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The purpose of this paper is to develop Pareto optimality conditions and constraint qualifications (CQs) for Multiobjective Programs with Cardinality Constraints (MOPCaC). In general, such problems are difficult to solve, not only because they involve a cardinality constraint that is neither continuous nor convex, but also because there may be a potential conflict between the various objective functions. Thus, we reformulate the MOPCaC based on the problem with continuous variables, namely the relaxed problem. Furthermore, we consider different notions of optimality (weak/strong Pareto optimal solutions). Thereby, we define new stationarity conditions that extend the classical Karush-Kuhn-Tucker (KKT) conditions of the scalar case. Moreover, we also introduce new CQs, based on the recently defined multiobjective normal cone, to ensure compliance with such stationarity conditions. Important statements are illustrated by examples. [ABSTRACT FROM AUTHOR]

In this paper we study the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such problems. In each iteration, with an auxiliary variable introduced to track the inner layer function values we compute stochastic gradients of the nested function using a subsampling strategy. To alleviate difficulties caused by possibly nonconvex constraints, we construct a stochastic approximation to the linearized augmented Lagrangian function to update the primal variable, which further motivates to update the dual variable in a weighted-average way. Moreover, to better understand the asymptotic dynamics of the update schemes we consider a deterministic continuous-time system from the perspective of ordinary differential equation (ODE). We analyze the Karush-Kuhn-Tucker measure at the output by the STEP method with constant parameters and establish its iteration and sample complexities to find an \epsilon-stationary point, ensuring that expected stationarity, feasibility as well as complementary slackness are below accuracy \epsilon. To leverage the benefit of the (near) initial feasibility in the STEP method, we propose a two-stage framework incorporating a feasibility-seeking phase, aiming to locate a nearly feasible initial point. Moreover, to enhance the adaptivity of the STEP algorithm, we propose an adaptive variant by adaptively adjusting its parameters, along with a complexity analysis. Numerical results on a risk-averse portfolio optimization problem and an orthogonal nonnegative matrix decomposition reveal the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Many data sets in biology, medicine, and other biostatistical areas deal with matrix‐valued time series. The case of a single univariate time series is very well developed in the literature; and single multi‐variate series (i.e., vector time series) though less well studied have also been developed. A class of matrix time series models is introduced for dealing with situations where there are multiple sets of multi‐variate time series data. Explicit expressions for a matrix autoregressive model along with its cross‐autocorrelation functions are derived. Stationarity conditions are also provided. Least squares estimators and maximum likelihood estimators of the model parameters and their asymptotic properties are derived. Results are illustrated through simulation studies and a real data application. [ABSTRACT FROM AUTHOR]

Background: In this work, we implement a data-driven approach using an aggregation of several analytical methods to study the characteristics of COVID-19 daily infection and death time series and identify correlations and characteristic trends that can be corroborated to the time evolution of this disease. The datasets cover twelve distinct countries across six continents, from January 22, 2020 till March 1, 2022. This time span is partitioned into three windows: (1) pre-vaccine, (2) post-vaccine and pre-omicron (BA.1 variant), and (3) post-vaccine including post-omicron variant. This study enables deriving insights into intriguing questions related to the science of system dynamics pertaining to COVID-19 evolution. Methods: We implement a set of several distinct analytical methods for: (a) statistical studies to estimate the skewness and kurtosis of the data distributions; (b) analyzing the stationarity properties of these time series using the Augmented Dickey-Fuller (ADF) tests; (c) examining co-integration properties for the non-stationary time series using the Phillips-Ouliaris (PO) tests; (d) calculating the Hurst exponent using the rescaled-range (R/S) analysis, along with the Detrended Fluctuation Analysis (DFA), for self-affinity studies of the evolving dynamical datasets. Results: We notably observe a significant asymmetry of distributions shows from skewness and the presence of heavy tails is noted from kurtosis. The daily infection and death data are, by and large, nonstationary, while their corresponding log return values render stationarity. The self-affinity studies through the Hurst exponents and DFA exhibit intriguing local changes over time. These changes can be attributed to the underlying dynamics of state transitions, especially from a random state to either mean-reversion or long-range memory/persistence states. Conclusions: We conduct systematic studies covering a widely diverse time series datasets of the daily infections and deaths during the evolution of the COVID-19 pandemic. We demonstrate the merit of a multiple analytics frameworks through systematically laying down a methodological structure for analyses and quantitatively examining the evolution of the daily COVID-19 infection and death cases. This methodology builds a capability for tracking dynamically evolving states pertaining to critical problems. [ABSTRACT FROM AUTHOR]

We propose a novel class of Markov processes for dealing with continuous positive time series data, which is constructed based on a latent gamma effect and named gamma-driven (GD) models. The GD processes possess desirable properties and features: (i) it can produce any desirable invariant distribution with support on R + , (ii) it is time-reversible, and (iii) it has the transition density function given in an explicit form. Estimation of parameters is performed through the maximum likelihood method combined with a Gauss Laguerre quadrature to approximate the likelihood function. The evaluation of the estimators and also confidence intervals of parameters are explored via Monte Carlo simulation studies. Two generalizations of the GD processes are also proposed to handle nonstationary and long-memory time series. We apply the proposed methodologies to analyze the daily realized volatility of the FTSE 100 equity index. [ABSTRACT FROM AUTHOR]

Purchasing Power Parity (PPP) doctrine has been a significant topic in the domain of international finance and economics. Several studies have been conducted on the issue of testing the soundness of the PPP hypothesis but a very few studies have been done for developing nations, particularly for India. This study tried to empirically test the PPP hypothesis for Indian rupee/US dollar (INR/USD) rate using quarterly data for the period 2001:1 – 2024:2. The stationarity of the relevant variables is examined by using the econometric tool of Augmented Dickey Fuller (ADF) and Phillip - Perron (PP) tests. To confirm empirical validity of PPP hypothesis, OLS regression technique is used. Autocorrelation problem is removed with the help of AR1 (Cochrane-Orcutt) and maximum likelihood procedures. The PPP model is estimated in naïve static form as well as the partial adjustment framework. The partial adjustment framework helps to find out the speed with which the actual exchange rate moves towards and reaches its equilibrium level. The empirical findings show that absolute PPP does not work well in its naïve static form, but it works well in partial adjustment framework with 2.5 quarters being speed of adjustment. The relative PPP is found to work well in both frameworks with 1.5 quarters as speed of adjustment. Thus, the policymakers may use the PPP hypothesis for exchange rate forecasting. Also, it is suggested that the policymakers should carefully consider the effect of internal or external shocks on PPP and tailor their monetary policy measures accordingly. [ABSTRACT FROM AUTHOR]

AbstractTime series analysis is increasingly popular across scientific domains. A key concept in time series analysis is stationarity, the stability of statistical properties of a time series. Understanding stationarity is crucial to addressing frequent issues in time series analysis such as the consequences of failing to model non-stationarity, how to determine the mechanisms generating non-stationarity, and consequently how to model those mechanisms (i.e., by differencing or detrending). However, many empirical researchers have a limited understanding of stationarity, which can lead to the use of incorrect research practices and misleading substantive conclusions. In this paper, we address this problem by answering these questions in an accessible way. To this end, we study how researchers can use detrending and differencing to model trends in time series analysis. We show via simulation the consequences of modeling trends inappropriately, and evaluate the performance of one popular approach to distinguish different trend types in empirical data. We present these results in an accessible way, providing an extensive introduction to key concepts in time series analysis, illustrated throughout with simple examples. Finally, we discuss a number of take-home messages and extensions to standard approaches, which directly address more complex time-series analysis problems encountered by empirical researchers. [ABSTRACT FROM AUTHOR]

The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well as its set-valued extensions. This approach leads to a more general and simpler version of fuzzy separation. The new model is capable of treating a wider range of optimization and variational problems. [ABSTRACT FROM AUTHOR]

We consider a stationary Markovian evolution with values on a finite disjointly partitioned set space I ⊔ E . The evolution is visible (in the sense of knowing the transition probabilities) on the states in I but not for the states in E . One only knows some partial information on the transition probabilities on E , the input and output transition probabilities and some constraints of the transition probabilities on E . Under some conditions we supply the transition probabilities on E that satisfies the maximum entropy principle. [ABSTRACT FROM AUTHOR]

The neuromotor control of the diaphragm muscle (DIAm) involves motor unit recruitment, sustained activity (incrementing and decrementing), and motor unit derecruitment, phases that may be modified to maintain ventilation across conditions. The primary goal of the present study was to investigate the effects of hypercapnia, which increases respiratory rate and tidal volume, on DIAm neuromotor control in awake rats. We recorded DIAm electromyography (EMG) with implanted chronic fine-wire electrodes in nine Sprague-Dawley rats during normocapnia and hypercapnia (7% CO2). The durations of motor unit recruitment/derecruitment were estimated by evaluating stationarity of DIAm EMG activity during normocapnia and hypercapnia; the motor unit recruitment/derecruitment durations were used to evaluate root mean square (RMS) EMG recruitment/derecruitment amplitudes. Overall, hypercapnia reduced the burst duration by ∼40% and increased respiratory rate by ∼50%. The change in the burst duration was primarily attributable to a 57% decrease in the peak-to-offset duration of the DIAm RMS EMG signal, suggesting a suppression of postinspiratory activity. Although neither the recruitment duration nor the onset-to-peak duration changed with hypercapnia, both the recruitment and peak amplitudes increased, by 11% and 23%, respectively. Therefore, although hypercapnia increases the number of motor units being recruited and their discharge rates, ventilation is primarily increased by increasing respiratory rate. Additionally, hypercapnia eliminated the decrementing sustained activity phase and consequently increased derecruitment amplitude by 171%. The results of the present study reveal that respiratory rate is increased chiefly by reducing the decrementing (i.e. "postinspiratory") phase of DIAm EMG activity. NEW & NOTEWORTHY: The neuromotor control of the diaphragm muscle (DIAm) in response to hypercapnia is not well understood. We show that both the number of motor units recruited and their discharge rates increase with hypercapnia, consistent with increased respiratory drive during hypercapnia. Potentially in response to this increased drive, the greatest effect of hypercapnia is on during the postinspiratory (descending) ramp of DIAm EMG activity, which shortens to facilitate higher respiratory rates. [ABSTRACT FROM AUTHOR]

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In this paper, we present the results of an econometric analysis for the stationarity of the analyzed long-time series of GDP and final public consumption, carried out by Augmented Dickey-Fuller Test in order to apply vector auto-regression model VAR(p). We use quarterly data on the movement of GDP and Public consumption of the Republic of North Macedonia for the time interval 2000Q1 - 2019Q4. The analysis was performed by using Eviews statistical analysis software was used for data processing, in which the VAR model is developed. In fact, this is starting procedure for the use of vector auto-regression. The VAR model has proven to be especially useful for describing the dynamic behavior of economic and financial time series and for forecasting. It often provides superior forecasts to those from univariate time series models and elaborate theory-based simultaneous equations models. The regression from the unit root test with the ADF test that used 3 lags proved that the DLNGDP series is stationary after 3 lags. [ABSTRACT FROM AUTHOR]

ObjectiveAiming at the problem that the working plane of inspection robots equipped with precision instruments can’t always maintain stable when moving on complex road surfaces such as bosses and trenches, an innovative design of the robot’s mobile chassis structure was proposed based on the contradiction analysis method and the material field model.MethodsA floating structure design was proposed and obstacle crossing analysis and driving smoothness analysis under complex road conditions such as bosses and trenches were conducted on the floating mobile chassis. The comparative simulation of the original structure chassis and improved mobile chassis moving under complex road conditions was conducted in Admas simulation software. A floating mobile chassis test prototype was built to conduct motion tests under complex road conditions.ResultsThe test results indicate that the floating mobile chassis has strong adaptability, and the working plane can maintain stable when crossing obstacles.

This study examined the impact of the exchange rate on non-hydrocarbon exports in Algeria. The main purpose of the research is to examine the relationship between the real effective exchange rate and the non-hydrocarbon export growth using the data of the Algerian economy. The data used are obtained from different sources: the real effective exchange rate is collected from International Financial Statistics published by the International Monetary Fund, while the non-hydrocarbon export growth is obtained from the Algeria Bank, and the gross domestic product variables are extracted from the official website of the World Bank. To conduct the study, the annual data for the three variables from 1980 to 2021 was considered; time series econometric techniques are used to check the existence of the relationship between variables. In the first step, the authors have performed the augmented Dickey-Fuller tests to check the stationarity of the three variables of interest. This test was computed for each variable with three models: the first model includes the constant term and the trend, the second model includes the constant term, and the third model was estimated without both the constant and the trend term. The stationary tests show that three variables (gross domestic product, the real effective exchange rate, and the non-hydrocarbon export growth) are integrated with order one, zero, and zero, respectively. In the second step, the exploration of the ARDL model between the three variables shows that the hypothesis that stipulates the existence of a significant relationship between the real effective exchange rate and the non-hydrocarbon export growth, on the one hand, is rejected, while the non-hydrocarbon export growth is, on the other hand, positively and statistically significantly correlated to the gross domestic product.

Our overarching goal in this paper was to both test and identify applications for a fundamental theorem of replacement-level populations known as the Stationary Population Identity (SPI), a mathematical model that equates the fraction of a population age x and the fraction with x years to live. Since true stationarity is virtually non-existent in human populations as well as in populations of non-human species, we used historical data on the memberships in both chambers of the U.S. Congress as population proxies. We conceived their fixed numbers (e.g., 100 Senators; 435 Representatives) as stationary populations, and their years served and years remaining as the equivalent of life lived and life remaining. Our main result was the affirmation of the mathematical prediction-i.e., the robust symmetry of years served and years remaining in Congress over the approximately 230 years of its existence (1789-2022). A number of applications emerged from this regularity and the distributional patterns therein including (1) new metrics such as Congressional half-life and other quantiles (e.g., 95% turnover); (2) predictability of the distribution of member's years remaining; (3) the extraordinary information content of a single number-the mean number of years served [i.e., derive birth (b) and death (d) rates; use of d as exponential rate parameter for model life tables]; (4) the concept of and metrics associated with period-specific populations (Congress); (5) Congressional life cycle concept with Formation, Growth, Senescence and Extinction Phases; and (6) longitudinal party transition rates for 100% Life Cycle turnover (Democrat/Republican) i.e., each seat from predecessor party-to-incumbent party and from incumbent party-to-successor party. Although our focus is on the use of historical data for Congressional members, we believe that most of the results are general and thus both relevant and applicable to most types of stationary or quasi-stationary populations including to the future world of zero population growth (ZPG).

We propose an extension of the double autoregressive (DAR) model: the sign-double autoregressive (SDAR) model, in the spirit of the GJR-GARCH model (also named the sign-ARCH model). Our model shares the important property of DAR models where a unit root does not imply non stationarity and it allows for asymmetry, as other alternatives in the literature such as the GJR-GARCH or asymmetric linear DAR and dual-asymmetry linear DAR models. We establish consistency and asymptotic normality of the quasi-maximum likelihood estimator in the context of the SDAR model. Furthermore, it is shown by simulations that the asymptotic properties also apply in finite samples. Finally, an empirical application shows the usefulness of our model specially in periods of supply/demand crises of oil disruptions, where spikes of volatility are very likely to be predominant. [ABSTRACT FROM AUTHOR]

The present study focused on examining the dynamic and causal relationships among selected world stock market indices. The growing importance of dynamic interactions among the stock indices have emerged as a focal point of research, driven by the recognition that financial markets are interconnected and interdependent. To achieve the above stated objective, multivariate vector autoregressive (VAR) approach is applied. For which the monthly time series data on the selected indices are obtained for the period 2010-2024. The required data was sourced from yahoofinance.com and the analysis was conducted using RStudio software version 2022.12.0+353 and MS Excel. We found that almost all the indices exhibit a positive and significant impact from their own past values on their future values and they are expected to increase over the next eight months. The impulse response function analysis reveals that only shocks in NSE are positively influenced by their own past values, along with the past values of other indices. Additionally, the FEVD test results indicate that most of the variance in each index is attributable to their own shocks, with the exception of TSX and DAX.

Rainfall intensity at a specific time is an important factor affecting the occurrence of combined sewer overflow (CSO). In this study, a statistical analysis of rainfall intensity frequency considering rainfall time (or cross-section) in the diurnal cycle were conducted based on the original 10-year rainfall intensity time series (the temporal resolution is 5 min). First, the stationarity of two different types of time series was evaluated by Augmented Dickey-Fuller (ADF) test and Phillips-Perron (PP) test, including the original rainfall time series and the diurnal cycle time series of five statistical characteristics (mean value (Mean), standard deviation (Std), coefficient of variation (Cv), skewness coefficient (Cs) and kurtosis coefficient (Kurt)). Moreover, the cumulative distribution function (CDF) of rainfall intensity at different cross-sections was analyzed. Finally, the best-fitting CDF of cross-section was used to quantify the CSO overflow frequency in the diurnal cycle under different thresholds. Results revealed that: (1) The original 10-year rainfall time series was second-order stationary time series. (2) The diurnal cycle time series of rainfall intensity statistics (Mean and Std) were non-stationary while those of rainfall intensity statistics (Cv, Cs and Kurt) were second-order stationary. (3) CDF of rainfall intensity at different cross-sections can be elaborated by the Generalized exponential distribution (Genexpon) and Generalized Pareto distribution (GPD) (R2 > 0.914). (4) CSO overflow has a high probability of occurring in three time intervals: (4:0–5:25), (15:35 − 16:40), and (20:30 − 22:55). Highlights: The original rainfall time series was second-order stationary. The diurnal cycle time series of Mean and Std were non-stationary. The diurnal cycle time series of Cv, Cs and Kurt were second-order stationary. CDF of rainfall intensity can be expressed as the generalized exponential distribution and generalized pareto distribution. CSO overflow has a high probability of occurring in three time intervals. [ABSTRACT FROM AUTHOR]

Forecasting stock prices is difficult because of the many unknowns and diverse factors that affect the financial market. Using time series data, the study attempts to assess how well the ARIMA (Auto Regressive Integrated Moving Average) model predicts the stock prices of Maersk, a significant participant in the global shipping industry. The research methodology is based on the Box-Jenkins approach, which includes model identification, estimation, and diagnostic checking to ensure reliable predictions. To ensure reliable time series forecasting, the analysis begins with the Augmented Dickey-Fuller (ADF) test, which checks for stationarity. The Akaike Information Criterion (AIC), which measures model complexity and predictive accuracy equally, serves as a guide for selecting models. The ARIMA model's performance is assessed by comparing predicted stock prices with actual observed values. The findings show the ARIMA model's usefulness in financial time series analysis by showing that it can accurately predict Maersk's stock prices. The model's suitability for stock price forecasting is confirmed by a variety of statistical metrics that validate its predictive ability. The usefulness of ARIMA models in financial forecasting is highlighted by this study, which provides insightful information to help analysts and investors make wise decisions. [ABSTRACT FROM AUTHOR]

A new non-linear stationary process for time series of counts is introduced. The process is composed of the survival and innovation component. The survival component is based on the generalized zero-modified geometric thinning operator, where the innovation process figures in the survival component as well. A few probability distributions for the innovation process have been discussed, in order to adjust the model for observed series with the excess number of zeros. The conditional maximum likelihood and the conditional least squares methods are investigated for the estimation of the model parameters. The practical aspect of the model is presented on some real-life data sets, where we observe data with inflation as well as deflation of zeroes so we can notice how the model can be adjusted with the proper parameter selection. [ABSTRACT FROM AUTHOR]

In this study I investigate the long-run impact of inflation on investment level in Turkiye for the period of 1990-2023 by utilizing ARDL estimation method. ADF unit root test findings implied that economic growth variable is stationary at level while inflation and investment variable are stationary at first differences. The results of ARDL bounds test disclosed that economic growth, inflation, and investment variables are co-integrated and thus they move together in the long-run. Regarding to the long-run coefficient estimation findings, as anticipated, statistically significant negative coefficient estimation for inflation variable and statistically significant positive coefficient estimation for economic growth variable were obtained. Put it differently, 1% increase in inflation level induces to a decrease in investment level by 0.2195% while 1% rise in economic growth leads to a jump in investment level by 0.3128%. Several diagnostic tests were conducted and the results of diagnostic tests indicated that the estimated ARDL(1,0,0) model is free from parameter instability, non-normality, autocorrelation, heteroscedasticity, and model misspecification problems. [ABSTRACT FROM AUTHOR]

This study examines the long run association between inflation and gross savings in Turkiye for the period of 1974-2023. ARDL estimation technique was utilized in all analyses. ADF unit root test findings indicated that variables of gross savings and consumer price inflation are integrated order one whereas economic growth variable is integrated order zero. ARDL bounds test implemented for cointegration analysis disclosed the presence of cointegration relationship among the variables of gross savings, consumer price inflation, and economic growth. Negative statistically significant coefficient estimation for inflation variable and positive statistically significant coefficient estimation for economic growth variable were obtained. In other words, if consumer price inflation jumps by 1% then gross savings drop by 0.2437% and if economic growth increases by 1% then gross savings augment by 0.0980%. [ABSTRACT FROM AUTHOR]

Predictive maintenance has gained importance due to industrialization. Harnessing advanced technologies like sensors and data analytics enables proactive interventions, preventing unplanned downtime, reducing costs, and enhancing workplace safety. They play a crucial role in optimizing industrial operations, ensuring the efficiency, reliability, and longevity of equipment, which have become increasingly vital in the context of industrialization. The analysis of time series' stationarity is a powerful and agnostic approach to studying variations and trends that may indicate imminent failures in equipment, thus contributing to the effectiveness of predictive maintenance in industrial environments. The present paper explores the use of the Augmented Dickey–Fuller p-value temporal variation as a possible method for determining trends in sensor time series and thus anticipating possible failures of a wood chip pump in the paper industry. [ABSTRACT FROM AUTHOR]

This study revisits income convergence among Turkish provinces for 1992-2019 and differs from most empirical literature due to its unique structural and methodological framework. Stochastic convergence is tested by employing a battery of panel stationarity tests that allow cross-sectional dependence and structural breaks. Breaks are further analyzed with respect to the nature of breaks as sharp and smooth. Sharp breaks are identified endogenously, while smooth breaks are accounted for using the Fournier approximation. Although due to its unique structural convergence is tested by employing a sectional dependence and respect to the nature of breaks endogenously, while smooth approximation. Although s-of stochastic convergence that at the provincial level, additional dimensions of procedure, outcomes about However, findings at the panel stochastic convergence. At the convergence is detected, there are no shreds of evidence of stochastic convergence at the panel level. Univariate test statistics demonstrate that at the provincial level, there is no single case that applies to all provinces. As additional dimensions of the data-generating process are evaluated in the testing procedure, outcomes about stochastic convergence slightly shift for provinces. However, findings at the panel level remain consistent and do not produce stochastic convergence. At the provincial level, mixed results are obtained. [ABSTRACT FROM AUTHOR]

This paper introduces stochastic covariance models in Hilbert spaces with stationary affine instantaneous covariance processes. We explore the applications of these models in the context of forward curve dynamics within fixed-income and commodity markets. The affine instantaneous covariance process is defined on positive self-adjoint Hilbert–Schmidt operators, and we prove the existence of a unique limit distribution for subcritical affine processes, provide convergence rates of the transition kernels in the Wasserstein distance of order p ∈ [ 1 , 2 ] , and give explicit formulas for the first two moments of the limit distribution. Our results allow us to introduce affine stochastic covariance models in the stationary covariance regime and to investigate the behaviour of the implied forward volatility for large forward dates in commodity forward markets. [ABSTRACT FROM AUTHOR]

The objective of this study is to analyze the temporal variability in water levels of Lake Mégantic (27.4 km2) during the period 1920–2020 in relation to anthropogenic and natural factors on the one hand, and its impact on the intensity and frequency of heavy flooding (recurring floods ≥ 10 years) of the Chaudière River of which it is the source, on the other hand. The application of four different Mann–Kendall tests showed a significant decrease in lake water levels during this period. The Lombard test revealed two breaks in the average daily maximum and average water levels, but only one break in the average daily minimum water levels. The first shift, which was smoothed, occurred between 1957 and 1963. It was caused by the demolition in 1956 of the first dam built in 1893 and the significant storage of water in the dams built upstream of the lake between 1956 and 1975. The second shift, which was rather abrupt, occurred between 1990 and 1993. It was caused by the voluntary and controlled lowering of the lake's water levels in 1993 to increase the surface area of the beaches for recreational purposes. However, despite this influence of anthropogenic factors on this drop in water levels, they are negatively correlated with the global warming climate index. It is therefore a covariation, due to anthropogenic factors whose impacts are exerted at different spatial scales, without a physical causal link. However, the winter daily minimum water levels, whose temporal variability has not been influenced by anthropogenic activities, are positively correlated with the NAO and AO indices, but negatively with PDO. Finally, since the transformation of Lake Mégantic into a reservoir following the construction of the Mégantic dam in 1893 and 1973 to control heavy flooding in the Chaudière River, all recurrent floods ≥ 10 years have completely disappeared in the section of this river located downstream of Lake Mégantic. However, the disappearance of these floods and the drop in water levels of Lake Mégantic have not significantly impacted the stationarity in the flow series of the Chaudière River since 1920. [ABSTRACT FROM AUTHOR]

‎Since pension funds are part of the social security system and have a socio-economic function, in order to maintain the value of the insured's savings, they should invest them, which will have a direct relationship with the money market and the capital market of each country. Due to the significant resources they have, pension funds affect the country's economic variables and, of course, are mostly affected by economic variables. This issue reveals the importance of examining how macroeconomic variables affect pension funds and the intensity of each one's impact, as well as the management of funds' resources in the face of the fluctuations of these variables‏. Therefore, in this ‎paper‎, the impact of pension funds on economic variables in 8 countries is investigated. Based on the results obtained in this research, the variables of short-term interest rate, exchange rate, and unemployment rate have an effect on the ratio of pension fund assets to GDP (as an indicator of performance).

In this study, we explored an asymmetric multivariate stochastic difference volatility model that extends various probabilistic and statistical properties previously discussed in the literature. We rigorously established that the model exhibits periodic stationarity and periodic ergodicity. Additionally, we delved into the robust consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE), providing a comprehensive analysis of its theoretical underpinnings. Finally, we demonstrated the practical applicability of our major findings through a series of pertinent applications. This work not only contributes to the existing body of knowledge on stochastic volatility modeling, but also opens new avenues for further research in this domain.

We use Brascamp-Lieb's inequality to obtain new decoupling inequalities for general Gaussian vectors, and in particular for finite stationary Gaussian processes. In the second case, we provide an application using a version by Bump and Diaconis of the strong Szegö limit theorem. We obtain sharp estimates on the decoupling coefficient of remarkable classes of Gaussian processes. [ABSTRACT FROM AUTHOR]

This article investigates some statistical and probabilistic properties of general threshold bilinear processes. Sufficient conditions for the existence of a causal, strictly and weak stationary solution for the equation defining a self-exciting threshold superdiagonal bilinear S E T B L process are derived. Then it is shown that under well-specified hypotheses the higher-order moments of the SETBL process are finite. As a result, the skewness and kurtosis indexes are explicitly computed. The exact autocorrelation function is derived with an arbitrarily fixed number of regimes. Also, the covariance functions of the process and its powers are evaluated and the second (respectively, higher)-order structure is shown to be similar to that of a linear process. This implies that the considered process admits an ARMA representation. Finally, necessary and sufficient conditions for the invertibility and geometric ergodicity of a SETBL model are established. Some examples illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In multivariate time series analysis, the Yule-Walker method refers to a system of equations relating the cross-covariances of a stationary vector autoregressive (VAR) model with the matrices of the autoregressive coefficients and the covariance matrix of the noise, both of which are unknown to be estimated. In Bayesian inference of VAR models, one of the key problems is the setting of the prior distributions on these unknown parameters. The Yule-Walker equations are used here to develop a novel prior specification that exploits the reparameterization of the unknowns in terms of the mean, the cross-covariances, and the covariance of the process. Further, the cross-covariance matrices are separated out in terms of the standard deviations and the correlations. All these new quantities are easier to handle because it is more common to have prior information on the mean and the correlation structure of a multiple time series rather than the underlying autoregressive coefficients and the white noise process. The proposed prior specification is suitable for both non informative and informative settings. Through the Yule-Walker based prior, parameter estimation and structure learning of the stationary VAR models are performed via Markov chain Monte Carlo methods. The methodology is illustrated via some synthetic data sets, a benchmark example, and an environmental time series. [ABSTRACT FROM AUTHOR]

This research paper delves into the substantial impact of commodity exchanges in India on the economy, specifically focusing on the areas of improved price discovery and the facilitation of systematic derivatives trading. Market participants, including hedgers and traders, effectively utilize futures contracts as strategic tools to control prices and capitalize on market volatility. Both agricultural and non-agricultural products are actively traded in the spot and futures markets, with metals emerging as the dominant category on the Multi Commodity Exchange (MCX). The process of price discovery within financial markets is a pivotal factor that ensures sustainable trading practices. Through an extensive study analyzing the relationship between spot and futures prices of seven metal derivatives traded on the MCX over a decade-long period, significant correlations have been identified across all cases. [ABSTRACT FROM AUTHOR]

Fractional Brownian motion approximation of queueing networks has been studied extensively. In the existing results related to this topic, the Hurst parameter of multidimensional fractional Brownian motion is only a constant H (0 < H < 1). However, just as pointed out by many scholars and practitioners, various Hurst parameters may be more appropriate. On the other hand, as a multivariate extension of fractional Brownian motion, operator fractional Brownian motion has operator self-similarity, and the dependence structure across the components of it is determined by the Hurst matrix. Moreover, it has also many potential applications in queueing theory. Inspired by these facts, we consider a queueing network with ON/OFF sources, and show that the workload process can be approximated by a reflected operator fractional Brownian motion under a heavy traffic condition. With this fact, it is important to consider stationarity. However, except for some special cases, there is no literature related to this topic. In our work, we construct an explicit stationary process associated with a two-dimensional reflected operator fractional Brownian motion. [ABSTRACT FROM AUTHOR]

Locomotor and balance disorders are major limitations for subjects with hemiparesis. The Timed Up and Go (TUG) test is a complex navigational task involving oriented walking and obstacle circumvention. We hypothesized that subjects with hemiparesis adopt a cautious gait during complex locomotor tasks. The primary aim was to compare spatio-temporal gait parameters, indicators of cautious gait, between the locomotor subtasks of the TUG (Go, Turn, Return) and a Straight-line walk in people with hemiparesis. Our secondary aim was to analyze the relationships between TUG performance and balance measures, compare spatio-temporal gait parameters between fallers and non-fallers, and identify the biomechanical determinants of TUG performance. Biomechanical parameters during the TUG and Straight-line walk were analyzed using a motion capture system. A repeated measures ANOVA and two stepwise ascending multiple regressions (with performance variables and biomechanical variables) were conducted. Gait speed, step length, and % single support phase (SSP) of the 29 participants were reduced during Turn compared to Go and Return and the Straight-line walk, and step width and % double support phase were increased. TUG performance was related to several balance measures. Turn performance (R2 = 63%) and Turn trajectory deviation followed by % SSP on the paretic side and the vertical center of mass velocity during Go (R2 = 71%) determined TUG performance time. People with hemiparesis adopt a cautious gait during complex navigation at the expense of performance. [ABSTRACT FROM AUTHOR]

Gamma processes are commonly used for modelling the accumulative deterioration of systems, in many fields. However, given a series of observations, it is not always easy to affirm that the choice of a gamma process modelling is a good choice. In particular, it would be of great interest to have a statistical test, i.e. a goodness-of-fit test, to answer this question. In this paper, a practical procedure combining three statistical tests is firstly proposed, whose aim is to reject the gamma process modelling as soon as the observations are clearly in contradiction with the basic properties of a homogeneous gamma process, observed with periodic inspections: stationarity, independence and gamma distribution for the increments. The procedure is then extended to non-homogeneous gamma process and aperiodic inspection times. The efficiency of the approach is investigated through numerical simulations, and on real data. [ABSTRACT FROM AUTHOR]

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In this study, we explored an asymmetric multivariate stochastic difference volatility model that extends various probabilistic and statistical properties previously discussed in the literature. We rigorously established that the model exhibits periodic stationarity and periodic ergodicity. Additionally, we delved into the robust consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE), providing a comprehensive analysis of its theoretical underpinnings. Finally, we demonstrated the practical applicability of our major findings through a series of pertinent applications. This work not only contributes to the existing body of knowledge on stochastic volatility modeling, but also opens new avenues for further research in this domain. [ABSTRACT FROM AUTHOR]

This study attempts to analyse the time series properties of exports, imports and exchange rate for the US. We empirically examine the presence of a cointegrating relationship between the exports, imports and the exchange rate using the monthly time series data from January, 1994 to September, 2023. The stationarity of the time series variables is tested using the Augmented Dickey-Fuller unit root test and the existence of a long run relationship between the variables is tested using Johansen's multivariate cointegration test. The findings from the study show that there is no cointegrating relationship between exports, imports and the exchange rate for the US, implying that the macroeconomic policies of the US are not effective enough to bring her exports and imports in long-run equilibrium. These findings from the study can provide significant implications for national policymakers and the researchers alike. [ABSTRACT FROM AUTHOR]

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This paper investigates the stability of threshold autoregressive models. We review recent research on stability issues from both a theoretical and empirical standpoint. We provide a sufficient condition for the stationarity and ergodicity of threshold autoregressive models by applying the concept of joint spectral radius to the switching system. The joint spectral radius criterion offers a generally applicable criterion to determine the stability in a threshold autoregressive model. [ABSTRACT FROM AUTHOR]

The use of digital devices to collect data in mobile health studies introduces a novel application of time series methods, with the constraint of potential data missing at random or missing not at random (MNAR). In time-series analysis, testing for stationarity is an important preliminary step to inform appropriate subsequent analyses. The Dickey–Fuller test evaluates the null hypothesis of unit root non-stationarity, under no missing data. Beyond recommendations under data missing completely at random for complete case analysis or last observation carry forward imputation, researchers have not extended unit root non-stationarity testing to more complex missing data mechanisms. Multiple imputation with chained equations, Kalman smoothing imputation, and linear interpolation have also been used for time-series data, however such methods impose constraints on the autocorrelation structure and impact unit root testing. We propose maximum likelihood estimation and multiple imputation using state space model approaches to adapt the augmented Dickey–Fuller test to a context with missing data. We further develop sensitivity analyses to examine the impact of MNAR data. We evaluate the performance of existing and proposed methods across missing mechanisms in extensive simulations and in their application to a multi-year smartphone study of bipolar patients. [ABSTRACT FROM AUTHOR]