MDSVfilter: MDSV Filtering
In Abdoulhaki/MDSV: Multifractal Discrete Stochastic Volatility

MDSVfilter

R Documentation

MDSV Filtering

Description

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

Usage

MDSVfilter(
  N,
  K,
  data,
  para,
  ModelType = 0,
  LEVIER = FALSE,
  calculate.VaR = TRUE,
  VaR.alpha = c(0.01, 0.05),
  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.
`para`	A vector of parameters use for the MDSV filtering on `data`. For more informations see Details.
`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.
`calculate.VaR`	Whether to calculate forecast Value at Risk during the estimation.
`VaR.alpha`	The Value at Risk tail level to calculate.

Details

The MDSVfilter help to simply filter a set of data with a predefined set of parameters. Like in MDSVfit, the likelihood calculation is performed in C++ through the Rcpp package. According to Augustyniak et al., (2021), the para consist on a vector of :

\omega probability of success of the stationnary distribution of the Markov chain. (0 < \omega < 1).
a highest persistance of the component of the MDSV process. (0 < a < 1).
b decroissance rate of the persistances. (1 < b).
\sigma^2 unconditionnal variance of the MDSV process.
\nu_0 states defined parameter. (0 < \nu_0 < 1).
\gamma parameter of the realized variances innovation. This parameter is required only if ModelType = 1 or ModelType = 2. (0 < \gamma).
\xi parameter of realized variances equation in joint estimation. This parameter is required only if ModelType = 2.
\phi parameter of realized variances equation in joint estimation. This parameter is required only if ModelType = 2.
\delta1 parameter of realized variances equation in joint estimation. This parameter is required only if ModelType = 2.
\delta2 parameter of realized variances equation in joint estimation. This parameter is required only if ModelType = 2.
l leverage effect parameter. This parameter is required only if LEVIER = TRUE. (0 < l).
\theta leverage effect parameter. This parameter is required only if LEVIER = TRUE. (0 < \theta < 1).

The leverage effect is taken into account according to the FHMV model (see Augustyniak et al., 2019). While filtering 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 MDSVfilter. This class has a summary, print and plot methods to summarize, print and plot the results. See summary.MDSVfilter, print.MDSVfilter and plot.MDSVfilter for more details.

Value

A list consisting of:

ModelType : type of model to be filtered.
LEVIER : wheter the filter 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.
data : data use for the filtering.
dates : vector or names of data designing the dates.
estimates : input 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.
Levier : numeric vector representing the leverage effect at each date. Levier is 1 when no leverage is detected
filtred_proba : matrix containing the filtred probabilities P(C_t=c_i | x_1,\dots, x_t) of the Markov Chain.
smoothed_proba : matrix containing the smoothed probabilities P(C_t=c_i | x_1,\dots, x_T) of the Markov Chain.
Marg_loglik : marginal log-likelihood corresponding to the log-likelihood of log-returns. This is only return when ModelType = 2.
VaR : Value-at-Risk compute empirically.

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

Augustyniak, M., Dufays, A., & Maoude, K.H.A. (2021). Multifractal Discrete Stochastic Volatility.

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_fit   <- MDSVfit(K = K, N = N, data = sp500, ModelType = ModelType, LEVIER = LEVIER)
# Model filtering
para      <-out_fit$estimates # parameter
out_filter<- MDSVfilter(K = K, N = N, data = sp500, para = para, ModelType = ModelType, LEVIER = LEVIER)
# Summary
summary(out_filter)
# Plot
plot(out_filter)


# 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

para      <- c(omega = 0.52, a = 0.99, b = 2.77, sigma = 1.95, v0 = 0.72, 
              xi = -0.5, varphi = 0.93, delta1 = 0.93, delta2 = 0.04, shape = 2.10,
              l = 0.78, theta = 0.876)
# Model filtering
out       <- MDSVfilter(K = K, N = N,data = nasdaq, para = para, ModelType = ModelType, LEVIER = LEVIER)
# Summary
summary(out)
# Plot
plot(out)

## End(Not run)

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