Forecasting Trends with Asset Prices

Abstract

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. Motivations

Robustness of Mathematical Models and Technical Analysis Strategies

“…In practice, the parameters are unknown and must be estimated. In Bel Hadj Ayed et al (2015a), the authors assess the feasibility of forecasting trends modeled by an unobserved mean-reverting diffusion. They show that, due to a weak signal-to-noise ratio, a bad calibration is very likely.…”

“…Several generalisations of this problem are possible (see Karatzas & Zhao (2001), Brendle (2006), Lakner (1998), Sass & Haussmann (2004), or Rieder & Bauerle (2005) for example) but all these models are confronted to the calibration problem. In Bel Hadj Ayed et al (2015a), the authors assess the feasibility of forecasting trends modeled by an unobserved mean-reverting diffusion. They show that, due to a weak signal-to-noise ratio, a bad calibration is very likely.…”

Performance Analysis of the Optimal Strategy Under Partial Information

“…This corresponds to the steady-state Kalman filter. The following proposition (see [1] for a proof) gives a first continuous representation of the steadystate Kalman filter: Proposition 2. The steady-state Kalman filter has a continuous time limit depending on the asset returns:…”

“…Here, we find that the steady-state trend estimator μ is an Ornstein Uhlenbeck process. In practice, the parameters (λ, σ µ , σ S ) are unknown and must be estimated (see [1] where the authors assess the feasibility of forecasting trends modeled by an unobserved meanreverting diffusion). In this paper, we assume that the parameters are known.…”

Robust utility maximization under model uncertainty via a penalization approach

“…This assumption clearly does not match the reality that investors are facing. Several works by Lakner (1995) andthen Bel Hadj Ayed et al (2017) address the utility maximization problem with an uncertain drift (however assuming some form of the prescribed dynamics or prior distribution of the drift).…”