Dynamic structural models with covariates for short-term forecasting of time series with complex seasonal patterns

Area of Science:

• Statistics
• Econometrics
• Time Series Analysis

Background:

• Accurate short-term forecasting of time series with complex seasonality is challenging.
• Existing models may not adequately capture dynamic changes in seasonal components.

Purpose of the Study:

• To present a novel framework for dynamic structural models with covariates.
• To improve short-term time series forecasting for data exhibiting complex seasonal patterns.

Main Methods:

• Utilizes a multiple sources of randomness formulation.
• Incorporates a noise model for seasonal components and time-varying coefficients.
• Employs a recursive maximum likelihood estimation procedure combining Kalman filter and covariance matrix adjustment.
• Applies a non-parametric bootstrap approach for enhanced forecasting.

Main Results:

• The proposed method effectively forecasts time series with complex seasonal patterns.
• The framework allows for estimation of system states, parameter standard errors, and prediction intervals.
• Empirical validation on two real time series demonstrates the framework's utility.

Conclusions:

• The dynamic structural model framework offers a robust approach to short-term time series forecasting.
• The integration of Kalman filtering and bootstrap methods enhances predictive accuracy and provides reliable uncertainty estimates.