Econometrics & Time-Series Methods

The method of element analysis is proposed here as an alternative to traditional wavelet-based approaches to analyzing perturbations in financial signals by scale. In this method, the processes that generate oscillations in financial signals are modelled as scaled, shifted, and isolated events that

There has been growing interest in applying NLP techniques in the financial domain, however, resources are extremely limited. This paper introduces StockEmotions, a new dataset for detecting emotions in the stock market that consists of 10,000 English comments collected from StockTwits, a financial

We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongs

This paper introduces Anticipatory Reinforcement Learning (ARL), a novel framework designed to bridge the gap between non-Markovian decision processes and classical reinforcement learning architectures, specifically under the constraint of a single observed trajectory. In environments characterised

We develop spectral portfolio theory by establishing a direct identification: neural network weight matrices trained on stochastic processes are portfolio allocation matrices, and their spectral structure encodes factor decompositions and wealth concentration patterns. The three forces governing sto

This study explores contagion in the Chinese stock market using Hawkes processes to analyze autocorrelation and cross-correlation in multivariate time series data. We examine whether market indices exhibit trending behavior and whether sector indices influence one another. By fitting self-exciting a

Major bank mergers and acquisitions (M&A) transform the financial market structure, but their valuation and spillover effects remain open to question. This study examines the market reaction to two M&A events: the 2005 creation of Mitsubishi UFJ Financial Group following the Financial Big Bang in Ja

Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a poor informative value as they miss the intrinsic multivaria

In this paper, we study an optimal dividend and capital-injection problem in a Cramér–Lundberg model where claim arrivals follow a Hawkes process, capturing clustering effects often observed in insurance portfolios. We establish key analytical properties of the value function and characterise the o

We investigate a number of Artificial Neural Network architectures (well-known and more ``exotic’’) in application to the long-term financial time-series forecasts of indexes on different global markets. The particular area of interest of this research is to examine the correlation of these indexes’

Stablecoins promise par convertibility, yet issuers must balance immediate liquidity against yield on reserves to keep the peg credible. We study this treasury problem as a continuous-time control task with two instruments: reallocating reserves between cash and short-duration government bills, and

Recent advances in quantum computing have demonstrated its potential to significantly enhance the analysis and forecasting of complex classical data. Among these, quantum reservoir computing has emerged as a particularly powerful approach, combining quantum computation with machine learning for mode

We study the problem of resource provisioning under stringent reliability or service level requirements, which arise in applications such as power distribution, emergency response, cloud server provisioning, and regulatory risk management. With chance-constrained optimization serving as a natural st

We study the asymptotic properties of the GLS estimator in multivariate regression with heteroskedastic and autocorrelated errors. We derive Wald statistics for linear restrictions and assess their performance. The statistics remains robust to heteroskedasticity and autocorrelation.

Short-term patterns in financial time series form the cornerstone of many algorithmic trading strategies, yet extracting these patterns reliably from noisy market data remains a formidable challenge. In this paper, we propose an entropy-assisted framework for identifying high-quality, non-overlappin

To the naked eye, stock prices are considered chaotic, dynamic, and unpredictable. Indeed, it is one of the most difficult forecasting tasks that hundreds of millions of retail traders and professional traders around the world try to do every second even before the market opens. With recent advances

This paper investigates the application of Transformer-based neural networks to stock price forecasting, with a special focus on the intersection of machine learning techniques and financial market analysis. The evolution of Transformer models, from their inception to their adaptation for time serie

We show that the state spaces of multifactor Markovian processes, coming from approximations of nonnegative Volterra processes, are given by explicit linear transformation of the nonnegative orthant. We demonstrate the usefulness of this result for applications, including simulation schemes and PDE

While the market impact of aggressive orders has been extensively studied, the impact of passive orders, those executed through limit orders, remains less understood. The goal of this paper is to investigate passive market impact by developing a microstructure model connecting liquidity dynamics and

As the increasing application of AI in finance, this paper will leverage AI algorithms to examine tail risk and develop a model to alter tail risk to promote the stability of US financial markets, and enhance the resilience of the US economy. Specifically, the paper constructs a multivariate multile

An insurance company, as a risk bearer, is exposed to the likelihood of running into ruin. This is the situation where the initial surplus falls below zero. There is the need to find the required start-up capital to hedge against insolvency. Most researchers, irrespective of whether the test for cla

The advances and development of various machine learning techniques has lead to practical solutions in various areas of science, engineering, medicine and finance. The great choice of algorithms, their implementations and libraries has resulted in another challenge of selecting the right algorithm a

Reducing financial risk is of paramount importance to investors, financial institutions, and corporations. Since the pioneering contribution of Johnson (1960), the optimal hedge ratio based on futures is regularly utilized. The current paper suggests an explicit and efficient method for testing the

The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear dependency structure among the assets. We describe the dynamics of the multivariate process of constituents with a copula model

Building on the one-to-one relationship between generalized FGM copulas and multivariate Bernoulli distributions, we prove that the class of multivariate distributions with generalized FGM copulas is a convex polytope. Therefore, we find sharp bounds in this class for many aggregate risk measures, s

This paper employs Topological Data Analysis (TDA) to detect extreme events (EEs) in the stock market at a continental level. Previous approaches, which analyzed stock indices separately, could not detect EEs for multiple time series in one go. TDA provides a robust framework for such analysis and i

We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for different behaviours across various times or regimes. To establ

The assessment of risk based on historical data faces many challenges, in particular due to the limited amount of available data, lack of stationarity, and heavy tails. While estimation on a short-term horizon for less extreme percentiles tends to be reasonably accurate, extending it to longer time

The stability of a complex financial system may be assessed by measuring risk contagion between various financial institutions with relatively high exposure. We consider a financial network model using a bipartite graph of financial institutions (e.g., banks, investment companies, insurance firms) o

We consider an offline learning problem for an agent who first estimates an unknown price impact kernel from a static dataset, and then designs strategies to liquidate a risky asset while creating transient price impact. We propose a novel approach for a nonparametric estimation of the propagator fr

This paper introduces the concept of a global financial market for environmental indices, addressing sustainability concerns and aiming to attract institutional investors. Risk mitigation measures are implemented to manage inherent risks associated with investments in this new financial market. We m

We propose a novel generative model for multivariate discrete-time time series data. Drawing inspiration from the construction of neural spline flows, our algorithm incorporates linear transformations and the signature transform as a seamless substitution for traditional neural networks. This approa

The US stock market experienced instability following the recession (2007-2009). COVID-19 poses a significant challenge to US stock traders and investors. Traders and investors should keep up with the stock market. This is to mitigate risks and improve profits by using forecasting models that accoun

We study the eigenvalue of the Wishart matrix, which is created from a time series with temporal correlation. When there is no correlation, the eigenvalue distribution of the Wishart matrix is known as the Marchenko-Pastur distribution (MPD) in the double scaling limit. When there is temporal correl

We develop a methodology that utilizes deep learning to simultaneously solve and estimate canonical continuous-time general equilibrium models in financial economics. We illustrate our method in two examples: (1) industrial dynamics of firms and (2) macroeconomic models with financial frictions. Thr

Copulas are widely used in financial economics as well as in other areas of applied mathematics. Yet, there is much arbitrariness in their choice. The author proposes “a natural copula” concept, which minimizes Wasserstein distance between distributions in some space, in which both these distributio

The concept of entropy is not uniquely relevant to the statistical mechanics but among others it can play pivotal role in the analysis of a time series, particularly the stock market data. In this area sudden events are especially interesting as they describe abrupt data changes which may have long-

We present a general framework for modelling the dynamics of limit order books, built on the combination of two modelling ingredients: the order flow, modelled as a general spatial point process, and market clearing, modelled via a deterministic mass transport operator acting on distributions of buy

Stock market forecasting is a classic problem that has been thoroughly investigated using machine learning and artificial neural network based tools and techniques. Interesting aspects of this problem include its time reliance as well as its volatility and other complex relationships. To combine the

In this paper we study optimal trading strategies in a financial market in which stock returns depend on a hidden Gaussian mean reverting drift process. Investors obtain information on that drift by observing stock returns. Moreover, expert opinions in the form of signals about the current state of

The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any non-negative integer $D$ for the total number of nestings. Standa

This study analyzes the dynamic interactions among the NASDAQ index, crude oil, gold, and the US dollar using a reduced-order modeling approach. Time-delay embedding and principal component analysis are employed to encode high-dimensional financial dynamics, followed by linear regression in the redu

We derive the explicit price of the perpetual American put option cancelled at the last passage time of the underlying above some fixed level. We assume the asset process is governed by a geometric spectrally negative Lévy process. We show that the optimal exercise time is the first epoch when asset

We present a simple unifying treatment of a broad class of applications from statistical mechanics, econometrics, mathematical finance, and insurance mathematics, where (possibly subordinated) Lévy noise arises as a scaling limit of some form of continuous-time random walk (CTRW). For each applicati

We study multivariate tail-dependence compatibility for complete and partial signed tail families, treating lower-tail, upper-tail, and mixed configurations in one geometric witness representation indexed by active coordinate sets and sign patterns. For a complete signed tail family, witness generat

Following years of controversial discussions about the risks of market-based redispatch, the German transmission network operators finally installed regional redispatch markets by the end of 2024. Since water electrolysers are eligible market participants, the otherwise downwards redispatched renewa

We propose a credit risk model for portfolios composed of green and brown loans, extending the ASRF framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gauss

An exponentially weighted moving model (EWMM) for a vector time series fits a new data model each time period, based on an exponentially fading loss function on past observed data. The well known and widely used exponentially weighted moving average (EWMA) is a special case that estimates the mean u

The geometric Brownian motion (GBM) is widely employed for modeling stochastic processes, yet its solutions are characterized by the log-normal distribution. This comprises predictive capabilities of GBM mainly in terms of forecasting applications. Here, entropy corrections to GBM are proposed to go

Predicting future direction of stock markets using the historical data has been a fundamental component in financial forecasting. This historical data contains the information of a stock in each specific time span, such as the opening, closing, lowest, and highest price. Leveraging this data, the fu

We prove a functional limit theorem for a pair of nearly unstable Hawkes processes coupled through a triangular cross-excitation mechanism, when the two kernels have distinct heavy-tail exponents. This heterogeneous regime produces two different degrees of roughness and, to the best of our knowledge

In this paper, we analyse the impacts of exogenous and endogenous factors on wealth distribution in the Bitcoin token economy, where wealth distribution refers to the distribution of BTC between economic participants or groups of economic participants. The objective of the paper is to analyse the im

In this paper we study the Fourier estimator of Malliavin and Mancino for the spot volatility. We establish the convergence of the trigonometric polynomial to the volatility’s path in a setting that includes the following aspects. First, the volatility is required to satisfy a mild integrability con

This study investigates the contribution of Intrinsic Mode Functions (IMFs) derived from economic time series to the predictive performance of neural network models, specifically Multilayer Perceptrons (MLP) and Long Short-Term Memory (LSTM) networks. To enhance interpretability, DeepSHAP is applied

Volatility clustering is one of the most robust stylized facts of financial markets, yet it is typically detected using moment-based diagnostics or parametric models such as GARCH. This paper shows that clustered volatility also leaves a clear imprint on the time-reversal symmetry of horizontal visi

Markets efficiency implies that the stock returns are intrinsically unpredictable, a property that makes markets comparable to random number generators. We present a novel methodology to investigate ultra-high frequency financial data and to evaluate the extent to which tick by tick returns resemble

We investigate the mechanisms by which medium-frequency trading agents are adversely selected by opportunistic high-frequency traders. We use reinforcement learning (RL) within a Hawkes Limit Order Book (LOB) model in order to replicate the behaviours of high-frequency market makers. In contrast to

This paper develops a novel framework for modeling the variance swap of multi-asset portfolios by employing the generalized variance approach, which utilizes the determinant of the covariance matrix of the underlying assets. By specifying the distribution of the log returns of the underlying assets

The present work tackles the money laundering detection problem. A new procedure is introduced which exploits structured time series of both qualitative and quantitative data by means of a transformer neural network. The first step of this procedure aims at learning representations of time series th

Accurate electricity price forecasting (EPF) is crucial for effective decision-making in power trading on the spot market. While recent advances in generative artificial intelligence (GenAI) and pre-trained large language models (LLMs) have inspired the development of numerous time series foundation

Using introduced concept of the exchange and inflation rates adequacy, the relevance of them to the determining factors is found. We established close positive relation between hryvnia / dollar exchange and inflation rates, fiscal deficit, price level of energy sources, and money supply. On this bas

We conduct a preliminary analysis of a pairs trading strategy using the Ornstein-Uhlenbeck (OU) process to model stock price spreads. We compare this approach to a naive pairs trading strategy that uses a rolling window to calculate mean and standard deviation parameters. Our findings suggest that t

We suggest employing log-ergodic processes to simulate the velocity of money in an ergodic manner. Our approach sheds light on economic behavior, policy implications, and financial dynamics by maintaining long-term stability. By bridging theory and practice, the partially ergodic model helps analyst

Cryptocurrencies are highly volatile financial instruments with more and more new retail investors joining the scene with each passing day. Bitcoin has always proved to determine in which way the rest of the cryptocurrency market is headed towards. As of today Bitcoin has a market dominance of close

This paper introduces BreakGPT, a novel large language model (LLM) architecture adapted specifically for time series forecasting and the prediction of sharp upward movements in asset prices. By leveraging both the capabilities of LLMs and Transformer-based models, this study evaluates BreakGPT and o

Financial AI empowers sophisticated approaches to financial market forecasting, portfolio optimization, and automated trading. This survey provides a systematic analysis of these developments across three primary dimensions: predictive models that capture complex market dynamics, decision-making fra

In this article, we employ physics-informed residual learning (PIRL) and propose a pricing method for European options under a regime-switching framework, where closed-form solutions are not available. We demonstrate that the proposed approach serves an efficient alternative to competing pricing tec

In the Venture Capital (VC) industry, predicting the success of startups is challenging due to limited financial data and the need for subjective revenue forecasts. Previous methods based on time series analysis often fall short as they fail to incorporate crucial inter-company relationships such as

In statistical analysis, many classic results require the assumption that models have finite mean or variance, including the most standard versions of the laws of large numbers and the central limit theorems. Such an assumption may not be completely innocent, and it may not be appropriate for datase

Recent advances in large language models (LLMs) have unlocked novel opportunities for machine learning applications in the financial domain. These models have demonstrated remarkable capabilities in understanding context, processing vast amounts of data, and generating human-preferred contents. In t

This paper explores the intersection of Natural Language Processing (NLP) and financial analysis, focusing on the impact of sentiment analysis in stock price prediction. We employ BERTopic, an advanced NLP technique, to analyze the sentiment of topics derived from stock market comments. Our methodol

Modeling financial data often relies on assumptions that may prove insufficient or unrealistic in practice. The Geometric Brownian Motion (GBM) model is frequently employed to represent stock price processes. This study investigates whether the behavior of weekly and monthly returns of selected equi

The Argentinian real estate market presents a unique case study characterized by its unstable and rapidly shifting macroeconomic circumstances over the past decades. Despite the existence of a few datasets for price prediction, there is a lack of mixed modality datasets specifically focused on Argen

Financial inclusion ensures that individuals have access to financial products and services that meet their needs. As a key contributing factor to economic growth and investment opportunity, financial inclusion increases consumer spending and consequently business development. It has been shown that

This study proposes a new exact simulation scheme of the Ornstein-Uhlenbeck driven stochastic volatility model. With the Karhunen-Loève expansions, the stochastic volatility path following the Ornstein-Uhlenbeck process is expressed as a sine series, and the time integrals of volatility and variance

We establish the weak convergence of the intensity of a nearly-unstable Hawkes process with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market model where orders to buy or sell an asset arrive according to a Hawkes process with power-law kernel. After suitable r

We present a standard form of master equations (ME) for general one-dimensional non-Markovian (history-dependent) jump processes, complemented by an asymptotic solution derived from an expanded system-size approach. The ME is obtained by developing a general Markovian embedding using a suitable set

This study outlines a comprehensive methodology utilizing copulas to discern inconsistencies in the behavior exhibited by pairs of financial assets. It introduces a robust approach to establishing the interrelationship between the returns of these assets, exploring potential measures of dependence a

The ARIMA (Autoregressive Integrated Moving Average model) has extensive applications in the field of time series forecasting. However, the predictive performance of the ARIMA model is limited when dealing with data gaps or significant noise. Based on previous research, we have found that cubic spli

We derive quantitative error bounds for deep neural networks (DNNs) approximating option prices on a $d$-dimensional risky asset as functions of the underlying model parameters, payoff parameters and initial conditions. We cover a general class of stochastic volatility models of Markovian nature as

The aim of this paper is to analyse the Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75% of total market capitalisation and compare their evolution with that of a wide variety of traditional assets: commodities with spot and fu

We consider an HJM model setting for Markov-chain modulated forward rates. The underlying Markov chain is assumed to induce regime switches on the forward curve dynamics. Our primary focus is on the interest rate and energy futures markets. After deriving HJM-drift conditions for the two markets, we

In this paper, we study the exponential utility indifference pricing of pure endowment policies within a stochastic-factor model for an insurer who also invests in a financial market. Our framework incorporates a hazard rate modeled as an observable diffusion process, while the risky asset price fol

This paper addresses stock price movement prediction by leveraging LLM-based news sentiment analysis. Earlier works have largely focused on proposing and assessing sentiment analysis models and stock movement prediction methods, however, separately. Although promising results have been achieved, a c

The efficiency of pension schemes in Kenya invites elevated interest owing to the increasing pension contribution amounts and the expectation that benefits paid out of these schemes would protect members from old age poverty. The study investigates the intervening effect of risk management on the re

This paper investigates a fundamental methodological flaw in the investment-cash flow sensitivity model of Fazzari, Hubbard, and Petersen (1988). The model comes from a full accounting identity in which some components are missing, generating what I term an Accounting Semi-Identity, that mechanicall

We introduce a new actuarial tail-shape index, the $θ$-index, based on a probability equal level relationship between Value at Risk and Expected Shortfall. The index is defined at each tail probability level as the parameter value for which Value at Risk coincides with Flexible Expected Shortfall, t

We introduce a class of short-rate models that exhibit a ``higher for longer’’ phenomenon. Specifically, the short-rate is modeled as a general time-homogeneous one-factor Markov diffusion on a finite interval. The lower endpoint is assumed to be regular, exit or natural according to boundary classi

Examples of stochastic processes whose state space representations involve functions of an integral type structure $$I_{t}^{(a,b)}:=\int_{0}^{t}b(Y_{s})e^{-\int_{s}^{t}a(Y_{r})dr}ds, \quad t\ge 0$$ are studied under an ergodic semi-Markovian environment described by an $S$ valued jump type process $

In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal couplings, as a generalization of well-known correlation statist

We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clustering feature by adding an independent compound Hawkes process to the Heston volati

The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreo

This research explores a relatively unexplored area of predicting cryptocurrency staking rewards, offering potential insights to researchers and investors. We investigate two predictive methodologies: a) a straightforward sliding-window average, and b) linear regression models predicated on historic

Portfolio’s optimal drivers for diversification are common causes of the constituents’ correlations. A closed-form formula for the conditional probability of the portfolio given its optimal common drivers is presented, with each pair constituent-common driver joint distribution modelled by Gaussian

This paper studies the mean-variance optimal portfolio choice of an investor pre-committed to a deterministic investment policy in continuous time in a market with mean-reversion in the risk-free rate and the equity risk-premium. In the tradition of Markowitz, optimal policies are restricted to a su

We consider a mean-field model of firms competing à la Cournot on a commodity market, where the commodity price is given in terms of a power inverse demand function of the industry-aggregate production. Investment is irreversible and production capacity depreciates at a constant rate. Production is

In most cases, insurance contracts are linked to the financial markets, such as through interest rates or equity-linked insurance products. To motivate an evaluation rule in these hybrid markets, Artzner et al. (2022) introduced the notion of insurance-finance arbitrage. In this paper we extend thei

We provide an event-level Hawkes microfoundation for a multitype inverse-Gaussian stochastic clock. We show that the event counts and integrated intensities of nearly critical multivariate linear Hawkes processes converge jointly to a multivariate pure-jump subordinator when reproduction delays have

Feller random measures generalize the Feller diffusion (the CIR process) by giving it memory. They arise as the scaling limits of nearly unstable Hawkes processes, and include the rough CIR process and its hyper-rough and discontinuous relatives. We show that every Feller random measure is the occup

Heavy-tailed phenomena appear across diverse domains –from wealth and firm sizes in economics to network traffic, biological systems, and physical processes– characterized by the disproportionate influence of extreme values. These distributions challenge classical statistical models, as their tails