The exponential model for the spectrum of a time series and its fractional extensions are based on the Fourier series expansion of the logarithm of the spectral density. The coefficients of the expansion form the cepstrum of the time series. After deriving the cepstrum of important classes of...

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 examine the joint predictability of return and cash flow within a present value framework, by imposing the implications from a long-run risk model that allow for both time-varying volatility and volatility uncertainty. We provide new evidence that the expected return variation and the...

We test for price discontinuities, or jumps, in a panel of high-frequency intraday returns for forty large-cap stocks and an equiweighted index from these same stocks. Jumps are naturally classified into two types: common and idiosyncratic. Common jumps affect all stocks, albeit to varying...

We develop a $C_{p}$ statistic for the selection of regression models with stationary and nonstationary ARIMA error term. We derive the asymptotic theory of the maximum likelihood estimators and show they are consistent and asymptotically Gaussian. We also prove that the distribution of the sum...

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...

The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is...

Structural change affects the estimation of economic signals, like the underlying growth rate or the seasonally adjusted series. An important issue, which has attracted a great deal of attention also in the seasonal adjustment literature, is its detection by an expert procedure. The...

We derive the optimal hedging ratios for a portfolio of assets driven by a Cointegrated Vector Autoregressive model (CVAR) with general cointegration rank. Our hedge is optimal in the sense of minimum variance portfolio. We consider a model that allows for the hedges to be cointegrated with the...

We review recent asymptotic results on some robust methods for multiple regression. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator...