High dimensional stochastic regression with latent factors, endogeneity and nonlinearity

By Jinyuan Chang, Bin Guo, Qiwei Yao. 2013

72 citations recorded by the source corpus.

We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors, and a vector white noise. We investigate the inference without imposing stationary conditions on the target multivariate time series, the regressors and the underlying factors. Furthermore we deal with the endogeneity that there exist correlations between the observed regressors and the unobserved factors. We also consider the model with nonlinear regression term which can be approximated by a linear regression function with a large number of regressors. The convergence rates for the estimators of regression coefficients, the number of factors, factor loading space and factors are established under the settings when the dimension of time series and the number of regressors may both tend to infinity together with the sample size. The proposed method is illustrated with both simulated and real data examples.

View Paper: https://www.semanticscholar.org/paper/57c71390556ce373afe50ae20b0c95ebb0797ab6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Jinyuan Chang
2. Jingjing He
3. Qiwei Yao
4. Lin Yang
5. Rong Chen
6. Dong Wang
7. Bin Guo
8. Xialu Liu

Citations in the corpus

• Constrained Factor Models for High-Dimensional Matrix-Variate Time Series (2017, unknown): “…factor analysis of such data either converts the matrix into a vector or modeling the row or column vectors separately (Chamberlain 1983, Chamberlain & Rothschild 1983, Bai 2003, Bai & Ng 2002, 2007, Forni et al. 2000, 2004, Pan & Yao 2008, Lam et al. 2011, Lam & Yao 2012, Chang et al. 2015).”
• Modelling matrix time series via a tensor CP-decomposition (2021, methodology): “Since rank(K1,q) = d, following Chang et al. (2015), we can estimate d as d̂ = arg min j∈[R] λ̂j+1(K̂1,q) + cn λ̂j(K̂1,q) + cn , (16) where R = bαmin(p, q)c for a prescribed constant α ∈ (0, 1) and some cn → 0+ as n → ∞.”
• Factor models for matrix-valued high-dimensional time series (2016, background): “…assumes that the factors should capture all dynamics of the observed process, hence the idiosyncratic noise process has no serial dependence (but may have strong cross-sectional dependence), see Pan and Yao (2008); Lam et al. (2011); Lam and Yao (2012); Chang et al. (2015); Liu and Chen (2016).”
• Principal component analysis for second-order stationary vector time series (2014, methodology): “j,t + n−k n y¯i,·y¯j,· − k n E(yi,t+kyj,t) = I 1+I 2 +I 3+I 4 +I 5, (7.4) where ¯yi,· = n−1 P n t=1yi,t and ¯yj,· = n −1 P t=1yj,t. By Davydov inequality, following the same arguments of Lemma 6.1 in Chang et al. (2013a), we have I 1 = Op(n−1/2), I 2 = Op(n−1), I 3 = Op(n−1), I 4 = Op(n−1), I 5 = Op”