Large Vector Auto Regressions

By Song Song, Peter J. Bickel. 2011

187 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/4e84ed439d38a0e916e028281590f9586193ad06

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Citations in the corpus

Oracle Efficient Estimation and Forecasting with the Adaptive Lasso and the Adaptive Group Lasso in Vector Autoregressions (2012, background): “Some exceptions are Wang ADAPTIVE LASSO AND ADAPTIVE GROUP LASSO IN VARS 3 et al. (2007), Caner and Knight (2011), Kock (2012), Medeiros and Mendes (2012), Song and Bickel (2011), Kock and Callot (2012) and Liao and Phillips (2012).”
Sparse Vector Autoregressive Modeling (2012, methodology): “Then, Lasso can be applied to select the AR coefficients and fit sVAR models, for example, see Valdés-Sosa (2005), Arnold, Liu, and Abe (2008), Lozano et al. (2009), Shojaie and Michailidis (2010), Song and Bickel (2011).”
Regularized estimation in sparse high-dimensional time series models (2013, background): “Some early attempts to establish consistency of VAR models under high-dimensional scaling include Song and Bickel (2011) and Kock and Callot (2012).”
High Dimensional and Banded Vector Autoregressions (2015, methodology): “advocated to use the group lasso penalization. A truncated weighted lasso penalization approach was proposed by Shojaie and Michailidis (2010) to exploring graphical granger causality in a VAR model. Song and Bickel (2011) proposed a lasso penalty for select the variables and lags simultaneously. Bo”
Principal component analysis for second-order stationary vector time series (2014, methodology): “Under different sparsity assumptions, VAR models have been estimated by LASSO regularization [Shojaie and Michailidis (2010), Song and Bickel (2011)], or by the Dantzig selector [Han, Lu and Liu (2015)].”
Oracle Inequalities for High Dimensional Vector Autoregressions (2012, methodology): “Song and Bickel (2011) have derived bounds for the LASSO similar to the ones mentioned in i) above.”
Challenges of Big Data Analysis (2013, unknown): “One solution is to re-sort to sparsity assumptions, under which new statistical tools have been developed [50,51].”
Granger Causality: A Review and Recent Advances (2021, background): “Asymptotic properties of the resulting estimators have also been investigated in high-dimensional settings, where p T (Song and Bickel, 2011; Basu and Michailidis, 2015).”
NETS: Network estimation for time series (2019, unknown): “This paper is also related to the literature on the estimation of sparse VARs (see Basu & Michailidis, 2015; Davis et al., 2016; Kock & Callot, 2015; Medeiros & Mendes, 2016; Song & Bickel, 2011).”
High dimensional stochastic regression with latent factors, endogeneity and nonlinearity (2013, methodology): “LASSO regularization has also been applied in VAR modelling; see, for example, Shojaie and Michailidis (2010) and Song and Bickel (2011).”
Autoregressive models for matrix-valued time series (2018, background): “…modeling with regularization (Davis et al., 2012; Basu and Michailidis, 2015; Guo et al., 2015; Han et al., 2015, 2016; Nicholson et al., 2015; Song and Bickel, 2011; Kock and Callot, 2015; Negahban and Wainwright, 2011; Nardi and Rinaldo, 2011, among others), and (ii) statistical or dynamic…”