Clustering heteroskedastic time series by model-based procedures

Financial time series are often characterized by similar volatility structures, often represented by GARCH processes. The detection of clusters of series displaying similar behavior could be important to understand the differences in the estimated processes, without having to study and compare the estimated parameters across all the series. This is particularly relevant dealing with many series, as in financial applications. The volatility of a time series can be characterized in terms of the underlying GARCH process. Using Wald tests and the AR metrics to measure the distance between GARCH processes, it is possible to develop a clustering algorithm, which can provide three classifications (with increasing degree of deepness) based on the heteroskedastic patterns of the time series. The number of clusters is detected automatically and it is not fixed a priori or a posteriori. The procedure is evaluated by simulations and applied to the sector indexes of the Italian marke

On methods to assess the significance of community structure in networks of financial time series

We consider the problem of determining whether the community structure found by a clustering algorithm applied to nancial time series is statistically signi cant, or is due to pure chance, when no other information than the observed values and a similarity measure among time series are available. As a subsidiary problem we also analyse the in uence of the choice of similarity measure in the accuracy of the clustering method. We propose two raw-data based methods for assessing robustness of clustering algorithms on time-dependent data linked by a relation of similarity: One based on community scoring functions that quantify some topological property that characterises ground-truth communities, and another based on random perturbations and quanti cation of the variation in the community structure. These methodologies are well-established in the realm of unweighted networks; our contribution are versions of these methodologies properly adapted to complete weighted networks.Peer ReviewedPostprint (published version

Testing for a set of linear restrictions in varma models using autoregressive metric: An application to granger causality test

In this paper we propose a test for a set of linear restrictions in a Vector Autoregressive Moving Average (VARMA) model. This test is based on the autoregressive metric, a notion of distance between two univariate ARMA models, M 0 and M 1 , introduced by Piccolo in 1990. In particular, we show that this set of linear restrictions is equivalent to a null distance d(M 0 , M 1 ) between two given ARMA models. This result provides the logical basis for using d(M 0 , M 1 ) = 0 as a null hypothesis in our test. Some Monte Carlo evidence about the finite sample behavior of our testing procedure is provided and two empirical examples are presented

Clustering mutual funds by return and risk levels

Mutual funds classifications, often made by rating agencies, are very common and sometimes criticized. In this work, a three-step statistical procedure for mutual funds classification is proposed. In the first step time series funds are characterized in terms of returns. In the second step, a clustering analysis is performed in order to obtain classes of homogeneous funds with respect to the risk levels. In particular, the risk is defined starting from an Asymmetric Threshold-GARCH model aimed todescribe minimum, normal and turmoil risk. The third step merges the previous two. An application to 75 European funds belonging to 5 different categories is given

On the classification of financial data with domain agnostic features

We compare a data-driven domain agnostic set of canonical features with a smaller collection of features that capture well-known stylized facts about financial asset returns. We show that these facts discriminate better different asset types than general-purpose features. Therefore, financial time series analysis is a domain where well-informed expert knowledge may not be disregarded in favor of agnostic representations of the data.info:eu-repo/semantics/publishedVersio

Tracing the temporal evolution of clusters in a financial stock market

We propose a methodology for clustering financial time series of stocks' returns, and a graphical set-up to quantify and visualise the evolution of these clusters through time. The proposed graphical representation allows for the application of well known algorithms for solving classical combinatorial graph problems, which can be interpreted as problems relevant to portfolio design and investment strategies. We illustrate this graph representation of the evolution of clusters in time and its use on real data from the Madrid Stock Exchange market.Comment: 22 pages, 3 figures (submitted for publication

Clustering of time series via non-parametric tail dependence estimation

We present a procedure for clustering time series according to their tail dependence behaviour as measured via a suitable copula-based tail coefficient, estimated in a non-parametric way. Simulation results about the proposed methodology together with an application to financial data are presented showing the usefulness of the proposed approach

On methods to assess the significance of community structure in networks of financial time series

We consider the problem of determining whether the community structure found by a clustering algorithm applied to financial time series is statistically significant, when no other information than the observed values and a similarity measure among time series is available. We propose two raw-data based methods for assessing robustness of clustering algorithms on time-dependent data linked by a relation of similarity: One based on community scoring functions that quantify some topological property that characterizes ground-truth communities, the other based on random perturbations and quantification of the variation in the community structure. These methodologies are well-established in the realm of unweighted networks; our contribution are versions adapted to complete weighted networks. We reinforce our assessment of the accuracy of the clustering algorithm by testing its performance on synthetic ground-truth communities of time series built through Monte Carlo simulations of VARMA processes