Multivariate Time Series

A firm in the early stages of financial distress exhibits characteristics different from those of healthy firms. As the economic condition of a firm worsens, its financial characteristics shift toward those of failed firms. Practitioners in the financial sector have long been interested in the early detection of a firm's slide toward insolvency. Several models have been developed with this purpose in mind, but these older models are static in nature. Therefore, a need exists for the development of business failure prediction models that assess the financial condition of firms sequentially over time. This article addresses this need by presenting a sequential business failure prediction model.

A problem of supervised learning from the multivariate time series (MTS) data where the target variable is potentially a highly complex function of MTS features is considered. This paper focuses on finding a compressed representation of MTS while preserving its predictive potential. Each time se- quence is decomposed into Chebyshev polynomials, and the decomposition coefficients are used as predictors in a statisti- cal learning model. The feature selection method capable of handling true multivariate effects is then applied to identify relevant Chebyshev features. MTS compression is achieved by keeping only those predictors that are pertinent to the re- sponse. The paper considers a problem of multivariate time series compression. We start with a dataset where each sample con- sists of several time series and a single response value. Indi- vidual series from the same sample correspond to the differ- ent variables with different physical characteristics generated by a process. Our g...

Prediction of future movement of stock prices has been a subject matter of many research work. On one hand, we have proponents of the Efficient Market Hypothesis who claim that stock prices cannot be predicted, on the other hand, there are propositions illustrating that, if appropriately modelled, stock prices can be predicted with a high level of accuracy. There is also a gamut of literature on technical analysis of stock prices where the objective is to identify patterns in stock price movements and profit from it. In this work, we propose a hybrid approach for stock price prediction using machine learning and deep learning-based methods. We select the NIFTY 50 index values of the National Stock Exchange (NSE) of India, over a period of four years: 2015 – 2018. Based on the NIFTY data during 2015 – 2018, we build various predictive models using machine learning approaches, and then use those models to predict the “Close” value of NIFTY 50 for the year 2019, with a forecast horizon of one week, i.e., five days. For predicting the NIFTY index movement patterns, we use a number of classification methods, while for forecasting the actual “Close” values of NIFTY index, various regression models are built. We, then, augment our predictive power of the models by building a deep learning-based regression model using Convolutional Neural Network (CNN) with a walk-forward validation. The CNN model is fine-tuned for its parameters so that the validation loss stabilizes with increasing number of iterations, and the training and validation accuracies converge. We exploit the power of CNN in forecasting the future NIFTY index values using three approaches which differ in number of variables used in forecasting, number of sub-models used in the overall models and, size of the input data for training the models. Extensive results are presented on various metrics for all classification and regression models. The results clearly indicate that CNN-based multivariate forecasting model is the most effective and accurate in predicting the movement of NIFTY index values with a weekly forecast horizon.

This article introduces the sparse group fused lasso (SGFL) as a statistical framework for segmenting sparse regression models with multivariate time series. To compute solutions of the SGFL, a nonsmooth and nonseparable convex program, we develop a hybrid optimization method that is fast, requires no tuning parameter selection, and is guaranteed to converge to a global minimizer. In numerical experiments, the hybrid method compares favorably to state-of-the-art techniques with respect to computation time and numerical accuracy; benefits are particularly substantial in high dimension. The method's statistical performance is satisfactory in recovering nonzero regression coefficients and excellent in change point detection. An application to air quality data is presented. The hybrid method is implemented in the R package sparseGFL available on the author's Github page.

I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate multivariate signal into a forecastable and an orthogonal white noise space. I present a provably converging algorithm with a fast eigenvector solution. Applications to financial and macro-economic data show that ForeCA can successfully discover informative structure in multivariate time series: structure that can be used for forecasting and classification.
The main methods for ForeCA are implemented in the R package ForeCA (cran.r-project.org/web/packages/ForeCA/index.html), which is publicly available on CRAN.

The detection of frequently occurring patterns, also called motifs, in data streams has been recognized as an important task. To find these motifs, we use an advanced event encoding and pattern discovery algorithm. As a large time series can contain hundreds of motifs, there is a need to support interactive analysis and exploration. In addition, for certain applications, such as

Prediction of future movement of stock prices has been a subject matter of many research work. On one hand, we have proponents of the Efficient Market Hypothesis who claim that stock prices cannot be predicted, on the other hand, there are propositions illustrating that, if appropriately modelled, stock prices can be predicted with a high level of accuracy. There is also a gamut of literature on technical analysis of stock prices where the objective is to identify patterns in stock price movements and profit from it. In this work, we propose a hybrid approach for stock price prediction using machine learning and deep learning-based methods. We select the NIFTY 50 index values of the National Stock Exchange (NSE) of India, over a period of four years: 2015-2018. Based on the NIFTY data during 2015-2018, we build various predictive models using machine learning approaches, and then use those models to predict the "Close" value of NIFTY 50 for the year 2019, with a forecast horizon of one week, i.e., five days. For predicting the NIFTY index movement patterns, we use a number of classification methods, while for forecasting the actual "Close" values of NIFTY index, various regression models are built. We, then, augment our predictive power of the models by building a deep learning-based regression model using Convolutional Neural Network (CNN) with a walk-forward validation. The CNN model is fine-tuned for its parameters so that the validation loss stabilizes with increasing number of iterations, and the training and validation accuracies converge. We exploit the power of CNN in forecasting the future NIFTY index values using three approaches which differ in number of variables used in forecasting, number of sub-models used in the overall models and, size of the input data for training the models. Extensive results are presented on various metrics for all classification and regression models. The results clearly indicate that CNN-based multivariate forecasting model is the most effective and accurate in predicting the movement of NIFTY index values with a weekly forecast horizon.

This paper investigates the impact of changes in the U.S. dollar/euro exchange rate on crude oil prices. The negative correlation of these two variables is ascribed to five possible channels: on the supply side, the purchasing power of oil export revenues and on the demand side, local prices in non-U.S. dollar regions, investments in crude oil-related asset markets, the monetary policy regime in oil-exporting countries and the efficiency of the currency market. We give evidence that using information on the U.S. dollar/euro exchange rate (and its determinants) significantly improves oil price forecasts. We discuss the possible implications these results might suggest with regard to the stabilization of oil prices or the adjustment of global imbalances.

... Available online 18 October 2005. Abstract. This paper presents a neural network approach to multivariate time-series analysis. ... Discussion following the Tiao and Tsay (1989) paper also addresses some of the problems with linear models for multivariate time series. ...

In this paper, we develop practical methods for modelling weak VARMA processes. In a first part, we propose new identified VARMA representations, the diagonal MA equation formand the final MA equation form, where the MA operator is diagonal and scalar respectively. Both of these representations have the important feature that they const itute relatively simple modifications of a VAR model (in contrast with the echelon representation). In a second part, we study the problem of estimating VARMA models by relatively simple methods,which only require linear regressions. We consider a generalization of the regression-based estimation method,proposed by Hannan and Rissanen (1982). The asymptotic properties of the estimator are derived under weak hypotheses on the innovations (uncorrelated and strong mixing) so as to broaden the class of models to which it can be applied. In a third part, we present a modified informat ion criterion which gives consistent estimates of the orders under the ...

Identifying temporally invariant components in complex multivariate time series is key to understanding the underlying dynamical system and predict its future behavior. In this Letter, we propose a novel technique, stationary subspace analysis (SSA), that decomposes a multivariate time series into its stationary and nonstationary part. The method is based on two assumptions: (a) the observed signals are linear superpositions

Prediction of future movement of stock prices has been a subject matter of many research work. On one hand, we have proponents of the Efficient Market Hypothesis who claim that stock prices cannot be predicted, on the other hand, there are propositions illustrating that, if appropriately modelled, stock prices can be predicted with a high level of accuracy. There is also a gamut of literature on technical analysis of stock prices where the objective is to identify patterns in stock price movements and profit from it. In this work, we propose a hybrid approach for stock price prediction using machine learning and deep learning-based methods. We select the NIFTY 50 index values of the National Stock Exchange (NSE) of India, over a period of four years: 2015 – 2018. Based on the NIFTY data during 2015 – 2018, we build various predictive models using machine learning approaches, and then use those models to predict the “Close” value of NIFTY 50 for the year 2019, with a forecast horizon...

We consider the problem of training a discriminative classifier given a set of labelled multivariate time series (a.k.a. multichannel signals or vector processes). We propose a novel kernel function that exploits the spectral information of tensors of fourth-order cross-cumulants associated to each multichannel signal. Contrary to existing approaches the arising procedure does not require an (often nontrivial) blind identification step. Nonetheless, insightful connections with the dynamics of the generating systems can be drawn under specific modeling assumptions. The method is illustrated on both synthetic examples as well as on a brain decoding task where the direction, either left of right, towards where the subject modulates attention is predicted from magnetoencephalography (MEG) signals. Kernel functions for unstructured data do not leverage the underlying dynamics of multichannel signals. A comparison with these kernels as well as with state-of-the-art approaches, including generative methods, shows the merits of the proposed technique.