18 research outputs found
Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes
The order of integration is valid to characterize linear processes; but it is not appropriate for non-linear worlds. We propose the concept of summability (a re-scaled partial sum of the process being Op(1)) to handle non-linearities. The paper shows that this new concept, S (d): (i) generalizes I (d); (ii) measures the degree of persistence as well as of the evolution of the variance; (iii) controls the balancedness of non-linear relationships; (iv) opens the door to the concept of co-summability which represents a generalization of co-integration for non-linear processes. To make this concept empirically applicable, an estimator for d and its asymptotic properties are provided. The finite sample performance of subsampling confidence intervals is analyzed via a Monte Carlo experiment. The paper finishes with the estimation of the degree of summability of the macroeconomic variables in an extended version of the Nelson-Plosser database.Co-integration, Co-summability, Integrated processes, Non-linear balanced relationships, Non-linear processes, Summability
Testing for multicointegration in panel data with common factors
The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis.common factors, cross-section dependence, i(2) processes, crossmulticointegration, panel data, multicointegration
Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes
The order of integration is valid to characterize linear processes; but it is not appropriate for non-linear
worlds. We propose the concept of summability (a re-scaled partial sum of the process being Op(1)) to
handle non-linearities. The paper shows that this new concept, S (δ): (i) generalizes I (δ); (ii) measures
the degree of persistence as well as of the evolution of the variance; (iii) controls the balancedness of
non-linear relationships; (iv) opens the door to the concept of co-summability which represents a
generalization of co-integration for non-linear processes. To make this concept empirically applicable,
an estimator for δ and its asymptotic properties are provided. The finite sample performance of
subsampling confidence intervals is analyzed via a Monte Carlo experiment. The paper finishes with
the estimation of the degree of summability of the macroeconomic variables in an extended version of
the Nelson-Plosser database
Co-summability from linear to non-linear cointegration
While co-integration theory is an ideal framework to study linear relationships among persistent
economic time series, the intrinsic linearity in the concepts of integration and co-integration makes it
unsuitable to study non-linear long run relations among persistent processes. This drawback hinders
the empirical analysis of modern macroeconomics, which often addresses asymmetric responses to
policy interventions, multiplicity of equilibria, transitions between regimes or polynomial approximations
to unknown functions.
In this paper, to cope with non-linear relations and consequently to generalise co-integration, we
formalise the idea of co-summability. It is built upon the concept order of summability developed by
Berenguer-Rico and Gonzalo (2013), which, in turn, was conceived to address non-linear
transformations of persistent processes. Theoretically, a co-summable relationship is balanced -in
terms of the variables involved having the same order of summability- and describes a long run
equilibrium that can be non-linear -in the sense that the errors have a lower order of summability. To
test for these types of equilibria, inference tools for balancedness and cosummability are designed and
their asymptotic properties are analysed. Their finite sample performance is studied via Monte Carlo
experiments.
The practical strength of co-summability theory is shown through two empirical applications.
Specifically, asymmetric preferences of central bankers and the environmental Kuznets curve
hypothesis are studied through the lens of co-summability.Financial support from the University of
Oxford, Institute for New Economic Thinking, Spanish Ministerio de Ciencia e Innovación (grants ECO2010-19357
and Consolider-2010), Comunidad de Madrid (grant Excelecon) and Bank of Spain (grant ER program) is
gratefully acknowledged
Normality testing after outlier removal
The cumulant based normality test after outlier removal is analyzed. It is shown that the standard least squares normalizations can be misleading in this context. The sample cumulants should be standardized according to the truncation imposed at the removal stage and the estimation method being used. New standardizations that lead to chi-squared inference are derived
Multicointegration, polynomial cointegration and I(2) cointegration with structural breaks. An application to the sustainability of the US external deficit.
In this paper we model the multicointegration relation, allowing for one structural break. Since multicointegration is a particular case of polynomial or I(2) cointegration, our proposal can also be applied in these cases. The paper proposes the use of a residualbased Dickey-Fuller class of statistic that accounts for one known or unknown structural break. Finite sample performance of the proposed statistic is investigated by using Monte Carlo simulations, which reveals that the statistic shows good properties in terms of empirical size and power. We complete the study with an empirical application of the sustainability of the US external deficit. Contrary to existing evidence, the consideration of one structural break leads to conclude in favour of the sustainability of the US external deficit.I(2) processes, multicointegration, polynomial cointegration, structural break, sustainability of external deficit.
Co-summability from linear to non-linear co-integration
This thesis opens a new set of econometric possibilities in the study of non-linear
long run relationships generalizing co-integration theory. This generalization is presented in three
di¤erent, although self-contained, chapters. Chapter 1 presents the order of summability and its
associated econometric tools. Chapter 2 develops the ideas of balancedness and co-summability
as well as the econometric theory to use them in practice. Their applicability is shown with two
empirical illustrations: asymmetric preferences of central bankers and the environmental Kuznets
curve. Chapter 3 derives the threshold present value model for asset pricing and tests it using the
techniques developed in the two previous chapters. The corresponding appendices, collecting all the
proofs, are at the end of each chapte
Summability of stochastic processes: a generalization of integration for non-linear processes
The order of integration is valid to characterize linear processes; but it is not appropriate for non-linear worlds. We propose the concept of summability (a re-scaled partial sum of the process being O-p(1)) to handle non-linearities. The paper shows that this new concept, S (delta): (i) generalizes I (delta); (ii) measures the degree of persistence as well as of the evolution of the variance; (iii) controls the balancedness of non-linear relationships; (iv) opens the door to the concept of co-summability which represents a generalization of co-integration for non-linear processes. To make this concept empirically applicable, an estimator for delta and its asymptotic properties are provided. The finite sample performance of subsampling confidence intervals is analyzed via a Monte Carlo experiment. The paper finishes with the estimation of the degree of summability of the macroeconomic variables in an extended version of the Nelson-Plosser database.Financial support from SEJ-2007-63098, ECO-2010-19357, CONSOLIDER 2010 (CSD 2006-00016), and EXCELECON S-2007/HUM-044 grants is gratefully acknowledged
Spatiotemporal Characteristics of the Largest HIV-1 CRF02_AG Outbreak in Spain: Evidence for Onward Transmissions
Background and Aim: The circulating recombinant form 02_AG (CRF02_AG) is the predominant clade among the human immunodeficiency virus type-1 (HIV-1) non-Bs with a prevalence of 5.97% (95% Confidence Interval-CI: 5.41–6.57%) across Spain. Our aim was to estimate the levels of regional clustering for CRF02_AG and the spatiotemporal characteristics of the largest CRF02_AG subepidemic in Spain.Methods: We studied 396 CRF02_AG sequences obtained from HIV-1 diagnosed patients during 2000–2014 from 10 autonomous communities of Spain. Phylogenetic analysis was performed on the 391 CRF02_AG sequences along with all globally sampled CRF02_AG sequences (N = 3,302) as references. Phylodynamic and phylogeographic analysis was performed to the largest CRF02_AG monophyletic cluster by a Bayesian method in BEAST v1.8.0 and by reconstructing ancestral states using the criterion of parsimony in Mesquite v3.4, respectively.Results: The HIV-1 CRF02_AG prevalence differed across Spanish autonomous communities we sampled from (p < 0.001). Phylogenetic analysis revealed that 52.7% of the CRF02_AG sequences formed 56 monophyletic clusters, with a range of 2–79 sequences. The CRF02_AG regional dispersal differed across Spain (p = 0.003), as suggested by monophyletic clustering. For the largest monophyletic cluster (subepidemic) (N = 79), 49.4% of the clustered sequences originated from Madrid, while most sequences (51.9%) had been obtained from men having sex with men (MSM). Molecular clock analysis suggested that the origin (tMRCA) of the CRF02_AG subepidemic was in 2002 (median estimate; 95% Highest Posterior Density-HPD interval: 1999–2004). Additionally, we found significant clustering within the CRF02_AG subepidemic according to the ethnic origin.Conclusion: CRF02_AG has been introduced as a result of multiple introductions in Spain, following regional dispersal in several cases. We showed that CRF02_AG transmissions were mostly due to regional dispersal in Spain. The hot-spot for the largest CRF02_AG regional subepidemic in Spain was in Madrid associated with MSM transmission risk group. The existence of subepidemics suggest that several spillovers occurred from Madrid to other areas. CRF02_AG sequences from Hispanics were clustered in a separate subclade suggesting no linkage between the local and Hispanic subepidemics
Heteroscedasticity testing after outlier removal
Given the effect that outliers can have on regression and specification testing, a vastly used robustification strategy by practitioners consists in: (i) starting the empirical analysis with an outlier detection procedure to deselect atypical data values; then (ii) continuing the analysis with the selected non-outlying observations. The repercussions of such robustifying procedure on the asymptotic properties of subsequent inferential procedures are, however, underexplored. We study the effects of such a strategy on testing for heteroscedasticity. Specifically, using weighted and marked empirical processes of residuals theory, we show that the White test implemented after the outlier detection and removal is asymptotically chi-square if the underlying errors are symmetric. In a simulation study, we show that-depending on the type of outliers-the standard White test can be either severely undersized or oversized, as well as have trivial power. The statistic applied after deselecting outliers has good finite sample properties under symmetry but can suffer from size distortions under asymmetric errors. Given these results, we devise an empirical modeling strategy to guide practitioners whose preferred approach is to remove outliers from the sample