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MADDALENA CAVICCHIOLI

Ricercatore t.d. art. 24 c. 3 lett. B presso: Dipartimento di Economia "Marco Biagi"


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Pubblicazioni

2021 - A matrix approach to the Beveridge-Nelson decomposition of Markov-Switching processes with applications to business cycle [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We provide simple matrix formulas for calculation of the Beveridge-Nelson decomposition in the Markov-switching multivariate case, where series are generated by vector ARIMA models with Markov-switching intercept term. The treatment is immediately extended for regime changes in the mean, distributed lags in the regime and cointegrated models with Markov switching. We apply the method to real data from an example representative of recently industrialized economies and from a classical study on US business cycle.


2021 - Learning from failure. Big data analysis for detecting the patterns of failure in innovative startups [Articolo su rivista]
Cavicchioli, M.; Kocollari, U.
abstract

This paper aims at identifying appropriate models for analyzing large dataset to serve a twofold goal: firstly, to better understand the dynamics impacting innovative startups’ performance and their managerial practice and, secondly, to detect their patterns of failure. Therefore, we investigate the interaction of economic-financial, context and governance dimensions of 4,185 Italian innovative startups created from 2012 to 2015. Once startups have been grouped, we focus only on those unsuccessful. Then failure patterns have been uncovered integrating the use of factor and cluster analysis, where factor scores for each firm are used to identify a set of homogeneous groups based on clustering methods. The integrated use of those large dimensional data techniques permits to classify items in rigorous ways and to unfold structures of the data, which are not apparent in the beginning. The analysis suggests that each pattern of failure is a multidimensional construct and as a consequence can generate different managerial implications. Therefore, an effective handling of failure requires management to use appropriate intervention targeted at the challenges faced at that particular pattern of failure in different firm’s age.


2021 - Statistical Inference for Mixture GARCH Models with Financial Application [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In this paper we consider mixture generalized autoregressive conditional heteroskedastic models, and propose a new iteration algorithm of type EM for the estimation of model parameters. The maximum likelihood estimates are shown to be consistent, and their asymptotic properties are investigated. More precisely, we derive simple expressions in closed form for the asymptotic covariance matrix and the expected Fisher information matrix of the ML estimator. Finally, we study the model selection and propose testing procedures. A simulation study and an application to financial real series illustrate the results.


2020 - A note on the asymptotic and exact Fisher information matrices of a Markov switching VARMA process [Articolo su rivista]
Cavicchioli, M.
abstract

We study the asymptotic and exact Fisher information (FI) matrices of Markov switching vector autoregressive moving average (MS VARMA) models. In a related paper (2017), we propose a method to derive an explicit expression in closed form for the asymptotic FI matrix of the underlying model, and use such a matrix to derive the asymptotic covariance matrix of the Gaussian maximum likelihood (ML) estimator of the parameters in the MS VARMA model. In this paper, the exact FI matrix of a Gaussian MS VARMA process is considered for a time series of length T in relation to the exact ML estimation method. Furthermore, we prove that the Gaussian exact FI matrix converges in probability to the asymptotic FI matrix when the sample size T goes to infinity.


2020 - Generalised Cepstral Models for the Spectrum of Vector Time Series [Articolo su rivista]
Cavicchioli, Maddalena
abstract

The paper treats the modeling of stationary multivariate stochastic processes via a frequency domain model expressed in terms of cepstrum theory. The proposed model nests the vector exponential model of Holan et al. (2017) as a special case, and extends the generalised cepstral model of Proietti and Luati (2019) to the multivariate setting, answering a question raised by the last authors in their paper. Contemporarily, we extend the notion of generalised autocovariance function of Proietti and Luati (2015) to vector time series. Then we derive explicit matrix formulas connecting generalised cepstral and autocovariance matrices of the process, and prove the consistency and asymptotic properties of the Whittle likelihood estimators of model parameters. Asymptotic theory for the special case of the vector exponential model is a signi ficant addition to the paper of Holan et al. (2017). We also provide a mathematical machinery, based on matrix differentiation, and computational methods to derive our results, which differ signi ficantly from those employed in the univariate case. The utility of the proposed model is illustrated through Monte Carlo simulation from a bivariate process characterized by a high dynamic range, and an empirical application on time varying minimum variance hedge ratios through the second moments of future and spot prices in the corn commodity market.


2020 - Invertibility and VAR Representations of Time-Varying Dynamic Stochastic General Equilibrium Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

I study the invertibility problem for time-varying Dynamic Stochastic General Equilibrium (DSGE) models. The question of interest is whether the shocks of a time-varying DSGE model can be recovered from an infinite time-varying VAR on the observable variables. Then I focus on DSGE models whose coefficients are driven by a Markov chain, and propose tractable methods to check their invertibility. Finally, I illustrate the validity of such methods via computations and examples. My results relate with the works of Amisano and Tristani (2010, 2011), Bekiros and Paccagnini (2013), Hallin (1980, 1983, 1986), Francq and Zako¨ıan (2001), and Franchi et al. (2013, 2015).


2020 - Nonresponse and measurement errors in income: matching individual survey data with administrative tax data [Working paper]
Lalla, M.; Cavicchioli, M.
abstract

A (local) survey on income carried out in the city of Modena in 2002 generated four categories of units: interviewees, refusals, noncontacts, and sometimes unused reserves. In this study, all units were matched with their corresponding records in the Ministry of Finance 2002 databases for fiscal incomes of 2001 and the 2001 Census. Considering all four categories, participation increased by education level and activity status, while it decreased among low or high incomes. Considering interviewees only, over- and under-reporting, as well as measurement errors, were investigated by comparing the surveyed income with fiscal income. Age and level of income were the main covariates affecting the behaviours of taxpayers.


2020 - Spectral Representation and Autocovariance Structure of Markov Switching DSGE Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We investigate the L2-structure of Markov switching Dynamic Stochastic General Equilibrium (MS DSGE) models and derive conditions for strict and second-order stationarity. Then we determine the autocovariance function of the process driven by a stationary MS DSGE model and give a stable VARMA representation of it. It turns out that the autocovariance structure of the process coincides with that of a standard VARMA. Finally, we propose a method to derive the spectral density in a matrix closed-form of MS DSGE models. Our results relate with the works of Francq and Zakoian, Krolzig, Zhang and Stine. Numerical and empirical illustrations complete the paper.


2020 - Unfolding the relationship between mortality, economic fluctuations and health in Italy [Articolo su rivista]
Cavicchioli, Maddalena; Pistoresi, Barbara
abstract

Despite the long run strong negative association between economic development and mortality, their short run relationship remains controversial. In the present work, we study comovement between mortality growth (overall, gender- and cause-specific) and economic fluctuations in Italy over the period 1862-2013. To this aim, we use Johansen (1991) procedure to jointly estimate the short and long run dynamics of the two variables, avoiding omitted variable bias in the cyclical co-movement extraction or spurious association attributable to trends. We also take into account possible asymmetric responses of mortality growth to shocks in GDP. We find that an increase of 1% in real GDP per capita induces a reduction in mortality rate of 0.27% for total population. Moreover, we observe that business cycle fluctuations do not affect mortality in the prewars era, where only the long run decrease matters driven by reduction in infections and accidents mortality. On the contrary, in the post-wars period, expansive phases of business cycle are associated with reduction in mortality growth and periods of recession generate an ever-deeper decrease. However, in this period, mortality for cancer is procyclical and significantly increasing in expansion: this reinforces the debate for controlling environmental factors.


2019 - Fourth Moment Structure of Markov Switching Multivariate GARCH Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We derive sufficient conditions for the existence of second and fourth moments of Markov switching multivariate generalized autoregressive conditional heteroscedastic processes in the general vector specification. We provide matrix expressions in closed form for such moments, which are obtained by using a Markov switching vector autoregressive moving-average representation of the initial process. These expressions are shown to be readily programmable in addition of greatly reducing the computational cost. As theoretical applications of the results, we derive the spectral density matrix of the squares and cross products, propose a new definition of multivariate kurtosis measure to recognize heavy-tailed features in financial real data, and provide a matrix expression in closed form of the impulse-response function for the volatility. An empirical example illustrates the results.


2019 - Learning from failure. Big Data analysis for detecting the patterns of failure in innovative startups [Relazione in Atti di Convegno]
Kocollari, Ulpiana; Cavicchioli, Maddalena
abstract

The purpose of the paper is to individuate appropriate models for analyzing large dataset in order to detect the patterns of failure in the case of innovative startups and understand the interaction of their economic, context and governance variables and their influence over the different patterns. The study is based on financial, governance and context data of all 180 Italian innovative startups failed from 2012 to 2015. The considered sample collects data on the entire population of Italian unsuccessful startups, so it is representative of this population as a whole. Failure patterns have been uncovered integrating the use of factor and cluster analyses, where the factor scores for each firm are used to identify a set of homogenous groups based on cluster analysis. The integrated use of those large dimensional data techniques permits to classify the data in rigorous ways and to unfold structures of the data, which are not apparent in the beginning. The analysis suggests that each pattern of failure is a multidimensional construct and as a consequence can generate different managerial implications. Therefore, an effective handling of failure requires management to use appropriate intervention targeted at the challenges faced at that particular pattern of failure in different firm’s age.


2018 - A HYBRID TOOL FOR HYBRID PROJECTS: HOW CROWDFUNDING CAN SCALE THE IMPACT OF SOCIAL ENTREPRENEURSHIP [Abstract in Atti di Convegno]
Kocollari, Ulpiana; Pedrazzoli, Alessia; Cavicchioli, Maddalena
abstract

Crowdfunding (CFD) is particularly relevant nowadays because it can support the growth of social oriented ventures and it can be seen as a hybrid financial tool. Its characteristics match with hybrid organizations aims, helping them in achieving the multiple purposes that they pursue. In fact, CFD combines the features of being at the same time a financial and a communication tool: it adds to financial support other benefits for social entrepreneurship as for example the attraction of media attention, the collection of market information and the opportunity to test social ideas and products to a large scale of potential beneficiaries. Therefore, CFD investors’ decisions are guided by both economic output and social value commitment. Academic research has demonstrated that there is a strict connection between CFD and social entrepreneurship as social dimension of the project is a signal of additional legitimacy for the crowd and can influence the campaign success. Reaching the CFD campaigns goals, social entrepreneur can promote both the economic and social sustainability of the initiative and foster dissemination to its actual and potential stakeholders. Even if the social orientation of the venture influences CFD success, less is known about the role of CFD in scaling social impact of the project through the campaign. In fact, scaling social impact is fundamental to the process of solving social problems through entrepreneurial activities. Studies on this topic individuate three different strategies used by social organization to scale their social impact: branching, affiliation, and dissemination. In particular, the dissemination one, that consists in increasing impact without expanding the organization size and revealing which elements of the project are relevant for the impact thriving, fits with CFD campaign aims. In this realm, the aim of this study is to investigate the role of CFD – as a hybrid financing tool, in scaling social impact through the campaign dissemination. In the case of CFD, the competencies attributed to social entrepreneur to promote social change - organizing, communicating and evaluating - are extended to the campaign tasks. On this vein, information about social projects published on three worldwide operating CFD platforms (Indiegogo, Chuffed.org and Startsomegood) are collected and subdivided in the three areas where scaling can be promoted. In particular, variables related to the organizing task is detected in the presence of a structured group or institutional supporters in the campaign, for promoting further the CFD project; concerning the communication purposes CFD variables can refer to the online entrepreneur’s relational power, campaign updates and comments; finally variables for evaluating CFD progress are those related to accountability of organizations instruments (as the presence of inputs, activities, social impact description, financial projections and business plan). The dependent variable - the scaling power of CFD social campaigns - is measured by the number of supporters (backers) involved through their economic (financing amount) and social (campaign shares in the web context) commitment to the project. From a practical perspective, the results contribute in the individuation of hybrid frameworks and tools for scaling social impact of social entrepreneurs engaged in CFD campaigns. From a theoretical perspective, the study advances the hybridization concepts matching the ones concerning organization design and the financing tool. Furthermore, these hybridization features are determinant for the scalability of the multi-purposes projects addressing social problems.


2018 - A Random Forests Approach to Assess Determinants of Central Bank Independence [Articolo su rivista]
Cavicchioli, Maddalena; Papana, Angeliki; Papana Dagiasis, Ariadni; Pistoresi, Barbara
abstract

In this paper we implement an efficient non-parametric statistical method, Random survival forests, for the selection of the determinants of Central Bank Independence (CBI) among a large database of political and economic variables for OECD countries. This statistical technique enables us to overcome omitted variables and overfitting problems. It turns out that the economic variables are major determinants compared to the political ones and linear and nonlinear effects of chosen predictors on CBI are found.


2018 - On mixture autoregressive conditional heteroskedasticity [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We consider mixture univariate autoregressive conditional heteroskedastic models, both with Gaussian or Student t-distributions, which were proposed in the literature for modeling nonlinear time series. We derive sufficient conditions for second order stationarity of these processes. Then we propose an algorithm in matrix form for the estimation of model parameters, and derive a formula in closed form for the asymptotic Fisher information matrix. Our results are proved by using the theory of time series models with Markov changes in regime. An illustrative example of the theoretical results and a real application on financial data complete the paper.


2018 - Statistical Analysis of Markov Switching DSGE Models [Relazione in Atti di Convegno]
Cavicchioli, Maddalena
abstract

We investigate statistical properties of Markov switching Dynamic Stochastic General Equilibrium (MS DSGE) models: L2 structure, stationarity, autocovariance function, and spectral density.


2017 - Asymptotic Fisher information matrix of Markov switching VARMA models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We study the Fisher information (FI) matrix of Markov switching vector autoregressive moving average (MS VARMA) models and derive an explicit expression in closed form for the asymptotic FI matrix of the underlying model. Our result is more general than the available one in the literature for linear VARMA models, which has been recently studied in Bao and Hua (2014), in two respects. First, we treat the variance of the error term in a more general setting rather than considering it as a nuisance parameter. Then, we consider non-trivial intercept in the MS VARMA model. Under general conditions, the asymptotic FI matrix can be used to derive the asymptotic covariance matrix of the Gaussian maximum likelihood estimator of the model parameters. Some examples and numerical applications illustrate the results.


2017 - Central Bank Independence, Financial Instability and Politics: New Evidence for OECD and Non-OECD Countries [Articolo su rivista]
Pistoresi, Barbara; Cavicchioli, Maddalena; Brevini, G.
abstract

This paper analyses the determinants of a new index of central bank independence, recently provided by Dincer and Eichengreen (2014), using a large database of economic, political and institutional variables. Our sample includes data for 31 OECD and 49 non-OECD economies and covers the period 1998-2010. To this aim, we implement factorial and regression analysis to synthesize information and overcome limitations such as omitted variables, multicollinearity and overfitting. The results confirm the role of the IMF loans program to guide all the economies in their choice of more independent central banks. Financial instability, recession and low inflation work in the opposite direction with governments relying extensively on central bank money to finance public expenditure and central banks’ political and operational autonomy is inevitably undermined. Finally, only for non-OECD economies, the degree of central bank independence responds to various measures of strength of political institutions and party political instability.


2017 - Central Bank Independence, financial instability and politics: new evidence for OECD and non-OECD countries [Working paper]
Pistoresi, B.; Cavicchioli, M.; Brevini, G.
abstract

This paper analyses the determinants of a new index of central bank independence, recently provided by Dincer and Eichengreen (2014), using a large database of economic, political and institutional variables. Our sample includes data for 31 OECD and 49 non-OECD economies and covers the period 1998-2010. To this aim, we implement factorial and regression analysis to synthesize information and overcome limitations such as omitted variables, multicollinearity and overfitting. The results confirm the role of the IMF loans program to guide all the economies in their choice of more independent central banks. Financial instability, recession and low inflation work in the opposite direction with governments relying extensively on central bank money to finance public expenditure and central banks’ political and operational autonomy is inevitably undermined. Finally, only for non-OECD economies, the degree of central bank independence responds to various measures of strength of political institutions and party political instability.


2017 - Estimation and asymptotic covariance matrix for stochastic volatility models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In this paper we compute the asymptotic variance-covariance matrix of the method of moments estimators for the canonical Stochastic Volatility model. Our procedure is based on a linearization of the initial process via the log-squared transformation of Breidt and Carriquiry (Modelling and prediction, honoring Seymour Geisel. Springer, Berlin, 1996). Knowledge of the asymptotic variance-covariance matrix of the method of moments estimators offers a concrete possibility for the use of the classical testing procedures. The resulting asymptotic standard errors are then compared with those proposed in the literature applying different parameter estimates. Applications on simulated data support our results. Finally, we present empirical applications on the daily returns of Euro-US dollar and Yen-US dollar exchange rates.


2017 - Higher order moments of Markov switching VARMA models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In this paper we derive matrix formulae in closed form for higher order moments and give sufficient conditions for higher order stationarity of Markov switching VARMA models. We provide asymptotic theory for sample higher order moments which can be used for testing multivariate normality. As an application, we propose new definitions of multivariate skewness and kurtosis measures for such models, and relate them with the existing concepts in the literature. Our work completes the statistical analysis developed in the fundamental paper of Francq and Zakoian (2001) and relates with the concepts of multivariate skewness and kurtosis proposed by Mardia (1970), Mori et al. (1993), and Kollo (2008). Under suitable assumptions, our results imply that the sample estimators of the skewness and kurtosis measures proposed by these authors are consistent and asymptotically normally distributed. Finally, we check our theory statements numerically via Monte Carlo simulations.


2017 - Markov Switching GARCH Models: Filtering, Approximations and Duality [Capitolo/Saggio]
Billio, Monica; Cavicchioli, Maddalena
abstract

This paper is devoted to show duality in the estimation of Markov Switching (MS) GARCH processes. It is well-known that MS GARCH models suffer of path dependence which makes the estimation step unfeasible with usual Maximum Likelihood procedure. However, by rewriting the model in a suitable state space representation, we are able to give a unique framework to reconcile the estimation obtained by filtering procedure with that coming from some auxiliary models proposed in the literature. Estimation on short-term interest rates shows the feasibility of the proposed approach.


2017 - Matrix Algebra and Invertibility Conditions for Linear Dynamic Stochastic General Equilibrium Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In this paper we analyze a class of state space models, called standard Dynamic Stochastic General Equilibrium (DSGE) models. Then we give necessary and sufficient conditions for the existence of infinite resp. finite order vector moving average (VMA) and vector autoregressive (VAR) representations of such models. Minimality of state space solutions of DSGE models is also discussed, and we show that it is very important in proving the necessary part of our statements. We also provide simple conditions for VARMA representations of DSGE models. The results are proved by using techniques of matrix algebra. Applications on classes of DSGE models currently used in economic analysis complete the paper.


2017 - Third and fourth moments of vector autoregressions with regime switching [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We derive matrix formulae in closed form for the unconditional third and fourth moments of a broad class of vector autoregressive time series with regime switching. First and second moments are well-known. New measures of multivariate skewness and kurtosis are introduced and basic properties are investigated. The knowledge of series level, variation, co-movements, skewness and kurtosis are useful to support model interpretation in real data application. Numerical examples complete the paper.


2016 - Determinants of Central Bank independence: a random forest approach [Working paper]
Cavicchioli, M.; Angeliki, Papana; Papana Diagasis, A.; Pistoresi, B.
abstract

In this paper we implement an effcient non-parametric statistical method, Random survival forests, for the selection of the determinants of Central Bank Independence (CBI) among a large data base of political and economic variables for OECD countries.This statistical technique enables us to overcome omitted variables and overftting problems. It turns out that the economic variables are major determinants compared to the political ones and linear andnonlinear effects of chosen predictors on CBI are found.


2016 - Eigenvalue Ratio Estimators for the Number of Common Factors [Articolo su rivista]
Cavicchioli, Maddalena; Forni, Mario; Lippi, Marco; Zaffaroni, Paolo
abstract

In this paper we introduce three dynamic eigenvalue ratio estimators for the number of dynamic factors. Two of them, the Dynamic Eigenvalue Ratio (DER) and the Dynamic Growth Ratio (DGR) are dynamic counterparts of the eigenvalue ratio estimators (ER and GR) proposed by Ahn and Horenstein (2013). The third, the Dynamic eigenvalue Difference Ratio (DDR), is a new one but closely related to the test statistic proposed by Onatsky (2009). The advantage of such estimators is that they do not require preliminary determination of discretionary parameters. Finally, a static counterpart of the latter estimator, called eigenvalue Difference Ratio estimator (DR), is also proposed. We prove consistency of such estimators and evaluate their performance under simulation. We conclude that both DDR and DR are valid alternatives to existing criteria. Application to real data gives new insights on the number of factors driving the US economy.


2016 - Statistical Analysis of Mixture Vector Autoregressive Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In this paper, we reconsider the mixture vector autoregressive model, which was proposed in the literature for modelling non-linear time series. We complete and extend the stationarity conditions, derive a matrix formula in closed form for the autocovariance function of the process and prove a result on stable vector autoregressive moving-average representations of mixture vector autoregressive models. For these results, we apply techniques related to a Markovian representation of vector autoregressive moving-average processes. Furthermore, we analyse maximum likelihood estimation of model parameters by using the expectation-maximization algorithm and propose a new iterative algorithm for getting the maximum likelihood estimates. Finally, we study the model selection problem and testing procedures. Several examples, simulation experiments and an empirical application based on monthly financial returns illustrate the proposed procedures.


2016 - Testing threshold cointegration in Wagner's Law: the role of military spending [Working paper]
Cavicchioli, M.; Pistoresi, B.
abstract

This paper uses historical data since mid-19th century to test the validity of Wagner's Law for the Italian economy. Unlike the previous studies, we accommodate possible nonlinear asymmetric effects of total goverment spending and GDP toward their long-run equilibrium. Our results show the presence of a threshold cointegrating relationship between the two variables with significantly different error correction adjustments in normal and extreme regimes. Particularly, we find the validity of Wagner's Law from 1862 to 2009, only when we take into account strong nonlinear responses of government spending during the WWI and WWII period. Robustness checks clearly recognize nonlinear behaviour of government expenditure driven by military spending


2016 - Testing threshold cointegration in Wagner’s Law: The role of military spending [Articolo su rivista]
Cavicchioli, Maddalena; Pistoresi, Barbara
abstract

This paper analyses historical data since the mid-19th century to find support for Wagner’s Law in the Italian economy. Unlike previous studies, we accommodate possible nonlinear asymmetric effects of government spending and GDP towards their long-run equilibrium. The results reveal a threshold cointegrating relationship between the two variables with significantly different error correction adjustments in normal and extreme regimes. A long-run tendency for the public sector to grow relative to GDP from 1862 to 2009 is observed only when nonlinearities generated by temporary higher military spending during wars are take into account.


2016 - Validating Markov Switching VAR Through Spectral Representations [Capitolo/Saggio]
Billio, Monica; Cavicchioli, Maddalena
abstract

We develop a method to validate the use of Markov Switching models in modelling time series subject to structural changes. Particularly, we consider multivariate autoregressive models subject to Markov Switching and derive close-form formulae for the spectral density of such models, based on their autocovariance functions and stable representations. Within this framework, we check the capability of the model to capture the relative importance of high- and low-frequency variability of the series. Applications to U.S. macroeconomic and financial data illustrate the behaviour at different frequencies.


2016 - Weak VARMA Representations of Regime-Switching State-Space Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We consider state-space representation of a multivariate dynamic process with Markov switching in both measurement and transition equations. Under appropriate moment conditions, we show that the autocovariance structure of such a process coincides with that of a stable VARMA model. This is potentially useful for statistical applications and for model selection as, for example, the identification of the regime number. Applications for classical Markov switching models and some numerical illustrations complete the paper.


2015 - Likelihood Ratio Test and Information Criteria for Markov Switching Var Models: An Application to the Italian Macroeconomy [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In this work we consider multivariate autoregressions subject to Markovian changes in regime. Estimation methods and filtering techniques for such processes are well established in the literature as well as the asymptotic distribution of the maximum likelihood estimators. Assuming the conditions under which the standard asymptotic distribution theory holds, the likelihood ratio (LR) has the null distribution. We give explicit formulae for LR tests of various hypotheses of interest in the context of Markov switching VAR models. The proposed LR statistic has a rather simple form as it reduces to the use of the estimated unrestricted and restricted variance-covariance matrices. Moreover, we derive simple expressions for some information criteria to address the question of linearity versus nonlinearity. An application to Italian macroeconomic data gives new insights on the number of regimes and the dynamics characterizing the economy.


2014 - ANALYSIS OF THE LIKELIHOOD FUNCTION FOR MARKOV-SWITCHING VAR(CH) MODELS [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In this work, we give simple matrix formulae for maximum likelihood estimates of parameters in a broad class of vector autoregressions subject to Markovian changes in regime. This allows us to determine explicitly the asymptotic variance-covariance matrix of the estimators, giving a concrete possibility for the use of the classical testing procedures. In the context of multivariate autoregressive conditional heteroskedastic models with changes in regime, we provide formulae for the analytic derivatives of the log likelihood. Then we prove the consistency of some maximum likelihood estimators and give some formulae for the asymptotic variance of the different estimators.


2014 - Autocovariance and Linear Transformations of Markov Switching VARMA Processes [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We study the autocovariance structure of a general Markov switching second-order stationary VARMA model. Then we give stable finite order VARMA(p* , q* ) representations for those M-state Markov switching VARMA(p, q) processes where the observables are uncorrelated with the regime variables. This allows us to obtain sharper bounds for p* and q* with respect to the ones existing in literature. Our results provide new insights into stochastic properties and facilitate statistical inference about the orders of MS-VARMA models and the underlying number of hidden states.


2014 - Business Cycle and Markov Switching Models with Distributed Lags: a Comparison between US and Euro area [Articolo su rivista]
Billio, Monica; Cavicchioli, Maddalena
abstract

Business cycle models are often investigated by using reduced form time series models, other than (or in alternative to) structural highly grounded in economic theory models. Reduced form VARMA with fixed parameters play a key role in business cycle analysis, but it is often found that by their very nature they do not typically capture the changing phases and regimes which characterize the economy. ln this paper we show that well-known state space systems used to analyse business cycle in several empirical works can be comprised into a broad class of non linear models, the MSI-VARMA. These processes are M-state Markov switching VARMA models for which the intercept term depends not only on the actual regime but also on the last r regimes. We give stable finite order VARMA representations for these processes, where upper bounds for the stable VARMA orders are elementary functions of the parameters of the initial switching model. If there is no cancellation, the bounds become equalities, and this solves the identification problem. This result allows us to study US and European business cycles and to determine the number of regimes most appropriate for the description of the economic systems. Two regimes are confirmed for the US economy; the European business cycle exhibits, instead, strong non-linearities and more regimes are necessary. This is taken into account when performing estimation and regime identification.


2014 - Determining the Number of Regimes in Markov-Switching VAR and VMA Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We give stable finite-order vector autoregressive moving average (p*; q*) representations for M-state Markov switching second-order stationary time series whose autocovariances satisfy a certain matrix relation. The upper bounds for p* and q* are elementary functions of the dimension K of the process, the number M of regimes, the autoregressive and moving-average orders of the initial model. If there is no cancellation, the bounds become equalities, and this solves the identification problem. Our classes of time series include every M-state Markov switching multi-variate moving-average models and autoregressive models in which the regime variable is uncorrelated with the observable. Our results include, as particular cases, those obtained by Krolzig (1997) and improve the bounds given by Zhang and Stine (2001) and Francq and Zakoïan (2001) for our classes of dynamic models. A Monte Carlo experiment and an application on foreign exchange rates complete the article.


2014 - On Spectral Representation of VARMA Models with Change in Regime [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We present various formulae in closed form for the spectral density of multivariate or univariate ARMA models subject to Markov switching, and describe some new properties of them. Many examples and numerical applications are proposed to illustrate the behaviour of the spectral density. This turns out to be useful in order to investigate various concepts of stationarity via spectral analysis.


2014 - Quasi Maximum Likelihood Inference for Stochastic Volatility Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In the present paper we consider the Quasi Maximum Likelihood (QML) procedure for the estimation of stationary Stochastic Volatility models. We prove the consistency of the QML estimators and compute explicitly their asymptotic variances. This allows us to obtain also consistent estimators of the asymptotic variances in explicit forms. The knowledge of the asymptotic variance-covariance matrix of the QML estimators gives a concrete possibility for the use of the classical testing procedures. Our results are related to those obtained in Ruiz (1994) and Bartolucci and De Luca (2001) (2003).


2013 - Acute Triangulations of Trapezoids and Pentagons [Articolo su rivista]
Cavicchioli, Maddalena
abstract

An acute triangulation of a polygon is a triangulation whose triangles have all their angles less than pi/2. The number of triangles in a triangulation is called the size of it. In this paper, we investigate acute triangulations of trapezoids and convex pentagons and prove new results about such triangulations with minimum size.This completes and improves in some cases the results obtained in two papers of Yuan (2010).


2013 - Inference Methods for Stochastic Volatility Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In the present paper we consider estimation procedures for stationary Stochastic Volatility models, making inferences about the latent volatility of the process. We show that a sequence of generalized least squares regressions enables us to determine the estimates. Finally, we make inferences iteratively by using the Kalman Filter algorithm.


2013 - On Asymptotic Properties of the QML Estimator for GARCH Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

This note can be considered as a continuation of a nice paper from Francq and Zakoian (2012) concerning with strict stationarity testing and estimation of GARCH models. We compute the asymptotic variances of the quasi-maximum likelihood estimators for stationary GARCH models.


2013 - Spectral Density of Markov Switching VARMA Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We review some results on stationarity and autocovariance function for Markov switching VARMA models. Then we derive a formula in closed form for the spectral density of such models, and describe some new properties of it. Our results complete those obtained by Pataracchia (2011) and Francq and Zakoian (2001).


2011 - Some Convergence Results on Dynamic Factor Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

We review some recent papers on a large dynamic factor model (LDFM) and its applications to structural macroeconomic analysis. Then we prove some convergence results concerning with the stochastic variables which define such a model.


2010 - Structural Macroeconomic Analysis for Dynamic Factor Models [Articolo su rivista]
Cavicchioli, Maddalena
abstract

In this work we review some recent papers concerned with large dynamic factor model (LDFM) and its applications to structural macroeconomic analysis. Using this theory, we present a new empirical application on the effects of technology and non technology shocks on hours worked.