Volume 6, Issue 1 -

In this article, we investigate and compare the behaviour of some bootstrap unit root tests in finite ARMA models with a constant and/or a trend and use them to obtain asymptotic results for the point optimal (hereafter PO) test, in terms of both size and power. We demonstrate the asymptotic validity of bootstrapping the PO test. We provide a feasible method for obtaining approximate critical values for the PO unit root test. Through simulations, we investigate how effective the bootstrap is in different sample sizes, correlative coefficients and close unity autoregressive roots in two different models. Our main objective is to show that the bootstrap PO test can be used in regression models with AR and MA errors and trending regressors. The results reported here provide an analytical investigation of the use of the bootstrap for PO tests with dependent data.The main contribution of this article has two features. First, we choose the PO test and make this powerful but unfeasible procedure both powerful and feasible, by plugging in a consistent estimation of the coefficient structure, and we show that the bootstrap PO test provides asymptotically valid critical values. Second, through simulation, our numerical results suggest that the bootstrap PO test performs well in having the correct size properties and retaining good power in the parametric (and semi-parametric) bootstrap procedure.

In this article, we extend the stationarity test proposed by Kurozumi and Tanaka (2010. “Reducing the size distortion of the KPSS test.” Journal of Time Series Analysis 31:415–26) to reduce size distortion with one structural break in data generating process. We find the bias up to the order of for four types of models containing structural breaks. Simulations on finite samples show a decrease of size distortions relative to other tests, thus receiving higher power.

The quasi-maximum likelihood estimator (QMLE) of parameters in the first-order moving average model can be biased in finite samples. We develop the second-order analytical bias of the QMLE and investigate whether this estimation bias can lead to biased feasible optimal forecasts conditional on the available sample observations. We find that the feasible multiple-step-ahead forecasts are unbiased under any nonnormal distribution, and the one-step-ahead forecast is unbiased under symmetric distributions.

The claim that linear filters are liable to induce spurious fluctuations has been repeated many times of late. However, there are good reasons for asserting that this cannot be the case for the filters that, nowadays, are commonly employed by econometricians. If these filters cannot have the effects that have been attributed to them, then one must ask what effects the filters do have that could have led to the aspersions that have been made against them.