Assessing Frequency Domain Causality in Cardiovascular Time Series with Instantaneous Interactions

2010 ◽  
Vol 49 (05) ◽  
pp. 453-457 ◽  
Author(s):  
G. Nollo ◽  
L. Faes
Keyword(s):  
Time Series ◽  
Frequency Domain ◽  
Multivariate Time Series ◽  
Real Data ◽  
Cardiovascular Physiology ◽  
Extended Model ◽  
Partial Directed Coherence ◽  
Model Combining ◽  
Lagged Effects ◽  
Simulation Results

Summary Background: The partial directed coherence (PDC) is commonly used to assess in the frequency domain the existence of causal relations between two time series measured in conjunction with a set of other time series. Although the multivariate autoregressive (MVAR) model traditionally used for PDC computation accounts only for lagged effects, instantaneous effects cannot be neglected in the analysis of cardiovascular time series. Objectives: We propose the utilization of an extended MVAR model for PDC computation, in order to improve the evaluation of frequency domain causality in the presence of zero-lag correlations among multivariate time series. Methods: A procedure for the identification of a MVAR model combining instantaneous and lagged effects is introduced. The coefficients of the extended model are used to estimate an extended PDC (EPDC). EPDC is compared to the traditional PDC on a simulated MVAR process and on real cardiovascular variability series. Results: Simulation results evidence that the presence of zero-lag correlations may produce misleading PDC profiles, while the correct causality patterns can be recovered using EPDC. Application on real data leads to spectral causality estimates which are better interpretable in terms of the known cardiovascular physiology using EPDC than PDC. Conclusions: This study emphasizes the necessity of including instantaneous effects in the MVAR model used for the computation of PDC in the presence of significant zero-lag correlations in multivariate time series.

Empirical analysis of time series using feature selection algorithms

2021 ◽  
Author(s):  
Mikhail Kanevski
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Feature Selection ◽  
Dimensional Space ◽  
Multivariate Time Series ◽  
Feature Space ◽  
Real Data ◽  
Theoretical Concepts ◽  
Wide Range ◽  
Linear And Nonlinear

<p>Nowadays a wide range of methods and tools to study and forecast time series is available. An important problem in forecasting concerns embedding of time series, i.e. construction of a high dimensional space where forecasting problem is considered as a regression task. There are several basic linear and nonlinear approaches of constructing such space by defining an optimal delay vector using different theoretical concepts. Another way is to consider this space as an input feature space – IFS, and to apply machine learning feature selection (FS) algorithms to optimize IFS according to the problem under study (analysis, modelling or forecasting). Such approach is an empirical one: it is based on data and depends on the FS algorithms applied. In machine learning features are generally classified as relevant, redundant and irrelevant. It gives a reach possibility to perform advanced multivariate time series exploration and development of interpretable predictive models.</p><p>Therefore, in the present research different FS algorithms are used to analyze fundamental properties of time series from empirical point of view. Linear and nonlinear simulated time series are studied in detail to understand the advantages and drawbacks of the proposed approach. Real data case studies deal with air pollution and wind speed times series. Preliminary results are quite promising and more research is in progress.</p>

scholarly journals A New Strategy of Hybrid Models using ARIMA, ANN, and DWT in Time Series Modelling

2021 ◽  
Vol 25 (1) ◽  
pp. 27-50
Author(s):  
Tsung-Lin Li ◽  
◽  
Chen-An Tsai ◽  
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Arima Model ◽  
Real Data ◽  
Hybrid Models ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Model Combining ◽  
Time Series Modelling ◽  
Significant Difference

Time series forecasting is a challenging task of interest in many disciplines. A variety of techniques have been developed to deal with the problem through a combination of different disciplines. Although various researches have proved successful for hybrid models, none of them carried out the comparisons with solid statistical test. This paper proposes a new stepwise model determination method for artificial neural network (ANN) and a novel hybrid model combining autoregressive integrated moving average (ARIMA) model, ANN and discrete wavelet transformation (DWT). Simulation studies are conducted to compare the performance of different models, including ARIMA, ANN, ARIMA-ANN, DWT-ARIMA-ANN and the proposed method, ARIMA-DWT-ANN. Also, two real data sets, Lynx data and cabbage data, are used to demonstrate the applications. Our proposed method, ARIMA-DWT-ANN, outperforms other methods in both simulated datasets and Lynx data, while ANN shows a better performance in the cabbage data. We conducted a two-way ANOVA test to compare the performances of methods. The results showed a significant difference between methods. As a brief conclusion, it is suggested to try on ANN and ARIMA-DWT-ANN due to their robustness and high accuracy. Since the performance of hybrid models may vary across data sets based on their ARIMA alike or ANN alike natures, they should all be considered when encountering a new data to reach an optimal performance.

scholarly journals Evaluation of multivariate time series clustering for imputation of air pollution data

2021 ◽  
Vol 10 (2) ◽  
pp. 265-285
Author(s):  
Wedad Alahamade ◽  
Iain Lake ◽  
Claire E. Reeves ◽  
Beatriz De La Iglesia
Keyword(s):  
Air Pollution ◽  
Time Series ◽  
Air Quality ◽  
Missing Data ◽  
Multivariate Time Series ◽  
Real Data ◽  
Economic Benefits ◽  
Air Pollutant ◽  
Monitoring Site ◽  
Concentration Data

Abstract. Air pollution is one of the world's leading risk factors for death, with 6.5 million deaths per year worldwide attributed to air-pollution-related diseases. Understanding the behaviour of certain pollutants through air quality assessment can produce improvements in air quality management that will translate to health and economic benefits. However, problems with missing data and uncertainty hinder that assessment. We are motivated by the need to enhance the air pollution data available. We focus on the problem of missing air pollutant concentration data either because a limited set of pollutants is measured at a monitoring site or because an instrument is not operating, so a particular pollutant is not measured for a period of time. In our previous work, we have proposed models which can impute a whole missing time series to enhance air quality monitoring. Some of these models are based on a multivariate time series (MVTS) clustering method. Here, we apply our method to real data and show how different graphical and statistical model evaluation functions enable us to select the imputation model that produces the most plausible imputations. We then compare the Daily Air Quality Index (DAQI) values obtained after imputation with observed values incorporating missing data. Our results show that using an ensemble model that aggregates the spatial similarity obtained by the geographical correlation between monitoring stations and the fused temporal similarity between pollutant concentrations produces very good imputation results. Furthermore, the analysis enhances understanding of the different pollutant behaviours and of the characteristics of different stations according to their environmental type.

scholarly journals Frequency Domain Repercussions of Instantaneous Granger Causality

2021 ◽  
Author(s):  
Luiz Antonio Baccalá ◽  
Koichi Sameshima
Keyword(s):  
Time Series ◽  
Transfer Function ◽  
Frequency Domain ◽  
Granger Causality ◽  
Partial Directed Coherence ◽  
Directed Transfer Function ◽  
Vector Autoregressive Models ◽  
Vector Autoregressive ◽  
Standard Vector ◽  
Domain Description

Using Directed Transfer Function (DTF) and Partial Directed Coherence (PDC) in their information version, this paper extends their theoretical framework to incorporate instantaneous Granger Causality (iGC)’s frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger Connectivity where interactions mediated without delay between time series can be easily detected.

scholarly journals Cointegration Testing Using Pseudolikelihood Ratio Tests

1997 ◽  
Vol 13 (2) ◽  
pp. 149-169 ◽  
Author(s):  
André Lucas
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Asymptotic Distributions ◽  
Nuisance Parameters ◽  
Vector Autoregressive Models ◽  
Vector Autoregressive ◽  
Higher Power ◽  
Simulation Results ◽  
Non Gaussian ◽  
Cointegration Testing

This paper considers pseudomaximum likelihood estimators for vector autoregressive models. These estimators are used to determine the cointegration rank of a multivariate time series process using pseudolikelihood ratio tests. The asymptotic distributions of these tests depend on nuisance parameters if the pseudolikelihood is non-Gaussian. This even holds if the likelihood is correctly specified. The nuisance parameters have a natural interpretation and can be consistently estimated. Some simulation results illustrate the usefulness of the tests: non-Gaussian pseudolikelihood ratio tests generally have a higher power than the Gaussian test of Johansen if the innovations demonstrate leptokurtic behavior.

scholarly journals Moving dynamic principal component analysis for non-stationary multivariate time series

2021 ◽  
Author(s):  
Fayed Alshammri ◽  
Jiazhu Pan
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Principal Component ◽  
Real Data ◽  
Component Analysis ◽  
Series Data ◽  
Dynamic Principal Component Analysis ◽  
Dynamic Relationships

AbstractThis paper proposes an extension of principal component analysis to non-stationary multivariate time series data. A criterion for determining the number of final retained components is proposed. An advance correlation matrix is developed to evaluate dynamic relationships among the chosen components. The theoretical properties of the proposed method are given. Many simulation experiments show our approach performs well on both stationary and non-stationary data. Real data examples are also presented as illustrations. We develop four packages using the statistical software R that contain the needed functions to obtain and assess the results of the proposed method.

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