arXiv subjects

Xingcheng Xu

Publications and source records attributed to Xingcheng Xu.

30 records · Page 2Linked to original sources

arXiv2024

Deep Learning for Multi-Country GDP Prediction: A Study of Model Performance and Data Impact

GDP is a vital measure of a country's economic health, reflecting the total value of goods and services produced. Forecasting GDP growth is essential for economic planning, as it helps governments, businesses, and investors anticipate trends, make informed decisions, and promote stability and growth. While most previous works focus on the prediction of the GDP growth rate for a single country or by machine learning methods, in this paper we give a comprehensive study on the GDP growth forecasting in the multi-country scenario by deep learning algorithms. For the prediction of the GDP growth where only GDP growth values are used, linear regression is generally better than deep learning algorithms. However, for the regression and the prediction of the GDP growth with selected economic indicators, deep learning algorithms could be superior to linear regression. We also investigate the influence of the novel data -- the light intensity data on the prediction of the GDP growth, and numerical experiments indicate that they do not necessarily improve the prediction performance. Code is provided at https://github.com/Sariel2018/Multi-Country-GDP-Prediction.git.

econ.GN↗

arXiv2024

Optimal Trade and Industrial Policies in the Global Economy: A Deep Learning Framework

We propose a deep learning framework, DL-opt, designed to efficiently solve for optimal policies in quantifiable general equilibrium trade models. DL-opt integrates (i) a nested fixed point (NFXP) formulation of the optimization problem, (ii) automatic implicit differentiation to enhance gradient descent for solving unilateral optimal policies, and (iii) a best-response dynamics approach for finding Nash equilibria. Utilizing DL-opt, we solve for non-cooperative tariffs and industrial subsidies across 7 economies and 44 sectors, incorporating sectoral external economies of scale. Our quantitative analysis reveals significant sectoral heterogeneity in Nash policies: Nash industrial subsidies increase with scale elasticities, whereas Nash tariffs decrease with trade elasticities. Moreover, we show that global dual competition, involving both tariffs and industrial subsidies, results in lower tariffs and higher welfare outcomes compared to a global tariff war. These findings highlight the importance of considering sectoral heterogeneity and policy combinations in understanding global economic competition.

econ.GN↗

arXiv2024

Rough Path Renormalization from Stratonovich to Itô for Fractional Brownian Motion

This paper develops an Itô-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters $ H \in (\frac{1}{3}, \frac{1}{2}] $, using the Lyons' rough path framework. This approach is designed to fill gaps in conventional stochastic calculus models that fail to account for temporal persistence prevalent in dynamic systems such as those found in economics, finance, and engineering. The pathwise-defined method not only meets the zero expectation criterion but also addresses the challenges of integrating non-semimartingale processes, which traditional Itô calculus cannot handle. We apply this theory to fractional Black-Scholes models and high-dimensional fractional Ornstein-Uhlenbeck processes, illustrating the advantages of this approach. Additionally, the paper discusses the generalization of Itô integrals to rough differential equations (RDE) driven by fBM, emphasizing the necessity of integrand-specific adaptations in the Itô rough path lift for stochastic modeling.

math.PR↗

arXiv2024

Lévy Area Analysis and Parameter Estimation for fOU Processes via Non-Geometric Rough Path Theory

This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path. Our approach is particularly suitable for high-frequency data. To formulate the parameter estimators, we introduce a theory of pathwise Itô integrals with respect to fractional Brownian motion. By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes, we demonstrate that our estimators are strongly consistent and pathwise stable. Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings, and may have practical implications for fields including finance, economics, and engineering.

math.PR↗

arXiv2024

Machine Learning for Economic Forecasting: An Application to China's GDP Growth

This paper aims to explore the application of machine learning in forecasting Chinese macroeconomic variables. Specifically, it employs various machine learning models to predict the quarterly real GDP growth of China, and analyzes the factors contributing to the performance differences among these models. Our findings indicate that the average forecast errors of machine learning models are generally lower than those of traditional econometric models or expert forecasts, particularly in periods of economic stability. However, during certain inflection points, although machine learning models still outperform traditional econometric models, expert forecasts may exhibit greater accuracy in some instances due to experts' more comprehensive understanding of the macroeconomic environment and real-time economic variables. In addition to macroeconomic forecasting, this paper employs interpretable machine learning methods to identify the key attributive variables from different machine learning models, aiming to enhance the understanding and evaluation of their contributions to macroeconomic fluctuations.

econ.GN↗

arXiv2024

It Ain't That Bad: Understanding the Mysterious Performance Drop in OOD Generalization for Generative Transformer Models

Large language models (LLMs) have achieved remarkable proficiency on solving diverse problems. However, their generalization ability is not always satisfying and the generalization problem is common for generative transformer models in general. Researchers take basic mathematical tasks like n-digit addition or multiplication as important perspectives for investigating their generalization behaviors. It is observed that when training models on n-digit operations (e.g., additions) in which both input operands are n-digit in length, models generalize successfully on unseen n-digit inputs (in-distribution (ID) generalization), but fail miserably on longer, unseen cases (out-of-distribution (OOD) generalization). We bring this unexplained performance drop into attention and ask whether there is systematic OOD generalization. Towards understanding LLMs, we train various smaller language models which may share the same underlying mechanism. We discover that the strong ID generalization stems from structured representations, while behind the unsatisfying OOD performance, the models still exhibit clear learned algebraic structures. Specifically, these models map unseen OOD inputs to outputs with learned equivalence relations in the ID domain, which we call the equivalence generalization. These findings deepen our knowledge regarding the generalizability of generative models including LLMs, and provide insights into potential avenues for improvement.

cs.LG↗

arXiv2023

Deep Generative Modeling with Backward Stochastic Differential Equations

This paper proposes a novel deep generative model, called BSDE-Gen, which combines the flexibility of backward stochastic differential equations (BSDEs) with the power of deep neural networks for generating high-dimensional complex target data, particularly in the field of image generation. The incorporation of stochasticity and uncertainty in the generative modeling process makes BSDE-Gen an effective and natural approach for generating high-dimensional data. The paper provides a theoretical framework for BSDE-Gen, describes its model architecture, presents the maximum mean discrepancy (MMD) loss function used for training, and reports experimental results.

cs.LG↗

arXiv2023

GAMMT: Generative Ambiguity Modeling Using Multiple Transformers

We introduce a novel model called GAMMT (Generative Ambiguity Models using Multiple Transformers) for sequential data that is based on sets of probabilities. Unlike conventional models, our approach acknowledges that the data generation process of a sequence is not deterministic, but rather ambiguous and influenced by a set of probabilities. To capture this ambiguity, GAMMT employs multiple parallel transformers that are linked by a selection mechanism, allowing for the approximation of ambiguous probabilities. The generative nature of our approach also enables multiple representations of input tokens and sequences. While our models have not yet undergone experimental validation, we believe that our model has great potential to achieve high quality and diversity in modeling sequences with uncertain data generation processes.

cs.LG↗

arXiv2021

General Signature Kernels

Suppose that $γ$ and $σ$ are two continuous bounded variation paths which take values in a finite-dimensional inner product space $V$. Recent papers have introduced the truncated and the untruncated signature kernel of $γ$ and $σ$, and showed how these concepts can be used in classification and prediction tasks involving multivariate time series. In this paper, we introduce general signature kernels and show how they can be interpreted, in many examples, as an average of PDE solutions, and hence how they can be computed using suitable quadrature rules. We extend this analysis to derive closed-form formulae for expressions involving the expected (Stratonovich) signature of Brownian motion. In doing so, we articulate a novel connection between signature kernels and the hyperbolic development map, the latter of which has been a broadly useful tool in the analysis of the signature. As an application we evaluate the use of different general signature kernels as the basis for non-parametric goodness-of-fit tests to Wiener measure on path space.

math.PR↗

arXiv2020

Explicit solutions for a class of nonlinear backward stochastic differential equations and their nodal sets

In this paper, we investigate a class of nonlinear backward stochastic differential equations (BSDEs) arising from financial economics, and give specific information about the nodal sets of the related solutions. As applications, we are able to obtain the explicit solutions to an interesting class of nonlinear BSDEs including the k-ignorance BSDE arising from the modeling of ambiguity of asset pricing.

math.PR↗

arXiv2018

Optimal probabilities and controls for reflecting diffusion processes

A solution to the optimal problem for determining vector fields which maximize (resp. minimize) the transition probabilities from one location to another for a class of reflecting diffusion processes is obtained in the present paper. The approach is based on a representation for the transition probability density functions. The optimal transition probabilities under the constraint that the drift vector field is bounded by a constant are studied in terms of the HJB equation. In dimension one, the optimal reflecting diffusion processes and the bang-bang diffusion processes are considered. We demonstrate by simulations that, even in this special case, the optimal diffusion processes exhibit an interesting feature of phase transitions. We also solve an optimal stochastic control problem for a class of stochastic control problems involving diffusion processes with reflection.

math.PR↗

arXiv2017

Critical radius and supremum of random spherical harmonics (II)

We continue the study, begun in \cite{FA}, of the critical radius of embeddings, via deterministic spherical harmonics, of fixed dimensional spheres into higher dimensional ones, along with the associated problem of the distribution of the suprema of random spherical harmonics. Whereas \cite{FA} concentrated on spherical harmonics of a common degree, here we extend the results to mixed degrees, obtaining larger lower bounds on critical radii than we found previously.

math.PR↗