Nonparametric estimation of the spectral density of amplitude-modulated time series with missing observations

2014 ◽  
Vol 93 ◽  
pp. 7-13 ◽  
Author(s):  
Sam Efromovich
Keyword(s):  
Time Series ◽  
Spectral Density ◽  
Nonparametric Estimation ◽  
Missing Observations

AN EVOLUTIONARY APPROACH FOR IMPUTING MISSING DATA IN TIME SERIES

2010 ◽  
Vol 19 (01) ◽  
pp. 107-121 ◽  
Author(s):  
JUAN CARLOS FIGUEROA GARCÍA ◽  
DUSKO KALENATIC ◽  
CESAR AMILCAR LÓPEZ BELLO
Keyword(s):  
Genetic Algorithm ◽  
Time Series ◽  
Missing Data ◽  
Genetic Structure ◽  
Evolutionary Algorithm ◽  
Fitness Function ◽  
Error Function ◽  
Missing Observations ◽  
Mean And Variance ◽  
Methodological Aspects

This paper presents a proposal based on an evolutionary algorithm for imputing missing observations in time series. A genetic algorithm based on the minimization of an error function derived from their autocorrelation function, mean, and variance is presented. All methodological aspects of the genetic structure are presented. An extended description of the design of the fitness function is provided. Four application examples are provided and solved by using the proposed method.

scholarly journals Time series analysis of trial-to-trial variability of MEG power spectrum during rest state, unattented listening and frequency-modulated tones classification

2021 ◽  
Author(s):  
Lech Kipiński ◽  
Wojciech Kordecki
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Power Spectrum ◽  
Spectral Density ◽  
Cognitive Task ◽  
Clinical Neuroscience ◽  
Rest State ◽  
Short Time ◽  
Low Complex ◽  
Dominant Frequencies

AbstractThe nonstationarity of EEG/MEG signals is important for understanding the functioning of human brain. From the previous research we know that even very short, i.e. 250—500ms MEG signals are variance-nonstationary. The covariance of stochastic process is mathematically associated with its spectral density, therefore we investigate how the spectrum of such nonstationary signals varies in time.We analyze the data from 148-channel MEG, that represent rest state, unattented listening and frequency-modulated tones classification. We transform short-time MEG signals to the frequency domain using the FFT algorithm and for the dominant frequencies 8—12 Hz we prepare the time series representing their trial-to-trial variability. Then, we test them for level- and trend-stationarity, unit root, heteroscedasticity and gaussianity and based on their properties we propose the ARMA-modelling for their description.The analyzed time series have the weakly stationary properties independently of the functional state of brain and localization. Only their small percentage, mostly related to the cognitive task, still presents nonstationarity. The obtained mathematical models show that the spectral density of analyzed signals depends on only 2—3 previous trials.The presented method has limitations related to FFT resolution and univariate models, but it is not computationally complicated and allows to obtain a low-complex stochastic models of the EEG/MEG spectrum variability.Although the physiological short-time MEG signals are in principle nonstationary in time domain, its power spectrum at the dominant frequencies varies as weakly stationary stochastic process. Described technique has the possible applications in prediction of the EEG/MEG spectral properties in theoretical and clinical neuroscience.

Design Wind Speeds Using Fast Fourier Transform

2011 ◽  
pp. 1576-1591
Author(s):  
Z.. Ismail ◽  
N. H. Ramli ◽  
Z.. Ibrahim ◽  
T. A. Majid ◽  
G. Sundaraj ◽  
...  
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Spectral Density ◽  
Fast Fourier Transform ◽  
Time Series Data ◽  
Absolute Magnitude ◽  
Stationary Pattern ◽  
Wind Speeds ◽  
Hidden Periodicities ◽  
Using Data

In this chapter, a study on the effects of transforming wind speed data, from a time series domain into a frequency domain via Fast Fourier Transform (FFT), is presented. The wind data is first transformed into a stationary pattern from a non-stationary pattern of time series data using statistical software. This set of time series is then transformed using FFT for the main purpose of the chapter. The analysis is done through MATLAB software, which provides a very useful function in FFT algorithm. Parameters of engineering significance such as hidden periodicities, frequency components, absolute magnitude and phase of the transformed data, power spectral density and cross spectral density can be obtained. Results obtained using data from case studies involving thirty-one weather stations in Malaysia show great potential for application in verifying the current criteria used for design practices.

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