The development of algorithmic trading has been one of the most prominent trends in finance and its applications. Hidden Markov Models (HMMs) help enhance the predictive power of statistical models and improve trading strategies for data scientists and algorithmic traders. In recent years there has been growing interest in investigating the pairs trading and multiple trading based on robust Kalman filtering (KF) using data-driven innovation volatility forecasts (DDIVF). KF algorithms were successfully applied in pairs trading with two cointegrated assets using DDIVF as a method for forecasting non-normal innovation volatility. In this paper a novel combined pairwise trading strategy is proposed by combining HMM and DDIVF to further optimize trading signals in different market regimes. The results of the numerical experiments on two cointegrated stocks show that the proposed profitable trading strategy using DDIVF-HMM outperforms the recently studied robust trading strategy using DDIVF alone.

Portfolio risk management is an important success factor in an organization’s ability to deliver more business value. Moreover, constructing a true resilient portfolio is impossible without the inclusion of higher-order moments such as skewness and kurtosis. Recently there has been a growing interest in using machine learning methods with empirical variance covariance matrix of returns to study Markowitz portfolio optimization. A major drawback is that the tangency portfolios constructed by using the existing portfolio risk measures such as portfolio standard deviation, value-at-risk (VaR), conditional value-at-risk (CVaR), maximum absolute deviation (MAD) are always affected by the larger skewness and kurtosis of the portfolio return. This paper develops a set of metrics that extend the traditional portfolio Sharpe ratio (PSR) to measures that include skewness and kurtosis. Using a random portfolio approach, the paper demonstrates how to use these new metrics and optimize portfolios. Inclusion of higher moments such as skewness and kurtosis in portfolio risk management acknowledges the risk of asymmetric and heavy-tailed returns and can help in constructing resilient portfolios. For portfolio optimization, simple yet effective novel data-driven resilient portfolio risk measures incorporating skewness and kurtosis are presented in this paper. The results show that the performance of maximum mean-risk portfolios using the proposed portfolio risk measures based on volatility correlation and sign correlation outperform the commonly used tangency portfolio using portfolio standard deviation.

Many of the challenges and opportunities of data science in finance involve recursive smoothing, forecasting, filtering and pattern mining. Recently there has been a growing interest in using filtered estimates for dynamic hedge ratios for pairs trading. Moreover, rolling estimates and forecasts are used for pattern mining in technical analysis. Kalman filtering algorithms were successfully applied in pairs trading with only two co-integrated assets. In this paper, pairs trading strategy is extended to multiple trading (with more than two assets) strategy. Recently proposed non-Gaussian maximum informative filtering algorithms for dynamic state space models are used to obtain the filtered estimates of hedge ratios and applied in multiple trading. It is shown that the proposed multiple trading strategy outperforms (with higher profits) the commonly used pairs trading strategy using real data. A data-driven approach for selecting a parameter which maximizes the Sharpe ratio (SR) to generate optimal trading signals is also discussed in some detail.

Interactions among animals can result in complex sensory signals containing a variety of socially relevant information, including the number, identity, and relative motion of conspecifics. How the spatiotemporal properties of such evolving naturalistic signals are encoded is a key question in sensory neuroscience. Here, we present results from experiments and modeling that address this issue in the context of the electric sense, which combines the spatial aspects of vision and touch, with the temporal aspects of audition. Wave-type electric fish, such as the brown ghost knifefish, Apteronotus leptorhynchus, used in this study, are uniquely identified by the frequency of their electric organ discharge (EOD). Multiple beat frequencies arise from the superposition of the EODs of each fish. We record the natural electrical signals near the skin of a "receiving" fish that are produced by stationary and freely swimming conspecifics. Using spectral analysis, we find that the primary beats, and the secondary beats between them ("beats of beats"), can be greatly influenced by fish swimming; the resulting motion produces low-frequency envelopes that broaden all the beat peaks and reshape the "noise floor". We assess the consequences of this motion on sensory coding using a model electroreceptor. We show that the primary and secondary beats are encoded in the afferent spike train, but that motion acts to degrade this encoding. We also simulate the response of a realistic population of receptors, and find that it can encode the motion envelope well, primarily due to the receptors with lower firing rates. We discuss the implications of our results for the identification of conspecifics through specific beat frequencies and its possible hindrance by active swimming.

In injured neurons, "leaky" voltage-gated sodium channels (Nav) underlie dysfunctional excitability that ranges from spontaneous subthreshold oscillations (STO), to ectopic (sometimes paroxysmal) excitation, to depolarizing block. In recombinant systems, mechanical injury to Nav1.6-rich membranes causes cytoplasmic Na(+)-loading and "Nav-CLS", i.e., coupled left-(hyperpolarizing)-shift of Nav activation and availability. Metabolic injury of hippocampal neurons (epileptic discharge) results in comparable impairment: left-shifted activation and availability and hence left-shifted I(Na-window). A recent computation study revealed that CLS-based I(Na-window) left-shift dissipates ion gradients and impairs excitability. Here, via dynamical analyses, we focus on sustained excitability patterns in mildly damaged nodes, in particular with more realistic Gaussian-distributed Nav-CLS to mimic "smeared" injury intensity. Since our interest is axons that might survive injury, pumps (sine qua non for live axons) are included. In some simulations, pump efficacy and system volumes are varied. Impacts of current noise inputs are also characterized. The diverse modes of spontaneous rhythmic activity evident in these scenarios are studied using bifurcation analysis. For "mild CLS injury", a prominent feature is slow pump/leak-mediated E(Ion) oscillations. These slow oscillations yield dynamic firing thresholds that underlie complex voltage STO and bursting behaviors. Thus, Nav-CLS, a biophysically justified mode of injury, in parallel with functioning pumps, robustly engenders an emergent slow process that triggers a plethora of pathological excitability patterns. This minimalist "device" could have physiological analogs. At first nodes of Ranvier and at nociceptors, e.g., localized lipid-tuning that modulated Nav midpoints could produce Nav-CLS, as could co-expression of appropriately differing Nav isoforms.