On tracking varying bounds when forecasting bounded time series
This work addresses a specific challenge in time series forecasting for domains like renewable energy, where bounds vary over time, representing an incremental advancement in method adaptation.
The paper tackles the problem of forecasting bounded time series with time-varying, unobserved bounds by introducing an extended log-likelihood estimation and designing algorithms, such as Online Normalized Gradient Descent, to track these bounds online, demonstrating its application in a wind power forecasting problem.
We consider a new framework where a continuous, though bounded, random variable has unobserved bounds that vary over time. In the context of univariate time series, we look at the bounds as parameters of the distribution of the bounded random variable. We introduce an extended log-likelihood estimation and design algorithms to track the bound through online maximum likelihood estimation. Since the resulting optimization problem is not convex, we make use of recent theoretical results on Normalized Gradient Descent (NGD) for quasiconvex optimization, to eventually derive an Online Normalized Gradient Descent algorithm. We illustrate and discuss the workings of our approach based on both simulation studies and a real-world wind power forecasting problem.