Cumulative sum algorithms for automatic detection of gas well parameter changes

The problem of the change point detection in a sequence of random variables is considered. The task arises in control of technological processes, particularly, in oil and gas production management. Some equipment parameters are to be controlled in order to detect a change of the equipment characteristics and, consequently, a breakdown of its technological regime. As a rule, the data observed are stochastic with the unknown distribution

Fixed accuracy estimation of parameters in a threshold autoregressive model

For parameters in a threshold autoregressive process, the paper proposes a sequential modification of the least squares estimates with a specific stopping rule for collecting the data for each parameter. In the case of normal residuals, these estimates are exactly normally distributed in a wide range of unknown parameters. On the base of these estimates, a fixed-size confidence ellipsoid covering true values of parameters with prescribed probability is constructed. In the i.i.d. case with unspecified error distributions, the sequential estimates are asymptotically normally distributed uniformly in parameters belonging to any compact set in the ergodicity parametric region. Small-sample behavior of the estimates is studied via simulation data

Оценка параметра и обнаружения разладок процесса AR(p)/ARCH(q) с неизвестными параметрами

The problem of parameter estimation and change point detection of process AR(p)/ARCH(q) is considered. Sequential estimators with bounded standard deviation are proposed and their asymptotic properties are studied. The obtained estimators are used in a sequential change-point detection algorithm; due to usage of the estimators the false alarm and delay probabilities are bounded from above. The results of simulation are presented

Доверительное неасимптотическое оценивание параметра авторегрессии AR(1) по зашумленным данным

For parameter in an AR(1) process corrupted by noise, the paper proposes the construction of confi-dence interval for unknown parameter with a prescribed coverage probability. The noises both in observable and in unobservable processes are assumed to be Gaussian with unknown variance. The estimation procedure is non-asymptotic and uses a special stopping rule. The results of numerical simulation by Monte-Carlo method are presented