Epidemiology of Coronavirus COVID-19: Forecasting the Future Incidence in Different Countries

Simulation and Inference for Stochastic Differential Equations: with R Examples

Most industrial products degrade with usage. To capture degradation patterns and schedule condition-based maintenance actions, it is necessary to model the degradation process and predict the system remaining useful life (RUL). In practice, the operating environments and loading conditions are dynamic and stochastic, which introduces extra randomness in the degradation process. To account for the dynamic environmental impacts, this article proposes a nonlinear Wiener process model with a random time-varying covariate. We model the dynamic covariate with an Ornstein–Uhlenbeck process, and link it to the time-varying degradation rate by an exponential form covariate-effect function. Therefore, the proposed Wiener process has a time-varying degradation rate impacted by the dynamic environment. We propose to estimate the model parameters by maximum likelihood estimation based on given observations of the degradation and covariate. We also propose a simulation-based procedure to obtain the RUL for the proposed model. The model is verified by Monte Carlo simulations. We apply the proposed model to a dust-cleaning fan degradation dataset and a lithium-ion battery degradation dataset, and the results show that the proposed model outperforms the existing degradation models in fitting the real data and RUL prediction. 

A Wiener Process Model With Dynamic Covariate for Degradation Modeling and Remaining Useful Life Prediction

This paper develops the optimal causal path algorithm and applies it within a fully-fledged statistical arbitrage framework to minute-by-minute data of the S&P 500 constituents from 1998 to 2015. S...

https://www.econstor.eu/bitstream/10419/173658/1/1011561689.pdf

Statistical arbitrage with optimal causal paths on high-frequency data of the S&P 500

We develop a multivariate statistical arbitrage strategy based on vine copulas—a highly flexible instrument for linear and nonlinear multivariate dependence modeling. In an empirical application on...

/pdf/statistical-arbitrage-with-vine-copulas-5fr3oxm7i5.pdf

Statistical arbitrage with vine copulas

This paper develops a pairs trading framework based on a mean-reverting jump–diffusion model and applies it to minute-by-minute data of the S&P 500 oil companies from 1998 to 2015. The established ...

https://www.econstor.eu/bitstream/10419/157807/1/885569830.pdf

Pairs trading with a mean-reverting jump–diffusion model on high-frequency data

This study derives an optimal pairs trading strategy based on a Levy-driven Ornstein–Uhlenbeck process and applies it to high-frequency data of the S&P 500 constituents from 1998 to 2015. Our model...

/pdf/optimal-trading-strategies-for-levy-driven-ornstein-542nrx4h86.pdf

Optimal trading strategies for Lévy-driven Ornstein–Uhlenbeck processes

This paper develops the regime classification algorithm and applies it within a fully-fledged pairs trading framework on minute-by-minute data of the S&P 500 constituents from 1998 to 2015. Specifi...

/pdf/a-flexible-regime-switching-model-with-pairs-trading-54e7ywbwm7.pdf

A flexible regime switching model with pairs trading application to the S&P 500 high-frequency stock returns

This study derives an optimal pairs trading strategy based on a Levy-driven Ornstein-Uhlenbeck process and applies it to high-frequency data of the S&P 500 constituents from1998 to 2015. Our model provides optimal entry and exit signals by maximizing the expected return expressed in terms of the first-passage time of the spread process. An explicit representation of the strategy's objective function allows for direct optimization without Monte Carlo methods. Categorizing the data sample into 10 economic sectors, we depict both the performance of each sector and the efficiency of the strategy in general. Results from empirical back-testing show strong support for the profitability of the model with returns after transaction costs ranging from 31.90 percent p.a. for the sector \Consumer Staples" to 278.61 percent p.a. for the sector \Financials". We find that the remarkable returns across all economic sectors are strongly driven by model parameters and sector size. Jump intensity decreases over time with strong outliers in times of high market turmoils. The value-add of our Levy-based model is demonstrated by benchmarking it with quantitative strategies based on Brownian motion-driven processes.

Optimal trading strategies for Lévy-driven Ornstein-Uhlenbeck processes

This paper develops a pairs trading framework based on a mean-reverting jump-diffusion model and applies it to minute-by-minute data of the S&P 500 oil companies from 1998 to 2015. The established statistical arbitrage strategy enables us to perform intraday and overnight trading. Essentially, we conduct a 3-step calibration procedure to the spreads of all pair combinations in a formation period. Top pairs are selected based on their spreads' meanreversion speed and jump behavior. Afterwards, we trade the top pairs in an out-of-sample trading period with individualized entry and exit thresholds. In the back-testing study, the strategy produces statistically and economically significant returns of 60.61 percent p.a. and an annualized Sharpe ratio of 5.30, after transaction costs. We benchmark our pairs trading strategy against variants based on traditional distance and time-series approaches and find its performance to be superior relating to risk-return characteristics. The mean-reversion speed is a main driver of successful and fast termination of the pairs trading strategy.

Pairs trading with a mean-reverting jump-diffusion model on high-frequency data

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