In this paper we consider a general first-order power ARCH process and, in particular, a special case in which the power parameter approaches zero. These considerations give us the autocorrelation function of the logarithms of the squared observations for first-order exponential and logarithmic...

In this paper a unified framework for testing the adequacy of an estimated GARCH model is presented. Parametric LM or LM type tests of no ARCH in standardized errors, linearity, and parameter constancy are proposed. The asymptotic null distributions of the tests are standard, which makes...

Many high frequency economic or financial time series display two empirical characteristics: high kurtosis and positive autocorrelation in the centred and squared observations. The first- order autocorrelation is typically low, and the autocorrelation function decays slowly. These series are...

The difficulty of predicting stock returns has recently motivated researchers to start looking for more powerful tests, and the current paper takes a step in this direction. Unlike existing tests, the test proposed here exploits the information contained in the heteroskedasticity of returns,...

This paper investigates statistical properties of the local generalized method of moments (LGMM) estimator for some time series models defined by conditional moment restrictions. First, we consider Markov processes with possible conditional heteroskedasticity of unknown forms and establish the...

In this paper, we propose two parametric alternatives to the standard GARCH model. They allow the variance of the model to have a smooth time-varying structure of either additive or multiplicative type. The suggested parameterisations describe both nonlinearity and structural change in the...

In this paper, we propose two parametric alternatives to the standard GARCH model. They allow the variance of the model to have a smooth time-varying structure of either additive or multiplicative type. The suggested parameterisations describe both nonlinearity and structural change in the...

This paper introduces a new confidence interval (CI) for the autoregressive parameter (AR) in an AR(1) model that allows for conditional heteroskedasticity of general form and AR parameters that are less than or equal to unity. The CI is a modification of Mikusheva's (2007a) modification of...

In recent years the Chinese stock market has experienced an astonishing growth and unprecedented development, but is also viewed as one of the most volatile markets, which has been called by many observers a “casino”. This study intends to examine the presence of heteroskedasticity and the...