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  • 1.
    He, Changli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Malmsten, Hans
    Teräsvirta, Timo
    Higher-order dependence in the general Power ARCH process and a special case2008In: Recent Advances In Linear Models and Related Areas / [ed] Shalabh, C. Heumann, Springer , 2008, p. 231-252Chapter in book (Other academic)
  • 2.
    He, Changli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Sandberg, Rickard
    Testing parameter constancy in unit root autoregressive models against multiple continuous structural changes2012In: Econometric Reviews, ISSN 0747-4938, E-ISSN 1532-4168, Vol. 31, no 1, p. 34-59Article in journal (Refereed)
    Abstract [en]

    This article considers tests for logistic smooth transition autoregressive (LSTAR) models accommodating multiple time dependent transitions between regimes when the data generating process is a random walk. The asymptotic null distributions of the tests, in contrast to the standard results in Lin and Teräsvirta (1994), are nonstandard. Monte Carlo experiments reveal that the tests have modest size distortions and satisfactory power against LSTAR models with multiple smooth breaks. The tests are applied to Swedish unemployment rates and the hysteresis hypothesis is over-turned in favour of an LSTAR model with two transitions between extreme regimes.

  • 3.
    He, Changli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Silvennoinen, Annastiina
    Teräsvirta, Timo
    Parameterizing unconditional skewness in models for financial time series2008In: Journal of Financial Econometrics, ISSN 1479-8409, E-ISSN 1479-8417, Vol. 6, no 2, p. 208-230Article in journal (Other academic)
    Abstract [en]

    In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modeling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution

  • 4.
    He, Changli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Strandberg, Rickard
    Dickey-Fuller type of tests against non-linear dynamic models2006In: Oxford Bulletin of Economics and Statistics, ISSN 0305-9049, E-ISSN 1468-0084, Vol. 68, no s1, p. 835-861Article in journal (Refereed)
    Abstract [en]

    In this paper, we introduce several test statistics testing the null hypothesis of a random walk (with or without drift) against models that accommodate a smooth nonlinear shift in the level, the dynamic structure and the trend. We derive analytical limiting distributions for all the tests. The power performance of the tests is compared with that of the unit-root tests by Phillips and Perron [Biometrika (1988), Vol. 75, pp. 335–346], and Leybourne, Newbold and Vougas [Journal of Time Series Analysis (1998), Vol. 19, pp. 83–97]. In the presence of a gradual change in the deterministics and in the dynamics, our tests are superior in terms of power.

  • 5.
    He, Changli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Teräsvirta, Timo
    An extended constant conditional correlation GARCH model and its fourth-moment structure2004In: Econometric Theory, ISSN 0266-4666, E-ISSN 1469-4360, Vol. 20, no 5, p. 904-926Article in journal (Refereed)
    Abstract [en]

    The constant conditional correlation general autoregressive conditional heteroskedasticity (GARCH) model is among the most commonly applied multivariate GARCH models and serves as a benchmark against which other models can be compared. In this paper we consider an extension to this model and examine its fourth-moment structure. The extension, first defined by Jeantheau (1998, Econometric Theory 14, 70–86), is motivated by the result found and discussed in this paper that the squared observations from the extended model have a rich autocorrelation structure. This means that already the first-order model is capable of reproducing a whole variety of autocorrelation structures observed in financial return series. These autocorrelations are derived for the first- and the second-order constant conditional correlation GARCH model. The usefulness of the theoretical results of the paper is demonstrated by reconsidering an empirical example that appeared in the original paper on the constant conditional correlation GARCH model.

  • 6.
    He, Changli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Teräsvirta, Timo
    Fourth Moment Structure of the Garch (p,q) Process1999In: Econometric Theory, Vol. 15, no 6Article in journal (Refereed)
    Abstract [en]

    In this paper, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH(p,q) process is given and also an expression for the moment itself. Furthermore, the autocorrelation function of the centered and squared observations of this process is derived. The statistical theory is further illustrated by a few special cases such as theGARCH(2,2)process and the ARCH(q) process.

  • 7.
    He, Changli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Teräsvirta, Timo
    Properties of moments of a family of GARCH processes1999In: Journal of Econometrics, ISSN 0304-4076, E-ISSN 1872-6895, Vol. 92, no 1, p. 173-192Article in journal (Refereed)
    Abstract [en]

    This paper considers the moments of a family of first-order GARCH processes. First, a general condition for the existence of any integer moment of the absolute values of the observations is given. Second, a general expression for this moment as a function of lower-order moments is derived. Third, the kurtosis and the autocorrelation function of the squared and absolute-valued observations are derived. The results apply to a number of different GARCH parameterizations. Finally, the existence, or lack thereof, of the theoretical counterpart to the so-called Taylor effect in some members of this GARCH family is discussed. Possibilities of extending the results to higher-order GARCH processes are indicated and potential applications of the statistical theory proposed.

  • 8.
    He, Changli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Teräsvirta, Timo
    Gónzalez, Andrés
    Testing parameter constancy in stationary vector autoregressive models against continuous change2008In: Econometric Reviews, ISSN 0747-4938, E-ISSN 1532-4168, Vol. 28, no 1-3, p. 225-245Article in journal (Refereed)
    Abstract [en]

    In this article we derive a parameter constancy test of a stationary vector autoregressive model against the hypothesis that the parameters of the model change smoothly over time. A single structural break is contained in this alternative hypothesis as a special case. The test is a generalization of a single-equation test of a similar hypothesis proposed in the literature. An advantage here is that the asymptotic distribution theory is standard. The performance of the tests is compared to that of generalized Chow-tests and found satisfactory in terms of both size and power.

  • 9.
    Li, Dao
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    He, Changli
    Dalarna University, School of Technology and Business Studies, Statistics.
    Forecasting with Vector Nonlinear Time Series Models2013Report (Other academic)
    Abstract [en]

    This work concerns forecasting with vector nonlinear time series models when errorsare correlated. Point forecasts are numerically obtained using bootstrap methods andillustrated by two examples. Evaluation concentrates on studying forecast equality andencompassing. Nonlinear impulse responses are further considered and graphically sum-marized by highest density region. Finally, two macroeconomic data sets are used toillustrate our work. The forecasts from linear or nonlinear model could contribute usefulinformation absent in the forecasts form the other model.

  • 10.
    Li, Dao
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    He, Changli
    Dalarna University, School of Technology and Business Studies, Statistics.
    Testing common nonlinear features in vector nonlinear autoregressive models2012Report (Other academic)
    Abstract [en]

    This paper studies a special class of vector smooth-transition autoregressive (VSTAR) models that contains common nonlinear features (CNFs), for which we proposed a triangular representation and developed a procedure of testing CNFs in a VSTAR model. We first test a unit root against a stable STAR process for each individual time series and then examine whether CNFs exist in the system by Lagrange Multiplier (LM) test if unit root is rejected in the first step. The LM test has standard Chi-squared asymptotic distribution. The critical values of our unit root tests and small-sample properties of the F form of our LM test are studied by Monte Carlo simulations. We illustrate how to test and model CNFs using the monthly growth of consumption and income data of United States (1985:1 to 2011:11).

  • 11.
    Meng, Xiangli
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    He, Changli
    Dalarna University, School of Technology and Business Studies, Statistics.
    Testing Seasonal Unit Roots in Data at Any Frequency, an HEGY approach2012Report (Other academic)
    Abstract [en]

    This paper generalizes the HEGY-type test to detect seasonal unit roots in data at any frequency, based on the seasonal unit root tests in univariate time series by Hylleberg, Engle, Granger and Yoo (1990). We introduce the seasonal unit roots at first, and then derive the mechanism of the HEGY-type test for data with any frequency. Thereafter we provide the asymptotic distributions of our test statistics when different test regressions are employed. We find that the F-statistics for testing conjugation unit roots have the same asymptotic distributions. Then we compute the finite-sample and asymptotic critical values for daily and hourly data by a Monte Carlo method. The power and size properties of our test for hourly data is investigated, and we find that including lag augmentations in auxiliary regression without lag elimination have the smallest size distortion and tests with seasonal dummies included in auxiliary regression have more power than the tests without seasonal dummies. At last we apply the our test to hourly wind power production data in Sweden and shows there are no seasonal unit roots in the series.

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