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 $C_{p}$ 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...

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...

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...

Yule (1926) introduced the concept of spurious or nonsense correlation, and showed by simulation that for some nonstationary processes, that the empirical correlations seem not to converge in probability even if the processes were inde- pendent. This was later discussed by Granger and Newbold...

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...

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the...