Maximum drawdown, recovery and momentum

We test predictability on asset price using stock selection rules based on maximum drawdown and consecutive recovery. Monthly momentum- and weekly contrarian-style portfolios ranked by the alternative selection criteria are implemented in various asset classes. Regardless of market, the alternative ranking rules are superior in forecasting asset prices and capturing cross-sectional return differentials. In a monthly period, alternative portfolios constructed by maximum drawdown measures dominate other momentum portfolios including the cumulative return-based momentum portfolios. Recovery-related stock selection criteria are the best ranking measures for predicting mean-reversion in a weekly scale. Prediction on future directions becomes more consistent, because the alternative portfolios are less riskier in various reward-risk measures such as Sharpe ratio, VaR, CVaR and maximum drawdown. In the Carhart four-factor analysis, higher factor-neutral intercepts for the alternative strategies are another evidence for the robust prediction by the alternative stock selection rules.Comment: 28 pages, 6 subfigures; minor revisio

Geometric shrinkage priors for K\"ahlerian signal filters

We construct geometric shrinkage priors for K\"ahlerian signal filters. Based on the characteristics of K\"ahler manifolds, an efficient and robust algorithm for finding superharmonic priors which outperform the Jeffreys prior is introduced. Several ans\"atze for the Bayesian predictive priors are also suggested. In particular, the ans\"atze related to K\"ahler potential are geometrically intrinsic priors to the information manifold of which the geometry is derived from the potential. The implication of the algorithm to time series models is also provided.Comment: 10 pages, published versio

K\"ahlerian information geometry for signal processing

We prove the correspondence between the information geometry of a signal filter and a K\"ahler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a K\"ahler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the K\"ahler potential. The Hermitian structure of the K\"ahler manifold is explicitly emergent if and only if the impulse response function of the highest degree in $z$ is constant in model parameters. The K\"ahlerian information geometry takes advantage of more efficient calculation steps for the metric tensor and the Ricci tensor. Moreover, $\alpha$-generalization on the geometric tensors is linear in $\alpha$. It is also robust to find Bayesian predictive priors, such as superharmonic priors, because Laplace-Beltrami operators on K\"ahler manifolds are in much simpler forms than those of the non-K\"ahler manifolds. Several time series models are studied in the K\"ahlerian information geometry.Comment: 24 pages, published versio

Application of K\"ahler manifold to signal processing and Bayesian inference

We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the K\"ahler manifold case. We find conditions for the information geometry of linear systems to be K\"ahler, and the relation of the K\"ahler potential to information geometric quantities such as $\alpha$-divergence, information distance and the dual $\alpha$-connection structure. The K\"ahler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the $\alpha$-generalization of the geometric objects. The Laplace--Beltrami operator is also simplified in the K\"ahler geometry. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the K\"ahler structure.Comment: 8 pages, submitted to the Proceedings of MaxEnt 1

K\"ahler information manifolds of signal processing filters in weighted Hardy spaces

We generalize K\"ahler information manifolds of complex-valued signal processing filters by introducing weighted Hardy spaces and smooth transformations of transfer functions. We prove that the Riemannian geometry of a linear filter induced from weighted Hardy norms for the smooth transformations of its transfer function is a K\"ahler manifold. Additionally, the K\"ahler potential of the linear system geometry corresponds to the square of the weighted Hardy norms of its composite transfer functions. Based on properties of K\"ahler manifolds, geometric objects on the manifolds of the linear systems in weighted Hardy spaces are computed in much simpler ways. Moreover, K\"ahler information manifolds of signal filters in weighted Hardy spaces incorporate various well-known information manifolds under the unified framework. We also cover several examples from time series models of which metric tensor, Levi-Civita connection, and K\"ahler potentials are represented with polylogarithms of poles and zeros from the transfer functions with weight vectors in exponential forms.Comment: 22 page

Capturing and Parsing the Mixed Properties of Light Verb Constructions in a Typed Feature Structure Grammar

One of the most widely used constructions in Korean is the so-called light verb construction (LVC) involving an active-denoting verbal noun (VN) together with the light verb ha-ta ‘do’. This paper first discusses the argument composition of the LVC, mixed properties of VNs which have provided a challenge to syntactic analyses with a strict version of X-bar theory. The paper shows the mechanism of multiple classification of category types with systematic inheritance can provide an effective way of capturing these mixed properties. The paper then restates the argument composition properties of the LVC and reenforces them with a constraint-based analysis. This paper also offers answers to the the puzzling syntactic variations in the LVC. Following these empirical and theoretical discussions is a short report on the implementation of the analysis within the LKB (Linguistics Knowledge Building) system