Functional linear models. Three types of linear model to consider:. Response is a function; covariates are multivariate. Response is scalar or multivariate; covariates are functional. Both response and covariates are functional. Functional response with multivariate covariates.
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the harmonic acceleration of β(t) . This smooths towards a shifted sinusoid.
Here we have a lot of possibilities. We can predict y(t) using the shape of x(s,t) over:
In this case we have to smooth β(s,t) with respect to both s and t.
The influence of temperature is nearly constant over the year.
Let’s see how the two fits compare.