# 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

Table 2: ARIMA time-series forecasting from 2003 to 2019. Generalized Autoregressive Conditional Heteroscedasticity (GARCH)  
GARCH is refined from the ARCH model, as proposed by [PERSON] [99]. This model overcomes the weaknesses of the ARCH model, as the ARCH model is of a very high order with huge number of parameter estimations [12]. GARCH is widely applied for economic and financial series forecasting. This model was found to have higher efficiency in forecasting when working with data of high volatility compared to ARIMA. The latter is limited in the autoregressive heteroscedasticity (ARCH) effect and is of linear time-series data, as it is assumed that the future value is in a linear relationship to time [12; 100]. From the review, GARCH has been deployed in different domains for forecasting data with high volatility, such as the prices of gold [28; 29], stocks and the financial market [30; 31; 32; 33], agricultural products [34], and power and electricity [12; 35] from 2005 to 2021. GARCH is proven to have better performance than ARIMA if the data have high volatility. This can be verified by conducting the Lagrange Multiplier (LM) test [28; 34]. The results indicate that ARIMA cannot predict well due to the volatility of the data. There are different refinements of GARCH, including Exponential GARCH (EGARCH) [12] (capturing asymmetric volatility of the data) and nonparametric GARCH (NPGARCH) [33] (removing the parameterized assumptions, which indicates that the data are in the relationship of square linear and stochastically volatile). Overall, GARCH is suitable for data with high volatility. However, for cases where the time-series data have a linear relationship, this model may not be able to model the time-series data well compared to the ARIMA approach. Table 3 summarizes the review on the studies of GARCH. \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
**Oil** & [PERSON] et al., 2015 [12] & Cotlook A (April 1982 to March 2012) & GARCH, EGARCH & EGARCH achieved the best performance with RMSE of 14.41 \\ \hline
**Gold** & [PERSON] et al., 2013 [28] & Kijaang Emas prices (July 2001 to September 2012) & GARCH & MAPE of 0.809767 \\ \cline{2-4}  & [PERSON] et al., 2019 [29] & Malaysia gold price (January 2003 to June 2014) & ARIMA, GARCH, ARIMA-GARCH & ARIMA-GARCH & ARIMA-GARCH achieved the most optimal result with a price error less than 2 \\ \hline
**Stock** & [PERSON] et al., 2021 [30] & West Texas Intermediate (January 2015 to May 2018) and CSI300 (May 2015 to 2016) & GARCH with nonlinear function & AIC of \(-\)1119.77 and \(-\)11373.6 for CSI300 and WTI dataset \\ \cline{2-4}  & [PERSON] and [PERSON], 2013 [31] & Bombay Stock Exchange and Shanghai Stock Exchange (1990 to 2013) & GARCH & AIC of \(-\)5.52662 and \(-\)5.260705 for BSE and SSE dataset \\ \cline{2-4}  & [PERSON] et al., 2018 [32] & Adaro energy share price (January 2014 to December 2016) & GARCH & MAPE of 2.16 \\ \hline
**Power** & [PERSON] et al., 2008 [33] & Power price in California of 2000 & NP-GARCH, GARCH, ARIMA & NP-GARCH achieved the lowest MPE of 3.62 and 4.86 \\ \hline
**Agricultural Product** & [PERSON] et al., 2014 [34] & Gram price in Delhi (January 2007 to April 2012) & GARCH, ARIMA & GARCH achieved the best performance with an average error of less than 2 \\ \hline
**Electricity** & [PERSON] et al., 2005 [35] & Spanish and California Power Market (September 1999 to November 2000) and (January 2000 to December 2000) & GARCH & FMSE of less than 6 and 69 for Spanish and California market \\ \hline \hline \end{tabular}
\end{table} 
Table 3: GARCH time-series forecasting from 2005 to 2021.