This paper explores nonlinear dynamics for the time series of the short term interest rate in the United States. The proposed model is an autoregressive threshold model augmented by conditional heteroskedasticity. The performance of the model is evaluated by considering its implications for the term structure of interest rates. The nonlinear dynamics imply a form of nonlin-earity in the levels ...

Using a multivariate generalized autoregressive conditional heteroskedasticity (GARCH-M) model, we investigate volatility spillovers in six Southeast Asian stock markets around the time of the 1997 Asian crisis. We focus on interactions with the U.S. market as a world financial market, and with the Japanese market as a regional financial market. We also use bivariate GARCH-M models to examine t...

The autocorrelation function of volatility in financial time series is fitted well by a superposition of several exponents. This case admits an explicit analytical solution of the problem of constructing the best linear forecast of a stationary stochastic process. We describe and apply the proposed analytical method for forecasting volatility. The leverage effect and volatility clustering are t...

In this paper we propose a generalised autoregressive conditional heteroskedasticity (GARCH) model-based test for a unit root. The model allows for two endogenous structural breaks. We test for unit roots in 156 US stocks listed on the NYSE over the period 1980 to 2007. We find that the unit root null hypothesis is rejected in 40% of the stocks, and only in four out of the nine sectors the null...

Starting from a robust, nonparametric definition of large returns ("excursions"), we study the statistics of their occurrences, focusing on the recurrence process. The empirical waiting-time distribution between excursions is remarkably invariant to year, stock, and scale (return interval). This invariance is related to self-similarity of the marginal distributions of returns, but the excursion...

4. Course Outline: (i) Review of Linear ARMA/ARIMA Time Series Models and their Properties. (ii) An Introduction to Spectral Analysis of Time Series. (iii) Fractional Differencing and Long Memory Time Series Modelling. (iv) Generalized Fractional Processes. Gegenbaur Processes. (v) Topics from Financial Time Series/Econometrics: ARCH and GARCH Models. (vi ) Time Series Modelling of Durations: A...

We study asymptotic properties of the local Whittle estimator of the long memory parameter for a wide class of fractionally integrated nonlinear time series models+ In particular, we solve the conjecture posed by Phillips and Shimotsu ~2004, Annals of Statistics 32, 656–692! for Type I processes under our framework, which requires a global smoothness condition on the spectral density of the sho...

This note investigates impacts of multivariate generalised autoregressive conditional heteroskedasticity (GARCH) errors on hypothesis testing for cointegrating vectors. The study reviews a cointegrated vector autoregressive model incorporating multivariate GARCH innovations and a regularity condition required for valid asymptotic inferences. Monte Carlo experiments are then conducted on a test ...