QMLKFMod: An R Package for Quasi-Maximum Likelihood Estimation via the Kalman Filter in RCA and GARCH Models

Abstract

R’s standard routines fit fixed-coefficient linear autoregressive and generalized autoregressive conditionally heteroscedastic (GARCH) models but cannot estimate random coefficient autoregressive (RCA) models, and they evaluate the GARCH likelihood under arbitrary initial values for the unobserved conditional variance. We present QMLKFMod, an R package implementing the quasi-maximum likelihood via Kalman filter (QMLKF) estimator for two classes of conditionally heteroscedastic time series: the RCA(p) model and the GARCH(p, q) model. For both, the package builds the Gaussian quasi-likelihood from the exact Kalman-filter innovation moments—requiring no assumption on presample values—optimises it by simulated annealing, and returns estimates with robust, heteroscedasticity- and autocorrelation-consistent (sandwich) standard errors, confidence intervals and Wald tests, making the asymptotic theory of the estimator operational. We document the exported functions and validate the package along three axes: (i) two Monte Carlo studies confirm that the standardised estimator is asymptotically Gaussian, that the empirical 95% coverage approaches the nominal level, and that the root mean squared error decays at the parametric rate; (ii) under heavy-tailed Student-t innovations the robust covariance retains coverage near 95% while the naive Gaussian covariance collapses to 73%, demonstrating the necessity of the sandwich form; and (iii) on GARCH(1, 2) and GARCH(2, 1) designs the estimator attains a uniformly smaller mean squared error than the classical quasi-maximum likelihood estimator. The methodology is illustrated on the daily returns of four European stock-market indices and the Moroccan MASI index.