MAT5 and MatØk5 project: The effect of temperature on electricity consumption in Sweden - modeling of correlation

Presentation of data and problem (Michael Bartels, Nordjysk Elhandel).

Last year the above data were analyzed using a multiple regression model of the form

y_t=b_0+b_1 T_t + b_2 max(0,T_t-17) + b_3 W_t + b_4 H_t + e_t

where for a day t, y_t is consumption, T_t is temperature, W_t is an indicator for weekend, H_t is an indicator for holiday and e_t is an error term. However, it became clear that a basic assumption - independent error terms e_t - was violated. This has implications both for inference regarding regression coefficients and prediction of consumption. In this year's project we will attemp to model and quantify the correlation in the residuals. The starting point will be a first-order auto regressive (AR(1)) model for the error terms.

Topics of relevance for the project include:

• Distribution of (e_1,...,e_T) when the e_i follow an AR(1) with normal innovation terms (mean, variance, covariance matrix, inverse covariance matrix, stationary vs. non-stationary version)
• Bayesian inference for AR(1).
• Prediction using an AR(1).
• Model assessment.
• Inference for a linear regression model with AR(1) error terms.
• If time allows: extensions of AR(1) (AR(p), integrated AR(1)...)