We extend the feature selection methodology to dependent data and propose a novel time series predictor selection scheme that accommodates statistical dependence in a more typical i.i.d sub-sampling based framework. Furthermore, the machinery of mixing stationary processes allows us to quantify the improvements of our approach over any base predictor selection method (such as lasso) even in a finite sample setting. Using the lasso as a base procedure we demonstrate the applicability of our methods to simulated and several real time series datasets.
Most existing predictor selection methods in time series are largely based on heuristics, @cite_22 or simply use plain lasso @cite_8 @cite_14 on the entire data and it is non-trivial to provide guarantees for such methods. For the specific case of vector auto regression (VAR) models, propose a grouped penalty based approach that provably identifies relevant lags and predictors in the asymptotic @math (number of time series) and @math (number of lags) regime. Our method is of a fundamentally distinct flavor in that we provide quantifiable improvement over any base predictor selection method, including the method in @cite_7 , even in the finite data (sample or dimension) setting. Moreover our approach also works for the more general VAR-X (VAR with exogenous) model and in general is independent of the base predictor selection mechanism.
@cite_14 @cite_22 @cite_7 @cite_8
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(2014) have recently demonstrated how to efficiently combine information from a set of popular technical indicators together with the standard Goyal and Welch (2008) predictor variables widely used in the equity premium forecasting literature to improve out-of-sample forecasts of the equity premium using a small number of principal components. We show that forecasts of the equity premium can be further improved by, first, incorporating broader macroeconomic data into the information set, second, improving the selection of the most relevant factors and combining the most relevant factors by means of a forecast combination regression, and third, imposing theoretically motivated positivity constraints on the forecasts of the equity premium. We find that in particular our proposed forecast combination approach, which combines forecasts of the most relevant (2014) and macroeconomic factors and further imposes positivity constraints on the equity premium forecasts, generates statistically significant and economically sizeable improvements over the best performing model of (2014). This chapter reviews methods for selecting empirically relevant predictors from a set of N potentially relevant ones for the purpose of forecasting a scalar time series. First, criterion-based procedures in the conventional case when N is small relative to the sample size, T, are reviewed. Then the large N case is covered. Regularization and dimension reduction methods are then discussed. Irrespective of the model size, there is an unavoidable tension between prediction accuracy and consistent model determination. Simulations are used to compare selected methods from the perspective of relative risk in one period ahead forecasts. One popular approach for nonstructural economic and financial forecasting is to include a large number of economic and financial variables, which has been shown to lead to significant improvements for forecasting, for example, by the dynamic factor models. A challenging issue is to determine which variables and (their) lags are relevant, especially when there is a mixture of serial correlation (temporal dynamics), high dimensional (spatial) dependence structure and moderate sample size (relative to dimensionality and lags). To this end, an integrated solution that addresses these three challenges simultaneously is appealing. We study the large vector auto regressions here with three types of estimates. We treat each variable's own lags different from other variables' lags, distinguish various lags over time, and is able to select the variables and lags simultaneously. We first show the consequences of using Lasso type estimate directly for time series without considering the temporal dependence. In contrast, our proposed method can still produce an estimate as efficient as an oracle under such scenarios. The tuning parameters are chosen via a data driven "rolling scheme" method to optimize the forecasting performance. A macroeconomic and financial forecasting problem is considered to illustrate its superiority over existing estimators. Accurate real-time tracking of influenza outbreaks helps public health officials make timely and meaningful decisions that could save lives. We propose an influenza tracking model, ARGO (AutoRegression with GOogle search data), that uses publicly available online search data. In addition to having a rigorous statistical foundation, ARGO outperforms all previously available Google-search–based tracking models, including the latest version of Google Flu Trends, even though it uses only low-quality search data as input from publicly available Google Trends and Google Correlate websites. ARGO not only incorporates the seasonality in influenza epidemics but also captures changes in people’s online search behavior over time. ARGO is also flexible, self-correcting, robust, and scalable, making it a potentially powerful tool that can be used for real-time tracking of other social events at multiple temporal and spatial resolutions.