Three Papers On Time Series Forecasting And Data Privacy

Abstract

The first paper applies receiver operating characteristic (ROC) analysis to microlevel, monthly time series of the M3-Competition. Forecasts from competing methods were used in binary decision rules to forecast exceptionally large declines in demand. Using the partial area under the ROC curve (PAUC) criterion as a forecast accuracy measure and paired-comparison testing via bootstrapping, we find that complex univariate methods perform best for this purpose. The second paper develops a multivariate forecasting model designed for forecasting the largest changes across many time series. Using the partial area under the curve (PAUC) metric, our results show statistical significance, a 35 percent improvement over OLS, and at least a 20 percent improvement over competing methods. The third paper considers a particular maximum likelihood estimator (MLE) and a computationally intensive Bayesian method for differentially private estimation of the linear mixed-effects model (LMM) with normal random errors. The differentially private MLE performs well compared to the regular MLE, and deteriorates as the protection increases for a problem in which the small-area variation is at the county level. The direct Bayesian approach for the same model uses an informative, reasonably diffuse prior to compute the posterior predictive distribution for the random effects and the empirical differential privacy is estimated.