Forecasting under model uncertainty: Non‐homogeneous hidden Markov models with Pòlya‐Gamma data augmentation

Koki, Constandina; Meligkotsidou, Loukia; Vrontos, Ioannis D.

doi:10.1002/for.2645

Cited by 15 publications

(20 citation statements)

References 69 publications

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“…In the present paper, we make an effort towards understanding price formation of the two largest cryptocurrencies, Bitcoin (BTC) and Ether (ETH), in terms of market capitalization. Our analysis uses a specific instance of the Non-Homogeneous Hidden Markov models, namely the Non-Homogeneous Pólya Gamma Hidden Markov model (NHPG) of [20], which has been shown to outperform similar models in conventional financial data, cf. [21].…”

Section: Summary and Resultsmentioning

confidence: 99%

“…Using the Non-Homogeneous Pólya-Gamma Hidden Markov Model (NHPG) of [20] on the Bitcoin (BTC) and Ether (ETH) price series and focusing on a data set of financial/economic predictors, we studied general properties of the cryptocurrency price series. While the NHPG algorithm exhibited good in-sample performance, it revealed that changes in the underlying two-state Markov process are frequent, thus indicating that the states are not persistent, contributing to the already high heteroskedasticity of both the Bitcoin and the Ether data series.…”

Section: Discussionmentioning

confidence: 99%

“…e., the parameters in the mean predictive regression equation and the parameters in the logistic regression equation for the transition probabilities. We follow the methodology of [20]. In brief, the authors propose the following MCMC sampling scheme for joint inference on model specification and model parameters.…”

Section: The Non-homogeneous Pólya-gamma Hidden Markov Modelmentioning

confidence: 99%

See 2 more Smart Citations

Do Cryptocurrency Prices Camouflage Latent Economic Effects? A Bayesian Hidden Markov Approach

Koki

Leonardos

Piliouras

2019

The 3rd Annual Decentralized Conference on Blockchain and Cryptocurrency

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With Bitcoin, Ether and more than 2000 cryptocurrencies already forming a multi-billion dollar market, a proper understanding of their statistical and financial properties still remains elusive. Traditional economic theories do not explain their characteristics and standard financial models fail to capture their statistic and econometric attributes such as their extreme variability and heteroskedasticity. Motivated by these findings, we study Bitcoin and Ether prices via a Non-Homogeneous Pólya Gamma Hidden Markov (NHPG) model that has been shown to outperform its counterparts in conventional financial data. The NHPG algorithm has good in-sample performance and identifies both linear and non-linear effects of the predictors. Our results indicate that all price series are heteroskedastic with frequent changes between the two states of the underlying Markov process. In a somewhat unexpected result, the Bitcoin and Ether prices, although correlated, are significantly affected by different variables. We compare long term to short term Bitcoin data and find that significant covariates may change over time. Limitations of the current approach—as expressed by the large number of significant predictors and the poor out-of-sample predictions—back earlier findings that cryptocurrencies are unlike any other financial asset and hence, that their understanding requires novel tools and ideas.

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Section: Summary and Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: The Non-homogeneous Pólya-gamma Hidden Markov Modelmentioning

confidence: 99%

See 1 more Smart Citation

Do Cryptocurrency Prices Camouflage Latent Economic Effects? A Bayesian Hidden Markov Approach

Koki

Leonardos

Piliouras

2019

The 3rd Annual Decentralized Conference on Blockchain and Cryptocurrency

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“…, where γ i j are parameter vectors to be estimated the dimensions of which correspond to vector v t . Note that for the identification of transition probabilities for each i there is a j so that γ i j is a vector of zeros (see Kaufmann, 2015;Koki, Meligkotsidou, and Vrontos, 2020, for the detailed model specification and estimation procedures). The selection of the variables in v t determines the time-dependence in transition probabilities and is subject to empirical verification.…”

Section: Nonhomogenous Markov Switchingmentioning

confidence: 99%

Markov Switching

Song¹,

Woźniak²

2021

Oxford Research Encyclopedia of Economics and Finance

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Markov switching models are a family of models that introduces time variation in the parameters in the form of their state, or regime-specific values. This time variation is governed by a latent discrete-valued stochastic process with limited memory. More specifically, the current value of the state indicator is determined by the value of the state indicator from the previous period only implying the Markov property. A transition matrix characterizes the properties of the Markov process by determining with what probability each of the states can be visited next period conditionally on the state in the current period. This setup decides on the two main advantages of the Markov switching models: the estimation of the probability of state occurrences in each of the sample periods by using filtering and smoothing methods and the estimation of the state-specific parameters. These two features open the possibility for interpretations of the parameters associated with specific regimes combined with the corresponding regime probabilities. The most commonly applied models from this family are those that presume a finite number of regimes and the exogeneity of the Markov process, which is defined as its independence from the model’s unpredictable innovations. In many such applications, the desired properties of the Markov switching model have been obtained either by imposing appropriate restrictions on transition probabilities or by introducing the time dependence of these probabilities determined by explanatory variables or functions of the state indicator. One of the extensions of this basic specification includes infinite hidden Markov models that provide great flexibility and excellent forecasting performance by allowing the number of states to go to infinity. Another extension, the endogenous Markov switching model, explicitly relates the state indicator to the model’s innovations, making it more interpretable and offering promising avenues for development.

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“…Section 2.1. Secondly, we model the log-price series data using a novel Hidden Markov (regime switching) model, namely the non-homogeneous Pólya Gamma Hidden Markov model (NHPG) of [24], cf. Section 2.2.…”

Section: Introductionmentioning

confidence: 99%

Do Cryptocurrency Prices Camouflage Latent Economic Effects? A Bayesian Hidden Markov Approach

2020

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We study the Bitcoin and Ether price series under a financial perspective. Specifically, we use two econometric models to perform a two-layer analysis to study the correlation and prediction of Bitcoin and Ether price series with traditional assets. In the first part of this study, we model the probability of positive returns via a Bayesian logistic model. Even though the fitting performance of the logistic model is poor, we find that traditional assets can explain some of the variability of the price returns. Along with the fact that standard models fail to capture the statistic and econometric attributes—such as extreme variability and heteroskedasticity—of cryptocurrencies, this motivates us to apply a novel Non-Homogeneous Hidden Markov model to these series. In particular, we model Bitcoin and Ether prices via the non-homogeneous Pólya-Gamma Hidden Markov (NHPG) model, since it has been shown that it outperforms its counterparts in conventional financial data. The transition probabilities of the underlying hidden process are modeled via a logistic link whereas the observed series follow a mixture of normal regressions conditionally on the hidden process. Our results show that the NHPG algorithm has good in-sample performance and captures the heteroskedasticity of both series. It identifies frequent changes between the two states of the underlying Markov process. In what constitutes the most important implication of our study, we show that there exist linear correlations between the covariates and the ETH and BTC series. However, only the ETH series are affected non-linearly by a subset of the accounted covariates. Finally, we conclude that the large number of significant predictors along with the weak degree of predictability performance of the algorithm back up earlier findings that cryptocurrencies are unlike any other financial assets and predicting the cryptocurrency price series is still a challenging task. These findings can be useful to investors, policy makers, traders for portfolio allocation, risk management and trading strategies.

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Forecasting under model uncertainty: Non‐homogeneous hidden Markov models with Pòlya‐Gamma data augmentation

Cited by 15 publications

References 69 publications

Do Cryptocurrency Prices Camouflage Latent Economic Effects? A Bayesian Hidden Markov Approach

Do Cryptocurrency Prices Camouflage Latent Economic Effects? A Bayesian Hidden Markov Approach

Markov Switching

Do Cryptocurrency Prices Camouflage Latent Economic Effects? A Bayesian Hidden Markov Approach

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