First-order linear ordinary differential equation for regression modelling
This paper discusses the data-driven regression modelling using firstorder linear ordinary differential equation (ODE). First, we consider a set of actual data and calculate the numerical derivative. Then, a general equation for the firstorder linear ODE is introduced. There are two parameters, nam...
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| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2024
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/10906/1/P16588_f1c1ba8ad6226f1e7b00e8b320332fa2.pdf http://eprints.uthm.edu.my/10906/ http://10.3233/FAIA231184 |
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| Summary: | This paper discusses the data-driven regression modelling using firstorder linear ordinary differential equation (ODE). First, we consider a set of actual
data and calculate the numerical derivative. Then, a general equation for the firstorder linear ODE is introduced. There are two parameters, namely the regression
parameters, in the equation, and their value will be determined in regression modelling. After this, a loss function is defined as the sum of squared errors to minimize
the differences between estimated and actual data. A set of necessary conditions
is derived, and the regression parameters are analytically determined. Based on
these optimal parameter estimates, the solution of the first-order linear ODE, which
matches the actual data trend, shall be obtained. Finally, two financial examples,
the sales volume of Proton cars and the housing index, are illustrated. Simulation
results show that an appropriate first-order ODE model for these examples can be
suggested. From our study, the practicality of using the first-order linear ODE for
regression modelling is significantly demonstrate |
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