Title: $L_2$ boosting for high dimensional locally stationary time series
Authors: Kashif Yousuf - Columbia University (United States) [presenting]
Serena Ng - Columbia University (United States)
Abstract: High dimensional time series analysis has attracted an increasing amount of attention in the econometrics literature in recent years. However, one of the main limiting assumptions made by most works on the topic is assuming stationarity and time invariant effects of the predictors. We study the theoretical properties of $L_2$ boosting for high dimensional time varying coefficient models, where the coefficients are modeled as smooth functions evolving over time and the predictors are locally stationary. We establish consistency of our procedures when using either componentwise local linear or local constant estimators as base learners. Dependence is quantified by functional dependence measures and the asymptotic properties of our methods depend on the moment conditions, the sparsity level, and the strength of dependence in the underlying processes, among other factors. Practical issues such as choosing the bandwidth for the base learners, and the number of boosting iterations are also addressed. Lastly finite sample performance of our procedures is shown through extensive simulation studies, and we include an application to macroeconomic forecasting.