Asymmetric Long-Memory GARCH: Sign-Dependent Kernel Injection in a Two-Dimensional Markov Chain
本文提出ALM-GARCH模型，通过不同幅度和核偏移处理正负创新，解决条件方差中的不对称长记忆问题，并在多个股票指数和比特币上验证了其有效性。
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GaussVLA: Geometry-Aware Spatial Reasoning for Vision-Language-Action Model
为解决VLA模型空间推理能力有限的问题，GaussVLA通过引入Gaussian Spatial Tokenizer和Depth-Aware Chain-of-Thought模块增强几何感知能力。
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Long-memory GARCH via a two-dimensional Markov chain
Traditional GARCH models struggle to capture the long memory and state-dependent characteristics of financial volatility. This work proposes a novel state-dependent GARCH model that, for the first time, integrates a two-dimensional Markov chain with a latent-variable power-law kernel. By allowing the level and slope of the power-law kernel to evolve dynamically according to the underlying state, the model achieves adaptive decay of historical shocks. This approach effectively captures long-memory features through a low-dimensional state space and establishes rigorous ergodicity guarantees via Foster–Lyapunov theory. Simulation and empirical results demonstrate pronounced low-frequency persistence in log-squared innovations, and the model attains competitive out-of-sample forecasting accuracy using only a two-state specification.
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Long-memory Markov chains with power-law intensities
This work addresses the challenge of constructing a tractable self-exciting point process that retains the long-memory characteristics of power-law decay while admitting a finite-dimensional Markovian representation. To this end, the authors propose a novel self-exciting point process in which a nonlinear Markov chain replaces the dependence on the entire event history, thereby enabling a finite-dimensional Markovian characterization of the intensity dynamics while preserving the local jump-and-slope update structure. This approach uniquely integrates power-law long memory with a finite state space, achieving both analytical tractability and computational feasibility. Theoretical analysis demonstrates that the latent state process reproduces long-memory behavior near the stability boundary and rigorously establishes the existence of a unique invariant distribution, along with key ergodic properties including irreducibility, aperiodicity, T-chain structure, and positive Harris recurrence.
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Forecasting duration in high-frequency financial data using a self-exciting flexible residual point process
This study addresses the challenge of modeling and forecasting inter-arrival times of limit order book events in high-frequency financial markets, which exhibit heavy-tailed distributions that are difficult to capture accurately. The authors propose a flexible residual point process model that integrates heavy-tailed inter-event time characteristics with a self-exciting decay structure, embedding empirical duration distributions within a self-exciting point process framework. Theoretical analysis establishes that, under suitable conditions, the model possesses desirable stochastic stability properties, including irreducibility, aperiodicity, positive Harris recurrence, and a unique stationary distribution. Empirical results based on ultra-high-frequency trading data demonstrate that the proposed approach significantly outperforms existing benchmark models in predicting event durations.
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Asymmetric Long-Memory GARCH: Sign-Dependent Kernel Injection in a Two-Dimensional Markov Chain
本文提出ALM-GARCH模型，通过不同幅度和核偏移处理正负创新，解决条件方差中的不对称长记忆问题，并在多个股票指数和比特币上验证了其有效性。
0 citationsRead paper
GaussVLA: Geometry-Aware Spatial Reasoning for Vision-Language-Action Model
为解决VLA模型空间推理能力有限的问题，GaussVLA通过引入Gaussian Spatial Tokenizer和Depth-Aware Chain-of-Thought模块增强几何感知能力。
0 citationsRead paper
Long-memory GARCH via a two-dimensional Markov chain
Traditional GARCH models struggle to capture the long memory and state-dependent characteristics of financial volatility. This work proposes a novel state-dependent GARCH model that, for the first time, integrates a two-dimensional Markov chain with a latent-variable power-law kernel. By allowing the level and slope of the power-law kernel to evolve dynamically according to the underlying state, the model achieves adaptive decay of historical shocks. This approach effectively captures long-memory features through a low-dimensional state space and establishes rigorous ergodicity guarantees via Foster–Lyapunov theory. Simulation and empirical results demonstrate pronounced low-frequency persistence in log-squared innovations, and the model attains competitive out-of-sample forecasting accuracy using only a two-state specification.
0 citationsRead paper
Long-memory Markov chains with power-law intensities
This work addresses the challenge of constructing a tractable self-exciting point process that retains the long-memory characteristics of power-law decay while admitting a finite-dimensional Markovian representation. To this end, the authors propose a novel self-exciting point process in which a nonlinear Markov chain replaces the dependence on the entire event history, thereby enabling a finite-dimensional Markovian characterization of the intensity dynamics while preserving the local jump-and-slope update structure. This approach uniquely integrates power-law long memory with a finite state space, achieving both analytical tractability and computational feasibility. Theoretical analysis demonstrates that the latent state process reproduces long-memory behavior near the stability boundary and rigorously establishes the existence of a unique invariant distribution, along with key ergodic properties including irreducibility, aperiodicity, T-chain structure, and positive Harris recurrence.
0 citationsRead paper
Forecasting duration in high-frequency financial data using a self-exciting flexible residual point process
This study addresses the challenge of modeling and forecasting inter-arrival times of limit order book events in high-frequency financial markets, which exhibit heavy-tailed distributions that are difficult to capture accurately. The authors propose a flexible residual point process model that integrates heavy-tailed inter-event time characteristics with a self-exciting decay structure, embedding empirical duration distributions within a self-exciting point process framework. Theoretical analysis establishes that, under suitable conditions, the model possesses desirable stochastic stability properties, including irreducibility, aperiodicity, positive Harris recurrence, and a unique stationary distribution. Empirical results based on ultra-high-frequency trading data demonstrate that the proposed approach significantly outperforms existing benchmark models in predicting event durations.
0 citationsRead paper