# Exploring Time-Series Forecasting Models for Dynamic Pricing in Digital Signage Advertising
## 3 Discussion
### DSA Data Analysis and Proposed Framework for Optimal Model Selection
#### 3.2.2 Weather and Temperature  
The weather and temperature have a significant impact on the crowd size of a location, especially for outdoor environments. The changes in the weather include changes in the air humidity and temperature [119]. The weather can have many changes in a short duration. With fast-changing weather, an hourly update to precisely calculate the prices of an advertising spot can be performed. As bad weather will negatively affect outdoor activities and events, this will result in lower prices of the advertisements at those spots. The temperature and air humidity data are analyzed. The data are complementary to each other. When the values of air humidity go down, the values of temperature go up. Figure 6 shows the changes in temperature and air humidity over 24 h on a randomly  
Figure 4: Popularity index changes in 30 days. Figure 5: Popularity index changes for the whole dataset. Figure 3: Popularity index comparison over 24 h for both weekdays and weekends. selected day to illustrate how these attributes change in a day. The data show an irregular movement in a longer time frame of 30 days and in the plot for the whole dataset, as shown in Figures 7 and 8, respectively. Generally, the temperature and air humidity show a movement that is contradictory to each other. The weather can affect the crowd size. An extremely high or low temperature will result in the crowd of a location to decrease. Notably, the environmental factors show a different data characteristic. Therefore, we observe that the data for each factor of the DSA show different characteristics. Based on the review studies, a framework is developed to analyze the data  
Figure 8: Temperature and air humidity for the whole dataset. Figure 6: Temperature and air humidity in 24 h.  
Figure 7: Temperature and air humidity in 30 days. for optimal model selection. A list of procedures and tests can be used to determine the data characteristics. A linearity test can be conducted through data visualization using a scatter plot by observing if the point cluster forms a diagonal line. The data stationarity can be checked by using the Augmented Dickey-Fuller (ADF) test [120]. A Lagrange Multiplier (LM) test is used to check the existence of the ARCH effect to assess the volatility in the dataset [5]. The p-values of both ADF and LM tests are used to indicate if the null hypotheses of the test are accepted to determine the stationarity and volatility of the data. In addition, dataset size is determined based on the number of observations in the dataset. Based the result from each test, the optimal price-forecasting method for each case can be determined. Note that the hybrid model is not included in the framework, as the hybrid models are the combination of two or more single models targeting different data characteristics, depending on the specific forecasting problems handled. Figure 9 illustrates the proposed framework, with the corresponding tests to determine the optimal model selection. From the above analysis, it is noticeable that each data point has different movements in time. The linearity, stationarity, and volatility tests for the environmental factors of the DSA dataset are performed to examine the data characteristics for each. Following the steps as illustrated in Figure 9, Table 12 shows the test results. Figure 10 shows the data visualization of the linearity test for the popularity index, temperature, and air humidity data. Based on Figure 10b,c, it is noticeable that the temperature and air humidity data show a linear relationship, respectively, as the points cluster along the diagonal line. Figure 9: Proposed framework for optimal model selection. From the interpreted results, SVM is the optimal model for modeling the popularity index, while ARIMA is suitable for modeling both temperature and air humidity. Multiple models can forecast the respective environmental factors instead of using a single model to fit all the factors.