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Interesting thought. Some questions and responses below.
It's not necessary, because there is a simple way you can get access to it: (design-wise, it would also not be desirable, since the user would have to "feed" information that the estimator should already know)
May I ask what your idea is, here? There might not be a "canonical" way to do this, but of course adding this - perhaps as a new estimator - is welcome. |
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In the context of time series, PolynomialTrendForecaster is simply an OLS where we add the explanatory variables t, t^2, ..., t^p and possibly t^0 if we allow an intercept, where p is the degree of the polynomial. If we make the standard assumption that the residuals of the fit are IID N(0, sigma^2), we use the fit to estimate sigma^2. A forecast has a Student's t-distribution with n-p (or n - (p+1)) d.f. where n = # of observations in the training set. It's fairly straightforward to carry this out. I wasn't sure that _fit was allowed to retain information, but if that's allowable then all is good. Thanks for the quick response. |
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hm, is this not sth that would be applicable to all forecasters, rather than just the polynomial trend one? As long as the assumption on iid residuals is satisfied. Similar to |
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oh, I see, only linear ones, probably.
Of course, how else would you "fit" 😄 |
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I am interested in enhancing the PolynomialTrendForecaster forecaster by implementing the predict_interval() method for it. My implementation requires as an input the index of the time series used to fit the model. Is it possible to add this as an additional argument to predict_interval()?
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