A bivariate semi-Pareto distribution is introduced
and characterized using geometric minimization.
Autoregressive minification models for bivariate random
vectors with bivariate semi-Pareto and bivariate Pareto
distributions are also discussed. Multivariate
generalizations of the distributions and the processes are briefly indicated.
We propose a novel, simple, efficient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box–Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re-sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re-sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data.
This paper proposes different estimators for the parameters of SemiPareto and Pareto autoregressive minification processes The asymptotic properties of the estimators are established by showing that the SemiPareto process is α-mixing. Asymptotic variances of different moment and maximum likelihood estimators are compared.
This paper presents gamma stochastic volatility models and investigates its distributional
and time series properties. The parameter estimators obtained by the
method of moments are shown analytically to be consistent and asymptotically
normal. The simulation results indicate that the estimators behave well. The insample
analysis shows that return models with gamma autoregressive stochastic
volatility processes capture the leptokurtic nature of return distributions and
the slowly decaying autocorrelation functions of squared stock index returns
for the USA and UK. In comparison with GARCH and EGARCH models, the
gamma autoregressive model picks up the persistence in volatility for the US
and UK index returns but not the volatility persistence for the Canadian and
Japanese index returns. The out-of-sample analysis indicates that the gamma
autoregressive model has a superior volatility forecasting performance compared
to GARCH and EGARCH models.
The average availability of a repairable system is the expected proportion of time that the system is operating in the interval [0, t]. The present article discusses the nonparametric estimation of the average availability when (i) the data on 'n' complete cycles of system operation are available, (ii) the data are subject to right censorship, and (iii) the process is observed upto a specified time 'T'. In each case, a nonparametric confidence interval for the average availability is also constructed. Simulations are conducted to assess the performance of the estimators.
In this article it is proved that the stationary Markov sequences generated by minification models are ergodic and uniformly mixing. These results are used to establish the optimal properties of estimators for the parameters in the model. The problem of estimating the parameters in the exponential minification model is discussed in detail.
When variables in time series context are non-negative, such as for volatility, survival
time or wave heights, a multiplicative autoregressive model of the type Xt = Xα
t−1Vt ,
0 ≤ α < 1, t = 1, 2, . . . may give the preferred dependent structure. In this paper,
we study the properties of such models and propose methods for parameter estimation.
Explicit solutions of the model are obtained in the case of gamma marginal distribution
Description:
Statistics and Probability Letters 82 (2012) 1530–1537
The standard models for statistical signal extraction assume that the signal and noise are
generated by linear Gaussian processes. The optimum filter weights for those models are
derived using the method of minimum mean square error. In the present work we study
the properties of signal extraction models under the assumption that signal/noise are
generated by symmetric stable processes. The optimum filter is obtained by the method of
minimum dispersion. The performance of the new filter is compared with their Gaussian
counterparts by simulation.
In this paper we try to fit a threshold autoregressive (TAR) model to time series data of monthly coconut oil prices at Cochin market. The procedure proposed by Tsay [7] for fitting the TAR model is briefly presented. The fitted model is compared with a simple autoregressive (AR) model. The results are in favour of TAR process. Thus the monthly coconut oil prices exhibit a type of non-linearity which can be accounted for by a threshold model.