SV.mle {astsa}

Stochastic Volatility Model with Feedback via MLE

Description

Fits a stochastic volatility model with feedback (optional) to a univariate time series of returns via quasi-MLE.

Usage

SV.mle(returns, gamma = 0, phi = 0.95, sQ = 0.1, alpha = NULL, sR0 = 1, mu1 = -3, sR1 = 2, 
        rho = NULL, feedback = FALSE)

Arguments

returns

single time series of returns

gamma

feedback coefficient - included if feedback=TRUE (does not have to be specified)

phi

initial value of the log-volatility AR parameter (does not have to be specified)

sQ

initial value of the standard deviation of log-volatility noise (does not have to be specified)

alpha

initial value of the log-returns^2 constant parameter (does not have to be specified)

sR0

initial value of the log-returns^2 normal mixture standard deviation parameter (component 0 - does not have to be specified)

mu1

initial value of the log-returns^2 normal mixture mean parameter (component 1 - does not have to be specified)

sR1

initial value of the log-returns^2 normal mixture standard deviation parameter (component 1 - does not have to be specified)

rho

correlation between the state noise and observation noise (so called "leverage"). If feedback=TRUE this will be included if given a proper numerical value; if NULL (default) it is not included because it is often not significant when the feedback coefficient is included.

feedback

if TRUE feedback is included in the model; default is FALSE.

Details

The returns are r_t (input this). The log-volatility process is x_t and y_t = \log r_t^2.

If feedback=TRUE, the model is

x_{t+1} = \gamma r_t + \phi x_t + \sigma w_t \qquad y_t = \alpha + x_t + \eta_t

where w_t is standard normal noise. The observation error \eta_t is a mixture of two normals, N(0, \sigma_0^2) and N(\mu_1, \sigma_1^2). The state and observation noise can be correlated if \rho is given a value between -1 and 1.

If feedback=FALSE, \gamma and \rho are not included in the model.

Value

Returned invisibly:

PredLogVol

one-step-ahead predicted log-volatility

RMSPE

corresponding root MSPE

Coefficients

table of estimates and estimated standard errors

In addition to the one step ahead predicted log-volatility, corresponding root MSPE, and table of estimates returned invisibly, the estimates and SEs are printed and a graph of (1) the data with the predicted log-volatility, and (2) the normal mixture are displayed in one graphic.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

SV.mcmc

Examples

## Not run: 

SV.mle(sp500.gr, feedback=TRUE)

SV.mle(nyse)

## End(Not run)