Small Autocorrelation Research Articles

Assessing digital financial inclusion and financial crises: The role of financial development in shielding against shocks.

Digital financial inclusion (DFI) has been proven to be a central factor in driving economic development and reducing inequality in countries. However, its impact on financial crises (FC) has yet to be clearly examined, particularly in the context of current Financial Development (FD). Therefore, this study examines the influence of DFI on FC across 52 countries from 2004 to 2020, focusing on how this impact varies with the level of FD. Using a combination of Threshold Regression (PTR) and Bayesian regression methods, the research first identifies structural breaks in the DFI-FC relationship, with FD as the threshold variable. Bayesian regression is then employed to address challenges such as small sample sizes, endogeneity, and autocorrelation, while assessing DFI's differential impact across countries with varying FD levels. The PTR analysis reveals a threshold value of 0.6036, indicating a non-linear DFI-FC relationship depending on FD levels. In low FD countries, DFI reduces the risk of FC, whereas in high FD countries, uncontrolled DFI increases it. Based on the results, we suggest that financial institutions should strengthen efforts to promote investment in digital technology by implementing digital skills training programs, providing capital to businesses and individuals, and facilitating support from financial institutions in countries with low FD. Meanwhile, for countries with high FD, regulatory authorities should establish stricter regulations and supervision mechanisms for digital financial activities to mitigate the risks of FC.

Strong long ties facilitate epidemic containment on mobility networks.

The analysis of connection strengths and distances in the mobility network is pivotal for delineating critical pathways, particularly in the context of epidemic propagation. Local connections that link proximate districts typically exhibit strong weights. However, ties that bridge distant regions with high levels of interaction intensity, termed strong long (SL) ties, warrant increased scrutiny due to their potential to foster satellite epidemic clusters and extend the duration of pandemics. In this study, SL ties are identified as outliers on the joint distribution of distance and flow in the mobility network of Shanghai constructed from 1 km × 1 km high-resolution mobility data. We propose a grid-joint isolation strategy alongside a reaction-diffusion transmission model to assess the impact of SL ties on epidemic propagation. The findings indicate that regions connected by SL ties exhibit a small spatial autocorrelation and display a temporal similarity pattern in disease transmission. Grid-joint isolation based on SL ties reduces cumulative infections by an average of 17.1% compared with other types of ties. This work highlights the necessity of identifying and targeting potentially infected remote areas for spatially focused interventions, thereby enriching our comprehension and management of epidemic dynamics.

Characterizing Rotational Dynamics and Heterogeneity via Single-Molecule Intensity Measurements.

Dynamic heterogeneity in glassy systems has typically been characterized at the single-molecule level by extracting rotational relaxation time scales from linear dichroism (LD) collected via two orthogonally polarized channels. However, in such measurements, localization precision is diminished due to photons lost relative to collection in a single detection channel. This poses challenges in characterizing rotational and translational dynamics simultaneously, as translational measurements require high localization precision. In this paper, we present a method for extracting rotational dynamics of glassy systems at the single-molecule level from intensity fluctuations of fluorescent probe molecules in a wide-field configuration without the use of a polarizing optical component. Through numerical analysis, we show that LD and intensity measurements probing rotational dynamics report similar, approximately second-order rotational correlation decays even at low signal to noise. Thus, within the assumptions of small, isotropic rotations, LD and intensity autocorrelation analysis should provide identical information on the time scale and heterogeneity of rotational dynamics. We then present experimental results that validate this numerical result, with direct comparison of LD and intensity-based approaches across probe molecules in both polymeric and small-molecule glass formers as well as across optical configurations. Our results demonstrate moderate correlation on a per-probe basis between rotational time scales obtained from both approaches, with deviations consistent with those expected in a dynamically heterogeneous system. We envision that this easily accessible strategy will be of use across disciplines for characterizing single-molecule rotational dynamics in limited signal situations and/or when high-precision localization is required.

Probabilistic analysis on the lateral capacity of suction caissons in spatially variable soils

This paper aims to investigate the ultimate lateral capacity of suction caissons embedded in clay with spatially varying undrained shear strength in the framework of probabilistic analysis for the first time. A non-stationary three-dimensional random field is used to represent the undrained shear strength with a linearly increasing trend with depths below the mudline. The stochastic finite difference method is employed to determine the probabilistic ultimate lateral capacity of suction caissons. The influences of the clay undrained strength heterogeneity κ, the coefficient of variation of undrained strength COVsu, and the autocorrelation distances on the probability density function (PDF) curves and cumulative distribution function (CDF) curves of the normalized ultimate lateral capacity N h are investigated . It is found that both the mean and standard deviation of normalized ultimate lateral capacity N h increase with the undrained strength heterogeneity κ, but the coefficient of variation of N h does not. Besides, the small autocorrelation distance of clay results in the low variability of normalized ultimate lateral capacity. This indicates the significance of probabilistic site characterization of the undrained strength of clay.

Unimodular Perfect and Nearly Perfect Sequences: a Variation of Björck’s Scheme

Constant Amplitude (CA), Zero Auto Correlation (ZAC) sequences (or CAZAC sequences, aka perfect sequences) have numerous applications. We generalize the CAZAC notion to what we term as CASAC by permitting small autocorrelations (SAC). We extend Björck’s classification result of two-valued CAZAC sequences by providing a complete classification of all almost 2-valued (i.e., two-valued except for the first position which uses a third value) CASAC sequences. While Björck’s original work dealt only with primes p, we extend his ideas to any abelian group of order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v\equiv 1\pmod {4}$ </tex-math></inline-formula> , as opposed to restricting just to the prime fields GF(p). Björck sequences have better ambiguity function than Zadoff-Chu sequences, making them suitable for radar and communications applications in the presence of high Doppler shifts. In fact, the discrete narrow band ambiguity function has an optimal bound in case of Björck sequences (as opposed to Gauss sequences). A one-parameter infinite family of CASAC we construct would have applications in Multiple-Input Multiple-Output (MIMO) areas. Toward MIMO applications, we introduce a performance measure we term as cross merit factor to study cross correlation behavior, generalizing the well-known notion of Golay Merit Factor (GMF).

Unravelling the multilevel and multi-dimensional impacts of building and tree on surface urban heat islands

The multilevel effects of landscape composition and configuration on daytime land surface temperature (LST) has been examined. However, how 2D and 3D characteristics of building and tree hierarchically interact to influence LST and how such effects vary diurnally were yet unknown. Using thermal satellite imagery, 2D and 3D characteristics of urban landscapes, and multilevel models (i.e. the random intercept model (RIM) and the random coefficient model (RCM)), we quantified the multi-dimensional and hierarchical effects of buildings and trees on LST as well as their diurnal contrast. Our results showed that combining landscape pattern and 3D urban morphology can capture more of the variation in diurnal LST than using them separately, regardless of single-level ordinary least squares (OLS) and multilevel models. Moreover, the multilevel models performed better than OLS models in explaining the impacts of landscape pattern and 3D urban morphology on LST for both day and night, and the RCM performed better than that the RIM. During the day, the standard deviations of the residual and autocorrelation in the residual for the RCM were 1.315 and 0.131, respectively, but 1.715 and 0.312 for OLS, respectively. Similarly, a smaller autocorrelation in the residual was produced by the RCM (0.155) than by OLS (0.366) at night. The spatial heterogeneity of LST was linked tightly to the percent cover of trees and the largest patch index of tree during the day, but was primarily dominated by the edge density of the buildings and the mean building height at night. Moreover, we found significant differences in the random effects of the composition and 3D urban morphology on the LST at the block level. The random impacts of the percent cover of buildings on both daytime and nighttime LSTs varied most across urban blocks. These findings provide urban planners and researchers a more thorough picture of LST-landscape associations from multi-dimensional and multilevel perspectives.

Dependent structure and risk analysis of S&amp;P 500 Index's continuously rising returns and continuously falling returns

PurposeThe stock market price time series can be divided into two processes: continuously rising and continuously falling. The authors can effectively prevent the stock market from crashing by accurately estimating the risk on continuously rising returns (CRR) and continuously falling returns (CFR).Design/methodology/approachThe authors add an exogenous variable into Log-autoregressive conditional duration (Log-ACD) model, and then apply our extended Log-ACD model and Archimedean copula to estimate the marginal distribution and conditional distribution of CRR and CFR. Plus, the authors analyze the conditional value at risk (CVaR) and present back-test results of the CVaR. The back-test shows that our proposed risk estimation method has a good estimation power for the risk of the CRR and CFR, especially the downside risk. In addition, the authors detect whether the dependent structure between the CRR and CFR changes using the change point test method.FindingsThe empirical results indicate that there is no change point here, suggesting that the results on the dependent structure and risk analysis mentioned above are stable. Therefore, major financial events will not affect the dependent structure here. This is consistent with the point that the CRR and CFR can be analyzed to obtain the trend of stock returns from a more macro perspective than daily stock returns scholars usually study.Practical implicationsThe risk estimation method of this paper is of great significance in understanding stock market risk and can provide corresponding valuable information for investment advisors and public policy regulators.Originality/valueThe authors defined a new stock returns, CRR and CFR, since it is difficult to analyze and predict the trend of stock returns according to daily stock returns because of the small autocorrelation among daily stock returns.

Intermittency of three-dimensional perturbations in a point-vortex model.

Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based on known physical properties of such 3D instabilities, we propose a simple, energy-conserving model describing this situation. It consists of a regularized 2D point-vortex flow coupled to localized 3D perturbations ("ergophages"), such that ergophages can gain energy by altering vortex-vortex distances through an induced divergent velocity field, thus decreasing point-vortex energy. We investigate the model in three distinct stages of evolution: (i) The linear regime, where the amplitude of the ergophages grows or decays exponentially on average, with an instantaneous growth rate that fluctuates randomly in time. The instantaneous growth rate has a small auto-correlation time, and a probability distribution featuring a power-law tail with exponent between -2 and -5/3 (up to a cutoff) depending on the point-vortex base flow. Consequently, the logarithm of the ergophage amplitude performs a Lévy flight. (ii) The passive-nonlinear regime of the model, where the 2D flow evolves independently of the ergophage amplitudes, which saturate by non-linear self-interactions without affecting the 2D flow. In this regime the system exhibits a new type of on-off intermittency that we name Lévy on-off intermittency, which we define and study in a companion paper [van Kan et al., Phys. Rev. E 103, 052115 (2021)1063-651X10.1103/PhysRevE.103.052115]. We compute the bifurcation diagram for the mean and variance of the perturbation amplitude, as well as the probability density of the perturbation amplitude. (iii) Finally, we characterize the fully nonlinear regime, where ergophages feed back on the 2D flow, and study how the vortex temperature is altered by the interaction with ergophages. It is shown that when the amplitude of the ergophages is sufficiently large, the condensate is disrupted and the 2D flow saturates to a zero-temperature state. Given the limitations of existing theories, our model provides a new perspective on 3D instabilities growing on 2D flows, which will be useful in analyzing and understanding the much more complex results of DNS and potentially guide further theoretical developments.

Significant Predictors of Henley Passport Index

Henley Passport Index (HPI) is a rank on the number of countries a passport holder of a country can travel VISA-free. Countries with high HPI ranking enjoy certain passport privileges. Little is known about the relationship between HPI and other global indices. This paper investigates the relationship between HPI and the trio of Corruption Perception Index (CPI), Global Peace Index (GPI), and World Happiness Report (WHR). The data of the country ranks of the 4 indices were obtained from the respective websites of the publishers of the indices. A final sample of 150 countries was analyzed after the cases of missing values were discarded. The result showed positive correlation between HPI and CPI (r = 0.768, p < 0.0005), GPI (r = 0.671, p < 0.005), and WHR (r = 0.775, p < 0.005), respectively. Regression analysis yielded an equation that showed that a unit increase in the country ranking of CPI, GPI, and WHR of countries increases the ranking of HPI by 0.196, 0.149, and 0.352, respectively. The coefficients of the independent variables are all significant at p value equals 0.05 and the model validation showed the absence of multicollinearity and the presence of small non-significant autocorrelation. The research concluded that countries with high passport privileges also have low corruption instances and conflicts and are perceived to be happy. The implications of this research were discussed.

On the bivariate Erdős–Kac theorem and correlations of the Möbius function

AbstractGiven a positive integer n let ω (n) denote the number of distinct prime factors of n, and let a be fixed positive integer. Extending work of Kubilius, we develop a bivariate probabilistic model to study the joint distribution of the deterministic vectors (ω(n), ω(n + a)), with n ≤ x as x → ∞, where n and n + a belong to a subset of ℕ with suitable properties. We thus establish a quantitative version of a bivariate analogue of the Erdős–Kac theorem on proper subsets of ℕ.We give three applications of this result. First, if y = x0(1) is not too small then we prove (in a quantitative way) that the y-truncated Möbius function μy has small binary autocorrelations. This gives a new proof of a result due to Daboussi and Sarkőzy. Second, if μ(n; u) :=e(uω(n)), where u ∈ ℝ then we show that μ(.; u) also has small binary autocorrelations whenever u = o(1) and $u\sqrt {\mathop {\log }\nolimits_2 x} \to \infty$, as x → ∞. These can be viewed as partial results in the direction of a conjecture of Chowla on binary correlations of the Möbius function.Our final application is related to a problem of Erdős and Mirsky on the number of consecutive integers less than x with the same number of divisors. If $y = x^{{1 \over \beta }}$, where β = β(x) satisfies certain mild growth conditions, we prove a lower bound for the number of consecutive integers n ≤ x that have the same number of y-smooth divisors. Our bound matches the order of magnitude of the one conjectured for the original Erdős-Mirsky problem.

Estimating Spatial Autocorrelation With Sampled Network Data

Spatial autocorrelation is a parameter of importance for network data analysis. To estimate spatial autocorrelation, maximum likelihood has been popularly used. However, its rigorous implementation requires the whole network to be observed. This is practically infeasible if network size is huge (e.g., Facebook, Twitter, Weibo, WeChat, etc.). In that case, one has to rely on sampled network data to infer about spatial autocorrelation. By doing so, network relationships (i.e., edges) involving unsampled nodes are overlooked. This leads to distorted network structure and underestimated spatial autocorrelation. To solve the problem, we propose here a novel solution. By temporarily assuming that the spatial autocorrelation is small, we are able to approximate the likelihood function by its first-order Taylor’s expansion. This leads to the method of approximate maximum likelihood estimator (AMLE), which further inspires the development of paired maximum likelihood estimator (PMLE). Compared with AMLE, PMLE is computationally superior and thus is particularly useful for large-scale network data analysis. Under appropriate regularity conditions (without assuming a small spatial autocorrelation), we show theoretically that PMLE is consistent and asymptotically normal. Numerical studies based on both simulated and real datasets are presented for illustration purpose.

On the arithmetic autocorrelation of the Legendre sequence

The Legendre sequence possesses several desirable features of pseudorandomness in view of different applications such as a high linear complexity (profile) for cryptography and a small (aperiodic) autocorrelation for radar, gps, or sonar. Here we prove the first nontrivial bound on its arithmetic autocorrelation, another figure of merit introduced by Mandelbaum for errorcorrecting codes.

Sequences with small correlation

The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or $$-1$$-1, called binary sequences, and sequences whose entries are complex numbers of unit magnitude, called unimodular sequences. Since the 1950s, there is sustained interest in sequences with small aperiodic autocorrelations relative to the sequence length. One of the main motivations is that a sequence with small aperiodic autocorrelations is intrinsically suited for the separation of signals from noise, and therefore has natural applications in digital communications. This survey reviews the state of knowledge concerning the two central problems in this area: How small can the aperiodic autocorrelations of a binary or a unimodular sequence collectively be and how can we efficiently find the best such sequences? Since the analysis and construction of sequences with small aperiodic autocorrelations is closely tied to the (often much easier) analysis of periodic autocorrelation properties, several fundamental results on corresponding problems in the periodic setting are also reviewed.

Estimating Spatial Autocorrelation with Sampled Network Data

Spatial autocorrelation is a parameter of importance for network data analysis. To estimate spatial autocorrelation, maximum likelihood has been popularly used. However, its rigorous implementation requires the whole network to be observed. This is practically infeasible if network size is huge (e.g., Facebook, Twitter, Weibo, WeChat, etc). In that case, one has to rely on sampled network data to infer about spatial autocorrelation. By doing so, network relationships (i.e., edges) involving unsampled nodes are overlooked. This leads to distorted network structure and underestimated spatial autocorrelation. To solve the problem, we propose here a novel solution. By temporarily assuming that the spatial autocorrelation is small, we are able to approximate the likelihood function by its first order Taylor's expansion. This leads to the method of approximate maximum likelihood estimator (AMLE), which further inspires the development of paired maximum likelihood estimator (PMLE). Compared with AMLE, PMLE is computationally superior and thus is particularly useful for large scale network data analysis. Under appropriate regularity conditions (without assuming a small spatial autocorrelation), we show theoretically that PMLE is consistent and asymptotically normal. Numerical studies based on both simulated and real datasets are presented for illustration purpose.

Implications of TCO Topography on Intermediate Reflector Design for a-Si/μc-Si Tandem Solar Cells—Experiments and Rigorous Optical Simulations

The influence of the transparent conducting oxide (TCO) topography was studied on the performance of a silicon oxide intermediate reflector layer (IRL) in a-Si/μc-Si tandem cells, both experimentally and by 3-D optical simulations. Therefore, cells with varying IRL thickness were deposited on three different types of TCOs. Clear differences were observed regarding the performance of the IRL as well as its ideal thickness, both experimentally and in the simulations. Optical modeling suggests that a small autocorrelation length is essential for a good performance. Design rules for both the TCO topography and the IRL thickness can be derived from this interplay.

EVD Dualdating Based Online Subspace Learning

Conventional incremental PCA methods usually only discuss the situation of adding samples. In this paper, we consider two different cases: deleting samples and simultaneously adding and deleting samples. To avoid the NP-hard problem of downdating SVD without right singular vectors and specific position information, we choose to use EVD instead of SVD, which is used by most IPCA methods. First, we propose an EVD updating and downdating algorithm, called EVD dualdating, which permits simultaneous arbitrary adding and deleting operation, via transforming the EVD of the covariance matrix into a SVD updating problem plus an EVD of a small autocorrelation matrix. A comprehensive analysis is delivered to express the essence, expansibility, and computation complexity of EVD dualdating. A mathematical theorem proves that if the whole data matrix satisfies the low-rank-plus-shift structure, EVD dualdating is an optimal rank-kestimator under the sequential environment. A selection method based on eigenvalues is presented to determine the optimal rank k of the subspace. Then, we propose three incremental/decremental PCA methods: EVDD-IPCA, EVDD-DPCA, and EVDD-IDPCA, which are adaptive to the varying mean. Finally, plenty of comparative experiments demonstrate that EVDD-based methods outperform conventional incremental/decremental PCA methods in both efficiency and accuracy.

Spatial scales of genetic patchiness in the western rock lobster Panulirus cygnus

In planktonic dispersers, impediments to dispersal, local selection or large variance in the reproductive success among individuals (sweepstakes reproductive success) can create genetic heterogeneity at local scales. While these processes are well recognized, relatively few studies have investigated the spatial scales over which genetic heterogeneity occurs and how it is distributed across species' ranges. We investigate population structure in the western rock lobster Panulirus cygnus, a commercially exploited species found in shallow and deep-water reef habitats along the Western Australia coastline. We screened 631 individuals from 9 locations across the species' range for genetic variation at 22 microsatellite loci. Consistent with expectations of exten- sive larval mixing during an extended planktonic stage, we found no significant genetic differen- tiation among locations (FST = 0.003, G''ST = 0.007). Despite the lack of large-scale geographic structure, small but significant positive spatial autocorrelation (SA) was detected over distances up to 40 km. Two-dimensional local SA analysis confirmed that fine-scale genetic heterogeneity was common throughout the species' range. An intriguing aspect of these results is that SA was based on juvenile and adult lobsters, suggesting restricted movement or spatial cohesion of indi- viduals after settlement.

Nonparametric HAC Estimation for Time Series Data with Missing Observations

The Newey and West (1987) estimator has become the standard way to estimate a heteroskedasticity and autocorrelation consistent (HAC) covariance matrix, but it does not immediately apply to time series with missing observations. We demonstrate that the intuitive approach to estimate the true spectrum of the underlying process using only the observed data leads to incorrect inference. Instead, we propose two simple consistent HAC estimators for time series with missing data. First, we develop the Amplitude Modulated estimator by applying the Newey-West estimator and treating the missing observations as non-serially correlated. Secondly, we develop the Equal Spacing estimator by applying the Newey-West estimator to the series formed by treating the data as equally spaced. We show asymptotic consistency of both estimators for inference purposes and discuss finite sample variance and bias tradeoff. In Monte Carlo simulations, we demonstrate that the Equal Spacing estimator is preferred in most cases due to its lower bias, while the Amplitude Modulated estimator is preferred for small sample size and low autocorrelation due to its lower variance.

Nonparametric HAC Estimation for Time Series Data with Missing Observations

The Newey and West (1987) estimator has become the standard way to estimate a heteroskedasticity and autocorrelation consistent (HAC) covariance matrix, but it does not immediately apply to time series with missing observations. We demonstrate that the intuitive approach to estimate the true spectrum of the underlying process using only the observed data leads to incorrect inference. Instead, we propose two simple consistent HAC estimators for time series with missing data. First, we develop the Amplitude Modulated estimator by applying the Newey-West estimator and treating the missing observations as non-serially correlated. Secondly, we develop the Equal Spacing estimator by applying the Newey-West estimator to the series formed by treating the data as equally spaced. We show asymptotic consistency of both estimators for inference purposes and discuss finite sample variance and bias tradeoff. In Monte Carlo simulations, we demonstrate that the Equal Spacing estimator is preferred in most cases due to its lower bias, while the Amplitude Modulated estimator is preferred for small sample size and low autocorrelation due to its lower variance.

Market Microstructure and Private Information: A Study on National Stock Exchange of India

This paper is an attempt to examine the impact of changes in market microstructure on stock return variances during exchange trading and nontrading hours for a sample of stocks listed in National Stock Exchange of India. The study has found that daytime return variance is higher than overnight return variance and opening return variance is higher than closing return variance. First order autocorrelations in opening returns have shown small but significant negative autocorrelations for more companies whereas closing returns have shown significant positive autocorrelation for few companies. Speed of adjustment estimated from opening returns has shown a tendency towards overreaction whereas closing returns have shown a tendency towards under reaction.