SearcharxivSearch

arXiv subjects

Aditya Maheshwari

Publications and source records attributed to Aditya Maheshwari.

At least 19 recordsLinked to original sources

Spillover-Informed Network Architecture for Global Volatility Forecasting

Spillover of volatility shocks across borders during turbulent periods makes accurate equity market volatility forecasts especially critical for risk management, derivatives pricing, and regulatory capital. In this paper, we examine whether volatility forecasts improve when models incorporate information on how markets are connected, and whether the choice of connection measure matters. Using daily data on 29 equity indices from every major region over 2015-2025, we let each market's forecast draw on the recent volatility of the markets linked to it, with the strength of each link set either by geography, return correlation, or the Diebold-Yilmaz (DY) spillover network estimated from the data. The spillover-informed forecasting model achieved an approximately 13\% reduction in out-of-sample QLIKE loss relative to the standard Heterogeneous AutoRegressive benchmark ($p<0.001$) and attained the highest model confidence set $p$-value among the models considered. Several benchmark models that do not explicitly incorporate cross-market structure were excluded from the 90\% model confidence set. The greatest improvements were observed during periods of elevated market stress: the COVID-19 crash, the Russian invasion of Ukraine, and the $2025$ US tariff shock, spillover-informed forecasts achieved approximately 21\% lower QLIKE loss than an otherwise identical network-blind model ($p = 0.018$), with no significant performance loss during calm periods. The advantage is economically material: a volatility-targeting investor would pay $322$-$373$ basis points per year, net of transaction costs, for spillover-informed forecasts, versus an insignificant $85$-$102$ basis point for the alternatives. Finally, when the model is left to infer connections on its own, it recovers the DY network from the forecast objective alone (permutation $p=0.0005$).

stat.AP

NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process

In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range dependence through a fractional Mittag-Leffler excitation kernel. Two neural architectures, namely a Long Short-Term Memory (LSTM) network and a Transformer, are developed to estimate the model parameters $(μ,γ,α,β)$ directly from sequences of inter-arrival times without requiring computationally intensive likelihood optimization. Experiments on synthetic data that both neural models significantly outperform the classical Maximum Likelihood Estimation (MLE) method, with the Transformer achieving the highest estimation accuracy (MSE = $0.1634$), followed by the LSTM (MSE = $0.1752$), compared to MLE (MSE = $2.8032$). An ablation study further examines the effects of key hyperparameters on model performance. The proposed framework is also on two real-world high-frequency datasets, namely AAPL NBBO transaction data and Montgomery County 911 emergency call records. Using a predictive validation approach, event sequences simulated from the estimated parameters closely reproduce the empirical distribution, tail behavior, and temporal dependence structure of the observed data. These results demonstrate that Transformer-based parameter estimation provides an accurate and efficient alternative to conventional estimation techniques for FHP and offers a promising framework for modeling event-driven systems with long-memory dynamics.

cs.LG

Parameter Estimation of Incomplete Gamma Subordinators

In this paper, we estimate the parameters of InG, InG-$ε$ and TInG subordinators which have been studied by Babulal \textit{et al} (see \cite{babulal}). We have modified the method of moments technique to use fractional moments of the InG and InG-$ε$ subordinator due to their infinite moments. For the TInG subordinator's parameter estimation, we have used the method of moments. We also compute the maximum likelihood estimator(MLE) for the parameter $α$ of the InG and InG-$ε$ subordinators using jump distribution of the process. We also discussed the asymptotic normality of MLE.

math.ST

SectEval: Evaluating the Latent Sectarian Preferences of Large Language Models

As Large Language Models (LLMs) becomes a popular source for religious knowledge, it is important to know if it treats different groups fairly. This study is the first to measure how LLMs handle the differences between the two main sects of Islam: Sunni and Shia. We present a test called SectEval, available in both English and Hindi, consisting of 88 questions, to check the bias-ness of 15 top LLM models, both proprietary and open-weights. Our results show a major inconsistency based on language. In English, many powerful models DeepSeek-v3 and GPT-4o often favored Shia answers. However, when asked the exact same questions in Hindi, these models switched to favoring Sunni answers. This means a user could get completely different religious advice just by changing languages. We also looked at how models react to location. Advanced models Claude-3.5 changed their answers to match the user's country-giving Shia answers to a user from Iran and Sunni answers to a user from Saudi Arabia. In contrast, smaller models (especially in Hindi) ignored the user's location and stuck to a Sunni viewpoint. These findings show that AI is not neutral; its religious ``truth'' changes depending on the language you speak and the country you claim to be from. The data set is available at https://github.com/secteval/SectEval/

cs.CL

NEXUS: A compact neural architecture for high-resolution spatiotemporal air quality forecasting in Delhi National Capital Region

Urban air pollution in megacities poses critical public health challenges, particularly in Delhi National Capital Region (NCR) where severe degradation affects millions. We present NEXUS (Neural Extraction and Unified Spatiotemporal) architecture for forecasting carbon monoxide, nitrogen oxide, and sulfur dioxide. Working with four years (2018--2021) of atmospheric data across sixteen spatial grids, NEXUS achieves R$^2$ exceeding 0.94 for CO, 0.91 for NO, and 0.95 for SO$_2$ using merely 18,748 parameters -- substantially fewer than SCINet (35,552), Autoformer (68,704), and FEDformer (298,080). The architecture integrates patch embedding, low-rank projections, and adaptive fusion mechanisms to decode complex atmospheric chemistry patterns. Our investigation uncovers distinct diurnal rhythms and pronounced seasonal variations, with winter months experiencing severe pollution episodes driven by temperature inversions and agricultural biomass burning. Analysis identifies critical meteorological thresholds, quantifies wind field impacts on pollutant dispersion, and maps spatial heterogeneity across the region. Extensive ablation experiments demonstrate each architectural component's role. NEXUS delivers superior predictive performance with remarkable computational efficiency, enabling real-time deployment for air quality monitoring systems.

cs.LG

IndicParam: Benchmark to evaluate LLMs on low-resource Indic Languages

While large language models excel on high-resource multilingual tasks, low- and extremely low-resource Indic languages remain severely under-evaluated. We present IndicParam, a human-curated benchmark of over 13,000 multiple-choice questions covering 11 such languages (Nepali, Gujarati, Marathi, Odia as low-resource; Dogri, Maithili, Rajasthani, Sanskrit, Bodo, Santali, Konkani as extremely low-resource) plus Sanskrit-English code-mixed set. We evaluated 20 LLMs, both proprietary and open-weights, which reveals that even the top-performing \texttt{Gemini-2.5} reaches 58\% average accuracy, followed by \texttt{GPT-5} (45) and \texttt{DeepSeek-3.2} (43.1). We additionally label each question as knowledge-oriented or purely linguistic to discriminate factual recall from grammatical proficiency. Further, we assess the ability of LLMs to handle diverse question formats-such as list-based matching, assertion-reason pairs, and sequence ordering-alongside conventional multiple-choice questions. \benchmark\ provides insights into limitations of cross-lingual transfer and establishes a challenging benchmark for Indic languages. The dataset is available at https://huggingface.co/datasets/bharatgenai/IndicParam. Scripts to run benchmark are present at https://github.com/ayushbits/IndicParam.

cs.CL

Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator

This paper introduces a variable-order stable subordinator (VOSS) $S^{α(t)}(t)$ with index $α(t)\in(0,1)$, where $α(t)$ is a right-continuous piecewise constant function. We drive the Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator (GSFPP-VO) defined by $\{N(S^{α(t)}(t))\}_{t \geq 0}$, obtained by time-changing a homogeneous Poisson process $\{N(t,λ)\}_{t\geq 0}$ with rate parameter $λ>0$ by an independent VOSS. Explicit expressions for the Laplace transform, probability generating function, probability mass function, and moment generating function of the GSFPP-VO are derived, and these quantities are shown to satisfy partial differential equations. Finally, we establish the associated generalized distributions, analyze the hitting-time properties, and characterize the Lévy measures of the GSFPP-VO.

math.PR

TwinFormer: A Dual-Level Transformer for Long-Sequence Time-Series Forecasting

TwinFormer is a hierarchical Transformer for long-sequence time-series forecasting. It divides the input into non-overlapping temporal patches and processes them in two stages: (1) a Local Informer with top-$k$ Sparse Attention models intra-patch dynamics, followed by mean pooling; (2) a Global Informer captures long-range inter-patch dependencies using the same top-$k$ attention. A lightweight GRU aggregates the globally contextualized patch tokens for direct multi-horizon prediction. The resulting architecture achieves linear $O(kLd)$ time and memory complexity. On eight real-world benchmarking datasets from six different domains, including weather, stock price, temperature, power consumption, electricity, and disease, and forecasting horizons $96-720$, TwinFormer secures $27$ positions in the top two out of $34$. Out of the $27$, it achieves the best performance on MAE and RMSE at $17$ places and $10$ at the second-best place on MAE and RMSE. This consistently outperforms PatchTST, iTransformer, FEDformer, Informer, and vanilla Transformers. Ablations confirm the superiority of top-$k$ Sparse Attention over ProbSparse and the effectiveness of GRU-based aggregation. Code is available at this repository: https://github.com/Mahimakumavat1205/TwinFormer.

cs.LG

NeuroMemFPP: A recurrent neural approach for memory-aware parameter estimation in fractional Poisson process

In this paper, we propose a recurrent neural network (RNN)-based framework for estimating the parameters of the fractional Poisson process (FPP), which models event arrivals with memory and long-range dependence. The Long Short-Term Memory (LSTM) network estimates the key parameters $μ>0$ and $β\in(0,1)$ from sequences of inter-arrival times, effectively modeling their temporal dependencies. Our experiments on synthetic data show that the proposed approach reduces the mean squared error (MSE) by about 55.3\% compared to the traditional method of moments (MOM) and performs reliably across different training conditions. We tested the method on two real-world high-frequency datasets: emergency call records from Montgomery County, PA, and AAPL stock trading data. The results show that the LSTM can effectively track daily patterns and parameter changes, indicating its effectiveness on real-world data with complex time dependencies.

cs.LG

ParamBench: A Graduate-Level Benchmark for Evaluating LLM Understanding on Indic Subjects

Large language models have been widely evaluated on tasks such as comprehension, summarization, code generation, etc. However, their performance on graduate-level, culturally grounded questions in the Indian context remains largely unexplored. Existing Indian benchmarks emphasise basic fact-orientated queries that offer limited assessment of a deeper disciplinary understanding tailored to the Indian setting. In this paper, we present ParamBench, consisting of more than 17K questions in the Hindi language, comprising questionnaires from 21 diverse subjects. These questions are primarily derived from a nationwide graduate-level entrance examination covering topics such as history, music, instruments, yoga, literature, philosophy, law, etc.~ specifically for the Indian context. Additionally, we assess the ability of LLMs to handle diverse question formats - such as list-based matching, assertion-reason pairs, and sequence ordering - alongside conventional multiple-choice questions. We evaluated the performance of more than 16 open source LLMs on this benchmark, observing that Gemma3-27B attains the highest overall accuracy of 56.4\%. Furthermore, subject-wise analysis indicates that even for the best-performing LLMs, performance remains weak on topics such as music, classical instruments, and law, underscoring persistent challenges in culturally grounded reasoning. The dataset and source code is present at https://github.com/ayushbits/ParamBench.

cs.CL

Geometrical subordinated Poisson processes and its extensions

In this paper, we study a generalized version of the Poisson-type process by time-changing it with the geometric counting process. Our work generalizes the work done by Meoli (2023) \cite{meoli2023some}. We defined the geometric subordinated Poisson process (GSPP), the geometric subordinated compound Poisson process (GSCPP) and the geometric subordinated multiplicative Poisson process (GSMPP) by time-changing the subordinated Poisson process, subordinated compound Poisson process and subordinated multiplicative Poisson process with the geometric counting process, respectively. We derived several distributional properties and many special cases from the above-mentioned processes. We calculate the asymptotic behavior of the correlation structure. We have discussed applications of time-changed generalized compound Poisson in shock modelling.

math.PR

Fractional counting process at Lévy times and its applications

Traditionally, fractional counting processes, such as the fractional Poisson process, etc. have been defined using fractional differential and integral operators. Recently, Laskin (2024) introduced a generalized fractional counting process (FCP) by changing the probability mass function (pmf) of the time fractional Poisson process using the generalized three-parameter Mittag-Leffler function. Here, we study some additional properties for the FCP and introduce a time-changed fractional counting process (TCFCP), defined by time-changing the FCP with an independent Lévy subordinator. We derive distributional properties such as the Laplace transform, probability generating function, the moments generating function, mean, and variance for the TCFCP. Some results related to waiting time distribution and the first passage time distribution are also discussed. We define the multiplicative and additive compound variants for the FCP and the TCFCP and examine their distributional characteristics with some typical examples. We explore some interesting connections of the TCFCP with Bell polynomials by introducing subordinated generalized fractional Bell polynomials. It is shown that the moments of the TCFCP can be represented in terms of the subordinated generalized fractional Bell polynomials. Finally, we present the application of the FCP in a shock deterioration model.

math.PR

Modelling and prediction of the wildfire data using fractional Poisson process

Modelling wildfire events has been studied in the literature using the Poisson process, which essentially assumes the independence of wildfire events. In this paper, we use the fractional Poisson process to model the wildfire occurrences in California between June 2019 - April 2023 and predict the wildfire events that explains the underlying memory between these events. We introduce method of moments and maximum likelihood estimate approaches to estimate the parameters of the fractional Poisson process, which is an alternative to the method proposed by Cahoy (2010). We obtain the estimates of the fractional parameter as 0.8, proving that the wildfire events are dependent. The proposed model has reduced prediction error by 90\% compared to the classical Poisson process model.

stat.AP

Tempered space-time fractional negative binomial process

In this paper, we define a tempered space-time fractional negative binomial process (TSTFNBP) by subordinating the fractional Poisson process with an independent tempered Mittag-Leffler Lévy subordinator. We study its distributional properties and its connection to partial differential equations. We derive the asymptotic behavior of its fractional order moments and long-range dependence property. It is shown that the TSTFNBP exhibits overdispersion. We also obtain some results related to the first-passage time.

math.PR

Hawkes process with tempered Mittag-Leffler kernel

In this paper, we propose an extension of the Hawkes process by incorporating a kernel based on the tempered Mittag-Leffler distribution. This is the generalization of the work presented in [10]. We derive analytical results for the expectation of the conditional intensity and the expected number of events in the counting process. Additionally, we investigate the limiting behavior of the expectation of the conditional intensity. Finally, we present an empirical comparison of the studied process with its limiting special cases.

math.PR

Lévy processes with jumps governed by lower incomplete gamma subordinator and its variations

In this paper, we study the Lévy process time-changed by independent Lévy subordinators, namely, the incomplete gamma subordinator, the $ε$-jumps incomplete gamma subordinator and tempered incomplete gamma subordinator. We derive their important distributional properties such as mean, variance, correlation, tail probabilities and fractional moments. The long-range dependence property of these processes are discussed. An application in insurance domain is studied in detail. Finally, we present the simulated sample paths for the subordinators.

math.PR

Tempered Fractional Hawkes Process and Its Generalization

Hawkes process (HP) is a point process with a conditionally dependent intensity function. This paper defines the tempered fractional Hawkes process (TFHP) by time-changing the HP with an inverse tempered stable subordinator. We obtained results that generalize the fractional Hawkes process defined in Hainaut (2020) to a tempered version which has \textit{semi-heavy tailed} decay. We derive the mean, the variance, covariance and the governing fractional difference-differential equations of the TFHP. Additionally, we introduce the generalized fractional Hawkes process (GFHP) by time-changing the HP with the inverse Lévy subordinator. This definition encompasses all potential (inverse Lévy) time changes as specific instances. We also explore the distributional characteristics and the governing difference-differential equation of the one-dimensional distribution for the GFHP.

math.PR

Parameter estimation and long-range dependence of the fractional binomial process

In 1990, Jakeman (see \cite{jakeman1990statistics}) defined the binomial process as a special case of the classical birth-death process, where the probability of birth is proportional to the difference between a fixed number and the number of individuals present. Later, a fractional generalization of the binomial process was studied by Cahoy and Polito (2012) (see \cite{cahoy2012fractional}) and called it as fractional binomial process (FBP). In this paper, we study second-order properties of the FBP and the long-range behavior of the FBP and its noise process. We also estimate the parameters of the FBP using the method of moments procedure. Finally, we present the simulated sample paths and its algorithm for the FBP.

math.ST