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We study online prediction of bounded stationary ergodic processes. To do so, we consider the setting of prediction of individual sequences and build a deterministic regression tree that performs asymptotically as well as the best L-Lipschitz constant predictors. Then, we show why the obtained regret bound entails the asymptotical optimality with respect to the class of bounded stationary ergodic processes.

In this paper we address the problem of predicting a time series using the ARMA (autoregressive moving average) model, under minimal assumptions on the noise terms. Using regret minimization techniques, we develop effective online learning algorithms for the prediction problem, without assuming that the noise terms are Gaussian, identically distributed or even independent. Furthermore, we show that our algorithm's performances asymptotically approaches the performance of the best ARMA model in hindsight.

In this paper we address the problem of predicting a time series using the ARMA (autoregressive moving average) model, under minimal assumptions on the noise terms. Using regret minimization techniques, we develop effective online learning algorithms for the prediction problem, without assuming that the noise terms are Gaussian, identically distributed or even independent. Furthermore, we show that our algorithm's performances asymptotically approaches the performance of the best ARMA model in hindsight.

Careful blood glucose monitoring and consistent insulin administration are necessary for managing diabetes. People with demanding schedules or little access to medical personnel may find this difficult. Fortunately, without having to visit a doctor every day, daily insulin dosage may now be customized to a person’s unique needs using technology and customised algorithms based on their food intake, exercise routines, and blood glucose levels. This information can be entered into a diabetes management app or device, where an algorithm will determine the proper insulin dosage and offer real-time feedback to assist maintain ideal blood glucose levels. A patient's dietary preferences, degree of physical activity, and blood sugar are taken into account for determining the proper bolus and basal insulin dosages in this study. According to the tracked body data, a patient’s appropriate insulin dosage is predicted using artificial neural network (ANN)-based models. Based on patient activity, food intake, exercise, and past insulin administration, insulin projections are created. To forecast an individual’s basal and bolus insulin requirements, long short-term memory (LSTM) and random forest regression models are employed. Accuracy of both models are tested and random forest regression shows better accuracy which is used in the prediction system. 

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a stationary and ergodic random process then the average number of mistakes converges, almost surely, to that of the optimum, given by the Bayes predictor. The desirable finite-sample properties of the predictor are illustrated by its performance for Markov processes. In such cases the predictor exhibits near optimal behavior even without knowing the order of the Markov process. Prediction with side information is also considered.

Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal pre-selection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used sub-optimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Ni\~no Southern Oscillation.

A computer program is described and presented for calculating finite memory predictors and prediction variances for autoregressive moving average time series models. The Cholesky decomposition algorithm is used, and a number of simplifying results are described and implemented in the program. (Author)

An algorithm is presented for conveniently calculating h step ahead minimum mean square linear predictors and prediction variances given a finite number of observations from a covariance stationary time series Y. It is shown that elements of the modified Cholesky decomposition of the covariance matrix of observations play the role in finite memory prediction that the coefficients in the infinite order moving average representation of Y play in infinite memory prediction. The algorithm is applied to autoregressive-moving average time series where further simplifications are shown to occur. A numerical example illustrating the basic points of the general algorithm is presented. (Author)

An algorithm is presented for conveniently calculating h step ahead minimum mean square linear predictors and prediction variances given a finite number of observations from a covariance stationary time series Y. It is shown that elements of the modified Cholesky decomposition of the covariance matrix of observations play the role in finite memory prediction that the coefficients in the infinite order moving average representation of Y play in infinite memory prediction. The algorithm is applied to autoregressive-moving average time series where further simplifications are shown to occur. A numerical example illustrating the basic points of the general algorithm is presented. (Author)

For oscillating time series, the prediction is often focused on the turning points. In order to predict the turning point magnitudes and times it is proposed to form the state space reconstruction only from the turning points and modify the local (nearest neighbor) model accordingly. The model on turning points gives optimal prediction at a lower dimensional state space than the optimal local model applied directly on the oscillating time series and is thus computationally more efficient. Monte Carlo simulations on different oscillating nonlinear systems showed that it gives better predictions of turning points and this is confirmed also for the time series of annual sunspots and total stress in a plastic deformation experiment.

A computer program is described and presented for calculating finite memory predictors and prediction variances for autoregressive moving average time series models. The Cholesky decomposition algorithm is used, and a number of simplifying results are described and implemented in the program. (Author)

A computer program is described and presented for calculating finite memory predictors and prediction variances for autoregressive moving average time series models. The Cholesky decomposition algorithm is used, and a number of simplifying results are described and implemented in the program. (Author)

Prediction of events is fundamental to both human and artificial agents. The main problem with previous prediction techniques is that they cannot predict events that have never been experienced before. This dissertation addresses the problem of predicting such novelty by developing algorithms and computational models inspired from recent cognitive science theories conceptual blending theory and event segmentation theory. We were able to show that prediction accuracy for event or state prediction can be significantly improved using these methods. The main contribution of this dissertation is a new class of prediction techniques inspired by conceptual blending that improves prediction accuracy overall and has the ability to predict even events that have never been experienced before. We also show that event segmentation theory, when integrated with these techniques, results in greater computational efficiency. We implemented the new prediction techniques, and more traditional alternatives such as Markov and Bayesian techniques, and compared their prediction accuracy quantitatively for three domains a role-playing game, intrusion-system alerts, and event prediction of maritime paths in a discrete-event simulator. Other contributions include two new unification algorithms that improve over a nave one, and an exploration of ways to maintain a minimum-size knowledge base without affecting prediction accuracy.

We establish rates of convergences in time series forecasting using the statistical learning approach based on oracle inequalities. A series of papers extends the oracle inequalities obtained for iid observations to time series under weak dependence conditions. Given a family of predictors and $n$ observations, oracle inequalities state that a predictor forecasts the series as well as the best predictor in the family up to a remainder term $\Delta_n$. Using the PAC-Bayesian approach, we establish under weak dependence conditions oracle inequalities with optimal rates of convergence. We extend previous results for the absolute loss function to any Lipschitz loss function with rates $\Delta_n\sim\sqrt{c(\Theta)/ n}$ where $c(\Theta)$ measures the complexity of the model. We apply the method for quantile loss functions to forecast the french GDP. Under additional conditions on the loss functions (satisfied by the quadratic loss function) and on the time series, we refine the rates of convergence to $\Delta_n \sim c(\Theta)/n$. We achieve for the first time these fast rates for uniformly mixing processes. These rates are known to be optimal in the iid case and for individual sequences. In particular, we generalize the results of Dalalyan and Tsybakov on sparse regression estimation to the case of autoregression.

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse.

The problems of moving average representations of weakly harmonizable processes, extending the corresponding results on stationary processes, is of interest both-theoretically and for applications. Completing some earlier work on the computational problems of conditional probabilities, some unresolved questions are highlighted with illustrations in another paper.

The purpose of this study was to combine knowledge of teacher demographic data with time-series forecasting methods to predict teacher turnover. Moving averages and exponential smoothing were used to forecast discrete time series. The study used data collected from the 22 largest school districts in Iowa, designated as FACT schools. Predictions were made for the 1968-69 school year and then validated with the actual data for that school year. Data were organized into 27 types, which were suggested by a literature review. Results of the study show that teachers with less than four years experience showed the highest amount of turnover, with married women under 30 having the highest rate, unmarried females under 30 being second, married males and unmarried males being third and fourth, respectively. (DB)

In real-time monitoring of hospital patients, high-quality inference of patients' health status using all information available from clinical covariates and lab tests are essential to enable successful medical interventions and improve patient outcomes. In this work, we develop and explore a Bayesian nonparametric model based on Gaussian process (GP) regression for hospital patient monitoring. Our method, MedGP, incorporates 24 clinical and lab covariates and supports a rich reference data set from which the relationships between these observed covariates may be inferred and exploited for high-quality inference of patient state over time. To do this, we develop a highly structured sparse GP kernel to enable tractable computation over tens of thousands of time points while estimating correlations among clinical covariates, patients, and periodicity in high-dimensional time series measurements of physiological signals. We apply MedGP to data from hundreds of thousands of patients treated at the Hospital of the University of Pennsylvania. MedGP has a number of benefits over current methods, including (i) not requiring an alignment of the time series data, (ii) quantifying confidence intervals in the predictions, (iii) exploiting a vast and rich database of patients, and (iv) providing interpretable relationships among clinical covariates. We evaluate and compare results from MedGP on the task of online state prediction for three different patient subgroups.

This article is from Healthcare Informatics Research , volume 16 . Abstract Objectives: To develop and evaluate time series models to predict the daily number of patients visiting the Emergency Department (ED) of a Korean hospital. Methods: Data were collected from the hospital information system database. In order to develop a forecasting model, we used, 2 years of data from January 2007 to December 2008 data for the following 3 consecutive months were processed for validation. To establish a Forecasting Model, calendar and weather variables were utilized. Three forecasting models were established: 1) average; 2) univariate seasonal auto-regressive integrated moving average (SARIMA); and 3) multivariate SARIMA. To evaluate goodness-of-fit, residual analysis, Akaike information criterion and Bayesian information criterion were compared. The forecast accuracy for each model was evaluated via mean absolute percentage error (MAPE). Results: The multivariate SARIMA model was the most appropriate for forecasting the daily number of patients visiting the ED. Because it's MAPE was 7.4%, this was the smallest among the models, and for this reason was selected as the final model. Conclusions: This study applied explanatory variables to a multivariate SARIMA model. The multivariate SARIMA model exhibits relativelyhigh reliability and forecasting accuracy. The weather variables play a part in predicting daily ED patient volume.

In this research the technology of complex Markov chains is applied to predict financial time series. The main distinction of complex or high-order Markov Chains and simple first-order ones is the existing of aftereffect or memory. The technology proposes prediction with the hierarchy of time discretization intervals and splicing procedure for the prediction results at the different frequency levels to the single prediction output time series. The hierarchy of time discretizations gives a possibility to use fractal properties of the given time series to make prediction on the different frequencies of the series. The prediction results for world's stock market indices is presented.

Time series prediction covers a vast field of every-day statistical applications in medical, environmental and economic domains. In this paper we develop nonparametric prediction strategies based on the combination of a set of 'experts' and show the universal consistency of these strategies under a minimum of conditions. We perform an in-depth analysis of real-world data sets and show that these nonparametric strategies are more flexible, faster and generally outperform ARMA methods in terms of normalized cumulative prediction error.

Motivated by a broad range of potential applications, we address the quantile prediction problem of real-valued time series. We present a sequential quantile forecasting model based on the combination of a set of elementary nearest neighbor-type predictors called "experts" and show its consistency under a minimum of conditions. Our approach builds on the methodology developed in recent years for prediction of individual sequences and exploits the quantile structure as a minimizer of the so-called pinball loss function. We perform an in-depth analysis of real-world data sets and show that this nonparametric strategy generally outperforms standard quantile prediction methods

In the nonlinear prediction of scalar time series, the common practice is to reconstruct the state space using time-delay embedding and apply a local model on neighborhoods of the reconstructed space. The method of false nearest neighbors is often used to estimate the embedding dimension. For prediction purposes, the optimal embedding dimension can also be estimated by some prediction error minimization criterion. We investigate the proper state space reconstruction for multivariate time series and modify the two abovementioned criteria to search for optimal embedding in the set of the variables and their delays. We pinpoint the problems that can arise in each case and compare the state space reconstructions (suggested by each of the two methods) on the predictive ability of the local model that uses each of them. Results obtained from Monte Carlo simulations on known chaotic maps revealed the non-uniqueness of optimum reconstruction in the multivariate case and showed that prediction criteria perform better when the task is prediction.

In this paper we show that different physiological states and pathological conditions may be characterized in terms of predictability of time series signals from the underlying biological system. In particular we consider systolic arterial pressure time series from healthy subjects and Chronic Heart Failure patients, undergoing paced respiration. We model time series by the regularized least squares approach and quantify predictability by the leave-one-out error. We find that the entrainment mechanism connected to paced breath, that renders the arterial blood pressure signal more regular, thus more predictable, is less effective in patients, and this effect correlates with the seriousness of the heart failure. The leave-one-out error separates controls from patients and, when all orders of nonlinearity are taken into account, alive patients from patients for which cardiac death occurred.

This article is from BMC Bioinformatics , volume 15 . Abstract Background: Time series models can play an important role in disease prediction. Incidence data can be used to predict the future occurrence of disease events. Developments in modeling approaches provide an opportunity to compare different time series models for predictive power. Results: We applied ARIMA and Random Forest time series models to incidence data of outbreaks of highly pathogenic avian influenza (H5N1) in Egypt, available through the online EMPRES-I system. We found that the Random Forest model outperformed the ARIMA model in predictive ability. Furthermore, we found that the Random Forest model is effective for predicting outbreaks of H5N1 in Egypt. Conclusions: Random Forest time series modeling provides enhanced predictive ability over existing time series models for the prediction of infectious disease outbreaks. This result, along with those showing the concordance between bird and human outbreaks (Rabinowitz et al. 2012), provides a new approach to predicting these dangerous outbreaks in bird populations based on existing, freely available data. Our analysis uncovers the time-series structure of outbreak severity for highly pathogenic avain influenza (H5N1) in Egypt.

Multi-task learning employs shared representation of knowledge for learning multiple instances from the same or related problems. Time series prediction consists of several instances that are defined by the way they are broken down into fixed windows known as embedding dimension. Finding the optimal values for embedding dimension is a computationally intensive task. Therefore, we introduce a new category of problem called dynamic time series prediction that requires a trained model to give prediction when presented with different values of the embedding dimension. This can be seen a new class of time series prediction where dynamic prediction is needed. In this paper, we propose a co-evolutionary multi-task learning method that provides a synergy between multi-task learning and coevolution. This enables neural networks to retain modularity during training for building blocks of knowledge for different instances of the problem. The effectiveness of the proposed method is demonstrated using one-step-ahead chaotic time series problems. The results show that the proposed method can effectively be used for different instances of the related time series problems while providing improved generalisation performance.

Multi-task learning employs shared representation of knowledge for learning multiple instances from the same or related problems. Time series prediction consists of several instances that are defined by the way they are broken down into fixed windows known as embedding dimension. Finding the optimal values for embedding dimension is a computationally intensive task. Therefore, we introduce a new category of problem called dynamic time series prediction that requires a trained model to give prediction when presented with different values of the embedding dimension. This can be seen a new class of time series prediction where dynamic prediction is needed. In this paper, we propose a co-evolutionary multi-task learning method that provides a synergy between multi-task learning and coevolution. This enables neural networks to retain modularity during training for building blocks of knowledge for different instances of the problem. The effectiveness of the proposed method is demonstrated using one-step-ahead chaotic time series problems. The results show that the proposed method can effectively be used for different instances of the related time series problems while providing improved generalisation performance.

In this paper we apply a new approach of the string theory to the real financial market. It is direct extension and application of the work [1] into prediction of prices. The models are constructed with an idea of prediction models based on the string invariants (PMBSI). The performance of PMBSI is compared to support vector machines (SVM) and artificial neural networks (ANN) on an artificial and a financial time series. Brief overview of the results and analysis is given. The first model is based on the correlation function as invariant and the second one is an application based on the deviations from the closed string/pattern form (PMBCS). We found the difference between these two approaches. The first model cannot predict the behavior of the forex market with good efficiency in comparison with the second one which is, in addition, able to make relevant profit per year.

Time series prediction has widespread application, ranging from predicting the stock market to trying to predict future locations of scud missiles. Recent work by Sauer and Casdagli has developed into the embedology theorem, which sets forth the procedures for state space manipulation and reconstruction for time series prediction. This includes embedding the time series into a higher dimensional space in order to form an attractor, a structure defined by the embedded vectors. Embedology is combined with neural technologies in an effort to create a more accurate prediction algorithm. These algorithms consist of embedology, neural networks, Euclidean space nearest neighbors, and spectral estimation techniques in an effort to surpass the prediction accuracy of conventional methods. Local linear training methods are also examined through the use of the nearest neighbors as the training set for a neural network. Fusion methodologies are also examined in an attempt to combine several algorithms in order to increase prediction accuracy. The results of these experiments determine that the neural network algorithms have the best individual prediction accuracies, and both fusion methodologies can determine the best performance. The performance of the nearest neighbor trained neural network validates the applicability of the local linear training set.

We tackle the issue of the blind prediction of a Gaussian time series. For this, we construct a projection operator build by plugging an empirical covariance estimation into a Schur complement decomposition of the projector. This operator is then used to compute the predictor. Rates of convergence of the estimates are given.

We present two approaches for next step linear prediction of long memory time series. The first is based on the truncation of the Wiener-Kolmogorov predictor by restricting the observations to the last $k$ terms, which are the only available values in practice. Part of the mean squared prediction error comes from the truncation, and another part comes from the parametric estimation of the parameters of the predictor. By contrast, the second approach is non-parametric. An AR($k$) model is fitted to the long memory time series and we study the error made with this misspecified model.

We present two approaches for next step linear prediction of long memory time series. The first is based on the truncation of the Wiener-Kolmogorov predictor by restricting the observations to the last $k$ terms, which are the only available values in practice. Part of the mean squared prediction error comes from the truncation, and another part comes from the parametric estimation of the parameters of the predictor. By contrast, the second approach is non-parametric. An AR($k$) model is fitted to the long memory time series and we study the error made with this misspecified model.

Thesis advisors, Christopher Frenzen, Philip Beaver

We report on a technique based on multi-agent games which has potential use in the prediction of future movements of financial time-series. A third-party game is trained on a black-box time-series, and is then run into the future to extract next-step and multi-step predictions. In addition to the possibility of identifying profit opportunities, the technique may prove useful in the development of improved risk management strategies.

A computer program is described and presented for calculating finite memory predictors and prediction variances for autoregressive moving average time series models. The Cholesky decomposition algorithm is used, and a number of simplifying results are described and implemented in the program. (Author)

A computer program is described and presented for calculating finite memory predictors and prediction variances for autoregressive moving average time series models. The Cholesky decomposition algorithm is used, and a number of simplifying results are described and implemented in the program. (Author)

This thesis uses multiple layer perceptrons (MLP) neural networks and Kohonen clustering networks to predict and assign confidence to nonlinear time series classifications. The nonlinear time series used for analysis is the Standard and Poor's 100 (S&P 100) index. The target prediction is classification of the daily index change. Financial indicators were evaluated to determine the most useful combination of features for input into the networks. After evaluation it was determined that net changes in the index over time and three short-term idicators result in better accuracy. A back-propagation trained MLP neural network was then trained with these features to get a daily classification prediction of up or down. Next, a Kohonen clustering network was trained to develop 30 different clusters.The predictions from the MLP network were labeled as correct or incorrect within each classification and counted in each category to determine a confidence for a given cluster. Test data was then run through both networks and predictions were assigned a confidence based on which cluster they belonged to. The results of these tests show that this method can improve the accuracy of predictions from 51% to 73%. Within a cluster accuracy is near 100% for some classifications. (KAR) p. 9-10

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A computer program is described and presented for calculating finite memory predictors and prediction variances for autoregressive moving average time series models. The Cholesky decomposition algorithm is used, and a number of simplifying results are described and implemented in the program. (Author)

A numerical and experimental study of time domain methods for modeling and parameter identification of structural systems is presented. Models are developed which can be used to predict the transient response of multiple- degree-of-freedom systems subjected to arbitrary input. The linear, discrete time transfer function is expressed in a form called the Autoregressive Moving Average (ARMA) model. The ARMA model is a minimum parameter model that may be parameterized with a minimum number of measured quantities. The ARMA model is contrasted to traditional models such as differential equation models and modal methods. The ARMA model indentification algorithms are also compared to time domain modal methods. Though it has proven useful for a number of low-order systems, the identification of the ARMA model is often hampered by the sensitivity of parameter estimates to measurement noise bias.

The outbreak of the COVID-19 pandemic occurred some time ago, making the world a pandemic. Based on this condition is important to predict early to prevent the COVID-19 disease if someday pandemic occurs. The aim of the study is to compare the analysis result of cumulative cases of COVID-19 using multiple linear regression (MLR), ridge regression (RR), and long short term memory (LSTM) models for cases study Java and Bali islands. We chose both islands as a case study because they have very dense populations. These three models are the most widely used time series-based prediction models and have relatively high accuracy values. The predictive variables used are the number of cumulative cases, the daily cases, and population density. The research data was taken from Kaggle and processed using google collabs. Data was taken from January 20, 2020, to August 8, 2020, and data training was carried out for 12 days. The results show the accuracy of LSTM is better than other models. it can be seen in the accuracy value (99.8%) of the model test result. The testing model uses R2, mean square error (MSE), and root mean square error (RMSE). 

The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process $X_0,X_1,...X_n$ has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for $\textbf{P}(X_{n+1}|X_0,X_1,...X_n)$ can be found which converges to the true estimator almost surely. Despite this result, for restricted classes of processes, or for sequences of estimators along stopping times, universal estimators can be found. We present here a survey of some of the recent work that has been done along these lines.

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on kernel methods. Motivated by the powerful framework of Hilbert space embeddings of distributions, in this paper we apply this methodology for the kernel embedding of an autoregressive process of order $p$. By doing so, we provide a non-linear version of an autoregressive process, that shows increased performance over the linear model in highly complex time series. We use the method proposed for one-step ahead forecasting of different time-series, and compare its performance against other non-linear methods.

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on kernel methods. Motivated by the powerful framework of Hilbert space embeddings of distributions, in this paper we apply this methodology for the kernel embedding of an autoregressive process of order $p$. By doing so, we provide a non-linear version of an autoregressive process, that shows increased performance over the linear model in highly complex time series. We use the method proposed for one-step ahead forecasting of different time-series, and compare its performance against other non-linear methods.

Maintaining inventory level to avoid high inventory costs is an issue for Cardiac Product Distribution Companies (CPDCs) because of the shortage of their products which affect their sale and causes loss of the customer. This research aims to provide a method for predicting the upcoming demand of the Balloon and Stents by using time series analysis (Auto Regression Integrated Moving Average) and Deep learning (Long-Short Term Memory). To conduct this research, data was collected from Pakistan’s leading cardiac product distributors to determine the method's performance. The findings were compared using Mean absolute error (MAE) and Root Mean Square Error (RMSE). Resulst conclude that the ARIMA algorithm successfully forecasts cardiac products sale.

We consider $\alpha$-mixing observations and deal with the estimation of the conditional mode of a scalar response variable $Y$ given a random variable $X$ taking values in a semi-metric space. We provide a convergence rate in $L^p$ norm of the estimator. A useful and typical application to functional times series prediction is given.

This volume was digitized and made accessible online due to deterioration of the original print copy.

Shang and Hyndman (2016) proposed grouped functional time series forecasting approach as a combination of individual forecasts using generalized least squares regression. We modify their methodology using generalized exponential smoothing technique for the most disaggregated series in order to obtain more robust predictor. We show some properties of our proposals using simulations and real data related to electricity demand prediction.

This paper proposes and examines the performance of a hybrid model called the wavelet radial bases function neural networks (WRBFNN). The model will be compared its performance with the wavelet feed forward neural networks (WFFN model by developing a prediction or forecasting system that considers two types of input formats: input9 and input17, and also considers 4 types of non-stationary time series data. The MODWT transform is used to generate wavelet and smooth coefficients, in which several elements of both coefficients are chosen in a particular way to serve as inputs to the NN model in both RBFNN and FFNN models. The performance of both WRBFNN and WFFNN models is evaluated by using MAPE and MSE value indicators, while the computation process of the two models is compared using two indicators, many epoch, and length of training. In stationary benchmark data, all models have a performance with very high accuracy. The WRBFNN9 model is the most superior model in nonstationary data containing linear trend elements, while the WFFNN17 model performs best on non-stationary data with the non-linear trend and seasonal elements. In terms of speed in computing, the WRBFNN model is superior with a much smaller number of epochs and much shorter training time. 

We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting) probability (or estimation of the density for real-valued time series), ii) on-line prediction, iii) regression and iv) classification (or so-called problems with side information). We show that so-called archivers (or data compressors) can be used as a tool for solving these problems. In particular, firstly, it is proven that any so-called universal code (or universal data compressor) can be used as a basis for constructing asymptotically optimal methods for the above problems. (By definition, a universal code can "compress" any sequence generated by a stationary and ergodic source asymptotically till the Shannon entropy of the source.) And, secondly, we show experimentally that estimates, which are based on practically used methods of data compression, have a reasonable precision.