Modeling nonlinear, nonstationary, vector time series : methods and applications.

Abstract

Methods for modeling nonlinear time series provide ways to extract and describe information from complex and dynamic processes. The class of nonlinear time series models is large. Rather than be exhaustive, we provide a review of two popular classes of nonlinear time series models: Momentum threshold autoregressive and functional coefficient autoregressive models. These models are then extended to vector time series. We illustrate utility by applying the models to real data examples in geology and photovoltaics, respectively. The layers of speleothems (stalactites and stalagmites) hold information on ancient climates. Geologists hypothesize that the layers of a speleothem correspond to annual deposits, similar to tree rings. In these same layers, the ratios of carbon-13 isotopes and of oxygen-18 isotopes provide information on the types of vegetation, which in turn, gives information into the climate at the time that vegetation lived. We apply a momentum threshold vector autoregressive model (VMTAR) to the 3- dimensional series. We show a vast improvement over the linear vector autoregressive (VAR) model, both statistically and from a geological perspective, thus providing a useful tool for describing the climates during the late and middle Holocene periods. Assessment of a utility scale photovoltaic (PV) power plant’s potential performance is a critical aspect in the initial plant design and construction, and accurate monitoring of plant efficiency is crucial to profitable plant operation. Both assessment and monitoring rely on temporally dense, but spatially sparse measurements of irradiance from sensors at the plant’s location. We propose a sensor design algorithm to answer the question, “What is the optimal number and layout of sensors for predicting solar irradiance?”. The algorithm makes use of vector functional coefficient autoregressive (VFCAR) models to determine if an optimal sensor design exists. To illustrate utility, we apply the algorithm to irradiance data collected from a 1.2 MW PV plant located in Lanai, Hawaii.