Change Point Detection and Estimation of the Two-Sided Jumps of Asset Returns Using a Modified Kalman Filter

Abstract

Abstract:In the first part of the paper, the positive and negative jumps of NASDAQ daily (log-) returns and three of its stocks are estimated based on the methodology presented by Theodosiadou et al. 2016, where jumps are assumed to be hidden random variables. For that reason, the use of stochastic state space models in discrete time is adopted. The daily return is expressed as the difference between the two-sided jumps under noise inclusion, and the recursive Kalman filter algorithm is used in order to estimate them. Since the estimated jumps have to be non-negative, the associated pdf truncation method, according to the non-negativity constraints, is applied. In order to overcome the resulting underestimation of the empirical time series, a scaling procedure follows the stage of truncation. In the second part of the paper, a nonparametric change point analysis concerning the (variance-) covariance is applied to the NASDAQ return time series, as well as to the estimated bivariate jump time series derived after the scaling procedure and to each jump component separately. A similar change point analysis is applied to the three other stocks of the NASDAQ index.

State Space Modeling with Non-Negativity Constraints Using Quadratic Forms

“…For example, in the Vasicek model [5] and its extension [6], the interest rates are considered to be hidden random variables subject to non-negative constraints, while in [7,8], the eigenvalues of the VAR process were restricted within the unit circle. Considering the use of state space models in the domain of finance, a discrete state space model could be implemented for the estimation of the hidden jump components of asset returns [9,10]. The use of jumps has been proposed for the description of the dynamics of asset prices since they can explain some of the empirical characteristics of the asset prices, e.g., the lack of a normal distribution or the existence of leptokurticity (see for example [11]).…”