A Bayesian framework for functional time series analysis

The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations and states, is very flexible but also easy to implement in many cases. For many kinds of data, such as continuous functions, we show how the general theory of stochastic processes provides a convenient tool to specify priors and transition probabilities of the model. Finally, we show how standard Markov chain Monte Carlo methods for posterior simulation can be employed under consistent discretizations of the data

TraTSA: A Transprecision Framework for Efficient Time Series Analysis

Time series analysis (TSA) comprises methods for extracting information in domains as diverse as medicine, seismology, speech recognition and economics. Matrix Profile (MP) is the state-of-the-art TSA technique, which provides the most similar neighbor to each subsequence of the time series. However, this computation requires a huge amount of floating-point (FP) operations, which are a major contributor ( 50%) to the energy consumption in modern computing platforms. In this sense, Transprecision Computing has recently emerged as a promising approach to improve energy efficiency and performance by using fewer bits in FP operations while providing accurate results. In this work, we present TraTSA, the first transprecision framework for efficient time series analysis based on MP. TraTSA allows the user to deploy a high-performance and energy-efficient computing solution with the exact precision required by the TSA application. To this end, we first propose implementations of TraTSA for both commodity CPU and FPGA platforms. Second, we propose an accuracy metric to compare the results with the double-precision MP. Third, we study MP’s accuracy when using a transprecision approach. Finally, our evaluation shows that, while obtaining results accurate enough, the FPGA transprecision MP (i) is 22.75 faster than a 72-core server, and (ii) the energy consumption is up to 3.3 lower than the double-precision executions.This work has been supported by the Government of Spain under project PID2019-105396RB-I00, and Junta de Andalucia under projects P18-FR-3433 and UMA18-FEDERJA-197. Funding for open access charge: Universidad de Málaga / CBUA

Accounting for outliers and calendar effects in surrogate simulations of stock return sequences

Surrogate Data Analysis (SDA) is a statistical hypothesis testing framework for the determination of weak chaos in time series dynamics. Existing SDA procedures do not account properly for the rich structures observed in stock return sequences, attributed to the presence of heteroscedasticity, seasonal effects and outliers. In this paper we suggest a modification of the SDA framework, based on the robust estimation of location and scale parameters of mean-stationary time series and a probabilistic framework which deals with outliers. A demonstration on the NASDAQ Composite index daily returns shows that the proposed approach produces surrogates that faithfully reproduce the structure of the original series while being manifestations of linear-random dynamics.Comment: 21 pages, 7 figure

Analysis of nonlinear oscillators using volterra series in the frequency domain Part I : convergence limits

The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation. Barrett(1965) proposed a time domain criterion to prove that the Volterra series converges with a given region for a class of nonlinear systems with cubic stiffness nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation

Statistical Software for State Space Methods

In this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We first provide some background on the history of state space methods for the analysis of time series. This is followed by a concise overview of linear Gaussian state space analysis including the modelling framework and appropriate estimation methods. We discuss the important class of unobserved component models which incorporate a trend, a seasonal, a cycle, and fixed explanatory and intervention variables for the univariate and multivariate analysis of time series. We continue the discussion by presenting methods for the computation of different estimates for the unobserved state vector: filtering, prediction, and smoothing. Estimation approaches for the other parameters in the model are also considered. Next, we discuss how the estimation procedures can be used for constructing confidence intervals, detecting outlier observations and structural breaks, and testing model assumptions of residual independence, homoscedasticity, and normality. We then show how ARIMA and ARIMA components models fit in the state space framework to time series analysis. We also provide a basic introduction for non-Gaussian state space models. Finally, we present an overview of the software tools currently available for the analysis of time series with state space methods as they are discussed in the other contributions to this special volume.