N. Balakrishna

Inverse Gaussian Autoregressive Models

A first‐order autoregressive process with one‐dimensional inverse Gaussian marginals is introduced. The innovation distributions are obtained in certain special cases. The unknown parameters are estimated using different methods and these estimators are shown to be consistent and asymptotically normal. Performance of the estimators is discussed using simulation experiments.

Bivariate semi-Pareto distributions and processes

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.

Parameter Estimation in Minification Processes

Abstract 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.

Markovian chi-square and gamma processes

A sequence {Xn, n [greater-or-equal, slanted] 1} of random variables such that each Xn has chi-square or gamma distribution can be generated from independent Gaussian sequences. We study the properties of such sequences. The Markov property of gamma and chi-square sequences is characterized. The extension of these results to continuous time processes is indicated. A general gamma Markov model based on sums of random numbers of independent exponential and gamma random variables is formulated and its properties are investigated.

Estimation of the mean of some stationary markov sequences

This paper deals with the estimation of the mean e of the stationary distribution of some Markov sequences. In particular, if one can identify the error variables from a given realization of the model, it is possible to obtain improved estimators based on the errors. A two stage procedure for determining the regression parameter without error and then estimating the mean is presented. The conditional least square and the best linear unbiased estimators of e are studied and compared with the traditional timeaverage. The asymptotic properties of these estimators are also established.

Inverse Gaussian Distribution for Modeling Conditional Durations in Finance

The durations between market activities such as trades and quotes provide useful information on the underlying assets while analyzing financial time series. In this article, we propose a stochastic conditional duration model based on the inverse Gaussian distribution. The non-monotonic nature of the failure rate of the inverse Gaussian distribution makes it suitable for modeling the durations in financial time series. The parameters of the proposed model are estimated by an efficient importance sampling method. A simulation experiment is conducted to check the performance of the estimators. These estimates are used to compute estimated hazard functions and to compare with the empirical hazard functions. Finally, a real data analysis is provided to illustrate the practical utility of the models.

Estimation for the semipareto processes

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.

Extreme value autoregressive model and its applications

This article proposes a first-order autoregressive model with Gumbel extreme value marginal distribution to analyze the time-series data. As the innovation distribution of the model does not admit a closed-form expression, the problem of estimation becomes complicated. In this article, we propose the method of conditional least squares, quasi maximum likelihood, and maximum likelihood for estimating model parameters. Simulation studies are carried out to assess the performance of these methods. Two sets of real data are analyzed to illustrate the applications of the proposed model.

Sequential interval estimation of the limiting interval availability for a bivariate stationary dependent sequence

In this paper, we consider the sequential confidence interval estimation of the limiting interval availability of a repairable system when the sequences of failure and repair times are generated by a bivariate stationary dependent sequence. The confidence interval and the proposed stopping rule are shown to be asymptotically consistent and efficient as the width of the interval approaches zero. In particular, we consider the sequential interval estimation of the limiting interval availability for a first-order bivariate exponential autoregressive process. A simulation study is also conducted to asses the performance of the proposed confidence interval.

Nonparametric Estimation of the Average Availability

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.