This paper revisits the topic of time-scale parameterizations of the Heston-Nandi GARCH (1,1) model to create a new, theoretically valid setting compatible with real financial data. We first estimate parameters using three US market indices and six frequencies to let data reveal the correct,...

We consider two likelihood ratio tests, so-called maximum eigenvalue and trace tests, for the null of no cointegration when fractional cointegration is allowed under the alternative, which is a first step to generalize the so-called Johansen's procedure to the fractional cointegration case. The...

We consider cointegration rank estimation for a p-dimensional Fractional Vector Error Correction Model. We propose a new two-step procedure which allows testing for further long-run equilibrium relations with possibly different persistence levels. The fi?rst step consists in estimating the...

In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following...

In this paper we consider a fractionally cointegrated error correction model and investigate asymptotic properties of the maximum likelihood (ML) estimators of the matrix of the cointegration relations, the degree of fractional cointegration, the matrix of the speed of adjustment to the...

This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with...

In an important generalization of zero frequency autoregressive unit root tests, Hylleberg, Engle, Granger, and Yoo (1990) developed regression-based tests for unit roots at the seasonal frequencies in quarterly time series. We develop likelihood ratio tests for seasonal unit roots and show that...

Seemingly absent from the arsenal of currently available "nearly efficient" testing procedures for the unit root hypothesis, i.e. tests whose local asymptotic power functions are indistinguishable from the Gaussian power envelope, is a test admitting a (quasi-)likelihood ratio interpretation. We...