
on Econometric Time Series 
By:  Anna Gloria Billé (Free University of BozenBolzano, Faculty of Economics and Management); Samantha Leorato (University of Rome Tor Vergata, Department of Economics and Finance) 
Abstract:  In this paper we propose a PartialMLE for a general spatial nonlinear probit model, i.e. SARAR(1,1)probit, defined through a SARAR(1,1) latent linear model. This model encompasses the SAE(1)probit model, considered by Wang et al. (2013), and the more interesting SAR(1)probit model. We perform a complete asymptotic analysis, and account for the possible finite sum approximation of the covariance matrix (QuasiMLE) to speed the computation. Moreover, we address the issue of the choice of the groups (couples, in our case) by proposing an algorithm based on a minimum KLdivergence problem. Finally, we provide appropriate definitions of marginal effects for this setting. Finite sample properties of the estimator are studied through a simulation exercise and a real data application. In our simulations, we also consider both sparse and dense matrices for the specification of the true spatial models, and cases of model misspecifications due to different assumed weighting matrices. 
Keywords:  spatial autoregressiveregressive probit model, nonlinear modeling, SARAR, partial maximum likelihood, quasi maximum likelihood, marginal effects 
JEL:  C13 C31 C35 C51 
Date:  2017–12 
URL:  http://d.repec.org/n?u=RePEc:bzn:wpaper:bemps44&r=ets 
By:  Rajae R. Azrak; Guy Melard 
Keywords:  Nonstationary process; time series; time dependent model; time varying model; locally statiionary processes 
Date:  2017–12 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/262612&r=ets 
By:  Massimo Franchi ("Sapienza" University of Rome); Paolo Paruolo (European Commission, Joint Research Centre) 
Abstract:  This paper derives a generalization of the GrangerJohansen Representation Theorem valid for Hvalued autoregressive (AR) processes, where H is an infinite dimensional separable Hilbert space, under the assumption that 1 is an eigenvalue of finite type of the AR operator function and that no other nonzero eigenvalue lies within or on the unit circle. A necessary and sucient condition for integration of order d = 1, 2,... is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces h, h = ,..,d, each one associated with components of the process integrated of order h. These results mirror the ones recently obtained in the nite dimensional case, with the only di erence that the number of cointegrating relations of order 0 is infinite. 
Keywords:  Functional autoregressive process, Unit roots, Cointegration, Common Trends, GrangerJohansen Representation Theorem. 
JEL:  C12 C33 
Date:  2017–12 
URL:  http://d.repec.org/n?u=RePEc:sas:wpaper:20175&r=ets 
By:  Antoine Lejay (TOSCA); Paolo Pigato (WIAS) 
Abstract:  In financial markets, low prices are generally associated with high volatilities and viceversa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and meanreversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous time version of the SelfExciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Tests are performed on the daily prices of 21 assets. They show empirical evidence for leverage and meanreversion effects, consistent with the results in the literature. 
Date:  2017–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1712.08329&r=ets 
By:  Yubo Tao (School of Economics, Singapore Management University); Peter C.B. Phillips (Cowles Foundation, Yale University); Jun Yu (School of Economics and Lee Kong Chian School of Business, Singapore Management University) 
Abstract:  This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A twostage approach that employs realized volatility is proposed for the continuous system estimation, asymptotic theory is developed, and test statistics to identify the different forms of extreme sample path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S\&P 500 index data over 19642015 reveals strong evidence against parameter constancy after early 1980, which strengthens after July 1997, leading to a long duration of what the model characterizes as extreme behaviour in real stock prices. 
Keywords:  Continuous time models, Explosive path, Extreme behaviour, Random coefficient autoregression, Infill asymptotics, Bubble testing 
JEL:  C13 C22 G13 
Date:  2017–12 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:3014&r=ets 
By:  Offer Lieberman (BarIlan University); Peter C.B. Phillips (Cowles Foundation, Yale University) 
Abstract:  Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include localtounity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size tends to infinity. The second approach allows for stochastic departures from unity, leading to stochastic unit root (STUR) specifications. This paper introduces a hybrid local stochastic unit root (LSTUR) specification that has both LUR and STUR components and allows for endogeneity in the time varying coefficient that introduces structural elements to the autoregression. This hybrid model generates trajectories that, upon normalization, have nonlinear diffusion limit processes that link closely to models that have been studied in mathematical finance, particularly with respect to option pricing. It is shown that some LSTUR parameterizations have a mean and variance which are the same as a random walk process but with a kurtosis exceeding 3, a feature which is consistent with much financial data. We develop limit theory and asymptotic expansions for the process and document how inference in LUR and STUR autoregressions is affected asymptotically by ignoring one or the other component in the more general hybrid generating mechanism. In particular, we show how confidence belts constructed from the LUR model are affected by the presence of a STUR component in the generating mechanism. The import of these findings for empirical research are explored in an application to the spreads on US investment grade corporate debt. 
Keywords:  Autoregression, Nonlinear diffusion, Stochastic unit roo, Timevarying coefficient 
JEL:  C22 
Date:  2017–11 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:3013&r=ets 
By:  Mateusz Buczyński (Faculty of Economic Sciences, University of Warsaw); Marcin Chlebus (Faculty of Economic Sciences, University of Warsaw) 
Abstract:  In the literature, there is no consensus which ValueatRisk forecasting model is the best for measuring a market risk in banks. In the study an analysis of ValueatRisk forecasting models quality over varying economic stability periods for main indices from stock exchanges was conducted. The VaR forecasts from GARCH(1,1), GARCHt(1,1), GARCHst(1,1), QMLGARCH(1,1), CAViaR and historical simulation models in periods with contrasting volatility trends (increasing, constantly high and decreasing) for countries economically developed (the USA – S&P 500, Germany  DAX and Japan – Nikkei 225) and economically developing (China – SSE COMP, Poland – WIG20 and Turkey – XU100) were compared. The data samples used in the analysis were selected from period 01.01.1999 – 24.03.2017. To assess the VaR forecasts quality: excess ratio, Basel traffic light test, coverage tests (Kupiec test, Christoffersen test), Dynamic Quantile test, cost functions and DieboldMarino test were used. Obtained results shows that the quality of ValueatRisk forecasts for the models varies depending on a volatility trend. However, GARCHst (1,1) and QMLGARCH(1,1) were found as the most robust models to the different volatility periods. The results shows, as well that the CAViaR model forecasts were less appropriate in the increasing volatility period. Moreover, no significant differences for the VaR forecasts quality were found for the developed and developing countries. 
Keywords:  risk management, value at risk, GARCH, CAViaR, historical simulation, quality of model assessment 
JEL:  G32 C52 C53 C58 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:war:wpaper:201729&r=ets 
By:  Helmut Lütkepohl; Tomasz Woźniak 
Abstract:  In order to identify structural shocks that affect economic variables, restrictions need to be imposed on the parameters of structural vector autoregressive (SVAR) models. Economic theory is the primary source of such restrictions. However, only overidentifying restrictions can be tested with statistical methods which limits the statistical validation of many justidentified SVAR models. In this study, Bayesian inference is developed for SVAR models in which the structural parameters are identified via Markovswitching heteroskedasticity. In such a model, restrictions that are justidentifying in the homoskedastic case, become overidentifying and can be tested. A set of parametric restrictions is derived under which the structural matrix is globally identified and a SavageDickey density ratio is used to assess the validity of the identification conditions. For that purpose, a new probability distribution is defined that generalizes the beta, F, and compound gamma distributions. As an empirical example, monetary models are compared using heteroskedasticity as an additional device for identification. The empirical results support models with money in the interest rate reaction function. 
Keywords:  Identification through heteroskedasticity, MarkovSwitching models, SavageDickey Density Ratio, monetary policy shocks, Divisia Money 
JEL:  C11 C12 C32 E32 
Date:  2017 
URL:  http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1707&r=ets 
By:  Zacharias Psaradakis (Birkbeck, University of London); Marián Vávra (National Bank of Slovakia) 
Abstract:  The paper considers the problem of testing for normality of the onedimensional marginal distribution of a strictly stationary and weakly dependent stochastic process. The possibility of using an autoregressive sieve bootstrap procedure to obtain critical values and Pvalues for normality tests is explored. The smallsample properties of a variety of tests are investigated in an extensive set of Monte Carlo experiments. The bootstrap version of the classical skewnesskurtosis test is shown to have the best overall performance in small samples. 
Keywords:  Autoregressive sieve bootstrap; Normality test; Weak dependence. 
Date:  2017–10 
URL:  http://d.repec.org/n?u=RePEc:bbk:bbkefp:1706&r=ets 