scholarly journals Realized Multi-Power Variation Process for Jump Detection in the Nigerian All Share Index

2021 ◽  
Vol 52 (3) ◽  
pp. 397-412
Author(s):  
Mabel Adeosun ◽  
Olabisi Ugbebor
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Models ◽  
Asymptotic Properties ◽  
Higher Order ◽  
Asymptotic Results ◽  
Jump Detection ◽  
Limit Distributions ◽  
Price Process ◽  
Variation Process ◽  
Asymptotic Variances

In this paper, we studied the particular cases of higher-order realized multipower variation process, their asymptotic properties comprising the probability limits and limit distributions were highlighted. The respective asymptotic variances of the limit distributions were obtained and jump detection models were developed from the asymptotic results. The models were obtained from the particular cases of the higher-order of the realized multipower variation process, in a class of continuous stochastic volatility semimartingale process. These are extensions of the method of jump detection by Barndorff-Nielsen and Shephard (2006), for large discrete data. An Empirical Application of the models to the Nigerian All Share Index (NASI) data shows that the models are robust to jumps and suggest that stochastic models with added jump components will give a better representation of the NASI price process.

scholarly journals Equilibrium Pricing in Incomplete Markets

2005 ◽  
Vol 40 (4) ◽  
pp. 833-848 ◽  
Author(s):  
Abdelhamid Bizid ◽  
Elyès Jouini
Keyword(s):  
Stochastic Volatility ◽  
Incomplete Markets ◽  
Stochastic Volatility Model ◽  
Time Model ◽  
Equilibrium Pricing ◽  
Discrete Time Model ◽  
Price Process ◽  
State Price ◽  
Volatility Model ◽  
Market Framework

AbstractGiven the exogenous price process of some assets, we constrain the price process of other assets that are characterized by their final payoffs. We deal with an incomplete market framework in a discrete-time model and assume the existence of the equilibrium. In this setup, we derive restrictions on the state-price deflators. These restrictions do not depend on a particular choice of utility function. We investigate numerically a stochastic volatility model as an example. Our approach leads to an interval of admissible prices that is more robust than the arbitrage pricing interval.

The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1

1973 ◽  
Vol 59 (4) ◽  
pp. 721-736 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Water Waves ◽  
Large Time ◽  
Vries Equation ◽  
Asymptotic Properties ◽  
Series Representation ◽  
Convergent Series ◽  
Asymptotic Results ◽  
De Vries ◽  
Method Of Solution

The method of solution of the Korteweg–de Vries equation outlined by Gardneret al.(1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.

Estimation of the variance for the multitype Galton–Watson process

1982 ◽  
Vol 19 (2) ◽  
pp. 408-414 ◽  
Author(s):  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimator ◽  
Asymptotic Results ◽  
Variance Matrix ◽  
Individual Offspring ◽  
Watson Process ◽  
Asymptotic Variances

This paper is concerned with the estimation of the variance for the multitype Galton-Watson process X = {Xn = (Xn(1),…, Xn(p)); n ≧ 0}. Two estimators for the variance matrix are obtained and asymptotic results for the estimators are given. The first is a maximum likelihood estimator based upon knowledge of individual offspring sizes, the second estimator is based on parent-offspring type combination counts only. Estimators for the asymptotic variances of the Asmussen and Keiding estimator and Becker estimator are also proposed.

Asymptotic properties of the least-squares method for estimating transfer functions and disturbance spectra

1992 ◽  
Vol 24 (02) ◽  
pp. 412-440 ◽  
Author(s):  
Lennart Ljung ◽  
Bo Wahlberg
Keyword(s):  
Transfer Function ◽  
Finite Order ◽  
Transfer Functions ◽  
Least Squares Method ◽  
Asymptotic Properties ◽  
Model Order ◽  
Asymptotically Normal ◽  
Strongly Consistent ◽  
True System ◽  
Asymptotic Variances

The problem of estimating the transfer function of a linear system, together with the spectral density of an additive disturbance, is considered. The set of models used consists of linear rational transfer functions and the spectral densities are estimated from a finite-order autoregressive disturbance description. The true system and disturbance spectrum are, however, not necessarily of finite order. We investigate the properties of the estimates obtained as the number of observations tends to ∞ at the same time as the model order employed tends to ∞. It is shown that the estimates are strongly consistent and asymptotically normal, and an expression for the asymptotic variances is also given. The variance of the transfer function estimate at a certain frequency is related to the signal/noise ratio at that frequency and the model orders used, as well as the number of observations. The variance of the noise spectral estimate relates in a similar way to the squared value of the true spectrum.

scholarly journals Testing for Unit Roots in Time Series Data

1989 ◽  
Vol 5 (2) ◽  
pp. 256-271 ◽  
Author(s):  
Sastry G. Pantula
Keyword(s):  
Likelihood Ratio ◽  
Time Series Data ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Unit Roots ◽  
Sequential Testing ◽  
Series Data ◽  
Stochastic Difference Equation ◽  
Asymptotic Results ◽  
Testing Procedures

Let Yt satisfy the stochastic difference equation for t = 1,2,…, where et are independent and identically distributed random variables with mean zero and variance σ2 and the initial conditions (Y−p+1,…, Y0) are fixed constants. It is assumed that the process is invertible and that the true, but unknown, roots m1,m2,…,mp of satisfy the hypothesis Hd: m1 = … = md = 1 and |mj| < 1 for j = d + 1,…,p. We present a reparameterization of the model for Yt that is convenient for testing the hypothesis Hd. We consider the asymptotic properties of (i) a likelihood ratio type “F-statistic” for testing the hypothesis Hd, (ii) a likelihood ratio type t-statistic for testing the hypothesis Hd against the alternative Hd−1. Using these asymptotic results, we obtain two sequential testing procedures that are asymptotically consistent.

THE NONSTATIONARY FRACTIONAL UNIT ROOT

1999 ◽  
Vol 15 (4) ◽  
pp. 549-582 ◽  
Author(s):  
Katsuto Tanaka
Keyword(s):  
Unit Root ◽  
Asymptotic Properties ◽  
Test Statistics ◽  
Finite Sample ◽  
Asymptotic Results ◽  
Simulation Experiments ◽  
Normality Assumption ◽  
Asymptotically Efficient ◽  
Uniformly Most Powerful ◽  
Fractional Unit

This paper deals with a scalar I(d) process {yj}, where the integration order d is any real number. Under this setting, we first explore asymptotic properties of various statistics associated with {yj}, assuming that d is known and is greater than or equal to ½. Note that {yj} becomes stationary when d < ½, whose case is not our concern here. It turns out that the case of d = ½ needs a separate treatment from d > ½. We then consider, under the normality assumption, testing and estimation for d, allowing for any value of d. The tests suggested here are asymptotically uniformly most powerful invariant, whereas the maximum likelihood estimator is asymptotically efficient. The asymptotic theory for these results will not assume normality. Unlike in the usual unit root problem based on autoregressive models, standard asymptotic results hold for test statistics and estimators, where d need not be restricted to d ≥ ½. Simulation experiments are conducted to examine the finite sample performance of both the tests and estimators.

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