We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (complexity) is of order T 2, where T is the length of the time series. Our algorithm allows calculation speed of order T log2 T . For moderate and large...

We consider the nonstationary fractional model Δ^{d}X_{t}=ε_{t} with ε_{t} i.i.d.(0,σ²) 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 discuss the role of the initial values...

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...

This manual describes the usage of the accompanying freely available software package for estimation and testing in the fractionally cointegrated vector autoregressive (VAR) model.

We suggest improved tests for cointegration rank in the vector au- toregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but of course the asymptotic results apply more generally....

We use a fractionally cointegrated vector autoregressive model to examine the relationship between Canadian political support and macroeconomic conditions. This model is well suited for the analysis because it allows multiple fractional time series and admits simple asymptotic inference for the...

In a recent paper Hualde and Robinson (2011) establish consistency and asymptotic normality for conditional sum-of-squares estimators, which are equivalent to conditional quasi-maximum likelihood estimators, in parametric fractional time series models driven by conditionally homoskedastic...

We examine forecasting performance of the recent fractionally cointegrated vector autoregressive (FCVAR) model. The model is applied to daily polling data of political support in the United Kingdom for 2010 - 2015. We compare with popular competing models and at various forecast horizons. Our...

This manual describes the usage of the accompanying freely available Matlab program for estimation and testing in the fractionally cointegrated vector autoregressive (FCVAR) model. This program replaces an earlier Matlab program by Nielsen and Morin (2014), and although the present Matlab...

In this paper we apply the recently developed fractionally cointegrated vector autoregressive (FCVAR) model to analyze price discovery in the spot and futures markets for five non-ferrous metals (aluminium, copper, lead, nickel, and zinc). The FCVAR model allows for long memory (fractional...