在人手一機的時代裡，每個人每分每秒都在數位裝置上新增時間序列資料，許多公司透過收集巨量的時間序列資料進行預測未來的狀態，例如：公司業務的成長性，股市可能的走向等。
而在近年興起的深度學習網路在時間序列資料上的預測得到很大的發展，因為模型特性在非線性特徵提取上有很好的效果。與此同時，線性時間序列預測的工具依舊有其價值，在綫性特徵的預測上效果很好，以及在前期建立模型的時間上有其巨大的優勢。
本研究主要關注結合線性時間序列預測模型與深度學習時間序列預測模型後的效能，同時希望藉由結合線性與非線性特徵的預測達到效能增加的效果。本研究主要使用python與keras做為實驗的平台，採用ARIMA與SMA進行線性的時間序列資料預測，搭配廣泛使用在時間序列資料預測的LSTM（long short-term memory）來測試兩者結合的效益。

During the internet era，we are constantly generate a large quantity time series data on every single digital device. Numerous companies utilize this wealth of time series data to forecast future states, such as business growth and potential movement of the price of financial instruments.
In recent years, deep learning networks have made significant advancements in time series forecasting, because of their effectiveness in extracting non-linear features. In the same time, linear time series forecasting models still hold values, particularly in predicting linear features and they still have great advantages in the period of building models.
This research primarily focuses on evaluating the performance of combining the linear time series forecasting models with the deep learning time series forecasting model. The goal is to achieve enhanced performance by combining both linear and non-linear feature predictions. This study mainly utilizes Python and Keras as the experimental platform. It employs ARIMA and SMA for linear time series data forecasting, and combines them with LSTM (long short-term memory), widely used in time series data prediction, to test the effectiveness of their integration.

第一章 前言 1
1-1 研究背景 1
1-2 研究動機與目的 1
1-3 論文綱要 2
第二章 背景知識與相關研究 3
2-1 時間序列資料簡介 3
2-1-1 時序性資料的要素： 3
2-1-2 時間序列資料點特性： 4
2-2 統計時序資料預測模型 6
2-2-1 Autoregressive自迴歸 6
2-2-2 Simple Moving Average簡單移動平均 6
2-2-3 ARIMA 7
2-2-3 Exponential Smoothing 9
2-3 深度學習時序資料預測模型——LSTM（Long Short Term Memory ） 11
2-4 相似論文 12
第三章 研究方法 13
3-1 訓練資料 13
3-2 資料預處理 22
3-3 參數選擇 22
3-3-3 LSTM 24
第四章 實驗結果與討論 26
4-1 SMA-LSTM實驗結果 26
4-1-1 APPL 26
4-1-2 BTC 28
4-1-3 PM25 30
4-1-4 Coffee Future 32
4-1-5 Covid19 34
4-1-6 SMA-LSTM 結果討論 36
4-2 ARIMA-LSTM實驗結果圖 37
4-2-1 APPL 37
4-2-2 BTC 39
4-2-3 PM25 41
4-2-4 Coffee Future 43
4-2-5 Covid19 45
4-2-6 ARIMA-LSTM結果討論 47
4-3 結果與討論 48
第五章 結論與未來展望 49
5-1 結論 49
5-2 未來展望 49
參考文獻 50

Ayoobi, N., Sharifrazi, D., Alizadehsani, R., Shoeibi, A., Gorriz, J. M., Moosaei, H., Khosravi, A., Nahavandi, S., Chofreh, A. G., & Goni, F. A. (2021). Time series forecasting of new cases and new deaths rate for COVID-19 using deep learning methods. Results in physics, 27, 104495.
Alassafi, M. O., Jarrah, M., & Alotaibi, R. (2022). Time series predicting of COVID-19 based on deep learning. Neurocomputing, 468, 335-344.
ASHUTOSH619-SUDO. (2020). M5 Forecasting With Conv1D and LSTM. https://www.kaggle.com/code/ashutosh619sudo/m5-forecasting-with-conv1d-and-lstm
Ayoobi, N., Sharifrazi, D., Alizadehsani, R., Shoeibi, A., Gorriz, J. M., Moosaei, H., Khosravi, A., Nahavandi, S., Chofreh, A. G., & Goni, F. A. (2021). Time series forecasting of new cases and new deaths rate for COVID-19 using deep learning methods. Results in physics, 27, 104495.
Bala, R., & Singh, R. P. (2019). Financial and non-stationary time series forecasting using LSTM recurrent neural network for short and long horizon. 2019 10th international conference on computing, communication and networking technologies (ICCCNT),
BANERJEE, P. (2020). ARIMA Model for Time Series Forecasting. https://www.kaggle.com/code/prashant111/arima-model-for-time-series-forecasting
Chimmula, V. K. R., & Zhang, L. (2020). Time series forecasting of COVID-19 transmission in Canada using LSTM networks. Chaos, Solitons & Fractals, 135, 109864.
chollet, F. (2022-06). Keras大神歸位：深度學習全面進化！用 Python 實作CNN、RNN、GRU、LSTM、GAN、VAE、Transformer (黃逸華、林采薇, Trans.). 旗標科技股份有限公司.
COSMA, A. (2018). Time Series - Exponential Smoothing. https://www.kaggle.com/code/andreicosma/time-series-exponential-smoothing
DOBRENZ, D. (2022). Forcasting Using Exponential Smoothing. https://www.kaggle.com/code/danieldobrenz/forcasting-using-exponential-smoothing
DUTTA, G. (2020). Temperature Prediction with Exponential Smoothing. https://www.kaggle.com/code/gauravduttakiit/temperature-prediction-with-exponential-smoothing
GUPTA, A. (2018). Bidirectional LSTM with Convolution. https://www.kaggle.com/code/eashish/bidirectional-gru-with-convolution
Haque, E., Tabassum, S., & Hossain, E. (2021). A comparative analysis of deep neural networks for hourly temperature forecasting. IEEE access, 9, 160646-160660.
Jahanbakht, M., Xiang, W., & Azghadi, M. R. (2021). Sea surface temperature forecasting with ensemble of stacked deep neural networks. IEEE Geoscience and Remote Sensing Letters, 19, 1-5.
Jin, X., Yu, X., Wang, X., Bai, Y., Su, T., & Kong, J. (2020). Prediction for Time Series with CNN and LSTM. Proceedings of the 11th international conference on modelling, identification and control (ICMIC2019),
Kyle. (2021-09-19). [Day4] 時間序列預測界的 OG：白話解釋 ARIMA 組成模型及步驟. https://ithelp.ithome.com.tw/articles/10267730
Li, A. W., & Bastos, G. S. (2020). Stock market forecasting using deep learning and technical analysis: a systematic review. IEEE access, 8, 185232-185242.
Lim, B., & Zohren, S. (2021). Time-series forecasting with deep learning: a survey. Philosophical Transactions of the Royal Society A, 379(2194), 20200209.
Lindemann, B., Müller, T., Vietz, H., Jazdi, N., & Weyrich, M. (2021). A survey on long short-term memory networks for time series prediction. Procedia CIRP, 99, 650-655.
Livieris, I. E., Pintelas, E., & Pintelas, P. (2020). A CNN–LSTM model for gold price time-series forecasting. Neural computing and applications, 32, 17351-17360.
Shastri, S., Singh, K., Kumar, S., Kour, P., & Mansotra, V. (2020). Time series forecasting of Covid-19 using deep learning models: India-USA comparative case study. Chaos, Solitons & Fractals, 140, 110227.
Siami-Namini, S., Tavakoli, N., & Namin, A. S. (2018). A comparison of ARIMA and LSTM in forecasting time series. 2018 17th IEEE international conference on machine learning and applications (ICMLA),
Siami-Namini, S., Tavakoli, N., & Namin, A. S. (2019). The performance of LSTM and BiLSTM in forecasting time series. 2019 IEEE International conference on big data (Big Data),
Song, H., Qiu, R. T., & Park, J. (2019). A review of research on tourism demand forecasting: Launching the Annals of Tourism Research Curated Collection on tourism demand forecasting. Annals of Tourism Research, 75, 338-362.
Sunny, M. A. I., Maswood, M. M. S., & Alharbi, A. G. (2020). Deep learning-based stock price prediction using LSTM and bi-directional LSTM model. 2020 2nd novel intelligent and leading emerging sciences conference (NILES),
Tung, E. R語言自學日記(12) -自迴歸移動平均模型(ARMA模型). https://medium.com/r-%E8%AA%9E%E8%A8%80%E8%87%AA%E5%AD%B8%E7%B3%BB%E5%88%97/r%E8%AA%9E%E8%A8%80%E8%87%AA%E5%AD%B8%E6%97%A5%E8%A8%98-12-%E8%87%AA%E8%BF%B4%E6%AD%B8%E7%A7%BB%E5%8B%95%E5%B9%B3%E5%9D%87%E6%A8%A1%E5%9E%8B-arma%E6%A8%A1%E5%9E%8B-c7bbfa045e05
Wang, Y., Zhu, S., & Li, C. (2019). Research on multistep time series prediction based on LSTM. 2019 3rd International Conference on Electronic Information Technology and Computer Engineering (EITCE),
Weber. (2021-07-04). ARIMA時間序列模型python應用-銅價格預測(一). https://adaptable-haze-butterfly-551.medium.com/arima%E6%99%82%E9%96%93%E5%BA%8F%E5%88%97%E6%A8%A1%E5%9E%8Bpython%E6%87%89%E7%94%A8-%E9%8A%85%E5%83%B9%E6%A0%BC%E9%A0%90%E6%B8%AC-%E4%B8%80-4f91693e3ec6
Yu, Y., Si, X., Hu, C., & Zhang, J. (2019). A review of recurrent neural networks: LSTM cells and network architectures. Neural computation, 31(7), 1235-1270.
Zeroual, A., Harrou, F., Dairi, A., & Sun, Y. (2020). Deep learning methods for forecasting COVID-19 time-Series data: A Comparative study. Chaos, Solitons & Fractals, 140, 110121.