We analyzed long-term temperature trends in Utah using a relatively new signal processing method called Empirical Mode Decomposition (EMD). We evaluated the available weather records in Utah and selected 52 stations, which had records longer than 60 years, for analysis. We analyzed daily temperature data, both minimum and maximums, using the EMD method that decomposes non-stationary data (data with a trend) into periodic components and the underlying trend. Most decomposition algorithms require stationary data (no trend) with constant periods and temperature data do not meet these constraints. In addition to identifying the long-term trend, we also identified other periodic processes in the data. While the immediate goal of this research is to characterize long-term temperature trends and identify periodic processes and anomalies, these techniques can be applied to any time series data to characterize trends and identify anomalies. For example, this approach could be used to evaluate flow data in a river to separate the effects of dams or other regulatory structures from natural flow or to look at other water quality data over time to characterize the underlying trends and identify anomalies, and also identify periodic fluctuations in the data. If these periodic fluctuations can be associated with physical processes, the causes or drivers might be discovered helping to better understand the system. We used EMD to separate and analyze long-term temperature trends. This provides awareness and support to better evaluate the extremities of climate change. Using these methods we will be able to define many new aspects of nonlinear and nonstationary data. This research was successful and identified several areas in which it could be extended including data reconstruction for time periods missing data. This analysis tool can be applied to various other time series records.

This thesis examines three decomposition techniques and their usability for economic and financial time series. The stock index DAX30 and the exchange rate from British pound to US dollar are used as representative economic time series. Additionally, autoregressive and conditional heteroscedastic simulations are analysed as benchmark processes to the real data. Discrete wavelet transform (DWT) uses wavelike functions to adapt the behaviour of time series on different time scales. The second method is the singular spectral analysis (SSA), which is applied to extract influential reconstructed modes. As a third algorithm, empirical mode decomposition (END) leads to intrinsic mode functions, who reflect the short and long term fluctuations of the time series. Some problems arise in the decomposition process, such as bleeding at the DWT method or mode mixing of multiple EMD mode functions. Conclusions to evaluate the predictability of the time series are drawn based on entropy - and recurrence - analysis. The cyclic behaviour of the decompositions is examined via the coefficient of variation, based on the instantaneous frequency. The results show rising predictability, especially on higher decomposition levels. The instantaneous frequency measure leads to low values for regular oscillatory cycles, irregular behaviour results in a high variation coefficient. The singular spectral analysis show frequency - stable cycles in the reconstructed modes, but represents the influences of the original time series worse than the other two methods, which show on the contrary very little frequency - stability in the extracted details.

Ο στόχος αυτής της εργασίας ήταν η αναγνώριση έξι βασικών κινήσεων του χεριού με χρήση δύο συστημάτων. Όντας θέμα διεπιστημονικού επιπέδου έγινε μελέτη της ανατομίας των μυών του πήχη, των βιοσημάτων, της μεθόδου της ηλεκτρομυογραφίας (ΗΜΓ) και μεθόδων αναγνώρισης προτύπων. Παράλληλα, το σήμα περιείχε αρκετό θόρυβο και έπρεπε να αναλυθεί, με χρήση του EMD, να εξαχθούν χαρακτηριστικά αλλά και να μειωθεί η διαστασιμότητά τους, με χρήση των RELIEF και PCA, για βελτίωση του ποσοστού επιτυχίας ταξινόμησης. Στο πρώτο μέρος γίνεται χρήση συστήματος ΗΜΓ της Delsys αρχικά σε ένα άτομο και στη συνέχεια σε έξι άτομα με το κατά μέσο όρο επιτυχημένης ταξινόμησης, για τις έξι αυτές κινήσεις, να αγγίζει ποσοστά άνω του 80%. Το δεύτερο μέρος περιλαμβάνει την κατασκευή αυτόνομου συστήματος ΗΜΓ με χρήση του Arduino μικροελεγκτή, αισθητήρων ΗΜΓ και ηλεκτροδίων, τα οποία είναι τοποθετημένα σε ένα ελαστικό γάντι. Τα αποτελέσματα ταξινόμησης σε αυτή την περίπτωση αγγίζουν το 75%. / The aim of this work was to identify six basic movements of the hand using two systems. Being an interdisciplinary topic, there has been conducted studying in the anatomy of forearm muscles, biosignals, the method of electromyography (EMG) and methods of pattern recognition. Moreover, the signal contained enough noise and had to be analyzed, using EMD, to extract features and to reduce its dimensionality, using RELIEF and PCA, to improve the success rate of classification. The first part uses an EMG system of Delsys initially for an individual and then for six people with the average successful classification, for these six movements at rates of over 80%. The second part involves the construction of an autonomous system EMG using an Arduino microcontroller, EMG sensors and electrodes, which are arranged in an elastic glove. Classification results in this case reached 75% of success.

本研究主要應用基於總體經驗模態分解法(EEMD)之倒傳遞類神經網路(BPNN)預測兩種不同的非線性時間序列數據，包括政大逐時用電量以及逐日歷史黃金價格。透過EEMD，這兩種資料會分別被拆解為數條具有不同物理意義的本徵模態函數(IMF)，而這讓我們可以將這些IMF視為各種影響資料的重要因子，並且可將拆解過後的IMF放入倒傳遞類神經網路中做訓練。 另外在本文中，我們也採用移動視窗法作為預測過程中的策略，另外也應用內插法和外插法於逐時用電量的預測。內插法主要是用於補點以及讓我們的數據變平滑，外插法則可以在某個範圍內準確預測後續的趨勢，此兩種方法皆對提升預測準確度占有重要的影響。 利用本文的方法，可在預測的結果上得到不錯的準確性，但為了進一步提升精確度，我們利用多次預測的結果加總平均，然後和只做一次預測的結果比較，結果發現多次加總平均後的精確度的確大幅提升，這是因為倒傳遞類神經網路訓練過程中其目標為尋找最小誤差函數的關係所致。 / In this paper, we applied the Ensemble Empirical Mode Decomposition (EEMD) based Back-propagation Neural Network (BPNN) learning paradigm to two different topics for forecasting: the hourly electricity consumption in NCCU and the historical daily gold price. The two data series are both non-linear and non-stationary. By applying EEMD, they were decomposed into a finite, small number of meaningful Intrinsic Mode Functions (IMFs). Depending on the physical meaning of IMFs, they can be regarded as important variables which are input into BPNN for training. We also use moving-window method in the prediction process. In addition, cubic spline interpolation as well as extrapolation as our strategy is applied to electricity consumption forecasting, these two methods are used for smoothing the data and finding local trend to improve accuracy of results. The prediction results using our methods and strategy resulted in good accuracy. However, for further accuracy, we used the ensemble average method, and compared the results with the data produced without applying the ensemble average method. By using the ensemble average, the outcome was more precise with a smaller error, it results from the procedure of finding minimum error function in the BPNN training.

L'objectif repose sur le traitement et l'analyse des signaux non-stationnaires, multi-composantes. <br />Pour le traitement (filtrage et débruitage), nous proposons de nouveaux outils fondés sur la Transformation de Huang (ou Décomposition modale empirique : EMD). Partant de l'opérateur de Teager-Kaiser, nous proposons un nouvel opérateur de mesure d'interaction entre deux signaux complexes. Nous établissons les liens théoriques avec les représentations temps-fréquence de la classe de Cohen. Nous montrons que c'est une mesure de similarité et qu'il est adapté à la détection de signaux. <br />Pour l'analyse, nous introduisons une nouvelle méthode temps-fréquence basée sur l'utilisation conjointe de l'EMD et de l'opérateur de Teager-Kaiser : la Transformation de Huang-Teager (THT). Pour illustrer ces concepts, des résultats de filtrage, de débruitage, de détection, d'analyse temps-fréquence de signaux sont présentés. Nous terminons par l'analyse et classification des échos de cibles sonars par THT.

La Décomposition Modale Empirique (EMD) est un outil de traitement de signal piloté par les données et dédié aux signaux non-stationnaires issus ou non de systèmes linéaires. L'idée de base de l'EMD est l'interpolation des extrema par des splines pour extraire de composantes oscillantes appelées modes empiriques intrinsèques (IMFs) et un résidu. Dans cette thèse, un nouvel algorithme de l'EMD est introduit où au lieu d'une interpolation rigide, un lissage est utilisé pour la construction des enveloppes supérieures et inférieures du signal à décomposer. Ce nouvel algorithme est plus robuste au bruit que l'EMD conventionnelle et réduit le nombre d'IMFs "artificielles" (sur-décomposition). En combinant le nouvel algorithme et la méthode de séparation d'énergie (ESA) basée sur l'Opérateur d'Energie de Teager-Kaiser (OETK), un nouveau schéma de démodulation des signaux AM-FM multi-composante appelé EMD-ESA est introduit. Différentes versions de l'EMD-ESA sont analysées en terme de performance. Pour l'analyse Temps-Fréquence (TF), une nouvelle formulation de la carte TF de l'EMD-ESA appelée Transformation de Teager-Huang (THT) est présentée. Cette nouvelle Représentation TF (RTF) ne présentant pas de termes d'interférences est comparée aux RTF classiques telles que le spectrogramme, le scalogramme, la distribution de Wigner-Ville Distribution (WVD), la Pseudo-WVD et la réallocation de la Pseudo-WVD. En combinant la nouvelle formulation de la THT et la transformée de Hough, une nouvelle méthode de détection des signaux multi-composante à modulation linéaire de fréquence dans le plan TF est présentée. Cette méthode de détection est appelée transformation de Teager-Huang-Hough (THHT). Les résultats de la THHT sont comparés à ceux de la transformée WVD-Hough. Finalement, l'analyse TF par THT et par des RTF classiques (WVD, spectrogramme, etc.) de signaux réels de rétrodiffusion par des coques cylindriques de dimensions et de caractéristiques physiques différentes est présentée. Les résultats obtenus montrent l'apport de la THT comme un outil TF.

This thesis examines three decomposition techniques and their usability for economic and financial time series. The stock index DAX30 and the exchange rate from British pound to US dollar are used as representative economic time series. Additionally, autoregressive and conditional heteroscedastic simulations are analysed as benchmark processes to the real data. Discrete wavelet transform (DWT) uses wavelike functions to adapt the behaviour of time series on different time scales. The second method is the singular spectral analysis (SSA), which is applied to extract influential reconstructed modes. As a third algorithm, empirical mode decomposition (END) leads to intrinsic mode functions, who reflect the short and long term fluctuations of the time series. Some problems arise in the decomposition process, such as bleeding at the DWT method or mode mixing of multiple EMD mode functions. Conclusions to evaluate the predictability of the time series are drawn based on entropy - and recurrence - analysis. The cyclic behaviour of the decompositions is examined via the coefficient of variation, based on the instantaneous frequency. The results show rising predictability, especially on higher decomposition levels. The instantaneous frequency measure leads to low values for regular oscillatory cycles, irregular behaviour results in a high variation coefficient. The singular spectral analysis show frequency - stable cycles in the reconstructed modes, but represents the influences of the original time series worse than the other two methods, which show on the contrary very little frequency - stability in the extracted details.:1. Einleitung 2. Datengrundlage 2.1. Auswahl und Besonderheiten ökonomischer Zeitreihen 2.2. Simulationsstudie mittels AR-Prozessen 2.3. Simulationsstudie mittels GARCH-Prozessen 3. Zerlegung mittels modernen Techniken der Zeitreihenanalyse 3.1. Diskrete Wavelet Transformation 3.2. Singulärsystemanalyse 3.3. Empirische Modenzerlegung 4. Bewertung der Vorhersagbarkeit 4.1. Entropien als Maß der Kurzzeit-Vorhersagbarkeit 4.2. Rekurrenzanalyse 4.3. Frequenzstabilität der Zerlegung 5. Durchführung und Interpretation der Ergebnisse 5.1. Visuelle Interpretation der Zerlegungen 5.2. Beurteilung mittels Charakteristika 6. Fazit

金融市場是個變化莫測的環境，看似隨機，在隨機中卻隱藏著某些特性與關係。不論是自然現象中的氣象預測或是金融領域中對下一時刻價格的預測, 都有相似的複雜性。 時間序列的預測一直都是許多領域中重要的項目之一, 金融時間序列的預測也不例外。在本論文中我們針對金融時間序列的非線性與非穩態關係引入類神經網路(ANNs) 與集合經驗模態分解法(EEMD), 藉由ANNs處理非線性問題的能力與EEMD處理時間序列信號的優點，並進一步與傳統上使用於金融時間序列分析的自回歸滑動平均模型(ARMA)進行複合式的模型建構，引入燭型圖概念嘗試進行高頻下的台指期貨TAIEX交易。在不計交易成本的績效測試下本研究的高頻交易模型有突出的績效，證明以ANNs、EEMD方法與ARMA組成的混合式模型在高頻時間尺度交易下有相當的發展潛力，具有進一步發展的價值。在處理高頻時間尺度下所產生的大型數據方面，引入平行運算架構SPMD(single program, multiple data)以增進其處理大型資料下的運算效率。本研究亦透過分析高頻時間尺度的本質模態函數(IMFs)探討在高頻尺度下影響台指期貨價格的因素。 / Financial market is complex, unstable and non-linear system, it looks like have some principle but the principle usually have exception. The forecasting of time series always an issue in several field include finance. In this thesis we propose several version of hybrid models, they combine Ensemble Empirical Mode Decomposition (EEMD), Back-Propagation Neural Networks(BPNN) and ARMA model, try to improve the forecast performance of financial time series forecast. We also found the physical means or impact factors of IMFs under high-frequency time-scale. For processing the massive data generated by high-frequency time-scale, we pull in the concept of big data processing, adopt parallel computing method ”single program, multiple data (SPMD)” to construct the model improve the computing performance. As the result of backtesting, we prove the enhanced hybrid models we proposed outperform the standard EEMD-BPNN model and obtain a good performance. It shows adopt ANN, EEMD and ARMA in the hybrid model configure for high-frequency trading modeling is effective and it have the potential of development.