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Two-prime Sidelnikov sequence introduced by Brandstätter et al. in 2010 was shown to enjoy nice pseudorandom properties. It was shown to be balanced only in the case $p$ and $q$ are twin primes or $p$ and $q$ are cousin primes with $p\equiv q\equiv 3(mod4)$. In the case $gcd(p-1,q-1)=2$, where $p$ and $q$ are two distinct primes, a modification of the binary two-prime Sidelnikov sequence is proposed in this paper. We show that the new defined sequence is always balanced. And we also study the autocorrelation of the new defined sequence showing that it possesses nice autocorrelation feature.

We introduce a new mathematical tool (a direction-dependent probe) to analyze the randomness of purported isotropic Gaussian random fields on the sphere. If the field is isotropic and Gaussian then the probe coefficients for a given direction should be realizations of uncorrelated scalar Gaussian random variables. To study the randomness of a field, we use the autocorrelation of the sequence of probe coefficients (which are just the Fourier coefficients $a_{\ell ,0}$ if the $z$-axis is taken in the probe direction). We introduce a particular function on the sphere (called the AC discrepancy) that accentuates the departure from Gaussianity and isotropy. We apply the probe to assess the full-sky cosmic microwave background (CMB) temperature maps produced by the Planck collaboration (PR2 2015 and PR3 2018), with special attention to the inpainted maps. We find that for some of the maps, there are many directions for which the departures are significant, especially near the galactic plane. We also look briefly at the noninpainted Planck maps, for which the computed AC discrepancy maps have a very different character, with features that are global rather than local.

The acceptance probability in Hybrid Monte Carlo simulations of QCD, in particular, its dependence on the lattice size, quark mass and the coupling, is discussed. Results on the tuning of parameters required in order to achieve low autocorrelations in the 2-d XY model are presented. In both phases of this model, the dynamical critical exponent is close to 2 for runs with trajectory lengths between 1 and 3 molecular dynamics units.

This investigation elucidates the feasibility of monitoring a process for which observational data are largely autocorrelated. Special causes typically affect not only the process mean but also the process variance. The EWMA control chart has recently been developed and adopted to detect small shifts in the process mean and/or variance. This work extends the EWMA control chart, called the generally weighted moving average (GWMA) control chart, to monitor a process in which the observations can be regarded as a first-order autoregressive process with a random error. The EWMA and GWMA control charts of residuals used to monitor process variability and to monitor simultaneously the process mean and variance are considered to evaluate how average run lengths (ARLs) differ in each case.

Since the pneumatic artificial muscle is usually employed to actuate the robot, it is inevitable that it will collide with obstacles and/or other objects such that there will be impacts. The typical impacts include the axial and radial ones. This paper detects these two kinds of impact by a designed differential pressure measurement system, and achieves the goal of identifying them by the autocorrelations of their differential pressure signals in both static and dynamic processes, which are the two main work processes of the pneumatic artificial muscle. In detail, first we design an experiment scheme by connecting the pneumatic artificial muscle to the differential pressure sensor through two pressure tubes; then the axial and radial impact signals are acquired via the impact experiments under different work conditions (impact strength, internal pressure, load, and impact position); finally, the identification of the axial and radial impact signals are achieved based on the autocorrelation technique with a well-selected threshold. The experiments illustrate the effectiveness of the whole method.

Detecting chaos in heavy-noise environments is an important issue in many fields of science and engineering. In this paper, first, a new criterion is proposed to recognize chaos from noise based on the distribution of energy. Then, a new method based on stationary wavelet transform (SWT) is presented for chaos detection that is recommended for data that contain more than 60% noise. This method is dependent on the distribution of signal’s energy in different frequency bands based on SWT for chaos detection which is robust to noisy environments. In this method, the effect of white noise and colored noise on the chaotic system is considered. As a case study, the proposed method is applied to detect chaos in two different oscillators based on memristor and memcapacitor. The simulation results are used to display the main points of the paper.

We describe azimuth structure commonly associated with elliptic and directed flow in the context of 2D angular autocorrelations for the purpose of precise separation of so-called nonflow (mainly minijets) from flow. We extend the Fourier-transform description of azimuth structure to include power spectra and autocorrelations related by the Wiener–Khintchine theorem. We analyze several examples of conventional flow analysis in that context and question the relevance of reaction plane estimation to flow analysis. We introduce the 2D angular autocorrelation with examples from data analysis and describe a simulation exercise which demonstrates precise separation of flow and nonflow using the 2D autocorrelation method. We show that an alternative correlation measure based on Pearson's normalized covariance provides a more intuitive measure of azimuth structure.

A Fourier Transform of Equal Symbols (FTES) was applied as a spectral density analysis method to identify DNA bases that repeat at any frequency in selected protein-coding genes. The analysis especially focused on identification of bases responsible for the dominant signal at frequency f=1/3 found in all protein-coding genes. The study included homologous sequences from two gene families and multiple unrelated sequences from single organisms. No signal pattern or spectrum specifically characterized either gene family. However, the patterns of bases comprising the signal at f=1/3 suggested the presence of a genome-specific label for protein-coding genes from the same genome. Data suggest that three factors form the informational basis for the signal structure at f=1/3: (1) codon base positional bias; (2) codon preference; and (3) codon arrangement. Quantitative measure of the contribution of each base to the period-3 signal suggests a basis to distinguish protein-coding genes from different organisms. Application of the FTES analysis characterized genes from Escherichia coli as different from the genes from Pseudomonas aeruginosa. Preliminary analyses of genes from these and three other bacteria by artificial neural nets, using FTES parameters, support our suggestion that the period-3 informational structure contains labels for the genomic origins of protein-coding genes. FTES analysis alone or in combination with other informational measures may reveal pathways and processes of gene flow into and through natural systems of microbial cell populations.

In time series analysis remaining autocorrelation in the errors of a model implies that it is failing to properly capture the structure of time-dependence of the series under study. This can be used as a diagnostic checking tool and as an indicator of the adequacy of the model.

Through the study of the errors of the model in the Lagrange Multiplier testing framework, in this paper we derive (and validate using simulated and real world examples) a hypothesis test which allows us to determine if there is some left autocorrelation in the error series. This represents a new diagnostic checking tool for fuzzy rule-based modelling of time series and is an important step towards statistically sound modelling strategy for fuzzy rule-based models.

In this paper, we shall discuss some statistical properties of the estimator of $C_p$ when sample observations are autocorrelated and affected by measurement errors. The presence of autocorrelation in production units is very common in many industries like chemical, food processing, pharmaceutical, paper, and mineral. At the same time some amount of measurement error is invariably present in the sample observations due to inaccurate measurement process. In this paper, we discuss the case of a first-order stationary autoregressive process where measurement error follows a Gaussian distribution. The comparison of the statistical properties of the estimator in this case with the error-free case is the subject matter of this paper.

This paper provides an investigation of the effects of an investment’s return moments on drawdown-based measures of risk, including Maximum Drawdown (MDD), Conditional Drawdown (CDD), and Conditional Expected Drawdown (CED). Additionally, a new end-of-period drawdown measure is introduced, which incorporates a psychological aspect of risk perception that previous drawdown measures had been unable to capture. While simulation results indicate many similarities in the first and second moments, skewness and kurtosis affect different drawdown measures in radically different ways. Thus, users should assess whether their choice of drawdown measure accurately reflects the kind of risk they want to measure.

This paper reports an empirical analysis of the relationship between return autocorrelation, trading volume and volatility, following the seminal paper by Campbell, Grossman and Wang (1992) using data for A shares traded on the Shanghai and Shenzhen stock exchanges for the period 1992–2002. Campbell et al. argue that autocorrelation of returns will be negatively related to trading volume given that market makers will need to be rewarded with higher returns for accommodating noise traders. For our full sample we find remarkably consistent support for the CGW hypothesis and results — return autocorrelations are negatively but non-linearly related to lagged trading volume and less strongly to volatility. These results are quite robust with respect to different messures of volume and volatility. We argue that this is a striking result in view of the substantial differences between the US market in the 1960s, 1970s and 1980s and the Chinese market of the 1990s. The relationship proves to be unstable over short sub-periods although whether this is due to the relatively short sample we use or to the inherent instability of the Chinese market in its first decade of operation will not be clear until much longer data sets are available for Chinese stock prices.

This paper reviews applications of signal processing techniques to a number of areas in the field of genetics. We focus on techniques for analyzing DNA sequences, and briefly discuss applications of signal processing to DNA sequencing, and other related areas in genetics that can provide biologically significant information to assist with sequence analysis.

This paper aims to analyze whether the financial crises of the past 20 years have reduced efficiency, in its weak form, in 19 stock markets belonging to the 20 most developed economies (G-20). The sample period comprises the period from 2 January 2000 to 5 February 2021 with the respective financial crises, namely, Dot-com, Argentina, Subprime, Sovereign debt, China stock market crash (2015–2016), UK’s withdrawal from the European Union and the global pandemic of 2020. The results highlight that most markets show signs of (in)efficiency in each sliding window (1000 days), that is, they show asymmetries and non-Gaussian distributions, and ${\alpha }_{\mathrm{\text{DFA}}}\ne 0.5$. These findings suggest that the random walk hypothesis is rejected in certain markets, which has implications for investors, since some returns may be expected, creating arbitrage and abnormal profit opportunities, contrary to the random walk and informational efficiency hypotheses. The results found also open room for market regulators to take steps to ensure better informational data across international financial markets.

Spatial data mining is the quantitative study of phenomena that are located in space. This paper investigates methods of mining patterns of a complex spatial data set (which generally describes any kind of data where the location in space of object holds importance). We based this research on the analysis of some spatial characteristics of certain objects. We began with describing the spatial pattern of events or objects with respect to their attributes; we looked at how to describe the spatial nature/characteristics of entities in an environment with respect to their spatial and non-spatial attributes. We also looked at modelling (predictive modelling/knowledge management of complex spatial systems), querying and implementing a complex spatial database (using data structure and algorithms). Critically speaking, the presence of spatial auto-correlation and the fact that continuous data types are always present in spatial data makes it important to create methods, tools and algorithms to mine spatial patterns in a complex spatial data set. This work is particularly useful to researchers in the field of data mining as it contributes a whole lot of knowledge to different application areas of data mining especially spatial data mining. It can also be useful in teaching and likewise for other study purposes.

We discuss the construction of designs for estimation of nonparametric regression models with autocorrelated errors when the mean response is to be approximated by a finite order linear combination of dilated and translated versions of the Daubechies wavelet bases with four vanishing moments. We assume that the parameters of the resulting model will be estimated by weighted least squares (WLS) or by generalized least squares (GLS). The bias induced by the unused components of the wavelet bases, in the linear approximation, then inflates the natural variation of the WLS and GLS estimates. We therefore construct our designs by minimizing the maximum value of the average mean squared error (AMSE). Such designs are said to be robust in the minimax sense. Our illustrative examples are constructed by using the simulated annealing algorithm to select an optimal $n$-point design, which are integers, from a grid of possible values of the explanatory or design variable $x$. We found that the integer-valued designs we constructed based on GLS estimation, have smaller minimum loss when compared to the designs for WLS or ordinary least squares (OLS) estimation, except when the correlation parameter $\rho$ approaches 1.

We completely determine the autocorrelations of the quaternary cyclotomic sequences over ${𝔽}_4$ of length $2p^m$ presented in [P. Ke and S. Zhang, New classes of quaternary cyclotomic sequence of length $2p^m$ with high linear complexity, Inf. Process. Lett. 112 (2012) 646–650] in general without the restrictions about $e$.

The fundamental frequency (F₀) plays a vital role in music signal analysis and processing. However, due to non-stationary noise, undesired physical vibration from the musical instruments, the robust estimation of F₀ remains a main challenge. In this paper, a F₀ estimation algorithm of music signals based on harmonic pattern match (HPM) is described to achieve more reliable estimation accuracy. The algorithm utilizes the autocorrelation both in the time domain and in the frequency domain, exploiting the spectrum subset to guide the search of F₀ candidates (FCs), and an efficient mechanism to evaluate the match between each FC and the harmonic pattern of the input signal. The harmonic pattern of the measured spectrum is presented by sub-pitch in each segmented sub-band. Finally, the estimated $$\hat{F}_0$$ is selected to best match the sub-pitches under a weighting strategy. Evaluation experiments were performed over a musical instruments database consisting of single pitched notes and the viability of the HPM algorithm was demonstrated to be competitive with several other F₀ estimators.

The estimation and significance testing of the first-order autoregressive (AR1) coefficient in short time series with trends are examined. The purpose is to identify the difficulties to which analysis procedures need to adjust for better results. The delta recursive AR1 estimator r_δ and the Sen–Theil trend estimator are viable for short sequence application. Significance testing for r_δ has low power. But the existence of trend has negligible influence in estimation and testing. The common practice of trend removal before AR1 estimation gives poorer results. Application to air quality data showed this could greatly change conclusions. Implication to analysis is discussed.

We study the long memory of order flow for each of three liquid currency pairs on a large electronic trading platform in the foreign exchange (FX) spot market. Due to the extremely high levels of market activity on the platform, and in contrast to existing empirical studies of other markets, our data enables us to perform statistically stable estimation without needing to aggregate data from different trading days. We find strong evidence of long memory, with a Hurst exponent $H\approx 0.7$, for each of the three currency pairs and on each trading day in our sample. We repeat our calculations using data that spans different trading days, and we find no significant differences in our results. We test and reject the hypothesis that the apparent long memory of order flow is an artifact caused by structural breaks, in favor of the alternative hypothesis of true long memory. We therefore conclude that the long memory of order flow in the FX spot market is a robust empirical property that persists across daily boundaries.