## 2 Related Work
### Challenges in Demand Forecasting  
Demand forecasting is a mature area of research [32]. Nonetheless, for accurate predictions of demand, many challenges remain to be addressed [32; 33; 34]. One of the major challenges is the curse of dimensionality. In demand forecasting, the predictor variables are lagged variables. The lagged variables are highly correlated. Consequently, even a moderate number of predictor variables may trigger the curse of dimensionality, and demand forecasting models often suffer from overfitting. Most of the existing CDFS do not take special measures to protect themselves against the curse [9; 17]. They train a single network (e.g., LSTM) with a set of lagged aggregate demand time series values to forecast the out-of-sample data.  
Another major challenge in demand forecasting is the presence of non-stationarity in demand time series [32; 33; 34]. In a non-stationary time series, the frequency content changesin time; all frequencies do not always exist. There are currently three main approaches for dealing with time-varying frequency components [35]. The first approach is to apply the differencing operator on-demand time series and remove these patterns from the time series. However, the main difficulty of the differencing approach is that it requires exact knowledge about the locations of all frequency components in the time series, which is by no means easy to capture.  
The second approach to deal with the time-varying frequency components is to enter a large number of non-seasonal lagged variables in a neural network (e.g., LSTM) during the training so that it automatically selects an optimal number of seasonal and non-seasonal lagged variables and models time-varying frequency components. Most of the existing resilient CDFS adopt this mechanism [9; 17]. This approach leads to a large number of lagged input variables in the model which might exacerbate the curse of dimensionality.  
The third approach to deal with the time-varying frequency components is to use a hybrid of wavelet transform and neural networks [35; 36]. This approach has been drawing increasingly more attention in recent years. This approach uses wavelet techniques to split the original time series into multiple component time series. A neural network (e.g., LSTM) is trained with the non-seasonal lagged variables generated from the component time series to forecast the future values of the original demand curve. Currently, more comparative studies are required to confirm the superiority of one approach over the other.  
Perhaps the biggest challenge in developing a demand forecasting model is that the older values of the demand time series are less useful than the newer ones as training data and become obsolete quickly, since the distribution of demand time series keeps changing with time [30]. Several studies suggest ensuring that the forecasting model adjusts rapidly to the changing distribution. Based on these studies, the higher penalty should be assigned to in-sample forecast errors on more recent demand observations during the training phase. However, this approach poses many practical problems. The key problem is how to weigh the values of demand time series appropriately in the presence of time-varying frequency components. An inadequate weighting scheme may cause more harm than good, as it may destroy the distribution of the original time series. Hence, the common practice is to keep adapting the forecasting model to the new observations as the sensors gather them without applying an arbitrary weighting scheme [9].