Short memory models contaminated by level shifts have similar long-memory features as fractionally integrated processes. This makes it hard to verify whether the true data generating process is a pure fractionally integrated process when employing standard estimation methods based on the...

We consider the problem of testing for unit root in time series where the error term of the series is near unit root. As the error term approaches unit root, existing tests no longer retain reasonable small sample properties. We introduce a test statistic that is well-behaved in small sample...

In this research note, we accomplish two objectives. First, we reexamine the reliability of unit root findings in the study by Said and Dickey (1984) and show that their results are internally consistent. Second, we provide new results from the reanalysis of the original data that were not...

We derive formulae for the asymptotic density and distribution functions of the t-statistic for autoregressive unit roots based on M-estimators. The distribution depends upon a nuisance parameter. Consequently, new critical values for this test have to be generated for each new estimator that is...

This paper introduces a novel way of differentiating a unit root from a stationary alternative. We write up the model consisting of zero and nonzero parameters. If the lagged dependent variable has a coefficient of zero, we know that the variable has a unit root. We exploit this property and...

In this paper I propose a novel optimal linear filter for smoothing, trend and signal extraction for time series with a unit root. The filter is based on the Singular Spectrum Analysis (SSA) methodology, takes the form of a particular moving average and is different from other linear filters...

This chapter examines the problems of dealing with trending type data when there is uncertainty over whether or not we really have unit roots in the data. This uncertainty is practical – for many macroeconomic and financial variables theory does not imply a unit root in the data however unit...

This paper uses wavelet theory to propose a frequency domain nonparametric and tuning parameter free family of unit root tests indexed by the fractional parameter d. The proposed test exploits the wavelet power spectrum of the observed series and its fractional partial sum to construct a test of...