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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

This paper extends the classical two-regime threshold autoregressive model by introducing hysteresis to its regime-switching structure, which leads to a new model: the hysteretic autoregressive model. The proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism. A sufficient condition is given for geometric ergodicity. Conditional least squares estimation is discussed, and the asymptotic distributions of its estimators and information criteria for model selection are derived. Simulation results and an example support the model. [ABSTRACT FROM AUTHOR]

This paper considers a local least absolute deviation estimation for unit root processes with generalized autoregressive conditional heteroskedastic (GARCH) errors and derives its asymptotic properties under only finite second-order moment for both errors and innovations. When the innovations are symmetrically distributed, the asymptotic distribution of the estimated unit root is shown to be a functional of a bivariate Brownian motion, and then two unit root tests are derived. The simulation results demonstrate that the tests outperform those based on the Gaussian quasi maximum likelihood estimators with heavy-tailed innovations and those based on the simple least absolute deviation estimators. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the use of an interactive hidden Markov model (IHMM) for modeling and analyzing default data in a sector. Under the IHMM, transitions of the hidden risk states of the sector depend on the observed number of bonds in the sector that default in the current time period. This incorporates the feedback effect of the number of defaults on the transitions of the hidden risk states. This feature seems to be more realistic and does not enjoy by the traditional HMMs. We then develop a “dynamic” version of the binomial expansion technique (BET) modulated by the IHMM for modeling the occurrence of defaults of bonds issued by firms in the same sector. Under the BET modulated by the IHMM, the number of bonds defaulting in each time period follows a Markov-modulated binomial distribution with the probability of defaulting of each bond depending on the states of the IHMM, which represent the hidden risk states of the sector. Efficient method will be presented for estimating the model parameters in the BET modulated by the IHMM. We shall compare the hidden risk state process extracted from the IHMM-modulated BET with that extracted from the BET modulated by HMM in order to illustrate the significance of the feedback effect using real data. We shall also present the estimation results for the BET modulated by the IHMM and compare them with those for the BET modulated by the HMM. [ABSTRACT FROM AUTHOR]

The recent paper by Peng & Yao (2003) gave an interesting extension of least absolute deviation estimation to generalised autoregressive conditional heteroscedasticity, GARCH, time series models. The asymptotic distributions of absolute residual autocorrelations and squared residual autocorrelations from the GARCH model estimated by the least absolute deviation method are derived in this paper. These results lead to two useful diagnostic tools which can be used to check whether or not a GARCH model fitted by using the least absolute deviation method is adequate. Some simulation experiments give further support to the asymptotic theory and a real data example is also reported. [ABSTRACT FROM AUTHOR]

We give several definitions of residual autocorrelations and derive their joint asymptotic distribution for the panel time series model of Hjellvik & Tjøstheim (1999a). A portmanteau goodness‐of‐fit test arises naturally from the asymptotic distribution. Simulation results show that the asymptotic standard errors compared satisfactorily with the empirical standard errors, that the goodness‐of‐fit test has reasonable empirical size, and that it is powerful enough to be useful with a modest sample size. The results of this paper are illustrated with a real‐data example. [ABSTRACT FROM PUBLISHER]

We propose a mixture autoregressive conditional heteroscedastic (MAR-ARCH) model for modeling nonlinear time series. The models consist of a mixture of K autoregressive components with autoregressive conditional heteroscedasticity; that is, the conditional mean of the process variable follows a mixture AR (MAR) process, whereas the conditional variance of the process variable follows a mixture ARCH process. In addition to the advantage of better description of the conditional distributions from the MAR model, the MAR-ARCH model allows a more flexible squared autocorrelation structure. The stationarity conditions, autocorrelation function, and squared autocorrelation function are derived. Construction of multiple step predictive distributions is discussed. The estimation can be easily done through a simple EM algorithm, and the model selection problem is addressed. The shape-changing feature of the conditional distributions makes these models capable of modeling time series with multimodal conditional distributions and with heteroscedasticity. The models are applied to two real datasets and compared to other competing models. The MAR-ARCH models appear to capture features of the data better than the competing models. [ABSTRACT FROM AUTHOR]

We consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity. Its asymptotic normality is established when the second moments of errors and innovations are finite. Several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach. A diagnostic tool, consisting of two portmanteau tests, is designed to check whether or not the estimated models are adequate. The simulation experiments give further support to our model and the results for the absolute returns of the Dow Jones Industrial Average Index daily closing price demonstrate their usefulness in modelling time series exhibiting the features of long memory, conditional heteroscedasticity and heavy tails. [ABSTRACT FROM AUTHOR]