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My goal is to predict electricity consumption given historic data for a time horizon of 36 hours. I understand how I can predict using GPs and historical consumption data; however, I also have access to temperature forecasts which is naturally highly correlated with electricity consumption.

What I would like to do is incorporate the temperature forecast into my simple GP model, that is, condition the 36-hours-ahead electricity consumption prediction also on the forecast temperature values at the corresponding time labels.

One very simple way I can think of is to model the electricity consumption using recent electricity consumption observations only, and scale the results up or down in accordance with the temperature forecast, using some linear regression approach. But this does not seem very elegant. Is there a better way to do this?

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    $\begingroup$ Please explain the acronym GP, is that 'Generalized Pareto?' Next, this paper by Rob Hyndman proposes a novel method for forecasting electricity consumption Forecasting Uncertainty in Electricity Smart Meter Data by Boosting Additive Quantile Regression ... ieeexplore.ieee.org/document/7423794. $\endgroup$
    – user78229
    Dec 4, 2017 at 13:34
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    $\begingroup$ GP refers to Gaussian Process, now clearified in the title. Regarding the paper you link I fail to realize how this method can be used to allow temperature predictions to contribute to the 36-hours-ahead electricity consumption forecast. $\endgroup$ Dec 4, 2017 at 13:49
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    $\begingroup$ Is it accurate to say that you are demanding a 'one-to-one,' exact recommendation wrt your query? That seems, not just onerous, but excesssive. Hyndman's BAQR approach is nonparametric. This means that it can fit any assumed distribution, including GP. As such, his method is proposed as a general, not exact, approach for forecasting electricity consumption. Do with it what you will. If you choose to ignore this comment, that's fine with me. $\endgroup$
    – user78229
    Dec 4, 2017 at 13:54
  • $\begingroup$ Well, an exact recommandation would of course be nice, but I am not expecting that and certainly not demanding it. As far as I can tell the BAQR approach moves to a probabilistic forecast in order capture the volatility of individual smart-meters. My data is aggregated from a large number of consumers and not nearly as volatile. I also have no experience with probabilistic forecasts; is that something I will have to consider in order to include temperature forecast in my prediction? Sorry in the case that my question makes noe sense, I am not very knowledged in this field. $\endgroup$ Dec 4, 2017 at 14:37
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    $\begingroup$ Some confusion here perhaps. GP is flagged in the question and comment by the OP as meaning Gaussian process. Nothing to do with generalized Pareto distribution. How best to predict electricity consumption remains the focus. $\endgroup$
    – Nick Cox
    Dec 4, 2017 at 15:09

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It seems to me that a suitable model for your application is a multivariate Gaussian Process, also known as "cokriging" in the geostatistical community, in which you can forecast two correlated variables simultaneously, while taking into account their dependencies, instead of separately obtaining forecasts for each of them.

In a univariate GP, the between-input correlation is represented through the covariance matrix. In a multivariate GP, both the between-input and between-output correlations are accounted for. The simplest way to do so is through separately modeling the covariance across inputs and across outputs and then the product would be a valid positive-definite covariance structure.

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