arXiv 5 May 2020 · Statistics — Methodology · publishedInternational Journal of Forecasting (2020) · 8 citations (OpenAlex)
arXiv:2005.03496 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes a new procedure to build factor models for high-dimensional unit-root time series by postulating that a $p$-dimensional unit-root process is a nonsingular linear transformation of a set of unit-root processes, a set of stationary common factors, which are dynamically dependent, and some idiosyncratic white noise components. For the stationary components, we assume that the factor process captures the temporal-dependence and the idiosyncratic white noise series explains, jointly with the factors, the cross-sectional dependence. The estimation of nonsingular linear loading spaces is carried out in two steps. First, we use an eigenanalysis of a nonnegative definite matrix of the data to separate the unit-root processes from the stationary ones and a modified method to specify the number of unit roots. We then employ another eigenanalysis and a projected principal component analysis to identify the stationary common factors and the white noise series. We propose a new procedure to specify the number of white noise series and, hence, the number of stationary common factors, establish asymptotic properties of the proposed method for both fixed and diverging $p$ as the sample size $n$ increases, and use simulation and a real example to demonstrate the performance of the proposed method in finite samples. We also compare our method with some commonly used ones in the literature regarding the forecast ability of the extracted factors and find that the proposed method performs well in out-of-sample forecasting of a 508-dimensional PM$_{2.5}$ series in Taiwan.
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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 | 19 | 3 | 100% |
| 2 | Tiao, G. C., and Tsay, R. S. (1989). Model specification in multivar… Journal of the Royal Statistical Society, B51, 157–213 self | 1.000 | 9 | 3 | 100% |
| 3 | Peña, D., and Poncela, P. (2006). Nonstationary dynamic factor analy… Journal of Statistical Planning and Inference, 136(4), 1237–1257 | 0.956 | 8 | 4 | 88% |
| 4 | Zhang, R., Robinson, P., and Yao, Q. (2019). Identifying cointegrati… Journal of the American Statistical Association, 114(526), 916–927 | 0.932 | 21 | 6 | 81% |
| 5 | Lam, C., and Yao, Q (2012) Factor modeling for high-dimensional time series: inference for the number of factors | 0.928 | 4 | 4 | 100% |
| 6 | Gao, Z., and Tsay, R. S (2020) Modeling high-dimensional time series: a factor model with dynamically dependent factors and diverging eigenvalues self | 0.880 | 22 | 6 | 68% |
| 7 | Bai, J., and Ng, S (2002) Determining the number of factors in approximate factor models | 0.874 | 7 | 2 | 100% |
| 8 | Banerjee, A., Marcellino, M., and Masten, I (2014) Forecasting with factor-augmented error correction models | 0.874 | 7 | 2 | 100% |
| 9 | Gao, Z., and Tsay, R. S (2019) A structural-factor approach for modeling high-dimensional time series and space-time data self | 0.737 | 3 | 3 | 67% |
| 10 | Box, G. E. P., and Tiao, G. C (1977) A canonical analysis of multiple time series | 0.737 | 3 | 2 | 100% |
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