Puyi Fang, Zhaoxing Gao, Ruey S. Tsay
arXiv 24 Apr 2023 · Econometrics · publishedJournal of Business and Economic Statistics (2025)
arXiv:2304.12134 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes a new approach to identifying the effective cointegration rank in high-dimensional unit-root (HDUR) time series from a prediction perspective using reduced-rank regression. For a HDUR process $\mathbf{x}_t\in \mathbb{R}^N$ and a stationary series $\mathbf{y}_t\in \mathbb{R}^p$ of interest, our goal is to predict future values of $\mathbf{y}_t$ using $\mathbf{x}_t$ and lagged values of $\mathbf{y}_t$. The proposed framework consists of a two-step estimation procedure. First, the Principal Component Analysis is used to identify all cointegrating vectors of $\mathbf{x}_t$. Second, the co-integrated stationary series are used as regressors, together with some lagged variables of $\mathbf{y}_t$, to predict $\mathbf{y}_t$. The estimated reduced rank is then defined as the effective cointegration rank of $\mathbf{x}_t$. Under the scenario that the autoregressive coefficient matrices are sparse (or of low-rank), we apply the Least Absolute Shrinkage and Selection Operator (or the reduced-rank techniques) to estimate the autoregressive coefficients when the dimension involved is high. Theoretical properties of the estimators are established under the assumptions that the dimensions $p$ and $N$ and the sample size $T \to \infty$. Both simulated and real examples are used to illustrate the proposed framework, and the empirical application suggests that the proposed procedure fares well in predicting stock returns.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bai, Jushan (2004) Estimating cross-section common stochastic trends in nonstationary panel data | 1.000 | 9 | 3 | 100% |
| 2 | Reinsel, Gregory C, Velu, Raja P, Chen, Kun (2022) Multivariate reduced-rank regression: theory and applications (2nd ed.). | 1.000 | 6 | 3 | 100% |
| 3 | Negahban, Sahand, Wainwright, Martin J (2011) Estimation of (near) low-rank matrices with noise and high-dimensional scaling | 1.000 | 5 | 3 | 100% |
| 4 | Poncela, Pilar (2006) Nonstationary dynamic factor analysis | 0.928 | 5 | 3 | 80% |
| 5 | Gao, Zhaoxing, Tsay, Ruey S (2021) Modeling high-dimensional unit-root time series self | 0.909 | 8 | 4 | 75% |
| 6 | Koo, Bonsoo, Anderson, Heather M, Seo, Myung Hwan, Yao, Wenying (2020) High-dimensional predictive regression in the presence of cointegration | 0.874 | 11 | 2 | 100% |
| 7 | Bai, Jushan, Ng, Serena (2002) Determining the number of factors in approximate factor models | 0.843 | 3 | 3 | 100% |
| 8 | Zhang, Rongmao, Robinson, Peter, Yao, Qiwei (2019) Identifying cointegration by eigenanalysis | 0.843 | 3 | 3 | 100% |
| 9 | Tsay, Ruey S (2014) Multivariate time series analysis: with R and financial applications self | 0.737 | 3 | 2 | 100% |
| 10 | Welch, Ivo, Goyal, Amit (2008) A comprehensive look at the empirical performance of equity premium prediction | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 48 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Robust Estimation in Network Vector Autoregression with Nonstationary Regressors | 0.405 | 1 | 1 |