Testing Of Nonstationarities In The Unit Circle,Long Memory Processes And Day Of The Week Effects In Financial Data

This paper examines a version of the tests of Robinson (1994) that enables one to test models of the form (1-Lk)dxt = ut, where k is an integer value, d may be any real number, and ut is I(0). The most common cases are those with k = 1 (unit or fractional roots) and k = 4 and 12 (seasonal unit or fractional models). However, we extend the analysis to cover situations such as (1-L5)d xt = ut, which might be relevant, for example, in the context of financial time series data. We apply these techniques to the daily Eurodollar rate and the Dow Jones index, and find that for the former series the most adequate specifications are either a pure random walk or a model of the form xt = xt-5 + εt, implying in both cases that the returns are completely unpredictable. In the case of the Dow Jones index, a model of the form (1-L5)d xt = ut is selected, with d constrained between 0.50 and 1, implying nonstationarity and mean-reverting behaviour

Testing of nonstationarities in the unit circle, long memory processes and the day of the week effects in financial data

This paper examines a version of the tests of Robinson (1994) that enables one to test models of the form (1-Lk)dxt = ut, where k is an integer value, d may be any real number, and ut is I(0). The most common cases are those with k = 1 (unit or fractional roots) and k = 4 and 12 (seasonal unit or fractional models). However, we extend the analysis to cover situations such as (1-L5)d xt = ut, which might be relevant, for example, in the context of financial time series data. We apply these techniques to the daily Eurodollar rate and Dow Jones index, and find that for the former series the most adequate specifications are either a pure random walk or a model of the form xt = xt-5 + εt, implying in both cases that the returns are completely unpredictable. In the case of Dow Jones index, a model of the form (1-L5)d xt = ut is selected, with d constrained between 0.50 and 1, implying nonstationarity and mean-reverting behaviour

Carbon-13 longitudinal relaxation time measurements and DFT-GIAO NMR computations for two ammonium ions of a tetraazamacrocyclic scorpiand system

Spin-lattice relaxation times, T1s, for 13C nuclei in two cations Hn1n+ (n = 1, 5)of N-(2-amino-ethyl)-cyclam (1, scorpiand) were determined by means of 13C{1H} NMR experiments in aqueous solution at pH 11.5 and 0.2. The theoretical study [modeling with OPLS-AA, B3LYP/6-31G(d) geometry optimizations, dispersion-corrected energies (DFT-D3), and DFT-GIAO predictions of the NMR chemical shifts (including an IEF-PCM simulation of hydration)] was also done for several conformers of the tautomer iso-H414+ not investigated before. The binding directions in protonated polyamino receptors necessary for efficient complexation of the nitrate anion(s) were briefly outlined, as well. All these results were discussed in terms of 'abnormal' 13C chemical shift changes found previously for the side-chain carbons of amine 1 in strongly acidic solution (HNO3). In conclusion, an earlier proposal of its association with NO3- at pH=1 was rejected. Instead, the participation of small amounts of a microspecies iso-H414+Dhydr under such conditions can be proposed.Publikacja w ramach programu Springer Open Choice/Open Access finansowanego przez Ministerstwo Nauki i Szkolnictwa Wyższego i realizowanego w ramach umowy na narodową licencję akademicką na czasopisma Springer w latach 2010-2013