In this article, we develop the asymptotic theory of Hwang and Basawa (2005) for explosive random coefficient autoregressive (ERCA) models. Applying the theory, we prove that a locally best invariant (LBI) test in McCabe and Tremayne (1995), which is for the null of a unit root (UR) process...

In this paper, we propose a simple methodology for investigating how shocks to trend and cycle are correlated in unidentified unobserved components models, in which the correlation is not identified. The proposed methodology is applied to U.S. and U.K. real GDP data. We find that the correlation...

In this note, I consider a general class of unobserved components (UC) models and derive a relevant inequality. This inequality implies that either of the two assumptions of standard UC models, namely, a random walk trend and uncorrelated shocks, is not satisfied if the impulse response measure...

The well known Jarque-Bera (JB) test for normality uses the sample mean and sample standard deviation for estimating the population mean and population standard deviation. Instead of the sample standard deviation, Gel and Gastwirth (2008) proposed to use a robust scale estimator, known as the...

The random coefficient autoregressive model has been utilized for modeling financial time series because it possesses features that are often observed in financial time series. When the mean of the random autoregressive coefficient is one, it is called the stochastic unit root model. This paper...

We introduce a matrix operator, which we call "vecd'' operator. This operator stacks up "diagonals'' of a symmetric matrix. This operator is more convenient for some statistical analyses than the commonly used "vech'' operator. We show an explicit relationship between the vecd and vech...