Matteo Barigozzi, Lorenzo Trapani
arXiv 10 Jun 2018 · Statistics — Methodology · 2 citations (OpenAlex)
arXiv:1806.03647 · PDF · DOI · OpenAlex · Extracted main text
We propose a procedure to determine the dimension of the common factor space in a large, possibly non-stationary, dataset. Our procedure is designed to determine whether there are (and how many) common factors (i) with linear trends, (ii) with stochastic trends, (iii) with no trends, i.e. stationary. Our analysis is based on the fact that the largest eigenvalues of a suitably scaled covariance matrix of the data (corresponding to the common factor part) diverge, as the dimension $N$ of the dataset diverges, whilst the others stay bounded. Therefore, we propose a class of randomised test statistics for the null that the $p$-th eigenvalue diverges, based directly on the estimated eigenvalue. The tests only requires minimal assumptions on the data, and no restrictions on the relative rates of divergence of $N$ and $T$ are imposed. Monte Carlo evidence shows that our procedure has very good finite sample properties, clearly dominating competing approaches when no common factors are present. We illustrate our methodology through an application to US bond yields with different maturities observed over the last 30 years. A common linear trend and two common stochastic trends are found and identified as the classical level, slope and curvature factors.
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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, J (2004) Estimating cross-section common stochastic trends in nonstationary panel data | 1.000 | 10 | 5 | 100% |
| 2 | Maciejowska, K (2010) Common factors in nonstationary panel data with a deterministic trend–estimation and distribution theory | 0.941 | 6 | 4 | 83% |
| 3 | Trapani, L (2017) A randomised testing procedure to determine the number of factors self | 0.843 | 15 | 6 | 60% |
| 4 | Zhang, R., P. Robinson, and Q. Yao (2018) Identifying cointegration by eigenanalysis | 0.811 | 4 | 2 | 100% |
| 5 | Ahn, S. C. and A. R. Horenstein (2013) Eigenvalue ratio test for the number of factors | 0.644 | 2 | 2 | 100% |
| 6 | Bai, J. and S. Ng (2002) Determining the number of factors in approximate factor models | 0.644 | 2 | 2 | 100% |
| 7 | Corradi, V. and N. R. Swanson (2006) The effects of data transformation on common cycle, cointegration, and unit root tests: Monte Carlo and a simple test | 0.644 | 2 | 2 | 100% |
| 8 | Zhang, B., G. Pan, and J. Gao (2017) CLT for largest eigenvalues and unit root tests for high-dimensional nonstationary time series | 0.644 | 2 | 2 | 100% |
| 9 | Bai, J. and S. Ng (2004) A panic attack on unit roots and cointegration | 0.585 | 3 | 1 | 100% |
| 10 | Duffie, D., L. Saita, and K. Wang (2007) Multi-period corporate default prediction with stochastic covariates | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 53 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | High-Dimensional Forecasting in the Presence of Unit Roots and Cointegration | 0.405 | 1 | 1 |
| 2 | Sequential monitoring for cointegrating regressions | 0.000 | 1 | 1 |