Frequency Domain Analysis Of Time Series Research Articles

Spectral analysis of high-dimensional time series

A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length, regularisation based methods can overcome the curse of dimensionality, but the existing ones lack theoretical justification. This paper develops the first non-asymptotic result for characterising the difference between the sample and population versions of the spectral density matrix, allowing one to justify a range of high-dimensional models for analysing time series. As a concrete example, we apply this result to establish the convergence of the smoothed periodogram estimators and sparse estimators of the inverse of spectral density matrices, namely precision matrices. These results, novel in the frequency domain time series analysis, are corroborated by simulations and an analysis of the Google Flu Trends data.

Testing for Granger Causality in the Frequency Domain: A Phase Resampling Method

abstractThis article introduces phase resampling, an existing but rarely used surrogate data method for making statistical inferences of Granger causality in frequency domain time series analysis. Granger causality testing is essential for establishing causal relations among variables in multivariate dynamic processes. However, testing for Granger causality in the frequency domain is challenging due to the nonlinear relation between frequency domain measures (e.g., partial directed coherence, generalized partial directed coherence) and time domain data. Through a simulation study, we demonstrate that phase resampling is a general and robust method for making statistical inferences even with short time series. With Gaussian data, phase resampling yields satisfactory type I and type II error rates in all but one condition we examine: when a small effect size is combined with an insufficient number of data points. Violations of normality lead to slightly higher error rates but are mostly within acceptable ranges. We illustrate the utility of phase resampling with two empirical examples involving multivariate electroencephalography (EEG) and skin conductance data.

Long-range dependence and asymptotic self-similarity in third order

The object of this paper is studying the topic of long-range dependence and asymp- totic self-similarity from the viewpoint of third-order time series analysis in frequency domain. The long-range dependent (LRD) time series in third-order is de¯ned by the bispectrum and by the bicovariances. A Tauber type connection between these two de¯nitions is shown.

Contributions of Professor Hirotugu Akaike in Statistical Science

Professor Hirotugu Akaike was awarded the 2006 Kyoto Prize for “his major contribution to statisticalscience and model ing with the Akaike Information Criterion (AIC)”. In 1973, he proposed the AIC as a naturalextension of the log-likelihood. The most natural way of applying the AIC is to use it as the model selection or order selection criterion. In the MAICE (minimum AIC estimation) procedure, the model with the minimum value of the AIC is selected as the best one among many possible models. This provided a versatile procedure for statistical modeling that is free from the ambiguities inherent in application of the hypothesis test procedure. However, the impact of the AIC is not limited to the realization of an automatic model selection procedure, and it eventually led to a paradigm shift in statisticalscience. In conventionalstatisticalinference, the theories of estimation and test are developed under the assumption of the presence of a true model. However, in statistical modeling, the model should be constructed based on the entire knowledge such as the established theory, empirical facts, current observations and even the objective of the analysis. Prof. Akaike gave a practical answer to the selection of the prior distribution of the Bayes model. Due to the development of information technologies, we can now access to huge amounts of data in various fields of science and social life. In this information and knowledge society, the Bayes modelis becoming a key technology. In this article, we shall look back at his research in five stages, namely, the launching period, frequency domain time series analysis, time series modeling, AIC and statistical modeling and Bayes modeling (Parzen et al. (1998)). It should be noted here that the reader will notice that his research was always performed based on the needs of researchers in the real-world.

Diving behaviour of whale sharks in relation to a predictable food pulse

We present diving data for four whale sharks in relation to a predictable food pulse (reef fish spawn) and an analysis of the longest continuous fine-resolution diving record for a planktivorous shark. Fine-resolution pressure data from a recovered pop-up archival satellite tag deployed for 206 days on a whale shark were analysed using the fast Fourier Transform method for frequency domain analysis of time-series. The results demonstrated that a free-ranging whale shark displays ultradian, diel and circa-lunar rhythmicity of diving behaviour. Whale sharks dive to over 979.5 m and can tolerate a temperature range of 26.4 degrees C. The whale sharks made primarily diurnal deep dives and remained in relatively shallow waters at night. Whale shark diving patterns are influenced by a seasonally predictable food source, with shallower dives made during fish spawning periods.

Alternans of ventricular gradient during percutaneous transluminal coronary angioplasty

We evaluated the influence of local myocardial ischemia induced by acute coronary occlusion during percutaneous transluminal coronary angioplasty (PTCA) on the ventricular gradients (VG) and investigated whether 2:1 alternans of VG occurs. Twenty-seven patients with angina pectoris, who had one-vessel coronary artery stenosis, were studied. The VG of each consecutive heartbeat before, during, and after PTCA over a 22-second interval was calculated using a microcomputer. The standard deviation and coefficient of variation of magnitude were used as indices of VG variability. Frequency-domain analysis of time series consisting of beat-to-beat VG magnitude for a 22-second interval was also performed by the maximum entropy method. The standard deviation and coefficient of variation of VG magnitude during PTCA were significantly greater than those before and after PTCA ( P < .01, P < .01, respectively), and the indices before PTCA were also significantly greater than those after PTCA ( P < .05). The maximum power spectrum peaks around 0.5 cycles/beat during PTCA were significantly greater than those after PTCA ( P < .01); this suggests that the enhancement of VG alternans is reflected by 2:1 alternans of the action potential in the acute local ischemic myocardium during PTCA.

Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models

The author considers frequency domain time series analysis, where smoothing in nonparametric spectrum estimation is data-dependent. Uniform convergence of spectrum estimates is established and applied to a semiparametric model, parameterized over possibly only a subset of the frequencies, in which disturbances have nonparametric autocorrelation. Optimal instruments depend on the disturbance spectrum and frequency response function, which is nonparametric in incomplete systems. The author justifies feasible, optimal parameter estimates. The degree of smoothing is allowed to depend on the data in a general way. The author proves consistency of a cross-validation method of automatic smoothing and applies it to a semiparametric model. Copyright 1991 by The Econometric Society.