Variable screening for high dimensional time series

Abstract

High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable screening discuss the time series setting, and even fewer works have developed methods which utilize the unique features of time series data. This paper introduces several model free screening methods based on the partial distance correlation and developed specifically to deal with time dependent data. Methods are developed both for univariate models, such as nonlinear autoregressive models with exogenous predictors (NARX), and multivariate models such as linear or nonlinear VAR models. Sure screening properties are proved for our methods, which depend on the moment conditions, and the strength of dependence in the response and covariate processes, amongst other factors. Dependence is quantified by functional dependence measures (Wu, 2005) and β-mixing coefficients, and the results rely on the use of Nagaev and Rosenthal type inequalities for dependent random variables. Finite sample performance of our methods is shown through extensive simulation studies, and we include an application to macroeconomic forecasting.

Boosting High Dimensional Predictive Regressions with Time Varying Parameters

“…The rest of the proof is essentially the same, if we replace the locally stationary variables with stationary ones. We borrow some arguments from the proof of theorem 2 in Yousuf (2018). The main technical tool we use is theorem 3 in Wu and Wu (2016).…”

“…In contrast, by using the moving average representation for ξ t = ∞ j=0 f j e i−j , we see the functional dependence measure is directly related to the data generating process: δ q (ξ t ) = O(f t ). Additionally, in many cases using functional dependence measures also requires less stringent assumptions (Yousuf, 2018;Wu, 2005). 8 We do note that functional dependence measures are restricted to a more limited class of processes, specifically those possessing the representation (3).…”

Machine learning advances for time series forecasting

“…The CSR forecast is calculated on these variables for different values of $$k$$. This approach is based on the Sure Independence Screening of Fan and Lv (2008), extended to dependent by Yousuf (2018), that aims to select a superset of relevant predictors among a very large set.…”

Testing Big Data in a Big Crisis: Nowcasting under COVID-19

“…Then aggregation is performed for each set of weights and each regressor, resulting in a number of new aggregated regressors equal to the number of original regressors multiplied by the number of weight sets. The selection of aggregated regressors is then performed using the generalized least squares screening (GLSS) proposed in Yousuf (2018). Values of parameters of the weight function originating the most significant aggregated regressors are stored and reused as initial values in a final maximum-likelihood estimation of the MIDAS regression.…”