Winsorized ARMA Estimation for Higher-Order Stochastic Volatility Models

Estimation, simulation, hypothesis testing, AR-order selection, and forecasting for univariate higher-order stochastic volatility SV(p) models. Supports Gaussian, Student-t, and Generalized Error Distribution (GED) innovations, with optional leverage effects. Estimation uses closed-form Winsorized ARMA-SV (W-ARMA-SV) moment-based methods that avoid numerical optimization. Hypothesis testing includes Local Monte Carlo (LMC) and Maximized Monte Carlo (MMC) procedures for leverage effects, heavy tails, and autoregressive order. AR-order selection is also available via information criteria (BIC/AIC) using the Kalman-filter quasi-likelihood and the Hannan-Rissanen ARMA residual variance. Forecasting is based on Kalman filtering and smoothing. See Ahsan and Dufour (2021) , Ahsan, Dufour, and Rodriguez-Rondon (2025) , and Ahsan, Dufour, and Rodriguez-Rondon (2026) for details.

wARMASVp

Overview

wARMASVp provides estimation, simulation, hypothesis testing, and forecasting for univariate higher-order stochastic volatility SV(p) models. It supports Gaussian, Student-t, and Generalized Error Distribution (GED) innovations, with optional leverage effects.

The estimation method is based on closed-form Winsorized ARMA-SV (W-ARMA-SV) moment-based estimators that avoid numerical optimization, making them fast and reliable.

Installation

You can install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("roga11/wARMASVp")

Features

Estimation: SV(p) models with Gaussian, Student-t, or GED errors via svp()
Leverage effects: Asymmetric volatility estimation for Gaussian SV(p)
Simulation: Generate SV(p) data with sim_svp()
Hypothesis testing: LMC and MMC procedures for autoregressive order, leverage, and heavy tails
Forecasting: Kalman filter-based h-step-ahead volatility forecasts via forecast_svp()
Standard errors: Simulation-based confidence intervals via svpSE()

Quick Start

library(wARMASVp)

# Simulate Gaussian SV(1)
y <- sim_svp(1000, phi = 0.95, sigy = 1, sigv = 0.3)

# Estimate
fit <- svp(y, p = 1)
summary(fit)

# Standard errors
se <- svpSE(fit, n_sim = 99)
se$CI

# Forecast
fc <- forecast_svp(fit, H = 10)
plot(fc)

References

Ahsan, M. N. and Dufour, J.-M. (2021). Simple estimators and inference for higher-order stochastic volatility models. Journal of Econometrics, 224(1), 181-197. doi:10.1016/j.jeconom.2021.03.008
Ahsan, M. N., Dufour, J.-M., and Rodriguez-Rondon, G. (2025). Estimation and inference for higher-order stochastic volatility models with leverage. Journal of Time Series Analysis, 46(6), 1064-1084. doi:10.1111/jtsa.12851
Ahsan, M. N., Dufour, J.-M., and Rodriguez-Rondon, G. (2026). Estimation and inference for stochastic volatility models with heavy-tailed distributions. Bank of Canada Staff Working Paper 2026-8. doi:10.34989/swp-2026-8