Abstract This paper presents a new prediction model for time series data by integrating a time-varying Geometric Brownian Motion model with a pricing mechanism used in financial engineering. Typical time series models such as Auto-Regressive Integrated Moving Average assumes a linear correlation structure in time series data. When a stochastic process is highly volatile, such an assumption can be easily violated, leading to inaccurate predictions. We develop a new prediction model that can flexibly characterize a time-varying volatile process without assuming linearity. We formulate the prediction problem as an optimization problem with unequal overestimation and underestimation costs. Based on real option theories developed in finance, we solve the optimization problem and obtain a predicted value, which can minimize the expected prediction cost. We evaluate the proposed approach using multiple datasets obtained from real-life applications including manufacturing, and finance. The numerical results demonstrate that the proposed model shows competitive prediction capability, compared with alternative approaches.

中文翻译：

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基于实物期权理论的波动过程数据驱动预测

摘要 本文通过将时变几何布朗运动模型与金融工程中使用的定价机制相结合，提出了一种新的时间序列数据预测模型。典型的时间序列模型（例如自回归综合移动平均线）假设时间序列数据中的线性相关结构。当随机过程高度不稳定时，很容易违反这种假设，从而导致预测不准确。我们开发了一种新的预测模型，可以灵活地表征随时间变化的易失性过程，而无需假设线性。我们将预测问题表述为一个具有不等高估和低估成本的优化问题。基于金融领域发展的实物期权理论，我们解决了优化问题并获得了一个预测值，这可以最小化预期的预测成本。我们使用从包括制造和金融在内的实际应用中获得的多个数据集来评估所提出的方法。数值结果表明，与替代方法相比，所提出的模型显示出具有竞争力的预测能力。