A model‐based approach for analog spatio‐temporal dynamic forecasting

Abstract

Analog forecasting has been applied in a variety of fields for predicting future states of complex nonlinear systems that require flexible forecasting methods. Past analog methods have almost exclusively been used in an empirical framework without the structure of a model-based approach. We propose a Bayesian model framework for analog forecasting, building upon previous analog methods but accounting for parameter uncertainty. Thus, unlike traditional analog forecasting methods, the use of Bayesian modeling allows one to rigorously quantify uncertainty to obtain realistic posterior predictive distributions. The model is applied to the long-lead time forecasting of mid-May averaged soil moisture anomalies in Iowa over a high-resolution grid of spatial locations. Sea surface temperature is used to find past time periods with similar trajectories to the current pre-forecast period. The analog model is developed on projection coefficients from a basis expansion of the soil moisture and sea surface temperature fields. Separate models are constructed for locations falling in each Iowa Crop Reporting District, and the forecasting ability of the proposed model is compared against a variety of alternative methods and metrics.

A hierarchical spatiotemporal analog forecasting model for count data

“…As with the response vector, if we assume linear projections, we can get projection coefficients by . McDermott and Wikle () show that these projection coefficients can be combined to form time lagged embedding matrices . That is, let q represent the number of periods lagged back in time, then for period t , we can define the following embedding matrix: …”

“…Bayesian models in general, and Bayesian hierarchical models in particular, provide a comprehensive modeling framework which account for multiple sources of uncertainty in ecological models (e.g., Wikle, ; Royle & Dorazio, ; Cressie, Calder, Clark, Hoef, & Wikle, ; to name a few); for a historical overview, see Ellison (). To date, there have been few attempts to cast “mechanism‐free’’ models within the Bayesian framework (McDermott & Wikle, ).…”

“…However, previous analog forecasting implementations have employed either some heuristic method that does not explicitly account for uncertainty associated with the choice or a multidimensional cross‐validation search (e.g., Arora, Little, & McSharry, ), to choose these values. The Bayesian framework described in McDermott and Wikle () allows for both the estimation and incorporation of model averaging over the various parameters in the analog model, thereby accounting for the uncertainty induced by their selection.…”

Deep echo state networks with uncertainty quantification for spatio‐temporal forecasting

“…In some cases, fairly standard linear regression or multivariate canonical correlation analysis methods can be used to generate effective long‐lead forecasts (e.g., Knaff & Landsea, ; Penland & Magorian, ). However, given the inherent nonlinearity of these systems, it has consistently been shown that well crafted nonlinear statistical methods often perform better than linear methods, at least for some spatial regions and time spans (e.g., Berliner, Wikle, & Cressie, ; Drosdowsky, ; Gladish & Wikle, ; Kondrashov, Kravtsov, Robertson, & Ghil, ; McDermott & Wikle, ; Tang, Hsieh, Monahan, & Tangang, ; Timmermann, Voss, & Pasmanter, ; Wikle & Hooten, ). It remains an active area of research to develop nonlinear statistical models for long‐lead forecasting, and there is a need to develop methods that are computationally efficient, are skillful, and can provide realistic uncertainty quantification in the presence of multiple time and spatial scales.…”

“…Solutions to this challenge require reducing the dimension of the state space, regularizing the parameter space, the incorporating of additional information (prior knowledge), and novel computational approaches (see the summary in Wikle, ). Parsimonious alternatives include analog methods (e.g., McDermott & Wikle, ; Zhao & Giannakis, ) and individual (agent)‐based models (e.g., Hooten & Wikle, ).…”