What are the specialities of applying locally weighted learning for time series forecasting?
I am trying to apply a nonparametric model ($K$-NN Regression) to forecast daily load curve (entire time series containing 24 points).
Throughout the model selection phase various hyperparameters (such as kernel function $\theta(z)$ and history length $m$ for the sliding window) are set. The bandwidth $K$ is set during the training phase using leave-out cross validation on the available training data determined by $m$.
I deal with the daily sesonality by having a separate model for each hour. I deal with weekly sesonality by clustering historic daily curves by weekday. However, there is a yearly cycle in the energy consumption (the housing consumes more energy in cold months). For which dont know how to account for.
My questions are:
What are the general approached for data normalization for time series forecasting applications? MinMax and Z-Factor should not work because we either don't know the upcoming min/max or the time series is nonstationary.
Can we use leave-out cross validation to find best $K$? From my understanding the historic x/y observations are independent from each other.
How do I get rid of long term cycles? One idea was to use only same month for training but that leaves me with too little data.
I have attached an example of the forecast time series down below and would appreciate any discussion on the matter.