Switching nonparametric regression models for multi-curve data
This work addresses the analysis of multi-curve data with switching patterns, such as in energy consumption, but is incremental as it builds on existing nonparametric and state-switching methods.
The authors tackled the problem of modeling multi-curve data with latent state processes by developing a switching nonparametric regression model, where each curve switches between smooth functions based on the state, and applied it to building power usage data, with simulation studies validating the estimates.
We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function to another. Thus each curve follows what we call a switching nonparametric regression model. We develop an EM algorithm to estimate the model parameters. We also obtain standard errors for the parameter estimates of the state process. We consider several types of state processes: independent and identically distributed, independent but depending on a covariate and Markov. Simulation studies show the frequentist properties of our estimates. We apply our methods to a data set of a building's power usage.