A new test statistic for searching hidden periodicities in time series and the derivation and numerical calculation of its power function

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

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Design Wind Speeds Using Fast Fourier Transform

Intelligent Information Technologies ◽

10.4018/978-1-59904-941-0.ch089 ◽

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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A robust method for shift detection in time series

Biometrika ◽

10.1093/biomet/asaa004 ◽

2020 ◽

Vol 107 (3) ◽

pp. 647-660

Author(s):

H Dehling ◽

R Fried ◽

M Wendler

Keyword(s):

Time Series ◽

Nonparametric Test ◽

Test Statistic ◽

Moment Conditions ◽

Limit Theory ◽

Dependent Observations ◽

U Statistics ◽

Shift Detection ◽

Heavy Tailed ◽

The Stability

Summary We present a robust and nonparametric test for the presence of a changepoint in a time series, based on the two-sample Hodges–Lehmann estimator. We develop new limit theory for a class of statistics based on two-sample U-quantile processes in the case of short-range dependent observations. Using this theory, we derive the asymptotic distribution of our test statistic under the null hypothesis of a constant level. The proposed test shows better overall performance under normal, heavy-tailed and skewed distributions than several other modifications of the popular cumulative sums test based on U-statistics, one-sample U-quantiles or M-estimation. The new theory does not involve moment conditions, so any transform of the observed process can be used to test the stability of higher-order characteristics such as variability, skewness and kurtosis.

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Synchronisation phenomenon in three blades rotor driven by regular or chaotic oscillations

MATEC Web of Conferences ◽

10.1051/matecconf/201814806002 ◽

2018 ◽

Vol 148 ◽

pp. 06002

Author(s):

Zofia Szmit ◽

Jerzy Warmiński

Keyword(s):

Time Series ◽

Numerical Calculation ◽

Duffing Oscillator ◽

Equations Of Motion ◽

Composite Beams ◽

Chaotic Oscillations ◽

Rotating System ◽

Chaotic Motions ◽

Structural Differences ◽

Different Types

The goal of the paper is to analysed the influence of the different types of excitation on the synchronisation phenomenon in case of the rotating system composed of a rigid hub and three flexible composite beams. In the model is assumed that two blades, due to structural differences, are de-tuned. Numerical calculation are divided on two parts, firstly the rotating system is exited by a torque given by regular harmonic function, than in the second part the torque is produced by chaotic Duffing oscillator. The synchronisation phenomenon between the beams is analysed both either for regular or chaotic motions. Partial differential equations of motion are solved numerically and resonance curves, time series and Poincaré maps are presented for selected excitation torques.

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TESTING THE ORDER OF FRACTIONAL INTEGRATION OF A TIME SERIES IN THE POSSIBLE PRESENCE OF A TREND BREAK AT AN UNKNOWN POINT

Econometric Theory ◽

10.1017/s0266466618000361 ◽

2018 ◽

Vol 35 (6) ◽

pp. 1201-1233 ◽

Cited By ~ 2

Author(s):

Fabrizio Iacone ◽

Stephen J. Leybourne ◽

A.M. Robert Taylor

Keyword(s):

Time Series ◽

Power Function ◽

Long Memory ◽

Fractional Integration ◽

Monte Carlo Study ◽

Local Power ◽

Finite Sample ◽

Lm Test ◽

Unknown Point ◽

Memory Parameter

We develop a test, based on the Lagrange multiplier [LM] testing principle, for the value of the long memory parameter of a univariate time series that is composed of a fractionally integrated shock around a potentially broken deterministic trend. Our proposed test is constructed from data which are de-trended allowing for a trend break whose (unknown) location is estimated by a standard residual sum of squares estimator applied either to the levels or first differences of the data, depending on the value specified for the long memory parameter under the null hypothesis. We demonstrate that the resulting LM-type statistic has a standard limiting null chi-squared distribution with one degree of freedom, and attains the same asymptotic local power function as an infeasible LM test based on the true shocks. Our proposed test therefore attains the same asymptotic local optimality properties as an oracle LM test in both the trend break and no trend break environments. Moreover, this asymptotic local power function does not alter between the break and no break cases and so there is no loss in asymptotic local power from allowing for a trend break at an unknown point in the sample, even in the case where no break is present. We also report the results from a Monte Carlo study into the finite-sample behaviour of our proposed test.

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