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Forecasting volatility with neural regression: a contribution to model adequacy.

A N Refenes¹, W T Holt

¹Department of Decision Sciences, London Business School, London NW1 4SA, UK.

IEEE Transactions on Neural Networks

|February 6, 2008

Summary

This study introduces a new misspecification testing method for neural networks, enhancing forecasting accuracy. The generalized Durbin-Watson statistic helps validate neural models, crucial for reliable predictions in finance.

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Area of Science:

Econometrics
Computational Statistics
Machine Learning

Background:

Neural networks offer advanced forecasting but suffer from overfitting and lack rigorous testing procedures.
Existing methods for model identification, selection, and adequacy testing are insufficient for neural networks.
Residual analysis is a necessary, though not sufficient, condition for validating data-generating processes.

Purpose of the Study:

To develop a methodology for neural model misspecification testing.
To introduce a generalized Durbin-Watson statistic for neural regression.
To establish rigorous procedures for neural model identification, selection, and adequacy testing.

Main Methods:

Generalization of the Durbin-Watson statistic for neural regression.
Derivation of a generalized influence matrix for neural estimators.
Monte Carlo simulations to compare test power against linear regressors.
Application to forecasting implied volatility innovations using high-frequency stock options data.

Main Results:

The proposed methodology provides a generalized Durbin-Watson statistic for neural networks.
Monte Carlo simulations demonstrate the test's power in detecting misspecification.
Application to implied volatility innovations confirmed nonlinear relationships and model adequacy.
Statistical tests validated variable significance and overall model adequacy.

Conclusions:

The developed misspecification testing methodology is essential for validating neural network models.
This work advances rigorous procedures for neural network model identification, selection, and adequacy testing.
The approach is effective in complex financial forecasting tasks, confirming nonlinear dynamics in implied volatility.