# Exploring Time-Series Forecasting Models for Dynamic Pricing in Digital Signage Advertising
## 2 Review on Time-Series Forecasting Studies
### Statistical Model
#### 2.1.1 Regression Model  
Autoregressive Integrated Moving Average (ARIMA)  
ARIMA is a linear regression model that works efficiently with stable correlated time-series data [82]. It can be applied to time-series forecasting problems in any domain based on the principle of univariate analysis. The model works well on stationary time-series data. The theoretical background of ARIMA is explained in [97]. Figure 2: The evolution of time-series forecasting models in different domains over two decades. Some studies have exemplified the applicability of ARIMA in forecasting time-series in different domains such as cryptocurrencies [13], stock [14; 15; 16], rubber and latex [17; 18], agricultural and e-commerce products [19; 20; 21; 27], gold [22; 23], and electricity [24; 25; 26] from 2003 to 2019 and demonstrated exceptionally promising results. From the studies made, ARIMA has difficulty when handling non-stationary time-series data, as it is trying to model the changes based on the historical time-series data with linearity assumptions when performing forecasting. It is noticed that the following factors will affect the model performance: sudden fluctuation [23], nonlinear and non-stationary time-series data [21], and multi-step ahead forecasting [98]. There are other variations of ARIMA introduced, such as ARIMA with the independent variable (ARIMAX) [17] and Seasonal ARIMA (SARIMA) [18] for multivariate modeling and seasonal time-series data problems, respectively. It is noticeable that ARIMA produces an exceptional performance when the data are linear and stationary. Table 2 summarizes the studies applying the ARIMA. \begin{table}
\begin{tabular}{p{85.4 pt} p{85.4 pt} p{85.4 pt} p{85.4 pt} p{85.4 pt}} \hline \hline
**Domain** & **Author** & **Dataset** & **Model** & **Result** \\ \hline \multirow{3}{*}{**Cryptocurrencies**} & [PERSON] et al., 2018 [13] & Cryptocurrencies (2013 to May 2018) & ARIMA & Accuracy of 86.424 \\ \hline \multirow{3}{*}{**Stock**} & [PERSON] et al., 2014 [14] & New York Stock Exchange and Nigerian Stock Exchange & ARIMA & R\({}^{2}\) of 0.0033 and 0.9972 \\ \cline{2-5}  & [PERSON] et al., 2014 [15] & Bovespa Index (January 2000 to December 2012) & ARIMA & MAPE of 0.064 \\ \cline{2-5}  & [PERSON], 2017 [16] & Indonesia Composite Stock Price Index & ARIMA & MAPE of 0.8431 \\ \hline \multirow{3}{*}{**Rubber**} & [PERSON] and [PERSON], 2016 [17] & Bangkok and World natural rubber price (January 2002 to December 2015) & ARIMAX & MAPE of 1.11 \\ \hline \multirow{2}{*}{**Latex**} & [PERSON] and [PERSON], 2018 [18] & Central Rubber Market of Hat Yai, Thailand & SARIMA & MAPE of 24.60 and 0.8768 of 14.90 \\ \hline \multirow{3}{*}{**Agricultural and e-commerce product**} & [PERSON] et al., 2016 [19] & Agricultural Produce Market Committee, Rampani (May 2003 to June 2015 & ARIMA & MAPE of 6.38 \\ \cline{2-5}  & [PERSON] et al., 2017 [20] & Price of cereal crops in Karnataka (2002 to 2016) & ARIMA & MAPE of 2.993, 1.859, 1.255 paddy, ragi, and maize, respectively \\ \cline{2-5}  & [PERSON] et al., 2018 [27] & Amazon product’s prices, with Google Trends data used as exogenous features & ARIMA & Achieves the lowest average MAPE of 4.77 \\ \cline{2-5}  & [PERSON] et al., 2019 [21] & Price in market Kadiri, India (January 2011 to December 2015) & ARIMA & MAPE of 2.30 \\ \hline \multirow{3}{*}{**Gold**} & Banhi and Gautam, 2016 [22] & Multi Commodity Exchange of India (November 2003 to January 2014) & ARIMA & MAPE of 3.145 \\ \cline{2-5}  & [PERSON], 2019 [23] & World Gold Council (July 2013 to June 2018) & ARIMA & Relative error of less than 1.2\% \\ \hline \multirow{3}{*}{**Electricity**} & [PERSON] et al., 2003 [24] & Spanish and California electricity market of 2000 & ARIMA & Mean errors of less than 11\% \\ \cline{2-5}  & [PERSON] et al., 2004 [25] & California power market of 1999 & ARIMA & MSE of 0.1148 \\ \cline{1-1} \cline{2-5}  & [PERSON] et al., 2011 [26] & EPEX power exchange & ARIMA & MAPE of 3.55 \\ \hline \hline \end{tabular}
\end{table}