Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (17)

Search Parameters:
Keywords = martingale test

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
18 pages, 1301 KiB  
Article
Numerical Investigation for the Temporal Fractional Financial Option Pricing Partial Differential Equation Utilizing a Multiquadric Function
by Jia Li, Tao Liu, Jiaqi Xu, Xiaoxi Hu, Changan Xu and Yanlong Wei
Fractal Fract. 2025, 9(7), 414; https://doi.org/10.3390/fractalfract9070414 - 26 Jun 2025
Viewed by 463
Abstract
This paper proposes a computational procedure to resolve the temporal fractional financial option pricing partial differential equation (PDE) using a localized meshless approach via the multiquadric radial basis function (RBF). Given that financial market information is best characterized within a martingale framework, the [...] Read more.
This paper proposes a computational procedure to resolve the temporal fractional financial option pricing partial differential equation (PDE) using a localized meshless approach via the multiquadric radial basis function (RBF). Given that financial market information is best characterized within a martingale framework, the resulting option pricing model follows a modified Black–Sholes (BS) equation, requiring efficient numerical techniques for practical implementation. The key innovation in this study is the derivation of analytical weights for approximating first and second derivatives, ensuring improved numerical stability and accuracy. The construction of these weights is grounded in the second integration of a variant of the multiquadric RBF, which enhances smoothness and convergence properties. The performance of the presented solver is analyzed through computational tests, where the analytical weights exhibit superior accuracy and stability in comparison to conventional numerical weights. The results confirm that the new approach reduces absolute errors, demonstrating its effectiveness for financial option pricing problems. Full article
Show Figures

Figure 1

26 pages, 4611 KiB  
Article
Predictive Patterns and Market Efficiency: A Deep Learning Approach to Financial Time Series Forecasting
by Darko B. Vuković, Sonja D. Radenković, Ivana Simeunović, Vyacheslav Zinovev and Milan Radovanović
Mathematics 2024, 12(19), 3066; https://doi.org/10.3390/math12193066 - 30 Sep 2024
Cited by 5 | Viewed by 3321
Abstract
This study explores market efficiency and behavior by integrating key theories such as the Efficient Market Hypothesis (EMH), Adaptive Market Hypothesis (AMH), Informational Efficiency and Random Walk theory. Using LSTM enhanced by optimizers like Stochastic Gradient Descent (SGD), Adam, AdaGrad, and RMSprop, we [...] Read more.
This study explores market efficiency and behavior by integrating key theories such as the Efficient Market Hypothesis (EMH), Adaptive Market Hypothesis (AMH), Informational Efficiency and Random Walk theory. Using LSTM enhanced by optimizers like Stochastic Gradient Descent (SGD), Adam, AdaGrad, and RMSprop, we analyze market inefficiencies in the Standard and Poor’s (SPX) index over a 22-year period. Our results reveal “pockets in time” that challenge EMH predictions, particularly with the AdaGrad optimizer at a size of the hidden layer (HS) of 64. Beyond forecasting, we apply the Dominguez–Lobato (DL) and General Spectral (GS) tests as part of the Martingale Difference Hypothesis to assess statistical inefficiencies and deviations from the Random Walk model. By emphasizing “informational efficiency”, we examine how quickly new information is reflected in stock prices. We argue that market inefficiencies are transient phenomena influenced by structural shifts and information flow, challenging the notion that forecasting alone can refute EMH. Additionally, we compare LSTM with ARIMA with Exponential Smoothing, and LightGBM to highlight the strengths and limitations of these models in financial forecasting. The LSTM model excels at capturing temporal dependencies, while LightGBM demonstrates its effectiveness in detecting non-linear relationships. Our comprehensive approach offers a nuanced understanding of market dynamics and inefficiencies. Full article
(This article belongs to the Section E5: Financial Mathematics)
Show Figures

Figure 1

23 pages, 1023 KiB  
Article
A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model
by Fanrong Zhao and Baoxue Zhang
Mathematics 2024, 12(16), 2588; https://doi.org/10.3390/math12162588 - 21 Aug 2024
Viewed by 1059
Abstract
The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional data cannot be approximated with a few principal components, [...] Read more.
The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional data cannot be approximated with a few principal components, we develop a second-order U-statistic using a pseudo-estimate for the unknown non-parametric component. Under some regularity conditions, the asymptotic normality of the proposed test statistic is established using the martingale central limit theorem. The proposed test is evaluated for finite sample properties through simulation studies and its application to real data. Full article
Show Figures

Figure 1

27 pages, 11976 KiB  
Article
Detection of Electromagnetic Seismic Precursors from Swarm Data by Enhanced Martingale Analytics
by Shane Harrigan, Yaxin Bi, Mingjun Huang, Christopher O’Neill, Wei Zhai, Jianbao Sun and Xuemin Zhang
Sensors 2024, 24(11), 3654; https://doi.org/10.3390/s24113654 - 5 Jun 2024
Cited by 1 | Viewed by 1713
Abstract
The detection of seismic activity precursors as part of an alarm system will provide opportunities for minimization of the social and economic impact caused by earthquakes. It has long been envisaged, and a growing body of empirical evidence suggests that the Earth’s electromagnetic [...] Read more.
The detection of seismic activity precursors as part of an alarm system will provide opportunities for minimization of the social and economic impact caused by earthquakes. It has long been envisaged, and a growing body of empirical evidence suggests that the Earth’s electromagnetic field could contain precursors to seismic events. The ability to capture and monitor electromagnetic field activity has increased in the past years as more sensors and methodologies emerge. Missions such as Swarm have enabled researchers to access near-continuous observations of electromagnetic activity at second intervals, allowing for more detailed studies on weather and earthquakes. In this paper, we present an approach designed to detect anomalies in electromagnetic field data from Swarm satellites. This works towards developing a continuous and effective monitoring system of seismic activities based on SWARM measurements. We develop an enhanced form of a probabilistic model based on the Martingale theories that allow for testing the null hypothesis to indicate abnormal changes in electromagnetic field activity. We evaluate this enhanced approach in two experiments. Firstly, we perform a quantitative comparison on well-understood and popular benchmark datasets alongside the conventional approach. We find that the enhanced version produces more accurate anomaly detection overall. Secondly, we use three case studies of seismic activity (namely, earthquakes in Mexico, Greece, and Croatia) to assess our approach and the results show that our method can detect anomalous phenomena in the electromagnetic data. Full article
(This article belongs to the Section Remote Sensors)
Show Figures

Figure 1

41 pages, 734 KiB  
Article
Do Consumption-Based Asset Pricing Models Explain the Dynamics of Stock Market Returns?
by Michael William Ashby and Oliver Bruce Linton
J. Risk Financial Manag. 2024, 17(2), 71; https://doi.org/10.3390/jrfm17020071 - 11 Feb 2024
Viewed by 2398
Abstract
We show that three prominent consumption-based asset pricing models—the Bansal–Yaron, Campbell–Cochrane and Cecchetti–Lam–Mark models—cannot explain the dynamic properties of stock market returns. We show this by estimating these models with GMM, deriving ex-ante expected returns from them and then testing whether the difference [...] Read more.
We show that three prominent consumption-based asset pricing models—the Bansal–Yaron, Campbell–Cochrane and Cecchetti–Lam–Mark models—cannot explain the dynamic properties of stock market returns. We show this by estimating these models with GMM, deriving ex-ante expected returns from them and then testing whether the difference between realised and expected returns is a martingale difference sequence, which it is not. Mincer–Zarnowitz regressions show that the models’ out-of-sample expected returns are systematically biased. Furthermore, semi-parametric tests of whether the models’ state variables are consistent with the degree of own-history predictability in stock returns suggest that only the Campbell–Cochrane habit variable may be able to explain return predictability, although the evidence on this is mixed. Full article
(This article belongs to the Special Issue Advanced Studies in Empirical Asset Pricing)
Show Figures

Figure 1

12 pages, 1000 KiB  
Article
Conformal Test Martingale-Based Change-Point Detection for Geospatial Object Detectors
by Gang Wang, Zhiying Lu, Ping Wang, Shuo Zhuang and Di Wang
Appl. Sci. 2023, 13(15), 8647; https://doi.org/10.3390/app13158647 - 27 Jul 2023
Viewed by 1710
Abstract
Unsupervised domain adaptation for object detectors addresses the problem of improving the cross-domain robustness of object detection from label-rich to label-poor domains, which has been explored in many studies. However, one important issue in terms of when to apply the domain adaptation algorithm [...] Read more.
Unsupervised domain adaptation for object detectors addresses the problem of improving the cross-domain robustness of object detection from label-rich to label-poor domains, which has been explored in many studies. However, one important issue in terms of when to apply the domain adaptation algorithm for geospatial object detectors has not been fully considered in the literature. In this paper, we tackle the problem of detecting the moment or change-point when the domain of geospatial images changes based on conformal test martingale. Beyond the simple introduction of this martingale-based process, we also propose a novel transformation approach to the original conformal test martingale to make change-point detection more efficient. The experiments are conducted with two partitions of our released large-scale remote sensing dataset and the experimental results empirically demonstrate the promising effectiveness and efficiency of our proposed algorithms for change-point detection. Full article
(This article belongs to the Special Issue Intelligent Computing and Remote Sensing)
Show Figures

Figure 1

19 pages, 430 KiB  
Article
Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions
by Peng Sun, Yincai Tang and Mingxiang Cao
Mathematics 2022, 10(22), 4339; https://doi.org/10.3390/math10224339 - 18 Nov 2022
Viewed by 1956
Abstract
In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, [...] Read more.
In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, respectively. Simulation results show that the proposed test procedure tends to outperform some existing test procedures. Full article
(This article belongs to the Special Issue Statistical Theory and Application)
Show Figures

Figure 1

16 pages, 427 KiB  
Article
Testing for the Presence of the Leverage Effect without Estimation
by Zhi Liu
Mathematics 2022, 10(14), 2511; https://doi.org/10.3390/math10142511 - 19 Jul 2022
Viewed by 2144
Abstract
Problem: The leverage effect plays an important role in finance. However, the statistical test for the presence of the leverage effect is still lacking study. Approach: In this paper, by using high frequency data, we propose a novel procedure to test if [...] Read more.
Problem: The leverage effect plays an important role in finance. However, the statistical test for the presence of the leverage effect is still lacking study. Approach: In this paper, by using high frequency data, we propose a novel procedure to test if the driving Brownian motion of an Ito^ semi-martingale is correlated to its volatility (referred to as the leverage effect in financial econometrics) over a long time period. The asymptotic setting is based on observations within a long time interval with the mesh of the observation grid shrinking to zero. We construct a test statistic via forming a sequence of Studentized statistics whose distributions are asymptotically normal over blocks of a fixed time span, and then collect the sequence based on the whole data set of a long time span. Result: The asymptotic behaviour of the Studentized statistics was obtained from the cubic variation of the underlying semi-martingale and the asymptotic distribution of the proposed test statistic under the null hypothesis that the leverage effect is absent was established, and we also show that the test has an asymptotic power of one against the alternative hypothesis that the leverage effect is present. Implications: We conducted extensive simulation studies to assess the finite sample performance of the test statistics, and the results show a satisfactory performance for the test. Finally, we implemented the proposed test procedure to a dataset of the SP500 index. We see that the null hypothesis of the absence of the leverage effect is rejected for most of the time period. Therefore, this provides a strong evidence that the leverage effect is a necessary ingredient in modelling high-frequency data. Full article
(This article belongs to the Section E5: Financial Mathematics)
Show Figures

Figure 1

26 pages, 1333 KiB  
Article
Exponentially Weighted Multivariate HAR Model with Applications in the Stock Market
by Won-Tak Hong and Eunju Hwang
Entropy 2022, 24(7), 937; https://doi.org/10.3390/e24070937 - 6 Jul 2022
Viewed by 2223
Abstract
This paper considers a multivariate time series model for stock prices in the stock market. A multivariate heterogeneous autoregressive (HAR) model is adopted with exponentially decaying coefficients. This model is not only suitable for multivariate data with strong cross-correlation and long memory, but [...] Read more.
This paper considers a multivariate time series model for stock prices in the stock market. A multivariate heterogeneous autoregressive (HAR) model is adopted with exponentially decaying coefficients. This model is not only suitable for multivariate data with strong cross-correlation and long memory, but also represents a common structure of the joint data in terms of decay rates. Tests are proposed to identify the existence of the decay rates in the multivariate HAR model. The null limiting distributions are established as the standard Brownian bridge and are proven by means of a modified martingale central limit theorem. Simulation studies are conducted to assess the performance of tests and estimates. Empirical analysis with joint datasets of U.S. stock prices illustrates that the proposed model outperforms the conventional HAR models via OLSE and LASSO with respect to residual errors. Full article
(This article belongs to the Special Issue Applications of Statistical Physics in Finance and Economics)
Show Figures

Figure 1

14 pages, 2469 KiB  
Article
Evaluating Horse Owner Expertise and Professional Use of Auxiliary Reins during Horse Riding
by Heidrun Gehlen, Julia Puhlmann, Roswitha Merle and Christa Thöne-Reineke
Animals 2021, 11(7), 2146; https://doi.org/10.3390/ani11072146 - 20 Jul 2021
Cited by 2 | Viewed by 12075
Abstract
Auxiliary reins are commonly used for the training of riders and horses as well as in daily training. They are often criticized when used incorrectly, as they will not help and can harm the horse by causing overwork, accidents, and injuries, which harm [...] Read more.
Auxiliary reins are commonly used for the training of riders and horses as well as in daily training. They are often criticized when used incorrectly, as they will not help and can harm the horse by causing overwork, accidents, and injuries, which harm the horse in the long term. They also often conceal causal rider problems while trying to achieve quick success. The aim of this paper was to investigate, with an online horse-owner questionnaire, which and how often auxiliary reins were used and whether they were used appropriately. Only participants who were currently using auxiliary reins were selected. Consequently, 823 participants were questioned, of which 362 were currently using auxiliary reins at least every two weeks. Auxiliary reins were mainly used according to their discipline: the running side rein was the most popular when working from the ground and the sliding ring martingale was the most popular for ridden equestrian activities. Most of the test subjects only attached the auxiliary reins after the warm-up phase, but half of the participants did not change them during the entire training session. Most participants (75%) could at least identify what the correct head position of the horse should look like. However, there were still too many (50%) who adjusted their horse too tightly and did not change anything at that time despite the related breathing problems. The study found that most participants used the reins responsibly, but there is still a need for clarification and information relating to the functions of the different auxiliary reins among horse owners. Full article
(This article belongs to the Section Animal Welfare)
Show Figures

Figure 1

10 pages, 263 KiB  
Review
Design and Analysis of Cancer Clinical Trials for Personalized Medicine
by Sin-Ho Jung
J. Pers. Med. 2021, 11(5), 376; https://doi.org/10.3390/jpm11050376 - 4 May 2021
Cited by 2 | Viewed by 1942
Abstract
Biomarkers play a key role in the development of personalized medicine. Cancer clinical trials with biomarker should be appropriately designed and analyzed reflecting the various factors, such as the phase of trials, the type of biomarker, the study objectives, and whether the used [...] Read more.
Biomarkers play a key role in the development of personalized medicine. Cancer clinical trials with biomarker should be appropriately designed and analyzed reflecting the various factors, such as the phase of trials, the type of biomarker, the study objectives, and whether the used biomarker is already validated or not. In this paper, we demonstrate design and analysis of two phase II cancer clinical trials, one with a predictive biomarker and the other with a prognostic biomarker. A statistical testing method and its sample size calculation method are presented for each of the trials. We assume that the primary endpoint of these trials is a time to event variable, but this concept can be used for any type of endpoint with associated testing methods. The test statistics and their sample size formulas are derived using the large sample approximation based on the martingale central limit theorem. Using simulations, we find that the test statistics control the type I error rate accurately and the sample sizes calculated using the formulas maintain the statistical power specified at the design stage. Full article
(This article belongs to the Section Epidemiology)
15 pages, 449 KiB  
Article
A Reliability Growth Process Model with Time-Varying Covariates and Its Application
by Xin-Yu Tian, Xincheng Shi, Cheng Peng and Xiao-Jian Yi
Mathematics 2021, 9(8), 905; https://doi.org/10.3390/math9080905 - 19 Apr 2021
Cited by 3 | Viewed by 2918
Abstract
The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of [...] Read more.
The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of the product under different operational environments. In this paper we introduce an AMSAA-based model considering the covariate effects to measure the influence of the time-varying environmental condition. The parameter estimation of the model is typically performed using maximum likelihood on the failure data. The statistical properties of the estimation in the model are comprehensively derived by the martingale theory. Further inferences including confidence interval estimation and hypothesis tests are designed for the model. The performance and properties of the method are verified in a simulation study, compared with the classical AMSAA model. A case study is used to illustrate the practical use of the model. The proposed approach can be adapted for a wide class of nonhomogeneous Poisson process based models. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
Show Figures

Figure 1

20 pages, 618 KiB  
Article
Efficiency Testing of Prediction Markets: Martingale Approach, Likelihood Ratio and Bayes Factor Analysis
by Mark Richard and Jan Vecer
Risks 2021, 9(2), 31; https://doi.org/10.3390/risks9020031 - 1 Feb 2021
Cited by 7 | Viewed by 4506
Abstract
This paper studies efficient market hypothesis in prediction markets and the results are illustrated for the in-play football betting market using the quoted odds for the English Premier League. Our analysis is based on the martingale property, where the last quoted probability should [...] Read more.
This paper studies efficient market hypothesis in prediction markets and the results are illustrated for the in-play football betting market using the quoted odds for the English Premier League. Our analysis is based on the martingale property, where the last quoted probability should be the best predictor of the outcome and all previous quotes should be statistically insignificant. We use regression analysis to test for the significance of the previous quotes in both the time setup and the spatial setup based on stopping times, when the quoted probabilities reach certain bounds. The main contribution of this paper is to show how a potentially different distributional opinion based on the violation of the market efficiency can be monetized by optimal trading, where the agent maximizes logarithmic utility function. In particular, the trader can realize a trading profit that corresponds to the likelihood ratio in the situation of one market maker and one market taker, or the Bayes factor in the situation of two or more market takers. Full article
Show Figures

Figure 1

35 pages, 584 KiB  
Article
Partial Cointegrated Vector Autoregressive Models with Structural Breaks in Deterministic Terms
by Takamitsu Kurita and Bent Nielsen
Econometrics 2019, 7(4), 42; https://doi.org/10.3390/econometrics7040042 - 6 Oct 2019
Cited by 9 | Viewed by 6111
Abstract
This paper proposes a class of partial cointegrated models allowing for structural breaks in the deterministic terms. Moving-average representations of the models are given. It is then shown that, under the assumption of martingale difference innovations, the limit distributions of partial quasi-likelihood ratio [...] Read more.
This paper proposes a class of partial cointegrated models allowing for structural breaks in the deterministic terms. Moving-average representations of the models are given. It is then shown that, under the assumption of martingale difference innovations, the limit distributions of partial quasi-likelihood ratio tests for cointegrating rank have a close connection to those for standard full models. This connection facilitates a response surface analysis that is required to extract critical information about moments from large-scale simulation studies. An empirical illustration of the proposed methodology is also provided. Full article
(This article belongs to the Special Issue Celebrated Econometricians: Katarina Juselius and Søren Johansen)
Show Figures

Figure 1

21 pages, 379 KiB  
Article
Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities
by Yijuan Liang and Xiuchuan Xu
Sustainability 2019, 11(3), 815; https://doi.org/10.3390/su11030815 - 4 Feb 2019
Cited by 3 | Viewed by 3944
Abstract
Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with [...] Read more.
Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with stochastic volatilities. First, a conditional Monte Carlo (CMC) pricing formula is constructed to reduce the dimension and variance of the MC simulation. Then, an efficient martingale control variate (CV), based on the martingale representation theorem, is designed by selecting volatility parameters in the approximated option price for further variance reduction. Numerical tests illustrated the sensitivity of the CMC method to correlation coefficients and the effectiveness and robustness of our martingale CV method. The idea in this paper is also applicable for the valuation of other derivatives with stochastic volatility. Full article
Back to TopTop