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We first construct a new generalized Hausman test for detecting the structural change in a multiplicative form of covariance matrix time series model. This generalized Hausman test is asymptotically pivotal, and has nontrivial power in detecting a broad class of alternatives. Moreover, we propose a new semiparametric covariance matrix time series model. The proposed model has a time-varying longrun component that takes the structural change into account, and a BEKK-type short-run component that captures the temporal dependence. We propose a twostep estimation procedure to estimate this semiparametric model, and establish the asymptotics of the related estimators. Finally, the importance of the generalized Hausman test and the semiparametric model is illustrated by means of simulations and an application to realized covariance matrix data. [ABSTRACT FROM AUTHOR]

We propose a new Conditional BEKK matrix-F (CBF) model for time-varying realized covariance (RCOV) matrices. This CBF model is capable of capturing a heavy-tailed RCOV, which is an important stylized fact, but is not handled adequately by Wishart-based models. To further mimic the long-memory feature of an RCOV, we introduce a special CBF model with a conditional heterogeneous autoregressive structure. Moreover, we provide a systematic study of the probabilistic properties and statistical inferences of the CBF model, including exploring its stationarity, establishing the asymptotics of its maximum likelihood estimator, and giving new inner-product-based tests for model checking. In order to handle a large-dimensional RCOV matrix, we construct two reduced CBF models: the variance-target CBF model (for a moderate but fixed-dimensional RCOV matrix), and the factor CBF model (for a high-dimensional RCOV matrix). For both reduced models, the asymptotic theory of the estimated parameters is derived. The importance of our methodology is illustrated by means of simulations and two real examples. [ABSTRACT FROM AUTHOR]

We propose novel one-sided omnibus tests for independence between two multivariate stationary time series. These new tests apply the Hilbert-Schmidt independence criterion (HSIC) to test the independence between the innovations of the time series. We establish the limiting null distributions of our HSIC-based tests under regular conditions. Next, our HSIC-based tests are shown to be consistent. A residual bootstrap method is used to obtain the critical values for the tests, and its validity is justified. Existing cross-correlation-based tests examine linear dependence. In contrast, our tests examine general dependence (including linear and non-linear), providing researchers with information that is more complete on the causal relationship between two multivariate time series. The merits of our tests are illustrated using simulations and a real-data example. [ABSTRACT FROM AUTHOR]

A buffered autoregression extends the classical threshold autoregression by allowing a buffer region for regime changes. In this study, we examine asymp-totic statistical inferences for the two-regime buffered autoregressive (BAR) model, with autoregressive unit roots. We propose a Sup-LR test for the nonlinear buffer effect in the possible presence of unit roots, and a class of unit root tests to identify the number of nonstationary regimes in the BAR model. The wild bootstrap method is suggested to approximate the critical values of the two tests. Simulation results show that the proposed unit root test outperforms the conventional augmented Dickey{Fuller test, and that the two wild bootstrap tests are robust to unknown heteroscedasticity. Two macroeconomic data examples, based on U.S. unemployment rates and real exchange rates, respectively, are provided to illustrate the methods. [ABSTRACT FROM AUTHOR]

The phenomenon of hysteresis has been observed in many economic time series, especially in unemployment rates. To study the hysteretic patterns at different quantiles, this study considers a conditional quantile estimation for hysteretic autoregressive models, and derives its asymptotic properties. Simulation experiments are conducted to evaluate the finite-sample performance of our method, and its usefulness is further demonstrated by an analysis of the growth rates of unemployment rates. [ABSTRACT FROM AUTHOR]

Note that A T () 1 p T max t T jy t 1 R t ()j 1 p T T X t=1 w 0 t (0 0)[R t (0) R t ()] In Li et al. (2015), the convergence of the estimated thresholds was shown to be T (^ r L r L0) = O p (1) and T (^ r U r U0) = O p (1). Under the unit root hypothesis, for any we have ~ t 1 () = ~ N T () + ~ A T () q ~ D T ()^ 2 where ~ N T () = 1 T T X t=1 ~ y t 1 ~ e t ~ R t () 1 T T X t=1 ~ y t 1 ~ w t 1 ~ R t () T X t=1 ~ w 2 t 1 ~ R t () ! Note that X 0 X is a special case of X 0 ()X and denote M =X 0 X=T. From Lemma 1.2, it can be obtained that M() is asymptotically block diagonal, then LR T () is LR T () =S 0 1 ()[M 11 () M 11 ()M 1 11 M 11 ()] 1 S 1 () +S 0 2 ()[M 22 () M 22 ()M 1 22 M 22 ()] 1 S 2 () +o p (1) = S 0 1 () p T M 11 () T M 11 () T M 11 T 1 M 11 () T 1 S 0 p T +S 0 2 ()[M 22 () M 22 ()M 1 22 M 22 ()] 1 S 2 () +o p (1) where 1 p T S 1 () = 1 p T T X t=1 y t 1 p T e t R t () 1 p T M 11 ()M 1 11 T X t=1 y t 1 p T e t) Z 1 0 W (s)dW (s;R()) R() Z 1 0 W (s)dW (s); S 2 () = 1 p T T X t=1 w t e t R t () 1 p T M 22 ()M 1 22 T X t=1 w t e t)G() 1 G; M 11 () T M 11 () T M 1 11 T M 11 () T)R()(1 R()) Z 1 0 W 2 (s)ds; and M 22 () M 22 ()M 1 22 M 22 ()!. [Extracted from the article]

20 LI, ZENG, ZHANG, LI AND LI Li, G., Li, Y., and Tsai, C.-L. (2015b). Additionally, 2 LI, ZENG, ZHANG, LI AND LI the equality holds if and only if = 0. Similarly, we can obtain that 2 = 0 2 from the equality Ef(y t x T t 2)(Ifx T t 0 2 >y t >x T t 2 g Ifx T t 0 2 y t >x T t 1 g Ifx T t 0 2 y t >x T t 2 g Ifx T t 0 1