Exact inference and optimal invariant estimation for the stability parameter of symmetric α-stable distributions

Exploiting tail shape biases to discriminate between stable and student t alternatives

“…For the stable class, the number m decreases to zero as the tails become thinner (one approaches the normal distribution). Sometimes an even larger number m is chosen such that the tail region comprises 30-40% of the entire sample size (see, e.g., Dufour & Kim, 2010;Mittnik, Paolella, & Rachev, 1998). The 10% rule is often followed in the literature when applied to the Hill estimator (see, e.g., Quintos, Fan, & Phillips, 2001;Ibragimov, Ibragimov, & Kattuman, 2013).…”

“…The 10% rule is often followed in the literature when applied to the Hill estimator (see, e.g., Quintos, Fan, & Phillips, 2001;Ibragimov, Ibragimov, & Kattuman, 2013). Sometimes an even larger number m is chosen such that the tail region comprises 30-40% of the entire sample size (see, e.g., Dufour & Kim, 2010;Mittnik, Paolella, & Rachev, 1998). However, our results suggest that one should use a relatively small number rather than a large number of upper-order statistics.…”

Simultaneous Indirect Inference, Impulse Responses and ARMA Models

“…Laslty, the confidence set is projected to construct impulse-response confidence bands, which entails maximizing and minimizing 3 Throughout this document, size and coverage are used interchangeably; see Andrews and Cheng (2012). 4 In this regard, our work relates to Dufour andValéry (2006, 2009) in stochastic volatility models, Dufour and Kurz-Kim (2010) and Beaulieu et al (2007Beaulieu et al ( , 2013Beaulieu et al ( , 2014 in models with fat-tailed fundamentals. each function over the non-rejected values of the parameters.…”

Four Essays on Identification-Robust Numerical and Statistical Tools with Applications to Dynamic Stochastic General Equilibrium Models

“…For the purpose of this chapter, more important than our specific under-identification result is the consequence of failing to detect its extent via popular toolkits such as GA and SA. Indeed, GA and SA converge to local optima that suggest misleading economic decisions on: (i) the nature of the New-Keynesian Phillips Curve [NKPC], (ii) determinacy of monetary policies, 3 Recent work with focus on identification challenges among others in this context include Fuhrer and Rudebusch (2004), Mavroeidis (2004, Benati (2008), Dufour et al (2006Dufour et al ( , 2010, Nason and Smith (2008), Canova and Sala (2009), Mavroeidis (2009), Iskrev (2010), Magnusson and Mavroeidis (2010), , Cochrane (2011), , , , Andrews and Mikusheva (2014), Basturk, Cakmakli, Ceyhan and van Dijk (2014), Castelnuovo and Fanelli (2014) and the surveys by Schorfheide (2013) and . and (iii) the persistence of the Taylor rule.…”

“…Equation (1.4.1) is a NKPC on which identification-robust test inversion based evidence is available by now; see e.g. Mavroeidis (2004, Dufour et al (2006Dufour et al ( , 2010, Nason and Smith (2008), Canova and Sala (2009), Mavroeidis (2009), Basturk, Cakmakli, Ceyhan andvan Dijk (2014) and the survey by . The restriction…”