Fractionally integrated processes have become a standard class of models to describe the long memory features of economic and financial time series data. However, it has been demonstrated in numerous studies that structural break processes and non-linear features can often be confused as being...

We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x_{t}=Delta^{-d}u_{t}, where d in (-1/2,1/2) is the fractional integration parameter and u_{t} is weakly dependent. The classical condition is existence of qmax(2,(d+1/2)^{-1}) moments...

We consider the nonstationary fractional model $\Delta^{d}X_{t}=\varepsilon _{t}$ with $\varepsilon_{t}$ i.i.d.$(0,\sigma^{2})$ and $d1/2$. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of $d$ conditional on initial values, and we...

We develop a model that can match two stylized facts of the term-structure. The first stylized fact is the predictability of excess returns on long-term bonds. Modeling this requires sufficient volatility and persistence in the price of risk. The second stylized fact is that long-term yields are...

This paper investigates the asymptotic properties of the Gaussian quasi-maximum-likelihood estimators (QMLE?s) of the GARCH model augmented by including an additional explanatory variable - the so-called GARCH-X model. The additional covariate is allowed to exhibit any degree of persistence as...

This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses the...

Empirical evidence from time series methods which assume the usual I(0)/I(1) paradigm suggests that the efficient market hypothesis, stating that spot and futures prices of a commodity should cointegrate with a unit slope on futures prices, does not hold. However, these statistical methods are...

The dynamic dependencies in financial market volatility are generally well described by a long-memory fractionally integrated process. At the same time, the volatility risk premium, defined as the difference between the ex-post realized volatility and the market’s ex-ante expectation thereof,...

This paper derives a semiparametric estimator of multivariate fractionally integrated processes covering both stationary and non-stationary values of d. We utilize the notion of the extended discrete Fourier transform and periodogram to extend the multivariate local Whittle estimator of Shimotsu...

In this paper, we propose new tests for long memory in stationary and nonstationary time series possibly perturbed by short-run noise which may be serially correlated. The tests are all based on semiparametric estimators and exploit the self-similarity property of long memory processes. We o¤er...