We provide a systematic comparison of the out-of-sample forecasts based on multivariate macroeconomic models and forecast combinations for the euro against the US dollar, the British pound, the Swiss franc and the Japanese yen. We use profit maximization measures based on directional accuracy and trading strategies in addition to standard loss minimization measures. When comparing predictive accuracy and profit measures, data snooping bias free tests are used. The results indicate that forecast combinations help to improve over benchmark trading strategies for the exchange rate against the US dollar and the British pound, although the excess return per unit of deviation is limited. For the euro against the Swiss franc or the Japanese yen, no evidence of generalized improvement in profit measures over the benchmark is found. (authors' abstract) / Series: Department of Economics Working Paper Series

This thesis focuses on mining association rules on multivariate time series. Com-mon association rule mining algorithms can usually only be applied to transactional data, and a typical application is market basket analysis. If we want to mine temporal association rules on time series data, changes need to be made. During temporal association rule mining, the temporal ordering nature of data and the temporal interval between the left and right patterns of a rule need to be considered. This thesis reviews some mining methods for temporal association rule mining, and proposes two similar algorithms for the mining of frequent patterns in single and multivariate time series. Both algorithms are scalable and efficient. In addition, temporal association rules are generated from the patterns found. Finally, the usability and efficiency of the algorithms are demonstrated by evaluating the results.

In this era of big data, multivariate time-series (MTS) data are prevalent in diverse domains and often high dimensional. However, there have been limited studies of building a capable classifier with MTS via classical machine learning methods that can deal with the double curse of dimensionality due to high variable dimension and long time series (large sample size). In this thesis, we propose two approaches to address this problem for multiclass classification with high dimensional MTS. Both approaches leverage the dynamics of an MTS captured by non-parametric modeling of its spectral density function. In the first approach, we introduce the reduced-rank spectral classifier (RRSC), which utilizes low-rank estimation and some new discrimination functions. We illustrate the efficacy of the RRSC with both simulations and real applications. For binary classification, we establish the consistency of the RRSC and provide an asymptotic formula for the misclassification error rates, under some regularity conditions. The second approach concerns the development of the random projection ensemble classifier for time series (RPECTS). This method first applies dimension reduction in the time domain via projecting the time-series variables into some low dimensional space, followed by measuring the disparity via some novel base classifier between the data and the candidate generating processes in the projected space. We assess the classification performance of our new approaches by simulations and compare them with some existing methods using real applications. Finally, we elaborate two R packages that implement the aforementioned methods.

Available statistical methodologies focus more on accommodating continuous variables, however recently dealing with count data has received high interest in the statistical literature. In this dissertation, we propose some statistical approaches to investigate linear and nonlinear dependencies between two discrete random variables, or between a discrete and continuous random variables. Copula functions are powerful tools for modeling dependencies between random variables. We derive copula-based population version of Spearman’s rho when at least one of the marginal distribution is discrete. In each case, the functional relationship between Kendall’s tau and Spearman’s rho is obtained. The asymptotic distributions of the proposed estimators of these association measures are derived and their corresponding confidence intervals are constructed, and tests of independence are derived. Then, we propose a Bayesian copula factor autoregressive model for time series mixed data. This model assumes conditional independence and shares latent factors in both mixed-type response and multivariate predictor variables of the time series through a quadratic timeseries regression model. This model is able to reduce the dimensionality by accommodating latent factors in both response and predictor variables of the high-dimensional time series data. A semiparametric time series extended rank likelihood technique is applied to the marginal distributions to handle mixed-type predictors of the high-dimensional time series, which decreases the number of estimated parameters and provides an efficient computational algorithm. In order to update and compute the posterior distributions of the latent factors and other parameters of the models, we propose a naive Bayesian algorithm with Metropolis-Hasting and Forward Filtering Backward Sampling methods. We evaluate the performance of the proposed models and methods through simulation studies. Finally, each proposed model is applied to a real dataset.

Developments in the field of data analytics provides a boost for small-sized factories. These factories are eager to take full advantage of the potential insights in the remotely collected data to minimise cost and maximise quality and profit. This project aims to process, cluster and visualise sensory data of a blow moulding machine in a plastic production factory. In collaboration with Lean Automation, we aim to develop a data visualisation solution to enable decision-makers in a plastic factory to improve their production process. We will investigate three different aspects of the solution: methods for processing multivariate time-series data, clustering approaches for the sensory-data cultivated, and visualisation techniques that maximises production process insights. We use a formative evaluation method to develop a solution that meets partners' requirements and best practices within the field. Through building the MTSI dashboard tool, we hope to answer questions on optimal techniques to represent, cluster and visualise multivariate time series data.

Information and modern computing technology advancements have led to a rise in the importance of maintenance, particularly in areas where a single components failure could have a significant impact on the overall systems performance. Numerous industries, including Alfa Laval, are operating on conditional-based systems that provide warnings only when a machine fails. In the worst instances, pro- longed downtime or machine failure can be costly in terms of money, time, and security [2]. The Alfa Laval company is interested in build- ing a smart alarm system that anticipates alarms and warnings based on sensor readings. For solving these issues, predictive maintenance using machine learning is one of the most effective approach to de- tect the machine condition in advance for maintenance and prevent it from real-time damage or faults. To obtain the best prescient machine learning model, we examined multi-linear and non-linear methods with tensor representation and the linear method as a baseline on real-time multi-sensor time-series datasets to build the smart alarm predictive system to anticipate cautions and warnings. As per the ex- perimental results, we are more certain that the non-linear (Tensor Convolutional Neural Network) method is more ideal than the other methods for the company’s multivariate time series datasets.

Anomaly detection plays a crucial role in various domains, such as transportation, cybersecurity, and industrial monitoring, where the timely identification of unusual patterns or outliers is of utmost importance. Traditional statistical techniques have limitations in handling complex and highdimensional data, which motivates the use of deep learning approaches. The project proposes designing and implementing deep neural networks, tailored explicitly for time series multivariate data from sensors incorporated in vehicles, to effectively capture intricate temporal dependencies and interactions among variables. As this project is conducted in collaboration with Scania, Sweden, the models are trained on datasets encompassing various vehicle sensor data. Different deep learning architectures, including Long Short-Term Memory (LSTM) networks and Convolutional Neural Networks (CNNs), are explored and compared to identify the most suitable model for anomaly detection tasks for the specified time series data and CNN found to perform well for the data used in the study. Furthermore, interpretability techniques are incorporated into the developed models to enhance their transparency and provide insights into the reasons behind detected anomalies. Interpretability is crucial in real-world applications to facilitate trust, understanding, and decision-making. Both model-agnostic and model-specific interpretability methods were employed to highlight the relevant features and contribute to the interpretability of the anomaly detection models. The performance of the proposed models is evaluated using test datasets with anomaly data, and comparisons are made against existing anomaly detection methods to demonstrate their effectiveness. Evaluation metrics such as precision, recall, false positive rate, F1 score, and composite F1 score are employed to assess the anomaly detection models' detection accuracy and robustness. For evaluating the interpretability method, Kolmogorov-Smirnov Test is used on counterfactual examples. The outcomes of this research project will contribute to developing advanced anomaly detection techniques that can effectively analyse time series multivariate data collected from sensors incorporated in vehicles. Incorporating interpretability techniques will provide valuable insights into the detected anomalies, enabling better decision-making and improved trust in the deployed models. These advancements can potentially enhance anomaly detection systems across various domains, leading to more reliable and secure operations.

The advent of music streaming has made it increasingly important for actors in the music industry to understand if tracks are going to succeed or not. This study investigates if it is possible to accurately classify the growth of the listener base of a music track based on multivariate time series with listener behavior data. 18 popular time series classification algorithms were used to build predictive models which were evaluated in a 10-fold cross-validation. We also examined the algorithms’ potential to deliver business value for a record label. Lastly, the possibilities and challenges of applying a data-driven business model in the music industry were investigated by performing a comparative analysis of a modern and traditional record label. Six algorithms were found to significantly outperform the baseline. Two algorithms based on convolutional kernels, RR and AMini, were found to present the biggest business value because of their accuracy and low time complexity. While it may be necessary for record labels to adopt data-driven business models to flourish in the modern market, there are difficulties regarding the competitiveness of digital solutions and complications in moving the focus from networking to developing technology. / Spridningen av musiktjänster har gjort det alltmer viktigt för aktörer i musikbranschen att förstå vilka låtar som kommer att lyckas och inte. Denna studie undersöker om det är möjligt att klassificera tillväxten av en låts lyssnarantal baserat på multivariata tidsserier innehållandes data om lyssnarbeteende. 18 populära algoritmer för tidsserieklassificering användes för att bygga prediktiva modeller som utvärderades med 10-delad korsvalidering. Vi undersökte sedan algoritmernas potential att skapa affärsvärde för ett skivbolag. Slutligen studerades möjligheter och utmaningar som datadrivna affärsmodeller presenterar i denna bransch genom en komparativ analys av ett modernt och traditionellt skivbolag. Sex algoritmer visade sig signifikant överträffa en baslinjeklassificerare. Vi fann att två algoritmer baserade på faltningskärnor, RR och AMini, kunde skapa störst affärsvärde på grund av deras noggrannhet samt låga tidskomplexitet. Det verkar vara nödvändigt för skivbolag att anamma datadrivna affärsmodeller för att frodas i den moderna marknaden, men det finns svårigheter som måste beaktas vad gäller konkurrenskraften för digitala lösningar samt förflyttandet av fokuset från nätverksbyggande till teknologiutveckling.

Mechanical devices in industriy are equipped with numerous sensors to capture thehealth state of the machines. The reliability of the machine’s health system depends on thequality of sensor data. In order to predict the health state of sensors, abnormal behaviourof sensors must be detected to avoid unnecessary cost.We proposed LSTM autoencoder in which the objective is to reconstruct input time seriesand predict the next time instance based on historical data, and we evaluate anomaliesin multivariate time series via reconstructed error. We also used exponential moving averageas a preprocessing step to smooth the trend of time series to remove high frequencynoise and low frequency deviation in multivariate time series data.Our experiment results, based on different datasets of multivariate time series of gasturbines, demonstrate that the proposed model works well for injected anomalies and realworld data to detect the anomaly. The accuracy of the model under 5 percent infectedanomalies is 98.45%.

Recent advances in technology have led to an explosion in data collection over time rather than in a single snapshot. For example, microarray technology allows us to measure gene expression levels in different conditions over time. Such temporal data grants the opportunity for data miners to develop algorithms to address domain-related problems, e.g. a time series of several different classes can be created, by observing various patient attributes over time and the task is to classify unseen patient based on his temporal observations. In time-sensitive applications such as medical applications, some certain aspects have to be considered besides providing accurate classification. The first aspect is providing early classification. Accurate and timely diagnosis is essential for allowing physicians to design appropriate therapeutic strategies at early stages of diseases, when therapies are usually the most effective and the least costly. We propose a probabilistic hybrid method that allows for early, accurate, and patient-specific classification of multivariate time series that, by training on a full time series, offer classification at a very early time point during the diagnosis phase, while staying competitive in terms of accuracy with other models that use full time series both in training and testing. The method has attained very promising results and outperformed the baseline models on a dataset of response to drug therapy in Multiple Sclerosis patients and on a sepsis therapy dataset. Although attaining accurate classification is the primary goal of data mining task, in medical applications it is important to attain decisions that are not only accurate and obtained early, but can also be easily interpreted which is the second aspect of medical applications. Physicians tend to prefer interpretable methods rather than black-box methods. For that purpose, we propose interpretable methods for early classification by extracting interpretable patterns from the raw time series to help physicians in providing early diagnosis and to gain insights into and be convinced about the classification results. The proposed methods have been shown to be more accurate and provided classifications earlier than three alternative state-of-the-art methods when evaluated on human viral infection datasets and a larger myocardial infarction dataset. The third aspect has to be considered for medical applications is the need for predictions to be accompanied by a measure which allows physicians to judge about the uncertainty or belief in the prediction. Knowing the uncertainty associated with a given prediction is especially important in clinical diagnosis where data mining methods assist clinical experts in making decisions and optimizing therapy. We propose an effective method to provide uncertainty estimate for the proposed interpretable early classification methods. The method was evaluated on four challenging medical applications by characterizing decrease in uncertainty of prediction. We showed that our proposed method meets the requirements of uncertainty estimates (the proposed uncertainty measure takes values in the range [0,1] and propagates over time). To the best of our knowledge, this PhD thesis will have a great impact on the link between data mining community and medical domain experts and would give physicians sufficient confidence to put the proposed methods into real practice. / Computer and Information Science