Volatility is a key variable in option pricing, trading, and hedging strategies. The purpose of this article is to improve the accuracy of forecasting implied volatility using an extension of genetic programming (GP) by means of dynamic training‐subset selection methods. These methods manipulate the training data in order to improve the out‐of‐sample patterns fitting. When applied with the static subset selection method using a single training data sample, GP could generate forecasting models, which are not adapted to some out‐of‐sample fitness cases. In order to improve the predictive accuracy of generated GP patterns, dynamic subset selection methods are introduced to the GP algorithm allowing a regular change of the training sample during evolution. Four dynamic training‐subset selection methods are proposed based on random, sequential, or adaptive subset selection. The latest approach uses an adaptive subset weight measuring the sample difficulty according to the fitness cases' errors. Using real data from S&P500 index options, these techniques are compared with the static subset selection method. Based on mean squared error total and percentage of non‐fitted observations, results show that the dynamic approach improves the forecasting performance of the generated GP models, especially those obtained from the adaptive‐random training‐subset selection method applied to the whole set of training samples.

Traditional parametric methods have limited success in estimating and forecasting the volatility of financial securities. Recent advance in evolutionary computation has provided additional tools to conduct data mining effectively. The current work applies the genetic programming in a Time Series Data Mining framework to characterize the S&P100 high frequency data in order to Forecast the one step ahead integrated volatility. Results of the experiment have shown to be superior to those derived by the traditional methods.

This work proposes a hybrid algorithm called Probabilistic Incremental Cartesian Genetic Programming (PI-CGP), which integrates an Estimation of Distribution Algorithm (EDA) with Cartesian Genetic Programming (CGP). PI-CGP uses a fixed-length problem representation and the algorithm constructs a probabilistic model of promising solutions. PI-CGP was evaluated on symbolic regression problems and next trading day stock price forecasting. On the symbolic regression problems PI-CGP did not outperform other approaches. The reason could be premature convergence and being trapped at a local minimum. However, PI-CGP was competitive at stock market forecasting. It was comparable to a fusion model employing a Hidden Markov Model (HMM). HMMs are extensively used for time-series forecasting. This result is promising considering the volatile nature of the stock market and that PI-CGP was not customized toward forecasting.

This paper presents the results from characterizing and predicting the release of droplets of metal from a welder. The welding process joins two pieces of metal into one by making a joint between them. An arcing current melts the tip of a wire, forming a metal droplet that elongates until it releases. The goal is to predict the moment when a droplet will release, which can improve the quality of the joint by allowing the droplet releases to be monitored and controlled. Because of the irregular, chaotic, and event nature of the droplet release, prediction is impossible using traditional time series methods. Using Time Series Data Mining techniques allows the droplet releases to be predicted with a high degree of accuracy. The Time Series Data Mining (TSDM) framework (Povinelli 1999; Povinelli and Feng 1998; Povinelli and Feng 1999) is applied to the prediction of welding droplet releases. Methods based on the TSDM framework are able to successfully characterize and predict complex, nonperiodic, irregular, and chaotic time series such as the release of metal droplets from a welder. This paper, which is divided into three sections, presents the results of applying the TSDM framework to this problem. The first section discusses the welding problem. The second section reviews the key TSDM concepts and an extension of the TSDM framework to multiple temporal patterns. The third section presents the prediction results. PROBLEM STATEMENT Welding joins two pieces of metal by forming a joint between them. As illustrated in Figure 1, a current arc is created between the welder and the metal to be joined. Wire is pushed out of the welder. The tip of the wire melts, forming a metal droplet that elongates (sticks out) until it releases. Predicting when a droplet of metal will release from a welder allows the quality of the metal joint to be monitored and controlled. The problem is to predict the releases { } , 1, t Y y t N = = , where t is a time index, and N is the number of observations, using the stickout { } , 1, t X x t N = = time series. This time series is a 1 Drs. C. Tolle, E. Larsen, D. Pace, and D. Iosty of INEEL gathered the data used in this paper. Their work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Materials and Materials Engineering, under DOE Idaho Operations Office Contract DE-AC07-94ID13223. measure of the droplet elongation. Because of the irregular, chaotic, and noisy nature of the droplet release, prediction is impossible using traditional time series methods. Figure 1 – Welding Process A sample of the stickout time series is illustrated in Figure 2. An electronic camera on the welding station measures the droplet stickout in pixels. It is sampled at 1kHz and comprised of approximately 5,000 observations. The release time series, also illustrated in Figure 2, indicates the release of a droplet (event) with a one and a non-release (nonevent) with a zero. It is synchronized with the stickout time series. Figure 2 – Welding Stickout and Release Time Series TIME SERIES DATA MINING METHOD Previous work (Povinelli 1999; Povinelli and Feng 1998; Povinelli and Feng 1999) presented the TSDM framework. Here the TSDM method for identifying multiple temporal pattern clusters is discussed. The TSDM method discussed here discovers hidden temporal patterns (vectors of length Q) characteristic of events (important occurrences) by time-delay embedding (Abarbanel 1996; Iwanski and Bradley 1998; Tolle 1997; Tolle and Gundersen 1998) an observed time series X into a reconstructed phase space, here simply called phase space. An event characterization function g is used to represent the eventness of a temporal pattern. An augmented phase space is formed by extending the phase space with g. The 150 160 170 180 190 200 40 0 42 0 44 0 46 0 48 0 50 0 52 0 54 0 56 0 58 0 60 0 t x t (p ix el s) stickout

This paper presents a hybrid prognosis approach of age-dependent hidden Markov model (HMM) and grey model (GM) for prediction of engineering asset health. Age-dependent HMM allows modeling the time duration of the hidden states and therefore is capable of prognosis. The estimated state duration probability distributions can be used to predict the remaining useful life (RUL) of the assets. The previous HMM based prognosis method assumed that the transition probabilities are only state-dependent. That is, the probability of making transition to a less healthy state does not increase with the age. In the proposed method, in order to characterize a deteriorating asset, an aging factor that discounts the probabilities of staying at current state while increasing the probabilities of transitions to less healthy states will be introduced. After the estimation of the aging factor, a grey model is used to compute the expected residual life (ERL) by redefining the hazard rate. With the asset health prognosis, the behavior of the asset condition can be predicted.

This paper introduces and illustrates a rough-set based approach to event prediction in multiple time series. The proposed approach uses two different versions of rough set theory to predict events occurrences and intensities. First, classical Indiscernibility relation-based Rough Set Approach (IRSA) is used to predict event classes and occurrences. Then, the Dominance-based Rough Set Approach (DRSA) is employed to predict the intensity of events. This paper presents the fundamental of the proposed approach and the conceptual architecture of a framework implementing this approach.

This paper develops the fundamental foundations of a technique for detection of faults in induction motors that is not based on the traditional Fourier transform frequency domain approach. The technique can extensively and economically characterize and predict faults from the induction machine adjustable speed drive design data. This is done through the development of dual-track proof-of-principle studies of fault simulation and identification. These studies are performed using our proven time stepping coupled finite element-state space method to generate fault case data. Then, the fault cases are classified by their inherent characteristics, so-called "signatures" or "fingerprints." These fault signatures are extracted or mined here from the fault case data using our novel time series data mining technique. The dual track of generating fault data and mining fault signatures was tested here on 3, 6, and 9 broken bar and broken end-ring connectors in a 208-V, 60-Hz, 4-pole, 1.2-hp, squirrel cage three-phase induction motor.

This paper describes a novel technique for determining a useful dimension for a time-delay embedding of an arbitrary time series, along with the individual time delays for each dimension. A binary-string genetic algorithm is designed to search for a variable number of time delays that minimize the standard deviation of the distance between each embedded data point and the centroid of the set of all data points, relative to the mean distance between each data point and the centroid. The geometric transformations of rotation and scaling are added to the algorithm to allow it to identify attractors that are not aligned with the data axes. Several artificial and real-world attractors and time series are analyzed to describe the types of attractors favorable to the use of this technique.

This paper addresses the question of how to develop forecasting models resulting from business processes that can be embodied in an intelligent decision support system. Moreover the design is suitable for evolving logistics and economic situations in which ports plan or foresee to have an improved economic role. The work presented in this paper also forms one component of a conceptual intelligent decision-making support system (i-DMSS) for port integration. The key objective of this work is to offer a model-based approach to Time Series Data Mining (TSDM) based on the assumptions that the time series may be produced by an underlying model, and that its flexibility is suitable to perform multivariate time-series analysis encompassing the notion of model selection and statistical learning known as the core of forecasting systems. The interrelated activities to induce domain knowledge are specified as the data collection principles, the descriptive modelling and normative modelling. Results indicate that for the period 2001 to 2005, the commodity throughput of coffee (tons) handled in the port of Buenaventura gains importance in the prediction of the Colombian national exports of coffee, thus indicating that the port operation was able to affect the economy in this regard. The previous period was strongly affected by outliers, creating a random walk process difficult to fit but feasible to produce due to unstable conditions evidenced in the economy.

This paper addresses the question of how to develop forecasting models resulting from business processes that can be embodied in an intelligent decision support system. Moreover the design is suitable for evolving logistics and economic situations in which ports plan or foresee to have an improved economic role. The key objective of this work is to offer a model-based approach to Time Series Data Mining (TSDM) based on the assumptions that the time series may be produced by an underlying model, and that its flexibility is suitable to perform multivariate time-series analysis encompassing the notion of model selection and statistical learning known as the core of forecasting systems. Results indicate that for the period 2001 to 2005, the commodity throughput of coffee (tons) handled in the port of Buenaventura gains importance in the prediction of the Colombian national exports of coffee, thus indicating that the port operation was able to affect the economy in this regard. The previous period was strongly affected by outliers, creating a random walk process difficult to fit but feasible to produce due to unstable conditions evidenced in the economy.

There are now domains where information is recorded over a period of time, leading to sequences of data known as time series. In many domains, like medicine, time series analysis requires to focus on certain regions of interest, known as events, rather than analyzing the whole time series. In this paper, we propose a framework for knowledge discovery in both one-dimensional and multidimensional time series containing events. We show how our approach can be used to classify medical time series by means of a process that identifies events in time series, generates time series reference models of representative events and compares two time series by analyzing the events they have in common. We have applied our framework on time series generated in the areas of electroencephalography (EEG) and stabilometry. Framework performance was evaluated in terms of classification accuracy, and the results confirmed that the proposed schema has potential for classifying EEG and stabilometric signals. The proposed framework is useful for discovering knowledge from medical time series containing events, such as stabilometric and electroencephalographic time series. These results would be equally applicable to other medical domains generating iconographic time series, such as, for example, electrocardiography (ECG).

There are now a great many domains where information is recorded by sensors over a limited time period or on a permanent basis. This data flow leads to sequences of data known as time series. In many domains, like seismography or medicine, time series analysis focuses on particular regions of interest, known as events, whereas the remainder of the time series contains hardly any useful information. In these domains, there is a need for mechanisms to identify and locate such events. In this paper, we propose an events definition language that is general enough to be used to easily and naturally define events in time series recorded by sensors in any domain. The proposed language has been applied to the definition of time series events generated within the branch of medicine dealing with balance-related functions in human beings. A device, called posturograph, is used to study balance-related functions. The platform has four sensors that record the pressure intensity being exerted on the platform, generating four interrelated time series. As opposed to the existing ad hoc proposals, the results confirm that the proposed language is valid, that is generally applicable and accurate, for identifying the events contained in the time series.

There are many processes under control. Nowadays all of them undergo through the automation procedure due to the rapid development of information technologies and computing devices. Because of the fact that many tasks of control deal with the elimination of situations, which can cause emergencies, automatic prediction of objective events in process streams becomes the popular problem decided by automation procedure. This work presents the new approach for intelligent analysis of processes represented by time series data. The main aim of our approach is prediction and detection of objective events. The idea of the technique is referred to the mapping of original time series into phase space and construction of the fuzzy prediction clusters of patterns in this phase space. Prediction stage consists of comparison of observed event with the prediction clusters according to the base of fuzzy rules.

The proper control of blood glucose levels in diabetic patients reduces serious complications. Yet tighter glycemic control increases the risk of developing hypoglycemia, a sudden drop in patients' blood glucose levels that causes coma and possibly death if proper action is not taken immediately. In this paper, we propose a hypoglycemia prediction model, using recent history of subcutaneous glucose measurements collected via Continuous Glucose Monitoring (CGM) sensors. The model is able to predict hypoglycemia events within a prediction horizon of thirty minutes accurately (sensitivity= 86.47%, specificity= 96.22, accuracy= 95.97%) using only the last two glucose measurements and the difference between them. More remarkably, this study shows the ability to develop a generalized prediction model suitable for predicting hypoglycemia events for the group of patients participating in the study.

The primary objective of engineering asset management is to optimize assets service delivery potential and to minimize the related risks and costs over their entire life through the development and application of asset health and usage management in which the health and reliability prediction plays an important role. In real-life situations where an engineering asset operates under dynamic operational and environmental conditions, the lifetime of an engineering asset is generally described as monitored nonlinear time-series data and subject to high levels of uncertainty and unpredictability. It has been proved that application of data mining techniques is very useful for extracting relevant features which can be used as parameters for assets diagnosis and prognosis. In this paper, a tutorial on nonlinear time-series data mining in engineering asset health and reliability prediction is given. Besides that an overview on health and reliability prediction techniques for engineering assets is covered, this tutorial will focus on concepts, models, algorithms, and applications of hidden Markov models (HMMs) and hidden semi-Markov models (HSMMs) in engineering asset health prognosis, which are representatives of recent engineering asset health prediction techniques.

The novel Time Series Data Mining (TSDM) framework is applied to analyzing financial time series. The TSDM framework adapts and innovates data mining concepts to analyzing time series data. In particular, it creates a set of methods that reveal hidden temporal patterns that are characteristic and predictive of time series events. This contrasts with other time series analysis techniques, which typically characterize and predict all observations. The TSDM framework and concepts are reviewed, and the applicable TSDM method is discussed. Finally, the TSDM method is applied to time series generated by a basket of financial securities. The results show that statistically significant temporal patterns that are both characteristic and predictive of events in financial time series can be identified.

The comparison of two time series and the extraction of subsequences that are common to the two is a complex data mining problem. Many existing techniques, like the discrete Fourier transform (DFT), offer solutions for comparing two whole time series. Often, however, the important thing is to analyse certain regions, known as events, rather than the whole times series. This applies to domains like the stock market, seismography or medicine. In this paper, we propose a method for comparing two time series by analysing the events present in the two. The proposed method is applied to time series generated by stabilometric and posturographic systems within a branch of medicine studying balance-related functions in human beings.

The comparison of two time series and the extraction of subsequences that are common to the two is a complex data mining problem. Many existing techniques, like the Discrete Fourier Transform (DFT), offer solutions for comparing two whole time series. Often, however, the important thing is to analyse certain regions, known as events, rather than the whole times series. This applies to domains like the stock market, seismography or medicine. In this paper, we propose a method for comparing two time series by analysing the events present in the two. The proposed method is applied to time series generated by stabilometric and posturographic systems within a branch of medicine studying balance-related functions in human beings.

The Time Series Data Mining framework developed by Povinelli is extended to perform weekly multiple time-step prediction and adapted to perform weekly stock selection from a broader market. The stock selections are combined into weekly portfolios, and techniques from Modern Portfolio Theory and the Capital Asset Pricing Model are adapted to optimize the portfolios. The contribution of this work is the combination of stock selection and portfolio optimization to develop a temporal data mining based stock trading strategy. Results show that investors can increase overall wealth, obtain optimal weekly portfolios that maximize return for a given level of portfolio risk, overcome trading costs associated with trading on a weekly basis, and outperform the market over a given time range.

Summary This paper describes a novel approach to river flood prediction using Time Series Data Mining which combines chaos theory and data mining to characterize and predict events in complex, nonperiodic and chaotic time series. Geophysical phenomena, including earthquakes, floods and rainfall, represent a class of nonlinear systems termed chaotic, in which the relationships between variables in a system are dynamic and disproportionate, however completely deterministic. Chaos theory provides a structured explanation for irregular behavior and anomalies in systems that are not inherently stochastic. While nonlinear approaches such as Artificial Neural Networks, Hidden Markov Models and Nonlinear Prediction are useful in forecasting of daily discharge values in a river, the focus of these approaches is on forecasting magnitudes of future discharge values rather than the prediction of floods. The described Time Series Data Mining methodology focuses on the prediction of events where floods constitute the events in a river daily discharge time series. The methodology is demonstrated using data collected at the St. Louis gauging station located on the Mississippi River in the USA. Results associated with the impact of earliness of prediction and the acceptable risk-level vs. prediction accuracy are presented.