  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, finance,
and environment. The numerical results demonstrate that the proposed model
shows competitive prediction capability, compared with alternative approaches.
