The Estimation of Time-varying Parameters – A Malliavin Calculus Approach

Abstract

The Malliavin derivative of the Malliavin calculus is used to estimate the time-varying amplitudes that appear in the sum of signals or time-varying regression models. A closed form solution is obtained for the estimates of the time-varying amplitudes. The duality principle of the Malliavin calculus is then used to find a numerically tractable expression for the estimates. Given are examples and comparisons to existing methods.

Keywords: Ito calculus, Malliavin calculus, Malliavin derivative, time-varying parameters, time-series analysis