scholarly journals Tail Behaviour of the Nifty-50 Stocks during Crises Periods

2021 ◽  
Vol 25 (4) ◽  
pp. 115-151
Keyword(s):  
Tail Behaviour

Tail asymptotics of an infinitely divisible space-time model with convolution equivalent Lévy measure

2021 ◽  
Vol 58 (1) ◽  
pp. 42-67 ◽  
Author(s):  
Mads Stehr ◽  
Anders Rønn-Nielsen
Keyword(s):  
Space Time ◽  
Time Interval ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Time Model ◽  
Spatial Object ◽  
Tail Behaviour ◽  
Fixed Radius ◽  
The Right ◽  
Space Time Model

AbstractWe consider a space-time random field on ${{\mathbb{R}^d} \times {\mathbb{R}}}$ given as an integral of a kernel function with respect to a Lévy basis with a convolution equivalent Lévy measure. The field obeys causality in time and is thereby not continuous along the time axis. For a large class of such random fields we study the tail behaviour of certain functionals of the field. It turns out that the tail is asymptotically equivalent to the right tail of the underlying Lévy measure. Particular examples are the asymptotic probability that there is a time point and a rotation of a spatial object with fixed radius, in which the field exceeds the level x, and that there is a time interval and a rotation of a spatial object with fixed radius, in which the average of the field exceeds the level x.

The tail behaviour of a random sum of subexponential random variables and vectors

Extremes ◽  
2007 ◽  
Vol 10 (1-2) ◽  
pp. 21-39 ◽  
Author(s):  
D. J. Daley ◽  
Edward Omey ◽  
Rein Vesilo
Keyword(s):  
Random Variables ◽  
Random Sum ◽  
Tail Behaviour

scholarly journals Tails of Stopped Random Products: The Factoid and Some Relatives

2008 ◽  
Vol 45 (04) ◽  
pp. 1161-1180
Author(s):  
Anthony G. Pakes
Keyword(s):  
Tail Behaviour ◽  
Random Product ◽  
Random Products ◽  
Heavy Tailed ◽  
First Time ◽  
Independent And Identically Distributed

The upper tail behaviour is explored for a stopped random product ∏j=1NXj, where the factors are positive and independent and identically distributed, andNis the first time one of the factors occupies a subset of the positive reals. This structure is motivated by a heavy-tailed analogue of the factorialn!, called the factoid ofn. Properties of the factoid suggested by computer explorations are shown to be valid. Two topics about the determination of the Zipf exponent in the rank-size law for city sizes are discussed.

scholarly journals Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times

2004 ◽  
Vol 111 (2) ◽  
pp. 237-258 ◽  
Author(s):  
A. Baltrūnas ◽  
D.J. Daley ◽  
C. Klüppelberg
Keyword(s):  
Busy Period ◽  
Tail Behaviour ◽  
Service Times

Large deviations in the supercritical branching process

1993 ◽  
Vol 25 (04) ◽  
pp. 757-772 ◽  
Author(s):  
J. D. Biggins ◽  
N. H. Bingham
Keyword(s):  
Distribution Function ◽  
Large Deviations ◽  
Population Size ◽  
Branching Process ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Large Deviation Theory ◽  
Tail Behaviour ◽  
The Moment ◽  
Deviation Theory

The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some ‘large-deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment-generating function of W translates to tail behaviour.

Time-varying asymmetry and tail thickness in long series of daily financial returns

2018 ◽  
Vol 22 (5) ◽  
Author(s):  
Błażej Mazur ◽  
Mateusz Pipień
Keyword(s):  
Shape Features ◽  
Forecasting Performance ◽  
Sample Density ◽  
Tail Behaviour ◽  
Term Variation ◽  
Density Forecasting ◽  
Out Of Sample ◽  
Time Invariant ◽  
Daily Returns

Abstract We demonstrate that analysis of long series of daily returns should take into account potential long-term variation not only in volatility, but also in parameters that describe asymmetry or tail behaviour. However, it is necessary to use a conditional distribution that is flexible enough, allowing for separate modelling of tail asymmetry and skewness, which requires going beyond the skew-t form. Empirical analysis of 60 years of S&P500 daily returns suggests evidence for tail asymmetry (but not for skewness). Moreover, tail thickness and tail asymmetry is not time-invariant. Tail asymmetry became much stronger at the beginning of the Great Moderation period and weakened after 2005, indicating important differences between the 1987 and the 2008 crashes. This is confirmed by our analysis of out-of-sample density forecasting performance (using LPS and CRPS measures) within two recursive expanding-window experiments covering the events. We also demonstrate consequences of accounting for long-term changes in shape features for risk assessment.

scholarly journals Geometry of the Poisson Boolean model on a region of logarithmic width in the plane

2011 ◽  
Vol 43 (03) ◽  
pp. 616-635
Author(s):  
Amites Dasgupta ◽  
Rahul Roy ◽  
Anish Sarkar
Keyword(s):  
Phase Transition ◽  
Half Space ◽  
Point Process ◽  
Poisson Point Process ◽  
Random Variable ◽  
Boolean Model ◽  
Side Length ◽  
Tail Behaviour ◽  
Critical Intensity ◽  
Poisson Boolean Model

Consider the region L = {(x, y): 0 ≤ y ≤ Clog(1 + x), x > 0} for a constant C > 0. We study the percolation and coverage properties of this region. For the coverage properties, we place a Poisson point process of intensity λ on the entire half space R + x R and associated with each Poisson point we place a box of a random side length ρ. Depending on the tail behaviour of the random variable ρ we exhibit a phase transition in the intensity for the eventual coverage of the region L. For the percolation properties, we place a Poisson point process of intensity λ on the region R 2. At each point of the process we centre a box of a random side length ρ. In the case ρ ≤ R for some fixed R > 0 we study the critical intensity λc of the percolation on L.

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