Statistical inference, the bootstrap, and neural-network modeling with application to foreign exchange rates.

Area of Science:

• * Statistics
• * Machine Learning
• * Econometrics

Background:

• * Feedforward neural networks are increasingly used for statistical modeling.
• * Determining the relevance of input variables is crucial for valid inference.
• * Existing methods may not adequately assess input importance in complex models.

Purpose of the Study:

• * To propose novel statistical tests for assessing input irrelevance in neural networks.
• * To enable valid statistical inference by identifying essential model inputs.
• * To investigate the predictability of foreign exchange rates using these tests.

Main Methods:

• * Development of tests for individual and joint irrelevance of network inputs.
• * Application of statistical resampling techniques (e.g., Monte Carlo simulations).
• * Empirical analysis of foreign exchange rate data.

Main Results:

• * Proposed tests demonstrate reasonable level and power in simulations.
• * Foreign exchange rates contain information useful for improved point prediction.
• * The predictive relationships within exchange rates are dynamic and evolve over time.

Conclusions:

• * The developed tests provide a robust framework for input selection in neural networks.
• * Statistical significance of inputs can be rigorously evaluated.
• * Foreign exchange markets exhibit time-varying predictability, offering opportunities for adaptive forecasting.