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 q≥2 and q1/(d+1/2)...

We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=Δ^(-d)u(t), where d є (-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 of the...

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 derive a functional central limit theorem for the empirical spectral measure or discretely averaged (integrated) periodogram of a multivariate long range dependent stochastic process in a degenerating neighborhood of the origin. We show that, under certain restrictions on the memory...

This paper deals with the sustainability of the US current account using fractional integration. We examine nominal and real exports and imports and their corresponding values deflated by GNP. The results show that only the variables deflated by GNP may contain unit roots, while nominal and real...

This paper deals with a multivariate long memory model for the specification of real output in the US, the UK, and Canada. We examine the orders of integration of the three time series first individually and then allow cross dependence between observations. Performing univariate analysis,...

In this paper we specify a multi-factor long-memory process that enables us to estimate the fractional differencing parameters at each frequency separately, and adopt this framework to model quarterly prices in three European countries (France, Italy and the UK). The empirical results suggest...

We analyze daily quotes of the BUX index, main index of the Budapest stock exchange, for period 2nd Jan. 1991–30th Sept. 2008, checking nonstationarity of series, stationarity of returns, applying the ARCH tests to the series. This period was not without its perils for the Hungarian economy....

In this article we show that multiple cycles can occur in financial and economic time series. We model these cycles by means of Gegenbauer processes, using a procedure that permits us to test multiple roots at fixed frequencies over time and thus, it permits us to approximate the length of each...

This paper estimates the long memory volatility model for 16 agricultural commodity futures returns from different futures markets, namely corn, oats, soybeans, soybean meal, soybean oil, wheat, live cattle, cattle feeder, pork, cocoa, coffee, cotton, orange juice, Kansas City wheat, rubber, and...