SPEAKER: Dimitris Politis, Distinguished Professor, Mathematics, UC San Diego
TITLE: “Model-free prediction and regression with an application to locally stationary time series”
ABSTRACT: The problem of prediction is revisited with a view towards going beyond the typical nonparametric setting, and reaching a fully model-free environment for predictive inference, i.e., point predictors and prediction intervals. Model-free prediction is based on the notion of transforming a given setup into one that is easier to work with, namely i.i.d. or Gaussian. A prime application is nonparametric regression; the model-free predictors are worked out, and bootstrap prediction intervals are constructed having asymptotic (conditional) validity. Moving to dependent data, with long time series, e.g. annual temperature measurements spanning over 100 years or daily financial returns spanning several years, it may be unrealistic to assume stationarity throughout the span of the dataset. We show how the model-free prediction principle can be applied to handle time series that are only locally stationary, i.e., they can be assumed to be (approximately) stationary only over short time-windows. One-step-ahead point predictors and prediction intervals are constructed, and the performance of model-free is compared to model-based prediction using models that incorporate a trend as well as heteroscedastic/correlated errors. A climate data example helps illustrate the efficacy of model-free prediction.
This joint Statistics/Economics colloquium is part of the STA 290 Seminar Series.
DATE: Tuesday, November 26th, 4:10pm
LOCATION: MSB 1143 (Statistics Seminar Room)
REFRESHMENTS: 3:30pm MSB 4110 (4th floor lounge)