Abstract
We are interested in obtaining forecasts for multiple time series, by taking into account the potential nonlinear relationships between their observations. For this purpose, we use a specific type of regression model on an augmented dataset of lagged time series. Our model is inspired by dynamic regression models (Pankratz 2012), with the response variable’s lags included as predictors, and is known as Random Vector Functional Link (RVFL) neural networks. The RVFL neural networks have been successfully applied in the past, to solving regression and classification problems. The novelty of our approach is to apply an RVFL model to multivariate time series, under two separate regularization constraints on the regression parameters.
Highlights
In this paper, we are interested in obtaining forecasts for multiple time series, by taking into account the potential nonlinear relationships between their observations
As a basis for our model, we will userandomized neural networks known as Random Vector Functional Link neural networks (RVFL networks hereafter)
To the best of our knowledge, randomized neural networks were introduced by Schmidt et al (1992), and the RVFL networks were introduced by Pao et al (1994)
Summary
We are interested in obtaining forecasts for multiple time series, by taking into account the potential nonlinear relationships between their observations. In addition to the direct link, there are new features: the hidden nodes (the dataset is augmented), that help to capture the nonlinear relationships between the time series These new features are obtained by random simulation over a given interval. We will obtain point forecasts and predictive distributions for the series, and see that in this RVFL framework, one (or more) variable(s) can be stressed, and influence the others About this last point, it means that it is possible, as in dynamic regression models (Pankratz 2012) to assign a specific future value to one regressor, and obtain forecasts of the remaining variables. Another advantage of the model described here is its ability to integrate multiple other exogenous variables, without overfitting in-sample data
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