This paper focuses on two applications of time series methods. The first proposes a simple transformation of the unit root form of stationary testing to infer about the validity of smoothing by second-order running averages of a series, or of the variables in a linear model (here opposing...

This paper inspects a grid search algorithm to estimate the AR(1) process, based on the joint estimation of the canonical AR(1) equation along with its reverse form. The method relies on the GLS principle, accounting for the covariance error structure of the special estimable system....

In this paper, we propose methods of the determination of the rank of matrix. We consider a rank test for an unobserved matrix for which an estimate exists having normal asymptotic distribution of order N1/2 where N is the sample size. The test statistic is based on the smallest estimated...

In this paper, we develop methods of the determination of the rank of random matrix. Using the matrix perturbation theory to construct or find a suitable bases of the kernel (null space) of the matrix and to determine the limiting distribution of the estimator of the smallest singular values. We...

In observational studies, confounding variables that affect both the exposure and an outcome of interest are a general concern. It is well known that failure to control for confounding variables adequately can worsen inference on an exposure's effect on outcome. In this paper, we explore how...