scholarly journals Symplectic Principal Component Analysis: A New Method for Time Series Analysis

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Min Lei ◽  
Guang Meng
Keyword(s):  
Dynamical System ◽  
Principal Component Analysis ◽  
Time Series ◽  
Symplectic Geometry ◽  
Time Series Data ◽  
Principal Component ◽  
Component Analysis ◽  
Series Data ◽  
Pca Method ◽  
Value Decomposition

Experimental data are often very complex since the underlying dynamical system may be unknown and the data may heavily be corrupted by noise. It is a crucial task to properly analyze data to get maximal information of the underlying dynamical system. This paper presents a novel principal component analysis (PCA) method based on symplectic geometry, called symplectic PCA (SPCA), to study nonlinear time series. Being nonlinear, it is different from the traditional PCA method based on linear singular value decomposition (SVD). It is thus perceived to be able to better represent nonlinear, especially chaotic data, than PCA. Using the chaotic Lorenz time series data, we show that this is indeed the case. Furthermore, we show that SPCA can conveniently reduce measurement noise.

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.

scholarly journals Challenges in estimating the impact of vaccination with sparse data

2018 ◽  
Author(s):  
Kayoko Shioda ◽  
Cynthia Schuck-Paim ◽  
Robert J. Taylor ◽  
Roger Lustig ◽  
Lone Simonsen ◽  
...  
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Simulation Analysis ◽  
Principal Component ◽  
Population Level ◽  
Series Data ◽  
Synthetic Control ◽  
Vaccine Impact ◽  
Pca Method ◽  
The Impact

ABSTRACTBackgroundThe synthetic control (SC) model is a powerful tool to quantify the population-level impact of vaccines, because it can adjust for trends unrelated to vaccination using a composite of control diseases. Because vaccine impact studies are often conducted using smaller subnational datasets, we evaluated the performance of SC models with sparse time series data. To obtain more robust estimates of vaccine effects from noisy time series, we proposed a possible alternative approach, “STL+PCA” method (seasonal-trend decomposition plus principal component analysis), which first extracts smoothed trends from the control time series and uses them to adjust the outcome.MethodsUsing both the SC and STL+PCA models, we estimated the impact of 10-valent pneumococcal conjugate vaccine (PCV10) on pneumonia hospitalizations among cases <12 months and 80+ years of age during 2004-2014 at the subnational level in Brazil. The performance of these models was also compared using simulation analyses.ResultsThe SC model was able to adjust for trends unrelated to PCV10 in larger states but not in smaller states. The simulation analysis confirmed that the SC model failed to select an appropriate set of control diseases when the time series were sparse and noisy, thereby generating biased estimates of the impact of vaccination when secular trends were present. The STL+PCA approach decreased bias in the estimates for smaller populations.ConclusionsEstimates from the SC model might be biased when data are sparse. The STL+PCA model provides more accurate evaluations of vaccine impact in smaller populations.

scholarly journals Forecasting of UV-Vis absorbance time series using artificial neural networks combined with principal component analysis

2016 ◽  
Vol 75 (4) ◽  
pp. 765-774
Author(s):  
Leonardo Plazas-Nossa ◽  
Thomas Hofer ◽  
Günter Gruber ◽  
Andres Torres
Keyword(s):  
Neural Networks ◽  
Principal Component Analysis ◽  
Time Series ◽  
Artificial Neural Networks ◽  
Principal Component ◽  
Component Analysis ◽  
Series Data ◽  
Visible Range ◽  
Artificial Neural ◽  
Uv Range

This work proposes a methodology for the forecasting of online water quality data provided by UV-Vis spectrometry. Therefore, a combination of principal component analysis (PCA) to reduce the dimensionality of a data set and artificial neural networks (ANNs) for forecasting purposes was used. The results obtained were compared with those obtained by using discrete Fourier transform (DFT). The proposed methodology was applied to four absorbance time series data sets composed by a total number of 5705 UV-Vis spectra. Absolute percentage errors obtained by applying the proposed PCA/ANN methodology vary between 10% and 13% for all four study sites. In general terms, the results obtained were hardly generalizable, as they appeared to be highly dependent on specific dynamics of the water system; however, some trends can be outlined. PCA/ANN methodology gives better results than PCA/DFT forecasting procedure by using a specific spectra range for the following conditions: (i) for Salitre wastewater treatment plant (WWTP) (first hour) and Graz West R05 (first 18 min), from the last part of UV range to all visible range; (ii) for Gibraltar pumping station (first 6 min) for all UV-Vis absorbance spectra; and (iii) for San Fernando WWTP (first 24 min) for all of UV range to middle part of visible range.

A Time-Series Trend Forecast Method Based on Principal Component Analysis

2012 ◽  
Vol 472-475 ◽  
pp. 2984-2987
Author(s):  
Shu Di Wei ◽  
Hui Huang Zhao
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Image Data ◽  
Principal Component ◽  
Component Analysis ◽  
Series Data ◽  
Text Data ◽  
Related Research ◽  
Time Series Method ◽  
Scan Data

The time-series is the collection of chronological varying numerical ordered by time. It has a wide existence of image data, text data, hand-written data and the brain scan data patterns. The present research of time-series concentrates on series data transformation, similarity search, forecast, classification, clustering and Visualization etc. Furthermore the trend forecast of time-series is the major basis of other related research. This paper analyses the existing time-series forecasting methods and puts forward a new time-series method based on principal component analysis. The example tests the validity of the method of other related research.

scholarly journals RESEARCH ON THE RELATIONSHIP BETWEEN INVESTOR SENTIMENT AND STOCK PRICE

2021 ◽  
Author(s):  
YI-MING DU ◽  
RUI DING ◽  
YI-LIN ZHANG ◽  
TING ZHANG ◽  
TAO ZHOU
Keyword(s):  
Principal Component Analysis ◽  
Behavioral Finance ◽  
Stock Price ◽  
Time Series Data ◽  
Investor Sentiment ◽  
Principal Component ◽  
Component Analysis ◽  
Series Data ◽  
Macroeconomic Factors ◽  
The Relationship

As one of the main contents of behavioral finance, investor sentiment has become a research hotspot in recent years. This paper takes the CSI300 index of China as the observation object, selects five emotional monthly time series data including lag one period from 2016 to 2020. The method of principal component analysis will be used to reduce the dimension of 10 groups of data. After eliminating the macroeconomic factors, the dimension reduction results are analyzed by the second principal component analysis to obtain the comprehensive index of emotion. Furthermore, a Vector Auto Regressive model (VAR) is established to investigate the relationship between ISIO and CSI300 of the stock market. The results show that investor sentiment and stock price interact with each other, but only in the short term. With more and more sufficient market information known, the effect is becoming insignificant.

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