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Rank Determination in Tensor Factor Model. (2022). Zhang, Cun-Hui ; Chen, Rong.
In: Papers.
RePEc:arx:papers:2011.07131.

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  1. Dynamic patterns and the latent community structure of sectoral volatility and jump risk contagion. (2024). Gao, Yang ; Zhao, Wandi.
    In: Emerging Markets Review.
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  2. Matrix-variate data analysis by two-way factor model with replicated observations. (2023). Guo, Jianhua ; Huang, Wei ; Gao, Zhigen ; Li, Yan.
    In: Statistics & Probability Letters.
    RePEc:eee:stapro:v:202:y:2023:i:c:s0167715223001281.

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  3. One-way or two-way factor model for matrix sequences?. (2023). Trapani, Lorenzo ; Yu, Long ; Kong, Xinbing ; He, Yong.
    In: Journal of Econometrics.
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  4. Econometrics of Machine Learning Methods in Economic Forecasting. (2023). Striaukas, Jonas ; Ghysels, Eric ; Babii, Andrii.
    In: Papers.
    RePEc:arx:papers:2308.10993.

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  5. Tensor Principal Component Analysis. (2022). Pan, Junsu ; Ghysels, Eric ; Babii, Andrii.
    In: Papers.
    RePEc:arx:papers:2212.12981.

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  1. Adopting similar procedures in the proof of Theorem 1 in Han et al. (2020), we can show Lemma 6. Lemma 7. Suppose Assumptions I, II, III, IV and V(a) hold. Let r1 ≤ r (j) 1 ≤ m1 < d1 for all 1 ≤ j ≤ i − 1, and m1 = O(r1). There exists an event Ω2 such that P(Ω2) ≥ 1 − e−d2 − T exp(−C1Tϑ ) − exp(−C2T), C1, C2 > 0, 1/ϑ = 1/θ1 + 2/θ2 and Ω2 is independent of iteration number i. Then, at i-th iteration, in the event Ω2, for any fixed m with m > r1, M(i) (r1, Û1) − M(i) (m, Û1,m) ≤ Cβd,T , where C > 0, βd,T = d1 Td1+δ0/2 + d 1/2 1 η (i) 1 Td1/2+3δ0/2 , and η (i) k = d 1/2 k dδ1−δ0/2−1/2 + d 1/2 k dδ1−1 .
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  50. Proof. See Lemma 2 in Han et al. (2020). Appendix C: Additional Simulation Results In this section, we show detailed comparison among IC1-IC5, and ER1-ER5 for the first part and third part simulation in Section 5. We also study a strong factor model with r1 = r2 = 2. (M0). Set r1 = r2 = 2. The univariate fijt follows AR(1) with AR coefficient φ11 = φ22 = 0.8 and φ12 = φ21 = 0.3; All elements of A1 and A2 are i.i.d N(0,1).
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  49. A Robust Criterion for Determining the Number of Factors in Approximate Factor Models. (2009). Capasso, Marco ; Barigozzi, Matteo ; Alessi, Lucia.
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