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Basis function regression is a very under-appreciated method for producing time series forecasts. I've found that it beats most of the methods described in thi

Basis function regression is a very under-appreciated method for producing time series forecasts. I've found that it beats most of the methods described in this article. Maybe I should make a blog post...

amrrs 7y ago
Sorry for ignorance. Did you mean to say Simple Linear regression or something else? Do you have any reference for that?
- chroem- 7y ago
  Yes, it's an extension of linear regression. You can incorporate different basis functions to model trend, seasonality, the effects of external regressors, different frequency components, etc. It gives you a lot more control over the forecast model.
  - riyadparvez 7y ago
    Are you referring to Generalized Additive Models (GAM)?
    - semi-extrinsic 7y ago
      I think GAMs are more for the case where you have many underlying input variables and a single resulting response.
      - XuMiao 7y ago
        This is a less studied senario for time series research: contextual forecasting. With enough contextual information, forecasting doesn't need to squeeze the information from its own history that hard.
- semi-extrinsic 7y ago
  Not OP, but as an example, imagine you want to fit the time series of measured monthly CO2 at Mauna Loa: https://www.esrl.noaa.gov/gmd/ccgg/trends/ https://www.esrl.noaa.gov/gmd/ccgg/trends/ Just by looking at the graph, you can see that fitting a linear combination of a constant term, t, t2 and sin(w*t) will give you a very accurate model that has five tuning parameters (four weights and one frequency).
- tgv 7y ago
  Here's an explanation: https://www.youtube.com/watch?v=rVviNyIR-fI https://www.youtube.com/watch?v=rVviNyIR-fI It's basically fitting on non-linear transformations of x.
- clircle 7y ago
  You can fit a basis function regression model with least squares.
starpilot 7y ago
Works if you have enough domain knowledge to prescribe the functions (priors). Not so good if it's a poorly understood or niche domain.

amrrs 7y ago

Sorry for ignorance. Did you mean to say Simple Linear regression or something else? Do you have any reference for that?

chroem- 7y ago
Yes, it's an extension of linear regression. You can incorporate different basis functions to model trend, seasonality, the effects of external regressors, different frequency components, etc. It gives you a lot more control over the forecast model.
- riyadparvez 7y ago
  Are you referring to Generalized Additive Models (GAM)?
  - semi-extrinsic 7y ago
    I think GAMs are more for the case where you have many underlying input variables and a single resulting response.
    - XuMiao 7y ago
      This is a less studied senario for time series research: contextual forecasting. With enough contextual information, forecasting doesn't need to squeeze the information from its own history that hard.
semi-extrinsic 7y ago
Not OP, but as an example, imagine you want to fit the time series of measured monthly CO2 at Mauna Loa: https://www.esrl.noaa.gov/gmd/ccgg/trends/ https://www.esrl.noaa.gov/gmd/ccgg/trends/ Just by looking at the graph, you can see that fitting a linear combination of a constant term, t, t2 and sin(w*t) will give you a very accurate model that has five tuning parameters (four weights and one frequency).
tgv 7y ago
Here's an explanation: https://www.youtube.com/watch?v=rVviNyIR-fI https://www.youtube.com/watch?v=rVviNyIR-fI It's basically fitting on non-linear transformations of x.
clircle 7y ago
You can fit a basis function regression model with least squares.

starpilot 7y ago

Works if you have enough domain knowledge to prescribe the functions (priors). Not so good if it's a poorly understood or niche domain.