Mitigating the choice of the duration in DDMS models through a parametric link

Area of Science:

• Econometrics
• Statistical Modeling
• Time Series Analysis

Background:

• Duration-dependent Markov-switching (DDMS) models are crucial for time series analysis.
• A key hyper-parameter, hidden state duration, lacks established estimation or testing procedures.
• Current ad hoc duration choices require heuristic justification, limiting model reliability.

Purpose of the Study:

• To propose and examine a novel methodology for mitigating the choice of duration in DDMS models.
• To enhance forecasting accuracy in DDMS models by increasing model flexibility.
• To introduce a new parametric link function for modeling transition probabilities in DDMS.

Main Methods:

• Utilized the asymmetric Aranda-Ordaz parametric link function to model transition probabilities.
• Replaced the commonly applied logit link function with the proposed asymmetric Aranda-Ordaz link.
• Conducted two Monte Carlo simulations and an empirical investigation using S&P500 volatility data.

Main Results:

• The proposed methodology effectively compensates for incorrect duration choices through the link function's parameter.
• The asymmetric Aranda-Ordaz link function increases the flexibility of DDMS models.
• Demonstrated the model's capability in forecasting the volatility of the S&P500 index.

Conclusions:

• The novel methodology offers a more robust approach to duration selection in DDMS models for forecasting.
• The asymmetric Aranda-Ordaz link function provides a flexible alternative to traditional link functions.
• The proposed model shows promise for practical applications in financial time series forecasting.