This thesis is an investigation of the time changing nature of financial markets. Financial
markets are complex systems having an intrinsic structure defined by the interplay of several
variables. The technological advancements of the ’digital age’ have exponentially increased
the amount of data available to financial researchers and industry professionals over the last
decade and, as a consequence, it has highlighted the key role of iterations amongst variables.
A critical characteristic of the financial system, however, is its time changing nature:
the multivariate structure of the systems changes and evolves through time. This feature
is critically relevant for classical statistical assumptions and has proven challenging to be
investigated and researched. This thesis is devoted to the investigation of this property,
providing evidences on the time changing nature of the system, analysing the implications
for traditional asset allocation practices and proposing a novel methodology to identify and
predict ‘market states’.
First, I analyse how classical model estimations are affected by time and what are the
consequential effects on classical portfolio construction techniques. Focusing on elliptical
models of daily returns, I present experiments on both in-sample and out-of-sample likelihood
of individual observations and show that the system changes significantly through
time. Larger estimation windows lead to stable likelihood in the long run, but at the cost of
lower likelihood in the short-term. A key implication of these findings is that the optimality
of fit in finance needs to be defined in terms of the holding period. In this context, I also
show that sparse models and information filtering significantly cope with the effects of non
stationarity avoiding the typical pitfalls of conventional portfolio optimization approaches.
Having assessed and documented the time changing nature of the financial system, I
propose a novel methodology to segment financial time series into market states that we
call ICC - Inverse Covariance Clustering. The ICC methodology allows to study the evolution of the multivariate structure of the system by segmenting the time series based on
their correlation structure. In the ICC framework, market states are identified by a reference
sparse precision matrix and a vector of expectation values. In the estimation procedure,
each multivariate observation is associated to a market state accordingly to a minimisation
of a penalized distance measure (e.g. likelihood, mahalanobis distance). The procedure is
made computationally very efficient and can be used with a large number of assets. Furthermore,
the ICC methodology allows to control for temporal consistency,S making it of
high practical relevance for trading systems. I present a set of experiments investigating
the features of the discovered clusters and comparing it to standard clustering techniques. I
show that the ICC methodology is successful at clustering different states of the markets in
an unsupervised manner, outperforming baseline standard models. Further, I show that the
procedure can be efficiently used to forecast off-sample future market states with significant
prediction accuracy.
Lastly, I test the significance of increasing number of states used to model equity returns
and how this parameter relates to the number of observations and the time consistency
of the states. I present experiments to investigate a) the likelihood of the overall model as
more states are spanned, b) the relevance of additional regimes measured by the number of
observations clustered. I found that the number of “market states” that optimally define the
system is increasing with the time spanned and the number of observations considered
