關於時間序列的異常檢測是一個很重要的領域，在許多領域中都具有廣泛的應用，例如金融、製造、醫療保健、網路安全等，可以幫助檢測可能的問題、預防損失或故障。
異常檢測尤其是單變量的異常檢測更是研究關注的重點，識別和標記那些與正常模式明顯不同的異常點或異常模式，這些異常可能是突然的、不尋常的事件，也可能是隨時間逐漸變化的趨勢，都需要我們透過結合領域知識和專業判斷異常。
本論文的目標是先將各種不同領域的時間序列單變量資料集進行預處理和分類，將資料及分類成平穩時序資料、週期性時序資料和非平穩且非週期性時序資料，接著再觀察不同的異常檢測方法對於三種時序資料的效能評估，尋找各種時序資料最佳的檢測方法，結果表明了機器學習的模型相比於統計模型和深度學習模型具有更佳的效能與普適性。

Anomaly detection on time series is an important field with wide applications in many domains, such as finance, manufacturing, healthcare, cybersecurity, etc., to help detect possible problems and prevent loss or failure.
Anomaly detection, especially univariate anomaly detection, is the focus of research. It identifies and marks abnormal points or abnormal patterns that are significantly different from normal patterns. These abnormalities may be sudden and unusual events, or they may be gradual over time. Changing trends require us to combine domain knowledge and professional judgment exceptions.
The objective of this paper is to preprocess and classify diverse time series univariate datasets from different domains. The data is categorized into stationary time series, periodic time series, and non-stationary and non-periodic time series.
Subsequently, different anomaly detection methods are evaluated for their performance on the three types of time series data to identify the optimal detection method for each type. The results show that the machine learning model has better performance and universality than statistical models and deep learning models.

致謝 II
摘 要 III
ABSTRACT IV
目 錄 V
圖目錄 VII
表目錄 VIII
第1章 前言 1
1-1 研究背景與動機 1
1-2 研究目的 1
1-3 論文綱要 2
第2章 背景知識 3
2-1 時間序列 3
2-2 異常檢測 4
2-2-1 異常的種類 4
2-3 時間序列分析 5
2-3-1 平穩時間序列 5
2-3-2 擴張迪基-福勒檢驗 6
2-3-3 週期性時間序列 7
2-3-4 自相關函數 8
2-3-5 皮爾森相關係數 8
2-4 統計模型 9
2-5 機器學習模型 10
2-5-1 監督式學習模型 10
2-5-2 非監督式學習模型 12
2-6 深度學習模型 13
第3章 研究方法 15
3-1 資料集 15
3-2 資料預處理 16
3-3 資料集分析 17
3-3-1 平穩檢測 17
3-3-2 週期性檢測 18
3-4 資料集選擇 19
3-5 異常檢測模型 20
3-5-1 ARIMA 21
3-5-2 Isolation Forest 21
3-5-3 LOF 22
3-5-4 KNN 22
3-5-5 LSTM 23
3-5-6 1D-CNN 25
3-5-7 LSTM Auto-Encoder 26
3-6 超參數調整 27
3-7 閾值設定 29
3-8 效能評估 30
第4章 實驗數據與結果討論 33
4-1 實驗環境 33
4-2 實驗結果 33
4-3 結果分析 34
第5章 結論與未來工作 37
5-1 結論 37
5-2 未來工作 38
第6章 參考文獻 39

[1]Chollet, F., Keras大神歸位：深度學習全面進化！用 Python 實作CNN、RNN、GRU、LSTM、GAN、VAE、Transformer. 2022.
[2]Chatfield, C., Time-series forecasting. 2000: CRC press.
[3]Ismail Fawaz, H., et al., Deep learning for time series classification: a review. Data mining and knowledge discovery, 2019. 33(4): pp. 917.
[4]Guralnik, V. and J. Srivastava. Event detection from time series data. in Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining. 1999.
[5]Zhang, L., et al. Accelword: Energy efficient hotword detection through accelerometer. in Proceedings of the 13th Annual International Conference on Mobile Systems, Applications, and Services. 2015.
[6]Blázquez-García, A., et al., A review on outlier/anomaly detection in time series data. ACM Computing Surveys (CSUR), 2021. 54(3): pp. 1.
[7]高健賓, 基於統計與深度學習之單變數時間序列異常檢測. 2019: pp. 4.
[8]Gupta, A., et al., Approaches and_Applications of Early Classification of Time Series:A Review. 2023: pp. 48.
[9]榮騰翎, IoT整合管理平台之異常檢測和事件警報系統. 2017: pp. 8.
[10]Choi, K., et al., Deep Learning for Anomaly Detection in Time-Series Data: Review, Analysis, and Guidelines. IEEE Access, 2021. 9: pp. 120044.
[11]Singh, A. A Gentle Introduction to Handling a Non-Stationary Time Series in Python. 2020; Available from: https://www.analyticsvidhya.com/blog/2018/09/non-stationary-time-series-python/.
[12]Elfeky, M.G., W.G. Aref, and A.K. Elmagarmid, Periodicity detection in time series databases. IEEE Transactions on Knowledge and Data Engineering, 2005: pp. 875.
[13]Fuller, W.A., Introduction to statistical time series. 2009: John Wiley & Sons.
[14]Cohen, I., et al., Pearson correlation coefficient. Noise reduction in speech processing, 2009: pp. 1.
[15]Akaike, H., A new look at the statistical model identification. IEEE transactions on automatic control, 1974. 19(6): pp. 716.
[16]Weisang, G. and Y. Awazu, Vagaries of the Euro: an Introduction to ARIMA Modeling. Case Studies In Business, Industry And Government Statistics, 2008: pp. 45.
[17]Alpaydin, E., Introduction to machine learning. 2020: MIT press.
[18]Kotsiantis, S.B., Decision trees: a recent overview. Artificial Intelligence Review, 2013. 39: pp. 261.
[19]Biau, G. and E. Scornet, A random forest guided tour. Test, 2016. 25: pp. 197.
[20]Zhang, Z., Introduction to machine learning: k-nearest neighbors. Annals of translational medicine, 2016.
[21]Arnold, L., et al. An introduction to deep learning. in European Symposium on Artificial Neural Networks (ESANN). 2011.
[22]Numenta. The Numenta Anomaly Benchmark (NAB). Available from: https://github.com/numenta/NAB.
[23]Statsmodels User Guide. Available from: https://www.statsmodels.org/stable/user-guide.html.
[24]Lee, S. and H.K. Kim, ADSaS: Comprehensive Real-time Anomaly Detection System. 2018.
[25]Al Farizi, W.S., I. Hidayah, and M.N. Rizal. Isolation forest based anomaly detection: A systematic literature review. in 2021 8th International Conference on Information Technology, Computer and Electrical Engineering (ICITACEE). 2021. IEEE.
[26]Alghushairy, O., et al., A review of local outlier factor algorithms for outlier detection in big data streams. Big Data and Cognitive Computing, 2020.
[27]Yu, Y., et al., A review of recurrent neural networks: LSTM cells and network architectures. Neural computation, 2019: pp. 1235.
[28]Meyer, D., Introduction to autoencoders. 2015.
[29]MENG, C., et al., A Time Convolutional Network Based Outlier Detection for Multidimensional Time Series in Cyber-Physical-Social Systems. 2020.
[30]隨機搜尋（Random Searching）演算法概述. Available from: https://www.796t.com/content/1544730847.html.
[31]plusone. 機器學習：交叉驗證！. Available from: https://ithelp.ithome.com.tw/articles/10197461.
[32]Lee, D.K., J. In, and S. Lee, Standard deviation and standard error of the mean. Korean journal of anesthesiology, 2015: pp. 220.
[33]Kumar, T. Solution of linear and non linear regression problem by K Nearest Neighbour approach: By using three sigma rule. in 2015 IEEE International Conference on Computational Intelligence & Communication Technology. 2015. IEEE.
[34]YC. 如何辨別機器學習模型的好壞？. Available from: https://ycc.idv.tw/confusion-matrix.html.
[35]Streiner, D.L. and G.R. Norman, “Precision” and “accuracy”: two terms that are neither. Journal of clinical epidemiology, 2006. 59(4): pp. 327.
[36]Buckland, M. and F. Gey, The relationship between recall and precision. Journal of the American society for information science, 1994. 45(1): pp. 12.
[37]Kundu, R. F1 Score in Machine Learning: Intro & Calculation. Available from: https://www.v7labs.com/blog/f1-score-guide.