# Exploring Time-Series Forecasting Models for Dynamic Pricing in Digital Signage Advertising
## 2 Review on Time-Series Forecasting Studies
### Hybrid Model  
Hybrid models are generally a combination of two or more models from the statistical and AI categories. The hybrid model is usually more robust than the single models, as it combines and complements the advantages of a single model to improve the forecasting accuracy. The hybrid model is widely used in different domains for dynamic pricing schemes, including the domain of stock [83; 84; 85; 94; 95], crude oil [86; 88; 89], energy [90], carbon [87; 91], electricity [92], and gold [93] from 2004 to 2021. Different combinations have been proven to successfully integrate the advantages of different models to improve the performance. For example, ANN-GARCH [93] accepted data nonlinearity and volatility. The proposed model demonstrated a significant advantage in modeling highly non-stationary and non-linear time-series data by outperforming any of the single models. From these studies, the hybrid model is proven to have better forecasting capability for time-series data.  
Although the hybrid model has demonstrated a promising outcome, such a model is usually highly complex and computationally intensive [118]. The determination of the models for combination is often tricky and challenging, as it requires an in-depth understanding of each method. Thus, a strong background of different models should be mastered and well-understood to decide on a suitable hybrid architecture. The hybrid models also have lower flexibility, since it is specifically designed to handle a particular problem. Table 9 shows the reviewed studies for the hybrid models.  
\begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Domain** & **Author** & **Dataset** & **Model** & **Result** \\ \hline \multirow{4}{*}{**Electricity**} & [PERSON] et al., 2007 [79] & PJM & RNN & MAPE of less than 10 \\ \cline{2-4}  & [PERSON] et al., 2018 [80] & New England ISO and PJM & LSTM, SVM, DT & LSTM has the best performance with an MAPE of lower than 39 \\ \cline{2-4}  & [PERSON] et al., 2018 [81] & Turkish electricity market of 2016 & LSTM, GRU, ANN & GRU has the best performance with an MAE of 5.36 \\ \hline \multirow{2}{*}{**Agricultural**} & [PERSON] et al., 2019 [82] & Beijing Xinfadi Market (August 2015 to July 2018) & RNN, ARIMA, BPNN & The RNN achieved the best performance with the lowest AAE of 0.49, 0.21, 0.15 \\ \hline \hline \end{tabular}
\end{table}
Table 8: _Cont._  
\begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Domain** & **Author** & **Dataset** & **Model** & **Result** \\ \hline \multirow{4}{*}{**Stock**} & [PERSON] and [PERSON], 2017 [83] & WIND database (January 2010 to September 2016) & HMM-GARCH & RMSE of 0.0238 and 0.0075 \\ \cline{2-4}  & [PERSON] and [PERSON], 2005 [85] & Ten stocks dataset (October 2020 to December 2002) & ARIMA, SVM, ARIMA-SVM & Hybrid model has the lowest MAE for the included ten stocks \\ \cline{2-4}  & [PERSON] et al., 2007 [94] & Daily stock price of Apple, IBM, and Dell from Yahoo Finance & ANN-GA-HMM & MAPE of 1.9247, 0.84871, and 0.699246 for the stock, respectively \\ \cline{2-4}  & [PERSON] and [PERSON], 2020 [84] & Ten stocks dataset (2015 to 2018) & DWT-ARIMA-GSXGB & RMSE of less than 20.3013 for the worst case, the general cases have an RMSE of less than 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Hybrid model time-series forecasting from 2004 to 2021.