bmgarch {bmgarch}

Estimate Bayesian Multivariate GARCH

Description

Draw samples from a specified multivariate GARCH model using 'Stan', given multivariate time-series. Currently supports CCC, DCC, BEKK, and pdBEKK model parameterizations.

Usage

bmgarch(
  data,
  xC = NULL,
  parameterization = "CCC",
  P = 1,
  Q = 1,
  iterations = 2000,
  chains = 4,
  standardize_data = FALSE,
  distribution = "Student_t",
  meanstructure = "constant",
  sampling_algorithm = "MCMC",
  ...
)

Arguments

data

Time-series or matrix object. A time-series or matrix object containing observations at the same interval.

xC

Numeric vector or matrix. Covariates(s) for the constant variance terms in C, or c, used in a log-linear model on the constant variance terms (Rast et al. 2020). If vector, then it acts as a covariate for all constant variance terms. If matrix, must have columns equal to number of time series, and each column acts as a covariate for the respective time series (e.g., column 1 predicts constant variance for time series 1).

parameterization

Character (Default: "CCC"). The type of of parameterization. Must be one of "CCC", "DCC", "BEKK", or "pdBEKK".

P

Integer. Dimension of GARCH component in MGARCH(P,Q).

Q

Integer. Dimension of ARCH component in MGARCH(P,Q).

iterations

Integer (Default: 2000). Number of iterations for each chain (including warmup).

chains

Integer (Default: 4). The number of Markov chains.

standardize_data

Logical (Default: FALSE). Whether data should be standardized to easy computations.

distribution

Character (Default: "Student_t"). Distribution of innovation: "Student_t" or "Gaussian"

meanstructure

Character (Default: "constant"). Defines model for means. Either 'constant' or 'ARMA'. Currently ARMA(1,1) only. OR 'VAR' (VAR1).

sampling_algorithm

Character (Default" "MCMC"). Define sampling algorithm. Either 'MCMC'for Hamiltonian Monte Carlo or 'VB' for variational Bayes. 'VB' is inherited from stan and is currently in heavy development – do not trust estimates.

...

Additional arguments can be ‘chain_id’, ‘init_r’, ‘test_grad’, ‘append_samples’, ‘refresh’, ‘enable_random_init’ etc. See the documentation in stan.

Details

Four types of paramerizations are implemented. The constant conditional correlation (CCC) and the dynamic conditional correlation (DCC; Engle2002,Engle2001a), as well as BEKK (Engle and Kroner 1995) and a BEKK model with positivity constraints on the diagonals of the ARCH and GARCH parameters "pdBEKK" (Rast et al. 2020).

The fitted models are 'rstan' objects and all posterior parameter estimates can be obtained and can be examined with either the 'rstan' toolbox, plotted and printed using generic functions or passed to 'bmgarch' functions to 'forecast' or compute 'model_weights' or compute fit statistics based on leave-future-out cross-validation.

Value

bmgarch object.

Author(s)

Philippe Rast, Stephen R. Martin

References

Engle RF, Kroner KF (1995). “Multivariate simultaneous generalized arch.” Econometric Theory, 11(1), 122–150. doi:10.1017/S0266466600009063.

Rast P, Martin SR, Liu S, Williams DR (2020). “A New Frontier for Studying Within-Person Variability: Bayesian Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models.” Psychological Methods. https://psyarxiv.com/j57pk/.()

Examples

## Not run: 
data(panas)
# Fit BEKK(1,1) mgarch model with a ARMA(1,1) meanstructure,
# and student-t residual distribution
fit <- bmgarch(panas, parameterization = "BEKK",
               P = 1, Q = 1,
               meanstructure = "arma",
               distribution = "Student_t")

# Summarize the parameters
summary(fit)

# Forecast 5 ahead
fit.fc <- forecast(fit, ahead = 5)
print(fit.fc)

# Plot mean forecasts
plot(fit.fc, type = "mean")

# Plot variance forecasts
plot(fit.fc, type = "var")

# Plot correlation forecasts
plot(fit.fc, type = "cor")

# Plot modeled data ("backcasted values").
plot(fit, type = "mean")

# Save "backcasted" values
fit.bc <- fitted(fit)

# Save estimated and forecasted data as a data.frame
df.fc <- as.data.frame(fit.fc)

# Access rstan's model fit object
mf <- fit$model_fit

# Return diagnostics and a plot of the first 10 parameters
rstan::check_hmc_diagnostics(mf)
rstan::plot(mf)

## End(Not run)