Daily electricity consumption forecasting is a classical problem. Existing
forecasting algorithms tend to have decreased accuracy on special dates like
holidays. This study decomposes the daily electricity consumption series into
three components: trend, seasonal, and residual, and constructs a two-stage
prediction method using piecewise linear regression as a filter and Dilated
Causal CNN as a predictor. The specific steps involve setting breakpoints on
the time axis and fitting the piecewise linear regression model with one-hot
encoded information such as month, weekday, and holidays. For the challenging
prediction of the Spring Festival, distance is introduced as a variable using a
third-degree polynomial form in the model. The residual sequence obtained in
the previous step is modeled using Dilated Causal CNN, and the final prediction
of daily electricity consumption is the sum of the two-stage predictions.
Experimental results demonstrate that this method achieves higher accuracy
compared to existing approaches.

日常电力消耗预测是一个经典问题，本研究通过使用分段线性回归和扩张因果卷积神经网络构建两阶段预测方法，将每日电力消耗系列拆分为趋势、季节和残差三个组件，并引入距离变量来挑战传统节日预测，最终预测结果通过两阶段预测的求和得出，实验结果表明该方法较现有方法具有更高的准确性。

基于分段线性回归和扩张因果卷积神经网络的中长期日电力消费预测

Mid-Long Term Daily Electricity Consumption Forecasting Based on  Piecewise Linear Regression and Dilated Causal CNN

We present a new piecewise linear regression methodology that utilizes
fitting a difference of convex functions (DC functions) to the data. These are
functions $f$ that may be represented as the difference $\phi_1 - \phi_2$ for a
choice of convex functions $\phi_1, \phi_2$. The method proceeds by estimating
piecewise-liner convex functions, in a manner similar to max-affine regression,
whose difference approximates the data. The choice of the function is
regularised by a new seminorm over the class of DC functions that controls the
$\ell_\infty$ Lipschitz constant of the estimate. The resulting methodology can
be efficiently implemented via Quadratic programming even in high dimensions,
and is shown to have close to minimax statistical risk. We empirically validate
the method, showing it to be practically implementable, and to have comparable
performance to existing regression/classification methods on real-world
datasets.

本文介绍了一种新的分段线性回归方法，利用凸函数差的拟合数据，通过分段凸函数的估计来近似数据。方法可以通过二次规划高效实现并在现实世界数据集上验证了它的可行性和性能。