# Exploring Time-Series Forecasting Models for Dynamic Pricing in Digital Signage Advertising
## 3 Discussion
### Summary of Suitable Data Characteristics for the Included Models  
In the review of the seven forecasting models, the importance of the different data characteristics in the optimal model selection for price forecasting is emphasized. Table 10 shows the suitability of data characteristics for each model. Each model has varying performance for the different data characteristics. The large dataset is generally built up with more than 100,000 observations, and the small dataset has fewer observations. This section presents a summary of the strengths and weaknesses of the models. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Domain** & **Author** & **Dataset** & **Model** & **Result** \\ \hline \multirow{8}{*}{**Crude oil**} & [PERSON] and [PERSON], 2014 [88] & Brent crude oil prices and WTI crude oil prices & ANN, WANN & WANN has the best performance with MAPE of 1.31 and 1.39 for Brent and WTI dataset \\ \cline{2-4}  & [PERSON] et al., 2015 [86] & WTI and Brent crude oil (January 1986 to 2005) and (May 1987 to June 2005) & EEMD-LSSVM-PSO-GARCH & MAPE of 1.27 and 1.53 for WRI and Brent dataset \\ \cline{2-4}  & [PERSON] and [PERSON], 2018 [89] & OPEC crude oil prices (January 2003 to September 2016) & ESM-ARIMA-NAR & MAPE of 2.44, obtained the lowest error compared to other single models \\ \hline \multirow{2}{*}{**Energy**} & [PERSON] et al., 2019 [90] & Iberian electricity market (February to July 2015) & ARIMA -MLR and ARIMA-Holt & ARIMA-Holt & ARIMA-Holt \\  & & & ARIMA-Holt & an MAPE of less than 5.07 for different day forecasting \\ \hline \multirow{8}{*}{**Carbon**} & [PERSON] and [PERSON], 2013 [87] & European Climate Exchange (ECX) of December 2010 and December 2012 & ARIMA-LSVM & RMSE of 0.0311 and 0.0309 for DEC10 and DEC12 \\ \cline{2-4}  & [PERSON] et al., 2021 [91] & EUA futures from Wind database & VMD-GARCH and LSTM & VMS-GARCH has the best performance with first ranking in terms of RMSE, MAE and MAPE \\ \hline \multirow{2}{*}{**Electricity**} & [PERSON] et al., 2011 [92] & Spanish electricity market of 2002 & Wavelet-ARIMA-RBFN & Error variances of less than 0.0049 \\ \hline \multirow{2}{*}{**Gold**} & [PERSON] and Minutolo, 2015 [93] & Gold Spot Price and Gold Future Price from Bloomberg (September 1999 to March 2014) & ANN-GARCH & MAPE of 0.6493 and 0.6621 \\ \hline \end{tabular}
\end{table} 
Table 9: _Cont._First, for regression models, ARIMA is suitable for linear and stationary data, whereas the GARCH model has a better performance when the data are high in volatility and is adaptable to non-stationary data. However, when the data have a linear relationship, ARIMA will have a better performance than GARCH. The stochastic model, HMM, introduced the hidden states that can simulate different volatility regimes. Therefore, it has better performance than a regression model such as GARCH when the data are high in volatility and there is a larger sample size. However, it should be noted that the hidden parameters of HMM are difficult to determine, and the algorithm will probably stop at a local maximum before reaching the most satisfactory result. Hence, this results in lower accuracy in price forecasting. As one of the ML models, SVM is more effective than statistical models such as ARIMA and GARCH in the sense of its better capability of working with the nonlinear, non-stationary, and highly volatile data. Unlike the regression models, SVM is not limited to working with data having a linear relationship or high volatility, the algorithm is convex optimized. This means that it can find the global optimum of the result. Therefore, it is better than HMM in reaching the most promising result. It can generalize well to previously unseen data, overcoming the existing problems such as forecasting a sudden fluctuation. However, if the dataset is too large, SVM might not perform well due to the memory and optimization constraints. The main advantage of RF compared to SVM is its ability in handling massive datasets.