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Automated Time Series Forecasting for Biosurveillance

in the above paper, page 4, two models, non-adaptive regression model, adaptive regression model, the non-adaptive regression model's parameter estimation method is "least squares", what is the parameter estimation for the adaptive regression model? is there any package in R to do parameter estimation for this kind of adaptive regression model? If I add more predictors in the adaptive regression model, can R still solve it? and how?

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