Forecasting trends with asset prices

TL;DR

This paper develops a stochastic asset price model with an unobservable trend, utilizing Kalman filtering and likelihood estimation to improve trend forecasting accuracy in financial time series.

Contribution

It introduces a closed-form likelihood and online computation methods for parameter estimation in a trend model with unobservable components.

Findings

Likelihood in closed form for the model

Two online methods for parameter estimation

Impact of mis-calibration on forecasting accuracy

Abstract

In this paper, we consider a stochastic asset price model where the trend is an unobservable Ornstein Uhlenbeck process. We first review some classical results from Kalman filtering. Expectedly, the choice of the parameters is crucial to put it into practice. For this purpose, we obtain the likelihood in closed form, and provide two on-line computations of this function. Then, we investigate the asymptotic behaviour of statistical estimators. Finally, we quantify the effect of a bad calibration with the continuous time mis-specified Kalman filter. Numerical examples illustrate the difficulty of trend forecasting in financial time series.