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Updated: May 5, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Correcting and combining time series forecasters.

Paulo Renato A Firmino¹, Paulo S G de Mattos Neto², Tiago A E Ferreira¹

¹Department of Statistics and Informatics, Federal Rural University of Pernambuco, 52171-900, Recife, Pernambuco, Brazil.

Neural Networks : the Official Journal of the International Neural Network Society

|November 19, 2013

Summary

This summary is machine-generated.

This study introduces a two-step method to improve forecasting models by correcting prediction errors using a recursive ARIMA algorithm. This enhances combined forecasting accuracy for financial time series data.

Keywords:

Artificial neural networks hybrid systems Linear combination of forecasts Maximum likelihood estimation Time series forecasters Unbiased forecasters

Related Experiment Videos

Last Updated: May 5, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Area of Science:

Time Series Analysis
Econometrics
Computational Finance

Background:

Traditional forecasting models often assume white noise residuals, which can be violated by uncaptured disturbances.
Accurate modeling of prediction errors is crucial for reliable time series forecasting.

Purpose of the Study:

To introduce a novel two-step method for correcting and combining forecasting models.
To address the violation of the white noise assumption in forecasting residuals.
To improve the accuracy of combined forecasts for financial time series.

Main Methods:

A recursive Autoregressive Integrated Moving Average (ARIMA) algorithm is used to model the stochastic process underlying prediction bias.
The ARIMA adjustment at each step is optimized using an information criterion, such as Akaike's Information Criterion.
A maximum likelihood combined estimator is applied to the bias-corrected predictions.

Main Results:

The proposed method effectively corrects biases in individual forecasting models, leading to white noise residuals.
Demonstrated improved forecasting performance on financial indices including Dow Jones, S&P500, Google, and Nasdaq.
Successfully combined predictions from Autoregressive Integrated Moving Average (ARIMA) and artificial neural networks models.

Conclusions:

The two-step correction and combination method offers a robust framework for enhancing time series forecasting accuracy.
The approach is particularly useful for financial market data where model assumptions may not hold.
This methodology provides a valuable tool for improving the reliability of combined forecasting systems.