Unit root tests in time series. Volume 2. Extensions and developments (Q482830)

The book is the second volume of [Zbl 1341.62019]. The aim of these tests is to decide whether a series is stationary. The author presents the most known models for non-stationary time series in connection with the unit root tests. The book does not study the models and methods from a mathematical point of view (no derivations of asymptotic properties or approximations of estimates or test statistics distributions). Rather, it gives an overview of models and decision procedures for non-stationary behavior of time series widely used in economic applications with exhausting lists of references. The book has 9 chapters. Chapter 1 offers a brief reminder of the models and methods described in the first volume together with an introduction of the change-point problem in regression. Chapter 2 named ``Functional form of nonparametric tests for unit roots'' shows that it is vital whether a unit root test is applied to original data or their logarithms. It shows how the tests may be modified using ranks, signs and runs. The fractional integrated time series \(I(d)\), \(d \in (0,1)\) are defined in Chapter 3. The estimation of \(d\) is considered together with Dickey-Fuller tests applied to these series. Chapter 4 deals with the problem of the semiparametric estimation of a long-memory parameter. Chapter 5 describes models of series with natural bounds. The AR models where coefficients change as a function of the deviation of an activating variable from its target or threshold value may serve as an example. The second example is the bounded random walk. Chapter 6 describes AR models with changing parameters after they exceeded a threshold. Chapter 7 presents procedures for testing a change in stochastic behavior of time series when a potential change point is known while Chapter 8 presents procedures for detecting a change (changes) when the change point(s) is (are) unknown. It also suggests how to estimate change point(s) if stationarity of series was rejected. Finally, Chapter 9 covers an impact of ARCH/GARCH type of heteroscedasticity on unit root tests.