Received: 31 October 2019
Revised: 2 May 2020
Accepted: 5 May 2020
DOI: 10.1002/qre.2673
RESEARCH ARTICLE
A hidden Markov model to detect regime changes in
cryptoasset markets
Paolo Giudici1
Iman Abu Hashish2
1
Department of Economics and
Management, University of Pavia, Pavia,
Italy
2
Department of Electrical, Computer and
Biomedical Engineering, University of
Pavia, Pavia, Italy
Correspondence
Paolo Giudici, Department of Economics,
University of Pavia, Via S. Felice 5, 27100
Pavia, Italy.
Email: giudici@unipv.it
Funding information
European Union's research and
innovation program “FIN-TECH: A
Financial supervision and Technology
compliance training programme”,
Grant/Award Number: 825215 (Topic:
ICT-35-2018 and Type of action: CSA).;
European Union's Horizon 2020,
Grant/Award Number: 825215
1
Abstract
The objective of this work is to understand the dynamics of cryptocurrency
prices. Specifically, how prices switch between different regimes, going from
“bull” to “stable” and “bear” times. For this purpose, we propose a hidden Markov model that aims at explaining the evolution of Bitcoin prices
through different, unobserved states. The implementation of the proposed
model includes a likelihood ratio test that allows to compare models with different states and with different covariance structures. Our empirical findings show
that the time movements of Bitcoin prices across different exchange markets are
well-described by the proposed model. In particular, a parsimonious model with
a diagonal covariance matrix leads to better predictions, compared with a model
with a full covariance matrix.
K E Y WO R D S
Bitcoin exchange markets, Bitcoin prices, hidden Markov models, likelihood ratio tests
BAC KG RO U N D
In the recent years, Financial Technology (FinTech) has been the center of attention due to its innovative solutions to
improve financial services (see, for instance, Schueffel1 ). Such solutions are mainly driven by three technologies, big
data analytics, artificial intelligence (AI), and blockchain technologies (see, for instance, Giudici2 ) and are affecting the
nature of the financial industry by creating new services that enable a wider level of inclusion to financial activities. In
particular, cryptocurrencies can be considered the main application of Blockchain technologies, and their popularity has
been growing significantly, along with their volatility, making it crucial to understand the dynamics of their prices.
The research on cryptocurrencies has been constantly growing, since Bitcoin was introduced by Satoshi Nakamoto.3
Corbet et al4 conducted a thorough systematic review of the research literature and reported that price dynamics is one
of the most popular research areas, together with market efficiency and cryptocurrency structure.
Crypto price dynamics was first investigated, from a theoretical viewpoint, by Dwyer5 who argued that the existence of a
quantity limit, along with the use of peer-to-peer networks, can create an economic equilibrium in which cryptocurrencies
have a positive value.
Trying to empirically understand the drivers of price dynamics, Bouoiyour et al6 applied a technique called empirical mode decomposition to assess Bitcoin prices formation and argued that, although Bitcoin is considered a speculative
asset, it is extremely driven by long-term fundamentals. However, Corbet et al7 studied the relationships between three
cryptocurrencies: Bitcoin, Litecoin, and Ripple, and their links with traditional financial assets, using a variance decomposition approach, and showed that the studied cryptocurrencies are strongly interconnected with each other and relatively
isolated from other financial assets. This result was confirmed by Ciaian et al,8 who applied autoregressive distributed lag
Qual Reliab Engng Int. 2020;1–9.
wileyonlinelibrary.com/journal/qre
© 2020 John Wiley & Sons, Ltd.
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GIUDICI AND ABU HASHISH
models to daily data of Bitcoin and other 16 cryptocurrencies and reported that the studied currencies are indeed interdependent among each other. They also found that the relationship is significantly stronger in the short-run rather than
in the long-run, consistently with the findings of Bouoiyour et al.6
Further arguments in favor of the endogenous nature of price dynamics have been provided by Blau,9 who studied the
dynamics of Bitcoin prices using GARCH models and found that price volatility does not depend on speculative trading,
and by Polasik et al,10 who provided a regression analysis of the investment characteristics of Bitcoin and found that
Bitcoin returns are mainly driven by endogenous causes, such as the sentiments on cryptocurrencies, or the total number
of transactions. Finally, along a similar line, Viglione11 found a positive relation in a cross-country correlation between
the level of technology and Bitcoin prices.
Recently, Giudici and Abu-Hashish12 proposed a vector autoregressive (VAR) model to understand the endogenous
nature of Bitcoin price dynamics and found that is largely driven by differences between the market exchanges in which
Bitcoins are traded. The present work develops this line of research employing, rather than a VAR model, a hidden Markov
model (HMM). While a VAR model directly models the dependency between the observed market exchange prices,
an HMM models the same dependency through the dynamics of its latent causes, attributed to time switches between
different market regimes.
In other words, to take into account the multivariate nature of cryptocurrency prices, we propose an HMM that explains
the time evolution of Bitcoin prices through the evolution of hidden unobserved states, which can be referred to different
equilibria of the crypto economy, consistently with the research of Dwyer.5 Doing so, we may be able to fully explain the
observed dependency between exchange prices that we previously found.12 This will be the case when, conditionally on
the latent state, Bitcoin exchange prices become independent (described by a diagonal covariance matrix) rather than still
interdependent (described by a full covariance matrix).
Our contribution to the literature is twofold. On one hand, as previously discussed, we contribute to the cryptocurrency
econometrics literature aimed at understanding the causes of Bitcoin price dynamics. On the other hand, we contribute
to the computational statistics literature, providing the implementation of an easy-to-use likelihood ratio test useful to
compare alternative HMM models.
The rest of the paper is organized as follows. In Section 2, we explain our proposed model and the data that will be
used to experiment it. In Section 3, the main empirical findings derived from the application of the model to the data are
presented. Finally, Section 4 contains some final remarks.
2
HIDDEN MARKOV C RY PTO MODELS
We propose to study price dynamics in cryptocurrency markets by means of HMMs.
A (discrete) HMM assumes that each observation Yt , for t = 1, … , T is generated by a stochastic process whose state Z
is a discrete random variable, hidden to the observer. The probability of observing Yt at any given time t can be described
by a statistical distribution, conditional on Zt , usually known up to a parameter 𝜃. It also assumes that the time transition
between subsequent states (Z1 , … , ZT ) follows a Markov chain, typically of first order.
More formally, the previous assumptions mean that the joint distribution of the observed time series Y1:T and of the
corresponding hidden states, Z1:T , can be factorized as follows:
P(Y1∶T , Z1∶T ) =
T
∏
P(Yt |Zt )P(Zt |Zt−1 ),
(2.1)
t=1
in which P(Z1 |Z0 ) = P(Z1 ) is the (unconditional) distribution of the initial state.
To further specify the probability distribution in ( 2.1), we need to define the conditional distributions P(Yt |Zt ) that link
the observed variables with the hidden states, the K × K state transition matrix which defines the conditional probabilities
P(Zt |Zt−1 ), and the probability distribution for the initial state P(Z1 ). HMMs are usually assumed to be time invariant,
which implies that the conditional distributions and the state transition matrices do not depend on t.
In our context, each observation Yt is a vector of market prices Yti , (i = 1, … , I; t = 1, … , T), one for each of the I
considered cryptocurrency exchanges. We assume that, at any given time point t, the vector Yt follows an HMM, specified
by the joint probability distribution in ( 2.1).
We also assume, given the multivariate nature of Yt , that each conditional distribution P(Yt |Zt ) is a multivariate Gaussian, with a zero mean vector and an unknown variance-covariance matrix 𝛴z , which depends on the state Z = z and
GIUDICI AND ABU HASHISH
Exchange market
Bitfinex
Bitstamp
Bittrex
Coinbase
Gemini
itBit
Kraken
Market share
13%
1%
1%
13%
0.3%
1%
10%
3
TABLE 1 Exchange markets by market share
which will be estimated using the available data, along with the transition matrix of the hidden states. The initial state
will be instead considered as a given constant value.
To apply the proposed model to the available data, we need to implement two computational algorithms: one to estimate the unknown parameters, and one to compare and test different model structures. The estimation of the unknown
parameters will be based on known methods. To estimate the variance covariance matrix, we will use the Maximum Likelihood Forward-Backward algorithm, and to estimate the transition matrix, we will use the Expectation Maximization
Baum-Welch algorithm.13
Differently, to compare alternative model structures, such as models with differing number of states, or models with
different variance-covariance matrices, we need to construct a new algorithm. To achieve this aim, we specifically implement in the Matlab software the likelihood ratio test statistics proposed by Giudici et al,14 which allows to compare a
diagonal covariance matrix model with a full covariance matrix model, for different number of states.
More precisely, we implemented the likelihood ratio (LR) statistics given by the following:
𝜆n = 2(Ln (𝜃̂n − Ln (𝜃̂0 )),
where 𝜃 n and 𝜃 0 are the maximum likelihood estimators under each of the considered models. Once the value of the LR
test is computed, the P value is calculated using the chi-square cumulative distribution function, with degrees of freedom
(d.f.) that vary depending on the considered model comparison.
The calculation of the LR statistics, and of the related P value, allows us to establish which model to select. It is of
interest, however, also to evaluate how accurate are the predictions obtained with the selected model. To perform this
task, we can employ our model to obtain forecasts on a (training) sample of data and, then, compare the forecasts with
the actual observations, on the remaining (test) set of data.
More formally, we implement the following procedure. Once the estimated values of the unknown parameters under the
selected model are obtained, we can insert them in equation (2.1) and accordingly calculate the conditional probability of
(Zt+1 ) given the series (Y1:T ), for each state Z. The state which receives the highest conditional probability is the predicted
state. Finally, the forecasts are obtained associating to the predicted state the mean of the exchange prices, under that
state.
To illustrate our proposed model, we consider, without loss of generality, the most important cryptocurrency: Bitcoin,
whose price in US dollars is observed. With no further loss of generality, and to reduce volatility issues, we consider daily
prices, obtained at the end of each day.
Our first aim is to assess whether Bitcoin prices in different exchange markets are correlated with each other, thus
exhibiting “endogenous” price variations. To understand this question, we have chosen a set of representative exchanges,
for which price data is available, in a sufficiently long period of time.
Specifically, we select seven of the most known exchanges: Bitfinex, Bitstamp, Bittrex, Coinbase, Gemini, ItBit, and
Kraken. The exchanges are reported in Table 1, along with their corresponding market shares, retrieved on November 21,
2018.15
From Table 1, note that the selected exchange markets represent about 40% of the total daily volume trades.
For each exchange market, we have collected daily closing data for a time period that goes from December 12, 2015,
to October 25, 2018. Data were obtained using the CryptoCompare API by implementing a Python script. This gives rise
to a database of 1,029 observations on seven variables. We remark that, differently from Giudici and Abu-Hashish,12 we
do not consider the HitBtc exchange market, as data is not available for the latest period of time. This is without loss of
generality, especially as HitBtc is a rather small market.
Figure 1 illustrates how Bitcoin prices evolved over the considered period of time, where each line in the figure
corresponds to the Bitcoin price evolution of one of the considered market exchanges.
4
GIUDICI AND ABU HASHISH
FIGURE 1 Bitcoin prices evolution over the considered period of
time [Colour figure can be viewed at wileyonlinelibrary.com]
TABLE 2 Summary statistics for Bitcoin prices
Price per exchange
Bitfinex
Bitstamp
Bittrex
Coinbase
Gemini
ItBit
Kraken
Mean
3,857.53
3,859.71
3,853.65
3,871.30
3,866.98
3,863.09
3,859.56
St. Dev.
4,025.72
4,035.09
4,023.48
4,059.16
4,050.82
4,045.71
4,031.61
Min
367.01
367.64
365.00
367.00
368.70
360.40
368.00
Max
19,210.00
19,187.78
19,261.10
19,650.00
19,499.99
19,357.97
19,356.90
Looking at Figure 1, it is obvious that Bitcoin prices in different exchange markets are highly correlated, but not perfectly
aligned. Moreover, at a first glance, prices went through different “equlibria” states: they were almost “stable” at the start
of the considered period of time until the beginning of 2017, when the well-known rise took place and the prices climbed
from a minimum of about 430 USD per Bitcoin to a maximum of almost 20,000 USD. This was followed by a fluctuation
in prices in 2018, a period of high volatility.
Table 2 shows a number of summary statistics for Bitcoin prices, complementary to Figure 1.
Table 2 confirms the divergence of Bitcoin prices within different exchange markets, not only in volatility and extreme
values but also in their mean, contrarily to the economic law of “one asset, one price.” Our hypothesis is that these
differences can be explained by endogenous relationships between market exchange prices, in turn explained by different
latent states of the crypto economy. From Table 2, note also that the standard deviation of the prices for the largest market
(Coinbase) is the highest.
In the next section, we apply our proposed model to empirically verify, on the available data, the validity of our
hypotheses.
3
EMPIRICAL FINDINGS
We considered three alternative types of hidden structures characterized, respectively, by two, three, and four hidden
states, conventionally labeled with (1, 2, 3, 4). We also considered two different types of variance-covariance matrices: a
full matrix and a more parsimonious diagonal matrix. Thus, we have a total of 3 × 2 alternative models. We will present,
unless otherwise specified, the results for a model with three states, both with a full and a diagonal matrix.
Figure 2 presents the time evolution of the three estimated hidden states, considering a full covariance matrix, and the
Bitstamp exchange market. The white line corresponds to periods in which the estimated hidden state is equal to zero,
the light purple line to periods in which the estimated hidden state is equal to one, and the dark purple line to periods in
which the estimated hidden state is equal to two.
From Figure 2, note that one hidden state is concentrated in the initial time period, when Bitcoin was relatively new and
rarely increasing, while the other two states alternate, between lower and higher prices, in the more recent time period.
GIUDICI AND ABU HASHISH
5
FIGURE 2 Time evolution of Bitstamp prices colored by
estimated hidden states with a full covariance matrix [Colour figure
can be viewed at wileyonlinelibrary.com]
FIGURE 3 Time evolution of Bitstamp prices colored by the
estimated hidden states with a diagonal covariance matrix [Colour
figure can be viewed at wileyonlinelibrary.com]
We remark that a full covariance matrix involves a model specification that assumes that, conditionally on the hidden
state, all exchanges are correlated with each other. This assumption may be too strong, as we expect that, the general
sentiment towards the bitcoin (for example, “bullish” or “bearish”), expressed by the hidden state, can explain most of
the pairwise correlations between the exchange prices, which thus become insignificant. For this reason, we consider a
more parsimonious model, characterized by a diagonal covariance matrix. This model implies that, conditionally on the
hidden state, the Bitcoin price of any market exchange is independent on the price of the others, at any time point. In
other words, the dynamics of the prices is fully explained by the dynamics of the hidden states, whereas the differences
between market exchanges are not significant.
Figure 3 presents the time evolution of the three estimated hidden states, considering a diagonal covariance matrix, and
the Bitstamp exchange market. Note that the first hidden state is still concentrated in the initial time period. However,
differently from what happens with a full covariance matrix, the second hidden state seems mostly concentrated in the
second period (a period in which the Bitcoin price was steadily rising), with the third state more spread, but concentrated
in the latest period.
Comparing the two previous graphs, it seems that, conditionally on having three states, a model with a diagonal
covariance matrix gives a better description of the “regime switches” implied by the data.
To confirm this result, from a more formal statistical viewpoint, we now calculate the chi-squared likelihood ratio test
statistics to compare a diagonal covariance matrix model with a full covariance matrix model, for three different number
of states (2, 3, or 4). Following what shown in Giudici et al,14 the degrees of freedom of the test can be obtained as the difference between the size of the parameter spaces under comparison. Recalling that we have 7 variables, when we compare
two models with different variance-covariance structure (full or diagonal) and the same number of states, the Chi squared
has thus, respectively, 14+14= 28 d.f. (two states), 14+14+14=42 d.f. (three states), and 14+14+14+14=56 d.f.(four states).
6
GIUDICI AND ABU HASHISH
TABLE 3 Likelihood ratio test—full versus diagonal covariance
Number of states
2
3
4
Likelihood ratio
51493.81
56931.07
50226.37
P value
3.12e − 51
2.34e − 54
7.12e − 49
TABLE 4 Likelihood ratio test—diagonal covariance
Number of states
3 vs. 2
3 vs. 4
Likelihood ratio
154.38
8440.61
P value
4.87e − 30
1.13e − 41
TABLE 5 Predictive performance (in terms of
root mean squared errors) of hidden Markov
models with two, three, or four states and,
respectively, a full or a diagonal variance
covariance matrix
Exchange 2
Bitfinex
Bitstamp
Bittrex
Coinbase
Gemini
itBit
Kraken
3
Full
2,498.78
2,491.52
2,598.19
2,467.18
2,478.71
2,424.51
2,503.19
Diagonal
2,802.85
2,798.33
2,792.86
2,800.36
2,793.26
2,821.31
2,792.50
4
Full
4,034.64
4,026.76
4,143.27
3,999.86
4,009.07
3,950.93
4,039.40
Diagonal
1,738.24
1,741.53
1,739.66
1,738.68
1,738.76
1,737.39
1,736.89
Full
4,898.90
4,889.83
5,013.77
4,861.94
4,871.61
4,809.42
4,903.52
Diagonal
708.67
741.29
740.42
733.07
734.05
739.42
737.94
Instead, when we compare two diagonal (full) models differing by one extra state, the chi-square distribution has 7
(21) d.f..
Table 3 presents the likelihood ratio test for the two considered covariance structures.
Table 3 clearly shows that a more parsimonious diagonal matrix model is always preferred to a full covariance matrix
model, for any number of states. This strongly supports our research hypotheses that market price and correlation
dynamics are fully explained by the dynamics of the unobserved, latent states.
To further assess which states configuration is more supported by the available data, we can compare, for a diagonal
covariance structure, models with different number of states. Table 4 shows the results.
From Table 4, note that the model with three states has a likelihood that is significantly higher than that of a simpler
model (two states), and than that of a more complex model (four states). Thus, the model which receives the highest
empirical likelihood from the observed data, and should therefore be selected, is a model with three hidden states. From an
economic viewpoint, this implies that the relatively young history of Bitcoin prices can be explained using three alternative
states of “bear,” “stable,” and “bull” markets.
Regardless of how it is constructed, any statistical model should be evaluated not only in terms of its likelihood, for the
data at hand, but also in terms of its predictive performance. To this aim, we now assess the predictive performance of our
proposed Hidden Markov model to understand if, besides being a good explainable model, it is also able to well predict
Bitcoin prices.
To this aim, we build our model with 80% of the data using the remaining 20% of the data as a test set. With the obtained
model, we predict the Bitcoin prices for the days in the test set, employing 1-day ahead rolling predictions, and compare
the predictions with the actual prices. Table 5 contains, for each exchange price, the root-mean-squared errors (RMSE)
of the predictions, for two, three, or four state models, respectively, using a full or diagonal variance covariance matrix.
Table 5 shows that the predictive performance of the proposed models is, overall, similar with RMSE of similar magnitudes. However, looking in detail, differences emerge. When a full covariance matrix is considered, the Bittrex exchange
(one of the least traded) is the most difficult to predict, and the itBit, along with the Coinbase exchange (one of the most
traded) is the least difficult to predict. When a diagonal covariance matrix is considered, errors are again similar, with
Bitstamp, the most traded, the most difficult to predict. This is consistent with the fact that highest volume exchanges are
more volatile and, therefore, more difficult to predict.
Table 5 also shows that the RMSE of the eight Bitcoin price predictions, under a diagonal covariance matrix, are always
lower than those obtained with a full matrix. A diagonal variance-covariance structure is therefore preferable, in line with
the likelihood ratio test results.
To further investigate the previous results, we could compare, from a predictive viewpoint, a diagonal and a full covariance matrix model, conditionally on a number of states equal to 4 (higher than before) and equal to 2 (lower than before).
Our results show that for the four states model, the predictive performance is significantly higher (lower RMSE) for a
diagonal covariance matrix, compared with a full one, in line with the results obtained with a three model states. Instead,
GIUDICI AND ABU HASHISH
Exchange
Bitfinex
Bitstamp
Bittrex
Coinbase
Gemini
ItBit
Kraken
RMSE VAR full
2,930.08
6,391.32
2,385.40
2,443.09
3,118.26
2,590.79
2,328.68
7
RMSE VAR diagonal
2,932.76
6,937.22
2,384.34
2,442.40
3,118.30
2,593.70
2,327.65
RMSE VAR equal
2,634.43
4,007.66
2,553.75
2,573.80
2,946.33
2,972.04
2,541.80
RMSE neural
2,256.44
2,056.24
2,242.83
2,183.24
2,050.66
2,283.33
2,028.67
TABLE 6 Predictive performance
of vector autoregressive models with,
respectively, a full, diagonal or equal
variance covariance matrix, and a
neural network with one hidden layer
and three nodes
Abbreviations: RMSE, tablenotes; VAR, vector autoregressive.
for the two states model, the full matrix model shows a slightly better performance. This is consistent with the fact that
the model with two states is very parsimonious and, therefore, the need to have a full covariance matrix emerges, as the
number of hidden states is too low to explain price dynamics.
To assess the merits of the proposed model, we should also compare it with possible competitors, either among more
classic econometric models or among machine learning models. Table 6 shows the RMSE of four different models: a VAR
model with a full variance-covariance matrix, a VAR model with a diagonal matrix, an “intermediate” VAR model with
a full variance-covariance matrix made up of equal correlations, and, finally, a neural network model, with one hidden
layer made up of three hidden nodes.
Comparing Table 6 with Table 5, note that our proposed hidden model, with a diagonal covariance matrix, is preferable
over VAR and neural network models, for all considered exchanges. However, a less parsimonious hidden model, with a
full covariance matrix, is worse than both VAR and neural models. This is consistent with the previously found results.
Note also that the neural network model, the one that more closely resembles hidden Markov models, is the second best
performing model. Note also that choosing an equal correlation structure does not help reducing the RMSE of a full
covariance matrix, in a substantial way.
4
CO NCLUDING REMARKS
In this paper, we have proposed a model that explains the observed time dynamics of Bitcoin prices, in different market
exchanges, by means of the latent time dynamics of a number of latent states, using an HMM that can model the regime
switches between different price vectors.
The model is quite general and can be extended to compare any number of exchange markets and any number of hidden
states, thanks to the employed likelihood ratio test strategy. It also shows a good predictive performance, when applied to
predict Bitcoin prices in an out-of-sample exercise.
We believe that our model could be extended to the simultaneous analysis of different cryptoassets, rather than different
exchanges, although the latter case is bound to be affected by a varying traded volume size. Another interesting extension
could be to apply the model to intra-day data, although this may involve a large price volatility, due to low liquidity effects.
Further directions of research may involve to overcome the limitations of the multivariate Gaussian assumption adopted
here. It is well known that Bitcoin price data are heavy tailed, and indeed our data confirm this assumption, according to the Shapiro-Wilk test statistics. Our model can thus be seen as a first approximation, to be improved within a
nonparametric context,16,17 or in a Bayesian context.18
ACKNOWLEDGMENTS
The authors would like to thank their colleagues at the FinTech lab of the University of Pavia for conducting useful
discussions. They also acknowledge useful discussion and suggestions from two anonymous referees. The research in the
paper has received funding from the European Union's Horizon 2020 research and innovation program “FIN-TECH: A
Financial supervision and Technology compliance training programme” under the grant agreement No. 825215 (Topic:
ICT-35-2018, Type of action: CSA).
ORCID
Paolo Giudici
https://orcid.org/0000-0002-4198-0127
8
GIUDICI AND ABU HASHISH
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AU THOR BIOGRAPHIES
Paolo Giudici is Professor of Statistics and Data Science at the Department of Economics and Management of the
University of Pavia. Academic supervisor of about 180 master's students and of 15 PhD students, currently working in
the financial industry, in IT/consulting companies or as academic researchers. Author of several scientific publications
(83 in Scopus, with 1,190 total citations and an h-index of 20). The main contributions to research are on the following:
multivariate graphical models; network models for financial stability; correlation networks for financial technologies;
operational risk management models; Bayesian data analysis; and model diagnostics, predictive accuracy, and explainability. Coordinator of 11 funded scientific projects, among which the European Horizon 2020 project “FIN-TECH:
Financial supervision and Technological compliance” (2019-2020) and the European VI programme project on “Multi
industry semantic based business intelligence” (2006-2010). Chief Editor of “Artificial Intelligence in Finance,” Frontiers. Associate Editor of “Digital Finance,” Springer and of “Risks,” MDPI. Researcher with CEPS on the monitoring of
COVID-19 contagion. Research fellow at the Bank for International Settlements, Basel. Research fellow at the University College London center for Blockchain technologies. Expert at the European Insurance and Occupational Pensions
Authority (EIOPA). Expert at the Italian ministry of development for the National AI strategy. Member of the scientific committee of the Association of Italian Financial Risk Managers, AssoFintech, the Cryptovalues association.
Member of the following: Italian Statistical Society(SIS), Italian Econometric Society (SIDE), European Big Data Value
Association (BDVA), European Network for Business and Industrial Statistics (ENBIS), and International Society for
Bayesian Analysis (ISBA). Principal investigator of research, training, and consulting projects for the following: the
Italian Banking Association, Intesa SanPaolo, Unicredit, UBI, BancoBpm, MPS, BPS, Creval, Accenture, KPMG, SAS,
Mediaset, and Sky.
Iman Abu Hashish received her PhD degree in Computer Engineering from the University of Pavia, Italy, in February
2020. She specializes in applied data science approaches with a particular interest in the domain of Financial Technology (FinTech). She is a review editor in Frontiers in Artificial Intelligence journal in the section of Artificial Intelligence
in Finance. Her research interests include artificial intelligence, domain-specific data science applications, machine
GIUDICI AND ABU HASHISH
learning, and deep learning. Dr Abu Hashish has several national and international publications in highly recognized
journals and IEEE conference proceedings.
How to cite this article: Giudici P, Abu Hashish I. A Hidden Markov Model to Detect Regime Changes in
Cryptoasset Markets. Qual Reliab Engng Int. 2020;1-9. https://doi.org/10.1002/qre.2673
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