Dynamic factor models with infinite-dimensional factor spaces: One-sided representations

By M. Forni, Marc Hallin, Marco Lippi, Paolo Zaffaroni. 2015

120 citations recorded by the source corpus.

Factor model methods recently have become extremely popular in the theory and practice of large panels of time series data. Those methods rely on various factor models which all are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forniet al. (2000). That paper, however, rests on Brillinger’s dynamic principal components. The corresponding estimators are two-sided filters whose performance at the end of the observation period or for forecasting purposes is rather poor. No such problem arises with estimators based on standard principal components, which have been dominant in this literature. On the other hand, those estimators require the assumption that the space spanned by the factors has finite dimension. In the present paper, we argue that such an assumption is extremely restrictive and potentially quite harmful. Elaborating upon recent results by Anderson and Deistler (2008a, b) on singular stationary processes with rational spectrum, we obtain one-sided representations for the GDFM without assuming finite dimension of the factor space. Construction of the corresponding estimators is also briefly outlined. In a companion paper, we establish consistency and rates for such estimators, and provide Monte Carlo results further motivating our approach.

Subfields: Computational Theory and Mathematics, Finance

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Citations in the corpus

Sufficient Forecasting Using Factor Models (2015, methodology): “For example, Forni et al. (2000, 2015) studied factor estimation based on projection, Liu et al. (2012), Xue and Zou (2012) and Fan et al. (2015b) employed rank-based methods for robust estimation of the covariance matrices, and Connor et al. (2012) applied a weighted additive nonparametric…”
Generalized dynamic factor models and volatilities: recovering the market volatility shocks (2016, unknown): “The analysis then can be conducted along the same ways as for the Y it 's in Section 3.1, applying the Forni et al. (2015) methodology to the 2n-dimensional panel (2.14).”
Generalized dynamic factor models and volatilities: estimation and forecasting (2017, methodology): “…of generality and for the simplicity ofn tation, thatn is an integer multiple of (q+1), that is,n = m(q+1) for somem ∈ N. Forni and Lippi (2011) and Forni et al. (2015b) show that, under Assumptions (A1)-(A3) and the mild additional condition of a rational spectrum, there exist anm(q+1)×m(q+1)…”
Dynamic factor model with infinite‐dimensional factor space: Forecasting (2016, methodology): “A motivation for studying model (2.1) without assumption (2.3), as argued in Forni et al. (2015, 2017), is that model (2.3) rules out cases as simple as xit = ci 1− diL ut + ξit = ci(ut + diut−1 + d 2 iut−2 + · · · ) + ξit, (2.5) i ∈ N, where ut is a scalar white noise.”
Statistical Inference for High-Dimensional Matrix-Variate Factor Models (2020, background): “Forni et al. (2015, 2017) proposed a full dynamic factor model for vector time series which include both covariance and auto-covariance.”
Principal Component Analysis of High-Frequency Data (2016, unknown): “The above factor models are static, as opposed to the dynamic factor models discussed in Forni et al. (2000, 2004), Forni and Lippi (2001), and their recent extensions with infinite-dimensional factor space discussed in Forni et al. (2015, 2017), for which frequency domain PCA is applied.”
Non-Stationary Dynamic Factor Models for Large Datasets (2016, methodology): “Last, our approach could be generalized to build an unrestricted Non-Stationary DMF, similar to the one proposed by Forni et al. (2017, 2015) for stationary data.”
Generalized Dynamic Principal Components (2016, methodology): “Forni, Hallin, Lippi, and Reichlin (2000) proposed a very general dynamic factor model allowing for an infinite number of factor lags and low correlation between any two idiosyncratic components. They show that the common component of the series can be consistently estimated by increasing the number”