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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Nonparametric estimation of functional dynamic factor model
AU - Martínez-Hernández, Israel
AU - Gonzalo, Jesús
AU - González-Farías, Graciela
PY - 2022/10/2
Y1 - 2022/10/2
N2 - Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for functional data. In this paper, we study functional factor models for time-dependent functional data. We propose nonparametric estimators under stationary and nonstationary processes. We obtain estimators that consider the time-dependence property. Specifically, we use the information contained in the covariances at different lags. We show that the proposed estimators are consistent. Through Monte Carlo simulations, we find that our methodology outperforms estimators based on functional principal components. We also apply our methodology to monthly yield curves. In general, the suitable integration of time-dependent information improves the estimation of the latent factors.
AB - Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for functional data. In this paper, we study functional factor models for time-dependent functional data. We propose nonparametric estimators under stationary and nonstationary processes. We obtain estimators that consider the time-dependence property. Specifically, we use the information contained in the covariances at different lags. We show that the proposed estimators are consistent. Through Monte Carlo simulations, we find that our methodology outperforms estimators based on functional principal components. We also apply our methodology to monthly yield curves. In general, the suitable integration of time-dependent information improves the estimation of the latent factors.
KW - Functional cointegration
KW - functional dynamic factor model
KW - functional time series
KW - I(1) functional process
KW - long-run covariance operator
U2 - 10.1080/10485252.2022.2080825
DO - 10.1080/10485252.2022.2080825
M3 - Journal article
VL - 34
SP - 895
EP - 916
JO - Journal of Nonparametric Statistics
JF - Journal of Nonparametric Statistics
SN - 1048-5252
IS - 4
ER -