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Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span

Torben Andersen (), Nicola Fusari (), Viktor Todorov () and Rasmus T. Varneskov ()
Additional contact information
Nicola Fusari: The Johns Hopkins University Carey Business School, Postal: The Johns Hopkins University Carey Business School, Baltimore, MD 21202, USA
Viktor Todorov: Northwestern University, Postal: Department of Finance, Kellogg School of Management, Northwestern University, Evanston, IL 60208, USA
Rasmus T. Varneskov: Northwestern University and CREATES, Postal: Department of Finance, Kellogg School of Management, Northwestern University, Evanston, IL 60208; CREATES, Aarhus, Denmark; Multi Assets at Nordea Asset Management, Copenhagen, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: We provide unifying inference theory for parametric nonlinear factor models based on a panel of noisy observations. The panel has a large cross-section and a time span that may be either small or large. Moreover, we incorporate an additional source of information provided by noisy observations on some known functions of the factor realizations. The estimation is carried out via penalized least squares, i.e., by minimizing the L_2 distance between observations from the panel and their model-implied counterparts, augmented by a penalty for the deviation of the extracted factors from the noisy signals for them. When the time dimension is fixed, the limit distribution of the parameter vector is mixed Gaussian with conditional variance depending on the path of the factor realizations. On the other hand, when the time span is large, the convergence rate is faster and the limit distribution is Gaussian with a constant variance. In this case, however, we incur an incidental parameter problem since, at each point in time, we need to recover the concurrent factor realizations. This leads to an asymptotic bias that is absent in the setting with a fixed time span. In either scenario, the limit distribution of the estimates for the factor realizations is mixed Gaussian, but is related to the limiting distribution of the parameter vector only in the scenario with a fixed time horizon. Although the limit behavior is very different for the small versus large time span, we develop a feasible inference theory that applies, without modification, in either case. Hence, the user need not take a stand on the relative size of the time dimension of the panel. Similarly, we propose a time-varying data-driven weighting of the penalty in the objective function, which enhances effciency by adapting to the relative quality of the signal for the factor realizations.

Keywords: Asymptotic Bias; Incidental Parameter Problem; Inference; Large Data Sets; Nonlinear Factor Model; Options; Panel Data; Stable Convergence; Stochastic Volatility (search for similar items in EconPapers)
JEL-codes: C51 C52 G12 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Date: 2018-01-10
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