TPLVM: Portfolio Construction by Student’s t-Process Latent Variable Model

Uchiyama, Yusuke; Nakagawa, Kei

doi:10.3390/math8030449

Cited by 8 publications

(7 citation statements)

References 25 publications

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“…Assume that the observed data

and the latent variable

are related as

by the Student’s t -process

. When we let

be the sequence of N observed data, and

be the sequence of N latent variables, we can define the following model as Student’s t -process latent variable model [ 10 ]:

Since the Student’s t -distribution converges to the Gaussian distribution in the limit of

, we can see that the Student’s t -process latent variable model embraces the Gaussian process latent variable model [ 20 ].…”

Section: Related Workmentioning

confidence: 99%

“…Assume that the observed data y∈R D and the latent variable x∈R Q are related as y = f (x) by the Student's t-process f ∼T P (m, K; ν). When we let Y∈R D×N be the sequence of N observed data, and X∈R Q×N be the sequence of N latent variables, we can define the following model as Student's t-process latent variable model [10]:…”

Section: Student's T-process Latent Variable Modelmentioning

confidence: 99%

“…The Student’s t -process is an extension of the Gaussian, for non-Gaussian distributed data such as asset returns. It has been proposed [ 9 ] and applied to the analysis of financial time-series and asset allocations, and it is confirmed for this model to estimate robustly [ 10 ].…”

Section: Introductionmentioning

confidence: 99%

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Entropy Based Student’s t-Process Dynamical Model

Nono

Uchiyama²,

Nakagawa

2021

Entropy

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Volatility, which represents the magnitude of fluctuating asset prices or returns, is used in the problems of finance to design optimal asset allocations and to calculate the price of derivatives. Since volatility is unobservable, it is identified and estimated by latent variable models known as volatility fluctuation models. Almost all conventional volatility fluctuation models are linear time-series models and thus are difficult to capture nonlinear and/or non-Gaussian properties of volatility dynamics. In this study, we propose an entropy based Student’s t-process Dynamical model (ETPDM) as a volatility fluctuation model combined with both nonlinear dynamics and non-Gaussian noise. The ETPDM estimates its latent variables and intrinsic parameters by a robust particle filtering based on a generalized H-theorem for a relative entropy. To test the performance of the ETPDM, we implement numerical experiments for financial time-series and confirm the robustness for a small number of particles by comparing with the conventional particle filtering.

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“…Assume that the observed data

and the latent variable

are related as

by the Student’s t -process

. When we let

be the sequence of N observed data, and

be the sequence of N latent variables, we can define the following model as Student’s t -process latent variable model [ 10 ]:

Since the Student’s t -distribution converges to the Gaussian distribution in the limit of

, we can see that the Student’s t -process latent variable model embraces the Gaussian process latent variable model [ 20 ].…”

Section: Related Workmentioning

confidence: 99%

Section: Student's T-process Latent Variable Modelmentioning

confidence: 99%

See 1 more Smart Citation

Entropy Based Student’s t-Process Dynamical Model

Nono

Uchiyama²,

Nakagawa

2021

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…See, e.g., Refs. [12][13][14][15] for an application of the Student's t distribution and Refs. [16][17][18][19]-for the Pareto distribution.…”

Section: Introductionmentioning

confidence: 99%

From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t-Distribution Case

et al. 2022

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Multivariate modelling of economics data is crucial for risk and profit analyses in companies. However, for the final conclusions, a whole set of variables is usually transformed into a single variable describing a total profit/balance of company’s cash flows. One of the possible transformations is based on the product of market variables. Thus, in this paper, we study the distribution of products of Pareto or Student’s t random variables that are ubiquitous in various risk factors analysis. We review known formulas for the probability density functions and derive their explicit forms for the products of Pareto and Gaussian or log-normal random variables. We also study how the Pareto or Student’s t random variable influences the asymptotic tail behaviour of the distribution of their product with the Gaussian or log-normal random variables and discuss how the dependency between the marginal random variables of the same type influences the probabilistic properties of the final product. The theoretical results are then applied for an analysis of the distribution of transaction values, being a product of prices and volumes, from a continuous trade on the German intraday electricity market.

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“…The TPR is realized by marginalization of the conditional GPR with a gamma distributed random precision or a Wishart distributed precision matrix. As with the GPR, the TPR is extended to latent variable modeling [8].…”

Section: Introductionmentioning

confidence: 99%

Student's T-process Regression on the Space of Probability Density Functions

Uchiyama¹,

Oka²,

Nono

2021

Stochastic Systems Theory and its Applications (SSS)

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This study provides an extension of the Student's tprocess regression (TPR) on the space of probability density functions as a method of system identification for the data set consist of noisy inputs and deterministic outputs with additive noises. With introducing the distance metrics of the probability density functions, the TPR can be naturally extended to the space of the probability density functions and thus prediction and hyper parameter estimation can be implemented by the same fashion of the ordinary model. In addition, with a numerical example of the proposed model, we introduce the Markov Chain Monte Carlo method for hyper parameter estimation.

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TPLVM: Portfolio Construction by Student’s t-Process Latent Variable Model

Cited by 8 publications

References 25 publications

Entropy Based Student’s t-Process Dynamical Model

Entropy Based Student’s t-Process Dynamical Model

From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t-Distribution Case

Student's T-process Regression on the Space of Probability Density Functions

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