| 1. |
- Höök, Lars Josef, et al.
(author)
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Efficient computation of the quasi likelihood function for discretely observed diffusion processes
- 2016
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In: Computational Statistics & Data Analysis. - : Elsevier BV. - 0167-9473 .- 1872-7352. ; 103, s. 426-437
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Journal article (peer-reviewed)abstract
- An efficient numerical method for nearly simultaneous computation of all conditional moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations is presented. The method is not restricted to any particular dynamics of the stochastic differential equation and is virtually insensitive to the sampling interval. The key contribution is that computational complexity is sublinear in terms of expensive operations in the number of observations as all moments can be computed offline in a single operation. Simulations show that the bias of the method is small compared to the random error in the estimates, and to the bias of comparable methods. Furthermore the computational cost is comparable (actually faster for moderate and large data sets) to the simple, but in some applications badly biased, the Euler–Maruyama approximation.
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| 2. |
- Cortese, Federico, et al.
(author)
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GENERALIZED INFORMATION CRITERIA FOR SPARSE STATISTICAL JUMP MODELS
- 2023
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In: Symposium i anvendt statistik 2023. - 9788798937036 ; , s. 68-78
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Book chapter (peer-reviewed)abstract
- We extend the generalized information criteria for high-dimensional penalizedmodels to sparse statistical jump models, a new class of statistically robust and computationally efficient alternatives to hidden Markov models. In a simulation study, we demonstrate that the new generalized information criteria selects the correct hyperparameters with high probability. Finally, providing an empirical application, we infer the key features that drive the return dynamics of the largest cryptocurrencies. We find that a four-state model best describes the dynamics of cryptocurrency returns. The states have natural market-based interpretations as they correspond to bull, bull-neutral, bear-neutral, and bear market regimes, respectively.
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| 3. |
- Cortese, Federico P., et al.
(author)
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What drives cryptocurrency returns? A sparse statistical jump model approach
- 2023
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In: Digital Finance. - 2524-6984.
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Journal article (peer-reviewed)abstract
- We apply the statistical sparse jump model, a recently developed, interpretable and robust regime-switching model, to infer key features that drive the return dynamics of the largest cryptocurrencies. The algorithm jointly performs feature selection, parameter estimation, and state classification. Our large set of candidate features are based on cryptocurrency, sentiment and financial market-based time series that have been identified in the emerging literature to affect cryptocurrency returns, while others are new. In our empirical work, we demonstrate that a three-state model best describes the dynamics of cryptocurrency returns. The states have natural market-based interpretations as they correspond to bull, neutral, and bear market regimes, respectively. Using the data-driven feature selection methodology, we are able to determine which features are important and which ones are not. In particular, out of the set of candidate features, we show that first moments of returns, features representing trends and reversal signals, market activity and public attention are key drivers of crypto market dynamics.
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| 5. |
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| 6. |
- Hultin, Hanna
(author)
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Generative models of limit order books
- 2021
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Licentiate thesis (other academic/artistic)abstract
- In this thesis generative models in machine learning are developed with the overall aim to improve methods for algorithmic trading on high-frequency electronic exchanges based on limit order books. The thesis consists of two papers.In the first paper a new generative model for the dynamic evolution of a limit order book, based on recurrent neural networks, is developed. The model captures the full dynamics of the limit order book by decomposing the probability of each transition of the limit order book into a product of conditional probabilities of order type, price level, order size, and time delay. Each such conditional probability is modeled by a recurrent neural network. In addition several evaluation metrics for generative models related to order execution are introduced. The generative model is successfully trained to fit both synthetic data generated by a Markov model and real data from the Nasdaq Stockholm exchange.The second paper explores reinforcement learning methods to find optimal policies for trading execution in Markovian models. A number of different approaches are implemented and compared, including a baseline time-weighted average price (TWAP) strategy, tabular Q-learning, and deep Q-learning based on predefined features as well as with the entire limit order book as input. The results indicate that it is preferable to use deep Q-learning with the entire limit order book as input to design efficient execution policies. In order to improve the understanding of the decisions taken by the agent, the learned action-value function for the deep Q-learning with predefined features is visualized as a function of selected features.
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| 7. |
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| 8. |
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| 9. |
- Larsson, Elisabeth, et al.
(author)
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Parameter Estimation in Finance Using Radial Basis Function Methods
- 2016
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Conference paper (peer-reviewed)abstract
- Given time series market observations for a price process, the parameters in an assumed underlying model can be determined through maximum likelihood estimation. Transition probability densities need to be estimated between each pair of data points. We show that Gaussian radial basis function approximation of the Fokker-Planck equations for the densities leads to a convenient mathematical representation. We present numerical results for one and two factor interest rate models.
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| 10. |
- Lindström, Erik, et al.
(author)
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A Diffusion Bridge Sampler for Drift- and Diffusion Dominated Models
- 2018
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Conference paper (peer-reviewed)abstract
- We introduce an adaptive algorithm for sampling multivariate diffusion bridges that performs well for both diffusion and drift dominated models.The algorithm combines the residual bridge sampler with adaptive MCMC, allowing the algorithm to make online improvements upon the ordinary residual bridge algorithm.The simulation study show that the proposed bridge sampler is performing at least as good as the residual bridge sampler on a diffusion dominated problem, and substantially better on a drift dominated problem.
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