scholarly journals Spectral methods for small sample time series: A complete periodogram approach

2021 ◽  
Author(s):  
Sourav Das ◽  
Suhasini Subba Rao ◽  
Junho Yang
Keyword(s):  
Time Series ◽  
Spectral Methods ◽  
Small Sample ◽  
Sample Time

scholarly journals Periodicity Detection Method for Small-Sample Time Series Datasets

2010 ◽  
Vol 4 ◽  
pp. BBI.S5983 ◽  
Author(s):  
Daisuke Tominaga
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Small Sample ◽  
Detection Methods ◽  
Series Data ◽  
Computational Time ◽  
Signal Pathways ◽  
Periodicity Detection ◽  
Sampling Points ◽  
Sample Time

Time series of gene expression often exhibit periodic behavior under the influence of multiple signal pathways, and are represented by a model that incorporates multiple harmonics and noise. Most of these data, which are observed using DNA microarrays, consist of few sampling points in time, but most periodicity detection methods require a relatively large number of sampling points. We have previously developed a detection algorithm based on the discrete Fourier transform and Akaike's information criterion. Here we demonstrate the performance of the algorithm for small-sample time series data through a comparison with conventional and newly proposed periodicity detection methods based on a statistical analysis of the power of harmonics. We show that this method has higher sensitivity for data consisting of multiple harmonics, and is more robust against noise than other methods. Although “combinatorial explosion” occurs for large datasets, the computational time is not a problem for small-sample datasets. The MATLAB/GNU Octave script of the algorithm is available on the author's web site: http://www.cbrc.jp/%7Etominaga/piccolo/ .

Time series analysis of Holocene climate data

1990 ◽  
Vol 330 (1615) ◽  
pp. 601-616 ◽  
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Time Domain ◽  
Small Sample ◽  
Climate Data ◽  
Holocene Climate ◽  
Series Analysis ◽  
Window Method ◽  
Band Limited ◽  
Periodic Components

Holocene climate records are imperfect proxies for processes containing complicated mixtures of periodic and random signals. I summarize time series analysis methods for such data with emphasis on the multiple-data-window technique. This method differs from conventional approaches to time series analysis in that a set of data tapers is applied to the data in the time domain before Fourier transforming. The tapers, or data windows, are discrete prolate spheroidal sequences characterized as being the most nearly band-limited functions possible among functions defined on a finite time domain. The multiple-window method is a small-sample theory and essentially an inverse method applied to the finite Fourier transform. For climate data it has the major advantage of providing a narrowband F -test for the presence and significance of periodic components and of being able to separate them from the non-deterministic part of the process. Confidence intervals for the estimated quantities are found by jackknifing across windows. Applied to 14 C records, this method confirms the presence of the ‘Suess wiggles’ and give an estimated period of 208.2 years. Analysis of the thickness variations of bristlecone pine growth rings shows a general absence of direct periodic components but a variation in the structure of the time series with a 2360-year period.

scholarly journals Estimating Dynamic Common-Correlated Effects in Stata

2018 ◽  
Vol 18 (3) ◽  
pp. 585-617 ◽  
Author(s):  
Jan Ditzen
Keyword(s):  
Estimation Procedure ◽  
American Statistical Association ◽  
Small Sample ◽  
Cross Sectional ◽  
Pooled Mean Group ◽  
Common Correlated Effects ◽  
Cross Sectional Dependence ◽  
The Common ◽  
The Mean ◽  
Sample Time

In this article, I introduce a new command, xtdcce2, that fits a dynamic common-correlated effects model with heterogeneous coefficients in a panel with a large number of observations over cross-sectional units and time periods. The estimation procedure mainly follows Chudik and Pesaran (2015b, Journal of Econometrics 188: 393–420) but additionally supports the common correlated effects estimator (Pesaran, 2006, Econometrica 74: 967–1012), the mean group estimator (Pesaran and Smith, 1995, Journal of Econometrics 68: 79–113), and the pooled mean group estimator (Pesaran, Shin, and Smith, 1999, Journal of the American Statistical Association, 94: 621–634). xtdcce2 allows heterogeneous or homogeneous coefficients and supports instrumental-variable regressions and unbalanced panels. The cross-sectional dependence test is automatically calculated and presented in the estimation output. Small-sample time-series bias can be corrected by “half-panel” jackknife correction or recursive mean adjustment. I carry out a simulation to prove the estimator's consistency.

scholarly journals Forecasting using cross-section average–augmented time series regressions

2020 ◽  
Author(s):  
Hande Karabiyik ◽  
Joakim Westerlund
Keyword(s):  
Time Series ◽  
Cross Section ◽  
Regression Models ◽  
Common Factor ◽  
Principal Component ◽  
Small Sample ◽  
Interactive Effects ◽  
Cross Sectional ◽  
Second Development ◽  
The Cross

Summary There is a large and growing body of literature concerned with forecasting time series variables by the use of factor-augmented regression models. The workhorse of this literature is a two-step approach in which the factors are first estimated by applying the principal components method to a large panel of variables, and the forecast regression is then estimated, conditional on the first-step factor estimates. Another stream of research that has attracted much attention is concerned with the use of cross-section averages as common factor estimates in interactive effects panel regression models. The main justification for this second development is the simplicity and good performance of the cross-section averages when compared with estimated principal component factors. In view of this, it is quite surprising that no one has yet considered the use of cross-section averages for forecasting. Indeed, given the purpose to forecast the conditional mean, the use of the cross-sectional average to estimate the factors is only natural. The present paper can be seen as a reaction to this. The purpose is to investigate the asymptotic and small-sample properties of forecasts based on cross-section average–augmented regressions. In contrast to most existing studies, the investigation is carried out while allowing the number of factors to be unknown.

Time Series Analysis in Pooled Cross-Sections

1986 ◽  
Vol 2 (3) ◽  
pp. 331-349 ◽  
Author(s):  
John J. Beggs
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Cross Sections ◽  
Spectral Methods ◽  
Time Series Data ◽  
Series Data ◽  
Cross Sectional ◽  
Series Analysis ◽  
Simulation Results ◽  
Spectral Representations

This article proposes the use of spectral methods to pool cross-sectional replications (N) of time series data (T) for time series analysis. Spectral representations readily suggest a weighting scheme to pool the data. The asymptotically desirable properties of the resulting estimators seem to translate satisfactorily into samples as small as T = 25 with N = 5. Simulation results, Monte Carlo results, and an empirical example help confirm this finding. The article concludes that there are many empirical situations where spectral methods canbe used where they were previously eschewed.

scholarly journals EC-GAN: Inferring Brain Effective Connectivity via Generative Adversarial Networks

2020 ◽  
Vol 34 (04) ◽  
pp. 4852-4859
Author(s):  
Jinduo Liu ◽  
Junzhong Ji ◽  
Guangxu Xun ◽  
Liuyi Yao ◽  
Mengdi Huai ◽  
...  
Keyword(s):  
Time Series ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Effective Connectivity ◽  
Small Sample ◽  
Fmri Data ◽  
Generative Adversarial Networks ◽  
The Real ◽  
Adversarial Networks ◽  
Fmri Time Series

Inferring effective connectivity between different brain regions from functional magnetic resonance imaging (fMRI) data is an important advanced study in neuroinformatics in recent years. However, current methods have limited usage in effective connectivity studies due to the high noise and small sample size of fMRI data. In this paper, we propose a novel framework for inferring effective connectivity based on generative adversarial networks (GAN), named as EC-GAN. The proposed framework EC-GAN infers effective connectivity via an adversarial process, in which we simultaneously train two models: a generator and a discriminator. The generator consists of a set of effective connectivity generators based on structural equation models which can generate the fMRI time series of each brain region via effective connectivity. Meanwhile, the discriminator is employed to distinguish between the joint distributions of the real and generated fMRI time series. Experimental results on simulated data show that EC-GAN can better infer effective connectivity compared to other state-of-the-art methods. The real-world experiments indicate that EC-GAN can provide a new and reliable perspective analyzing the effective connectivity of fMRI data.

scholarly journals Testing financial time series for autocorrelation: Robust Tests

2020 ◽  
Vol 27 (3) ◽  
pp. e96
Author(s):  
Nelson Omar Muriel Torrero
Keyword(s):  
Time Series ◽  
Stock Returns ◽  
Financial Time Series ◽  
Real Data ◽  
Small Sample ◽  
Small Sample Properties ◽  
Robust Tests ◽  
Daily Stock Returns ◽  
Portmanteau Statistics ◽  
Empirical Size

Two modified Portmanteau statistics are studied under dependence assumptions common in financial applications which can be used for testing that heteroskedastic time series are serially uncorrelated without assuming independence or Normality. Their asymptotic distribution is found to be null and their small sample properties are examined via Monte Carlo. The power of the tests is studied under the MA and GARCH-in-mean alternatives. The tests exhibit an appropriate empirical size and are seen to be more powerful than a robust Box-Pierce to the selected alternatives. Real data on daily stock returns and exchange rates is used to illustrate the tests.

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