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Trends in terrestrial temperature variability are perhaps more relevant for species viability than trends in mean temperature. In this paper, we develop methodology for estimating such trends using multi-resolution climate data from polar orbiting weather satellites. We derive two novel algorithms for computation that are tailored for dense, gridded observations over both space and time. We evaluate our methods with a simulation that mimics these data's features and on a large, publicly available, global temperature dataset with the eventual goal of tracking trends in cloud reflectance temperature variability., Comment: Published in AAAI-19

We derive generalization error bounds for traditional time-series forecasting models. Our results hold for many standard forecasting tools including autoregressive models, moving average models, and, more generally, linear state-space models. These non-asymptotic bounds need only weak assumptions on the data-generating process, yet allow forecasters to select among competing models and to guarantee, with high probability, that their chosen model will perform well. We motivate our techniques with and apply them to standard economic and financial forecasting tools---a GARCH model for predicting equity volatility and a dynamic stochastic general equilibrium model (DSGE), the standard tool in macroeconomic forecasting. We demonstrate in particular how our techniques can aid forecasters and policy makers in choosing models which behave well under uncertainty and mis-specification., Comment: 34 pages, 3 figures

The literature on statistical learning for time series assumes the asymptotic independence or ``mixing' of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an estimator for the $\beta$-mixing rate based on a single stationary sample path and show it is $L_1$-risk consistent., Comment: 9 pages, accepted by AIStats. CMU Statistics Technical Report