MDSVfit: MDSV Fitting

In Abdoulhaki/MDSV: Multifractal Discrete Stochastic Volatility

MDSV Fitting

Description

Method for fitting the MDSV model on log-retruns and realized variances (uniquely or jointly).

Usage

MDSVfit(
  N,
  K,
  data,
  ModelType = 0,
  LEVIER = FALSE,
  start.pars = list(),
  dis = "lognormal",
  ...
)

Arguments

N	An integer designing the number of components for the MDSV process
K	An integer designing the number of states of each MDSV process component
data	A univariate or bivariate data matrix. Can only be a matrix of 1 or 2 columns. If data has 2 columns, the first one has to be the log-returns and the second the realized variances.
ModelType	An integer designing the type of model to be fit. 0 for univariate log-returns, 1 for univariate realized variances and 2 for joint log-return and realized variances.
LEVIER	if TRUE, estime the MDSV model with leverage.
start.pars	List of staring parameters for the optimization routine. These are not usually required unless the optimization has problems converging.
...	Further options for the solnp solver of the Rsolnp package or for fixing some parameters (see @details ).
fixed.pars	A vector of the position of the parameters of the model to be fixed
fixed.values	A vector containing the value of parameters of the model to be fixed. Must have the same length as fixed.pars

Details

The MDSV optimization routine set of feasible starting points which are used to initiate the MDSV recursion. The likelihood calculation is performed in C++ through the Rcpp package. The optimization is perform using the solnp solver of the Rsolnp package and additional options can be supply to the fonction. The leverage effect is taken into account according to the FHMV model (see Augustyniak et al., 2019). While fitting an univariate realized variances data, log-returns are required to add leverage effect. AIC and BIC are computed using the formulas :

• AIC : L - k

• BIC : L - (k/2)*log(n)

where L is the log-likelihood, k is the number of parameters and n the number of observations in the dataset. The class of the output of this function is MDSVfit. This class has a summary, print and plot methods to summarize, print and plot the results. See summary.MDSVfit, print.MDSVfit and plot.MDSVfit for more details. To fixe some parameter in the optimization, you can use the deux optionnal parameters :

Value

A list consisting of:

• ModelType : type of model to be fitted.

• LEVIER : wheter the fit take the leverage effect into account or not.

• N : number of components for the MDSV process.

• K : number of states of each MDSV process component.

• convergence : 0 if convergence, 1 if not.

• estimates : estimated parameters.

• LogLikelihood : log-likelihood of the model on the data.

• AIC : Akaike Information Criteria of the model on the data.

• BIC : Bayesian Information Criteria of the model on the data.

• data : data use for the fitting.

References

Augustyniak, M., Bauwens, L., & Dufays, A. (2019). A new approach to volatility modeling: the factorial hidden Markov volatility model. Journal of Business & Economic Statistics, 37(4), 696-709. https://doi.org/10.1080/07350015.2017.1415910

See Also

For filtering MDSVfilter, bootstrap forecasting MDSVboot, simulation MDSVsim and rolling estimation and forecast MDSVroll.

Examples

## Not run: 
# MDSV(N=2,K=3) without leverage on univariate log-returns S&P500
data(sp500)         # Data loading
N         <- 2      # Number of components
K         <- 3      # Number of states
ModelType <- 0      # Univariate log-returns
LEVIER    <- FALSE  # No leverage effect

# Model estimation
out       <- MDSVfit(K = K, N = N, data = sp500, ModelType = ModelType, LEVIER = LEVIER)
# Summary
summary(out)
# Plot
plot(out,c("dis","nic"))


# MDSV(N=3,K=3) with leverage on joint log-returns and realized variances NASDAQ
data(nasdaq)      # Data loading
N         <- 3    # Number of components
K         <- 3    # Number of states
ModelType <- 2    # Joint log-returns and realized variances
LEVIER    <- TRUE # No leverage effect

# Model estimation
out       <- MDSVfit(K = K, N = N, data = nasdaq, ModelType = ModelType, LEVIER = LEVIER)
# Summary
summary(out)
# Plot
plot(out,"nic")

## End(Not run)

Abdoulhaki/MDSV documentation built on July 6, 2024, 4:03 p.m.