## 6 Results and Conclusions  
There are many well-known datasets, such as S&P 500, weather data, etc. We did not use these datasets because there have already been many experiments conducted on these data. Thus, we extracted a time series dataset from a real-world example. The time series used in this research was extracted from a software debugging web platform that projects the tendency of how frequently a specific tag is asked in blogs. Comparing the forecasting performances of some of the most used and famous models on a real-world time series gives clear insight into how accurate the models can perform. We tested the most used models: MLP, RNN, LSTM, CNN, and the wavenet variant of CNN. They all have the same or similar complexity. All the models tested in this work were constructed in Google's Colaboratory environment. The models were powered by TensorFlow version \"2.8.2\" and tensorflow.keras API version \"2.8.0\", which are supported by Google for numerical computing, training, and running neural networks [49]. A list of the tested models and their basic specifications, such as the number of layers, the number of units in the layers, filters, etc., are presented in Table 1.  
The prediction performance of the models is presented in Table 2. The metrics used to represent the forecasting performances were mean absolute error (MAE) and mean squared error (MSE). MAE computes the absolute values of the error, which are the differences between the predicted results and actual values. MSE computes the square of the errors. \begin{table}
\begin{tabular}{c c c} \hline \hline
**MODEL** & **LAYERS** & **FUNCTIONS** \\ \hline Dense & 3 Dense & ReLu, Linear \\ Stateless RNN & 2 RNN, 1 Dense & tanh, Linear \\ Stateful RNN & 2 RNN, 1 Dense & tanh, Linear \\ LSTM & 2 LSTM, 1 Dense & tanh-Sigmoid, Linear \\ CNN Hybrid & 1 CNN, 2 LSTM, 1 Dense & ReLu, tanh, Linear \\ Fully CNN & 6 CNN, 1 CNN & ReLu \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tested models and properties. Figure 16: Representation of the full CNN model. Figure 17: Forecasting performance of the fully CNN model. Consequently, MSE penalizes large errors more than MAE. If large errors are potentially more dangerous and cost much more than smaller errors, MSE is more beneficial than MAE. According to the performance metrics, the fully convolutional layer model was the most successful in both MAE and MSE metrics. Especially, in terms of the MSE, which penalizes large errors more, the fully convolutional model achieved very successful forecasting performance. After the fully CNN Model, the most successful model was the LSTM model. Using the CNN layer as a pre-processing unit did not positively affect the forecasting performance of the LSTM model. Another important result is the success of the dense model. The dense model, consisting of two simple layers with ten units, also performed well when compared with its simplicity and compactness. The RNN models, both stateless and stateful versions, performed poorly. This is partly because RNN models suffer from transferring long-term information, which is known as the vanishing gradient problem. The accuracy of time series prediction usually decreases as the forecast horizon increases. To measure the strength of the algorithms, we conducted more analyses using shorter window lengths. For example, on 5-day-long windows, the accuracy of the algorithms increased, and the model performances are compared in Table 3.  
Another important metric for the tested models was the execution time and complexity. To enlighten this, the number of units, filters used in each layer, and the execution times are presented in Table 4. The metrics are acquired on a Python 3 Google Compute Engine (GPU mode) with 12.7 RAM. To test the wavenet model's resilience, we also conducted a preliminary test by using S&P 500 stock data between 16 December 2011 and 9 November 2017. According to this