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Research output: Working paper › Research

**Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span.** / Andersen, Torben Gustav; Fusari, Nicola ; Todorov, Viktor; Varneskov, Rasmus T.

Research output: Working paper › Research

Andersen, TG, Fusari, N, Todorov, V & Varneskov, RT 2018 'Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span' Institut for Økonomi, Aarhus Universitet, Aarhus.

Andersen, T. G., Fusari, N., Todorov, V., & Varneskov, R. T. (2018). *Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span*. Institut for Økonomi, Aarhus Universitet. CREATES Research Papers, No. 2018-03

Andersen TG, Fusari N, Todorov V, Varneskov RT. 2018. Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span. Aarhus: Institut for Økonomi, Aarhus Universitet.

Andersen, Torben Gustav et al. *Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span*. Aarhus: Institut for Økonomi, Aarhus Universitet. (CREATES Research Papers; Journal number 2018-03). 2018., 74 p.

Andersen TG, Fusari N, Todorov V, Varneskov RT. Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span. Aarhus: Institut for Økonomi, Aarhus Universitet. 2018 Jan 10.

Andersen, Torben Gustav ; Fusari, Nicola ; Todorov, Viktor ; Varneskov, Rasmus T. / **Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span**. Aarhus : Institut for Økonomi, Aarhus Universitet, 2018. (CREATES Research Papers; No. 2018-03).

@techreport{27911954585d4d0a9c867c6a3812c694,

title = "Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span",

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",

author = "Andersen, {Torben Gustav} and Nicola Fusari and Viktor Todorov and Varneskov, {Rasmus T.}",

year = "2018",

month = jan,

day = "10",

language = "English",

series = "CREATES Research Papers",

publisher = "Institut for {\O}konomi, Aarhus Universitet",

number = "2018-03",

type = "WorkingPaper",

institution = "Institut for {\O}konomi, Aarhus Universitet",

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TY - UNPB

T1 - Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span

AU - Andersen, Torben Gustav

AU - Fusari, Nicola

AU - Todorov, Viktor

AU - Varneskov, Rasmus T.

PY - 2018/1/10

Y1 - 2018/1/10

N2 - 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.

AB - 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.

KW - Asymptotic Bias, Incidental Parameter Problem, Inference, Large Data Sets, Nonlinear Factor Model, Options, Panel Data, Stable Convergence, Stochastic Volatility

M3 - Working paper

T3 - CREATES Research Papers

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

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -