Nonparametric additive factor models using sieve methods
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This paper proposes a nonparametric additive factor model where the common components depend on the latent factors through unknown smooth functions. Our approach is novel in the literature on nonlinear factor models as we propose a general and rigorous framework for identification, specify a general nonparametric and flexible estimation procedure based on sieve methods, and derive consistency results. The key point of our strategy relies on the specification of an asymptotic parameter space for the factors. Estimation is then obtained by using sieve approximations of this infinite dimensional factor space. We prove convergence of the sieve estimators as both time and cross-sectional sizes increase at appropriate rates. The finite sample performance of the estimators is illustrated in extensive numerical experiments. Finally, we show relevance and usefulness of our method by an application to a nonlinear CAPM on S P500 data.
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