11 research outputs found
Expectile hidden Markov regression models for analyzing cryptocurrency returns
In this paper we develop a linear expectile hidden Markov model for the
analysis of cryptocurrency time series in a risk management framework. The
methodology proposed allows to focus on extreme returns and describe their
temporal evolution by introducing in the model time-dependent coefficients
evolving according to a latent discrete homogeneous Markov chain. As it is
often used in the expectile literature, estimation of the model parameters is
based on the asymmetric normal distribution. Maximum likelihood estimates are
obtained via an Expectation-Maximization algorithm using efficient M-step
update formulas for all parameters. We evaluate the introduced method with both
artificial data under several experimental settings and real data investigating
the relationship between daily Bitcoin returns and major world market indices
Quantile and expectile copula-based hidden Markov regression models for the analysis of the cryptocurrency market
The role of cryptocurrencies within the financial systems has been expanding
rapidly in recent years among investors and institutions. It is therefore
crucial to investigate the phenomena and develop statistical methods able to
capture their interrelationships, the links with other global systems, and, at
the same time, the serial heterogeneity. For these reasons, this paper
introduces hidden Markov regression models for jointly estimating quantiles and
expectiles of cryptocurrency returns using regime-switching copulas. The
proposed approach allows us to focus on extreme returns and describe their
temporal evolution by introducing time-dependent coefficients evolving
according to a latent Markov chain. Moreover to model their time-varying
dependence structure, we consider elliptical copula functions defined by
state-specific parameters. Maximum likelihood estimates are obtained via an
Expectation-Maximization algorithm. The empirical analysis investigates the
relationship between daily returns of five cryptocurrencies and major world
market indices.Comment: 35 pages, 6 figures. arXiv admin note: text overlap with
arXiv:2301.0972
A review of probabilistic forecasting and prediction with machine learning
Predictions and forecasts of machine learning models should take the form of
probability distributions, aiming to increase the quantity of information
communicated to end users. Although applications of probabilistic prediction
and forecasting with machine learning models in academia and industry are
becoming more frequent, related concepts and methods have not been formalized
and structured under a holistic view of the entire field. Here, we review the
topic of predictive uncertainty estimation with machine learning algorithms, as
well as the related metrics (consistent scoring functions and proper scoring
rules) for assessing probabilistic predictions. The review covers a time period
spanning from the introduction of early statistical (linear regression and time
series models, based on Bayesian statistics or quantile regression) to recent
machine learning algorithms (including generalized additive models for
location, scale and shape, random forests, boosting and deep learning
algorithms) that are more flexible by nature. The review of the progress in the
field, expedites our understanding on how to develop new algorithms tailored to
users' needs, since the latest advancements are based on some fundamental
concepts applied to more complex algorithms. We conclude by classifying the
material and discussing challenges that are becoming a hot topic of research.Comment: 83 pages, 5 figure
New insights on hidden Markov models for time series data analysis
The goal of this thesis is to develop novel methods for the analysis of financial data by using hidden Markov models based approaches. The analysis focuses on univariate and multivariate financial time series, modeling interrelationships between financial returns throughout different statistical methods, such as graphical models, quantile and expectile regressions. The dissertation is divided into three chapters, each of them examining different classes of assets returns for a comprehensive risk analysis. The methodologies we propose are illustrated using real-world data and simulation studies
GAMLSS for high-dimensional data – a flexible approach based on boosting
Generalized additive models for location, scale and shape (GAMLSS) are a popular semi-parametric modelling approach that, in contrast to conventional GAMs, regress not only the expected mean but every distribution parameter (e.g. location, scale and shape) to a set of covariates. Current fitting procedures for GAMLSS are infeasible for high-dimensional data setups and require variable selection based on (potentially problematic) information criteria. The present work describes a boosting algorithm for high-dimensional GAMLSS that was developed to overcome these limitations. Specifically, the new algorithm was designed to allow the simultaneous estimation of predictor effects and variable selection. The proposed algorithm was applied to data of the Munich Rental Guide, which is used by
landlords and tenants as a reference for the average rent of a flat depending on its characteristics and spatial features. The net-rent predictions that resulted from the high-dimensional GAMLSS were found to be highly competitive while covariate-specific prediction intervals showed a major improvement over classical GAMs
Recommended from our members
New regression methods for measures of central tendency
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel UniversityMeasures of central tendency have been widely used for summarising statistical data, with the mean being the most popular summary statistic. However, in reallife applications it is not always the most representative measure of central location, especially when dealing with data which is skewed or contains outliers. Alternative
statistics with less bias are the median and the mode. Median and quantile regression has been used in different fields to examine the effect of factors at different points of the distribution. Mode estimation, on the other hand, has found many applications in cases where the analysis focuses on obtaining information about the most typical value or pattern. This thesis demonstrates that mode also plays an important role in the analysis of big data, which is becoming increasingly important in many sectors of the global economy.
However, mode regression has not been widely applied, even though there is a clear conceptual benefit, due to the computational and theoretical limitations of the existing estimators. Similarly, despite the popularity of the binary quantile regression model, computational straight forward estimation techniques do not exist.
Driven by the demand for simple, well-found and easy to implement inference tools, this thesis develops a series of new regression methods for mode and binary quantile regression. Chapter 2 deals with mode regression methods from the Bayesian perspective and presents one parametric and two non-parametric methods of inference. Chapter 3 demonstrates a mode-based, fast pattern-identification method for big data and proposes the first fully parametric mode regression method, which effectively uncovers the dependency of typical patterns on a number of covariates. The proposed approach is demonstrated through the analysis of a decade-long dataset on the Body Mass Index and associated factors, taken from the Health Survey for England. Finally, Chapter 4 presents an alternative binary quantile regression approach, based on the nonlinear least asymmetric weighted squares, which can be implemented using standard statistical packages and guarantees a unique solution