in US dollars

log_return

logarithmic return

...

Summary tables of model parameters

Description

Extract parameters, transformed parameters and latent log volatility along with standard error, z-value and p-value

Usage

## S3 method for class 'stochvolTMB'
summary(object, ..., report = c("all", "fixed", "transformed", "random"))

Arguments

Value

data.table with parameter estimates, standard error, z-value and approximated p-value.

Calculate quantiles based on predictions from the predictive distribution

Description

Calculate quantiles based on predictions from the predictive distribution

Usage

## S3 method for class 'stochvolTMB_predict'
summary(object, ..., quantiles = c(0.025, 0.975), predict_mean = TRUE)

Arguments

Value

A list of data.tables. One for y, h and h_exp.