The foreign exchange market is one of the largest and most active financial markets with enormous daily trading volumes. Exchange rates are influenced by the interactions of a large number of agents, each operating with different intentions and on different time scales. This gives rise to nonlinear and non-stationary behaviour which complicates modelling. This research proposes a neural network based model trained on data filtered with a novel Empirical Mode Decomposition (EMD) filtering method for the forecasting of exchange rates. One minor and two major exchange rates are evaluated in this study. Firstly the ideal prediction horizons for trading are calculated for each of the exchange rates. The data is filtered according to this ideal prediction horizon using the EMD-filter. This EMD-filter dynamically filters the data based on the apparent number of intrinsic modes in the signal that can contribute towards prediction over the selected horizon. The filter is employed to filter out high frequency noise and components that would not contribute to the prediction of the exchange rate at the chosen timescale. This results in a clearer signal that still includes nonlinear behaviour. An artificial neural network predictor is trained on the filtered data using different sampling rates that are compatible with the cut-off frequency. The neural network is able to capture the nonlinear relationships between historic and future filtered data with greater certainty compared to a neural network trained on unfiltered data. Results show that the neural network trained on EMD-filtered data is significantly more accurate at prediction of exchange rates compared to the benchmark models of a neural network trained on unfiltered data and a random walk model for all the exchange rates. The EMD-filtered neural network’s predicted returns for the higher sample rates show higher correlations with the actual returns, and significant profits can be made when applying a trading strategy based on the predictions. Lower sample rates that just marginally satisfy the Nyquist criterion perform comparably with the neural network trained on unfiltered data; this may indicate that some aliasing occurs for these sampling rates as the EMD low-pass filter has a gradual cut-off, leaving some high frequency noise within the signal. The proposed model of the neural network trained on EMD-filtered data was able to uncover systematic relationships between the filtered inputs and actual outputs. The model is able to deliver profitable average monthly returns for most of the tested sampling rates and forecast horizons of the different exchange rates. This provides evidence that systematic predictable behaviour is present within exchange rates, and that this systematic behaviour can be modelled if it is properly separated from high frequency noise. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

The foreign exchange market is one of the largest and most active financial markets with enormous daily trading volumes. Exchange rates are influenced by the interactions of a large number of agents, each operating with different intentions and on different time scales. This gives rise to nonlinear and non-stationary behaviour which complicates modelling. This research proposes a neural network based model trained on data filtered with a novel Empirical Mode Decomposition (EMD) filtering method for the forecasting of exchange rates. One minor and two major exchange rates are evaluated in this study. Firstly the ideal prediction horizons for trading are calculated for each of the exchange rates. The data is filtered according to this ideal prediction horizon using the EMD-filter. This EMD-filter dynamically filters the data based on the apparent number of intrinsic modes in the signal that can contribute towards prediction over the selected horizon. The filter is employed to filter out high frequency noise and components that would not contribute to the prediction of the exchange rate at the chosen timescale. This results in a clearer signal that still includes nonlinear behaviour. An artificial neural network predictor is trained on the filtered data using different sampling rates that are compatible with the cut-off frequency. The neural network is able to capture the nonlinear relationships between historic and future filtered data with greater certainty compared to a neural network trained on unfiltered data. Results show that the neural network trained on EMD-filtered data is significantly more accurate at prediction of exchange rates compared to the benchmark models of a neural network trained on unfiltered data and a random walk model for all the exchange rates. The EMD-filtered neural network’s predicted returns for the higher sample rates show higher correlations with the actual returns, and significant profits can be made when applying a trading strategy based on the predictions. Lower sample rates that just marginally satisfy the Nyquist criterion perform comparably with the neural network trained on unfiltered data; this may indicate that some aliasing occurs for these sampling rates as the EMD low-pass filter has a gradual cut-off, leaving some high frequency noise within the signal. The proposed model of the neural network trained on EMD-filtered data was able to uncover systematic relationships between the filtered inputs and actual outputs. The model is able to deliver profitable average monthly returns for most of the tested sampling rates and forecast horizons of the different exchange rates. This provides evidence that systematic predictable behaviour is present within exchange rates, and that this systematic behaviour can be modelled if it is properly separated from high frequency noise. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

Nan Wan is a half-closed embayment in the most southern part of Taiwan. While facing the Luzon Strait, it also connects to the Pacific Ocean in its southeast, and is adjacent the Taiwan Strait and the South China Sea . In view of general oceanic circulation, Nan Wan Bay happens to lie to the rim of South China Sea circumfluence and Kuroshio where a variety of water mass exchange has taken place, causing saline intrusion and mixed of water. Seasonal variation and tidal fluctuations also contribute to the exchange of water masses. The Third Nuclear Power Station of Taiwan Power Company is located in Nan Wan with its thermal discharge outlet adjacent to Maobitou to the west of the bay in order to minimize the effect of warm water discharge on the local marine ecology and coral . A long-term monitoring program on water temperature and other environmental factors has been set up implemented .this research report will first describe the archives regarding the hydrology in Nan Wan in support of monitoring the process in temperature variation . Previous research efforts are found somehow unable reveal precisely the physical mechanism leading to water temperature variations in the bay, due to limited facilities, short of information or poor analytical tools. This report adopts 14 records of water temperature at the thermal outlet of the Third Nuclear Power Station for signal analysis. As to non-linear and unstable data analysis, it is based on the Hilbert-Huang Transform. HHT includes Empirical Mode Decomposition, EMD which could decompose the raw data into numerous Intrinsic Mode Function, IMF. It is allowed to comprehend the main causes for the rising and dropping of water temperature based on the variation of spectroscopy by transferring through Hilbert and analyzing via IMF. Furthermore, the characteristic of each quantity could be developed according to the quantities acquired from the former method of HHT. The analytical report of water temperature covers 14 records dating from 1999 to 2003. In light of the analytical report, tide and wind account for the main cause of the temperature variation in waters while demanding information to ensure whether it is influenced by other factors like internal waves, water masses or landforms, etc. In addition, the report compares the difference in the same of data between FFT and HHT and moreover concludes the advantages and disadvantages as reference for researches.

Conventional rotating machine vibration monitoring techniques are based on the assumption that changes in the measured structural response are caused by deterioration in the condition of the rotating machine. However, due to variations of the rotational speed, the measured signal may be non-stationary and difficult to interpret. For this reason, the order tracking technique is introduced. One of main advantages of order tracking over traditional vibration monitoring lies in its ability to clearly identify non-stationary vibration data and to a large extent exclude the influences of varying rotational speed. In recent years, different order tracking techniques have been developed. Each of these has their own pros and cons in analyzing rotating machinery vibration signals. In this research, three existing order tracking techniques are extensively investigated and combined to further explore their abilities in the context of condition monitoring. Firstly, computed order tracking is examined. This allows non-stationary effects due to the variation of rotational speed to be largely excluded. However, this technique was developed to deal with the entire raw signal and therefore looses the ability to focus on each individual order of interest. Secondly, Vold-Kalman filter order tracking is considered. It is widely reported that this technique overcomes many of the limitations of other order tracking methods and extracts order signals into the time domain. However because of the adaptive nature of the Vold-Kalman filter, the non-stationary effects due to the rotational speed will remain in the extracted order waveform, which is not ideal for conventional signal processing methods such as Fourier analysis. Yet, the strict mathematical filter (the Vold-Kalman filter is based upon two rigorous mathematical equations, namely the data equation and the structural equation, to realize the filter) gives this technique an excellent ability to focus on the orders of interest. Thirdly, the empirical mode decomposition method is studied. In the literature, this technique is claimed to be an effective diagnostic tool for various kinds of applications including diagnosis of rotating machinery faults. Its unique empirical way of extracting non-stationary and non-linear signals allows it to capture machine fault information which is intractable by other order tracking methods. But since there is no precise mathematical definition for an intrinsic mode function in empirical mode decomposition and – as far as could be ascertained – no published assessment of the relationship between an order and an intrinsic mode function, this technique has not been properly considered by analysts in terms of order tracking. As a result, its abilities have not really been explored in the context of order related vibrations in rotating machinery. In this research, the relationship between an order and an intrinsic mode function is discussed and it is treated as a special kind of order tracking method. In stead of focusing individually on each order tracking technique, the current work synthesizes different order tracking techniques. Through combination, exchange and reconciliation of ideas between these order tracking techniques, three improved order tracking techniques are developed for the purpose of enhancing order tracking analysis in condition monitoring. The techniques are Vold-Kalman filter and computed order tracking (VKC-OT), intrinsic mode function and Vold-Kalman filter order tracking (IVK-OT) and intrinsic cycle re-sampling (ICR). Indeed, these improved approaches contribute to current order tracking practice, by providing new order tracking methods with new capabilities for condition monitoring of systems which are intractable by traditional order tracking methods, or which enhances results obtained by these traditional methods. The work commences with a discussion of the inter-relationship between the order tracking methods which are considered in the thesis, and exposition of the scope of the work and an explanation of the way these independent order tracking techniques are integrated in the thesis. To demonstrate the abilities of the improved order tracking techniques, two simulation models are established. One is a simple single-degree-of-freedom (SDOF) rotor model with which VKC-OT and IVK-OT techniques are demonstrated. The other is a simplified gear mesh model through which the effectiveness of the ICR technique is proved. Finally two experimental set-ups in the Sasol Laboratory for Structural Mechanics at the University of Pretoria are used for demonstrating the improved approaches for real rotating machine signals. One test rig was established to monitor an automotive alternator driven by a variable speed motor. A stator winding inter-turn short was artificially introduced. Advantages of the VKC-OT technique are presented and features clear and clean order components under non-stationary conditions. The diagnostic ability of the IVK-OT technique of further decomposing an intrinsic mode function is also demonstrated via signals from this test rig, so that order signals and vibrations that modulate orders in IMFs can be separated and used for condition monitoring purposes. The second experimental test rig is a transmission gearbox. Artificially damaged gear teeth were introduced. The ICR technique provides a practical alternative tool for fault diagnosis. It proves to be effective in diagnosing damaged gear teeth. / Thesis (PhD)--University of Pretoria, 2011. / Mechanical and Aeronautical Engineering / unrestricted

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.

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.

The idea of time series forecasting techniques is that the past has certain information about future. So, the question of how the information is encoded in the past can be interpreted and later used to extrapolate events of future constitute the crux of time series analysis and forecasting. Several methods such as qualitative techniques (e.g., Delphi method), causal techniques (e.g., least squares regression), quantitative techniques (e.g., smoothing method, time series models) have been developed in the past in which the concept lies in establishing a model either theoretically or mathematically from past observations and estimate future from it. Of all the models, time series methods such as autoregressive moving average (ARMA) process have gained popularity because of their simplicity in implementation and accuracy in obtaining forecasts. But, these models were formulated based on certain properties that a time series is assumed to possess. Classical decomposition techniques were developed to supplement the requirements of time series models. These methods try to define a time series in terms of simple patterns called trend, cyclical and seasonal patterns along with noise. So, the idea of decomposing a time series into component patterns, later modeling each component using forecasting processes and finally combining the component forecasts to obtain actual time series predictions yielded superior performance over standard forecasting techniques. All these methods involve basic principle of moving average computation. But, the developed classical decomposition methods are disadvantageous in terms of containing fixed number of components for any time series, data independent decompositions. During moving average computation, edges of time series might not get modeled properly which affects long range forecasting. So, these issues are to be addressed by more efficient and advanced decomposition techniques such as Wavelets and Empirical Mode Decomposition (EMD). Wavelets and EMD are some of the most innovative concepts considered in time series analysis and are focused on processing nonlinear and nonstationary time series. Hence, this research has been undertaken to ascertain the predictability of nonstationary time series using wavelet and Empirical Mode Decomposition (EMD) based ARMA models. The development of wavelets has been made based on concepts of Fourier analysis and Window Fourier Transform. In accordance with this, initially, the necessity of involving the advent of wavelets has been presented. This is followed by the discussion regarding the advantages that are provided by wavelets. Primarily, the wavelets were defined in the sense of continuous time series. Later, in order to match the real world requirements, wavelets analysis has been defined in discrete scenario which is called as Discrete Wavelet Transform (DWT). The current thesis utilized DWT for performing time series decomposition. The detailed discussion regarding the theory behind time series decomposition is presented in the thesis. This is followed by description regarding mathematical viewpoint of time series decomposition using DWT, which involves decomposition algorithm. EMD also comes under same class as wavelets in the consequence of time series decomposition. EMD is developed out of the fact that most of the time series in nature contain multiple frequencies leading to existence of different scales simultaneously. This method, when compared to standard Fourier analysis and wavelet algorithms, has greater scope of adaptation in processing various nonstationary time series. The method involves decomposing any complicated time series into a very small number of finite empirical modes (IMFs-Intrinsic Mode Functions), where each mode contains information of the original time series. The algorithm of time series decomposition using EMD is presented post conceptual elucidation in the current thesis. Later, the proposed time series forecasting algorithm that couples EMD and ARMA model is presented that even considers the number of time steps ahead of which forecasting needs to be performed. In order to test the methodologies of wavelet and EMD based algorithms for prediction of time series with non stationarity, series of streamflow data from USA and rainfall data from India are used in the study. Four non-stationary streamflow sites (USGS data resources) of monthly total volumes and two non-stationary gridded rainfall sites (IMD) of monthly total rainfall are considered for the study. The predictability by the proposed algorithm is checked in two scenarios, first being six months ahead forecast and the second being twelve months ahead forecast. Normalized Root Mean Square Error (NRMSE) and Nash Sutcliffe Efficiency Index (Ef) are considered to evaluate the performance of the proposed techniques. Based on the performance measures, the results indicate that wavelet based analyses generate good variations in the case of six months ahead forecast maintaining harmony with the observed values at most of the sites. Although the methods are observed to capture the minima of the time series effectively both in the case of six and twelve months ahead predictions, better forecasts are obtained with wavelet based method over EMD based method in the case of twelve months ahead predictions. It is therefore inferred that wavelet based method has better prediction capabilities over EMD based method despite some of the limitations of time series methods and the manner in which decomposition takes place. Finally, the study concludes that the wavelet based time series algorithm could be used to model events such as droughts with reasonable accuracy. Also, some modifications that could be made in the model have been suggested which can extend the scope of applicability to other areas in the field of hydrology.

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