QMLKFMod: An Package for Quasi-Maximum Likelihood Estimation via the Kalman Filter in RCA and GARCH Models
Year: 2026
Type: article
Abstract: R's standard routines cannot estimate random coecient autoregressive (RCA) models. We present QMLKFMod, an R package for Gaussian quasi-maximum likelihood estimation of RCA(p) models, with a diagonal or a full covariance matrix of the random coecients, and of GARCH(p, q) models, built on the Kalman-lter formulation (QMLKF) whose asymptotic theory has recently been completed. For the RCA(p) model the Kalman lter is conditionally exact and delivers the exact conditional mean and variance. For the GARCH(p, q) model the quasi-Kalman lter of the squared returns coincides with the GARCH recursion once its start-up has decayed: the QMLKF is the classical quasi-maximum likelihood estimator equipped with an explicit start-up rule, and the two are asymptotically equivalent. The package evaluates the criteria and their analytic gradients in compiled code and reports the standard errors of the companion theorya sandwich covariance for RCA models, valid unˆ der nite fourth moments of the innovations only, and (ˆ κ − 1)J −1 for GARCH models, valid without any moment condition on the returnstogether with heteroscedasticity and autocorrelation consistent variants and a boundary-aware test of the absence of random coecients. Monte Carlo studies run with the released package conrm the asymptotic approximations, including for an RCA process with EX 4 t = ∞ and a GARCH process with Eε 4 t = ∞ . They also show that, under heavy-tailed innovations, the naive covariance under-covers while the sandwich intervals are much closer to the nominal level, and that in persistent GARCH models the start-up of the lter matters in nite samples, the default start-up being as accurate as the direct recursion started at the sample variance. The package is illustrated on four European stock-market indices, where the RCA(1) model captures ARCH-type heteroscedasticity but is outperformed by a GARCH(1, 1), and on the DM/USD exchange rate.
Author: BENMOUMEN, Mohammed
Institution: Mohamed I University
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7224797940