Nonlinearities and fractional integration in the US unemployment rate

This paper proposes a model of the US unemployment rate which accounts for both its asymmetry and its long memory. Our approach introduces fractional integration and nonlinearities simultaneously into the same framework, using a Lagrange Multiplier procedure with a standard null limit distribution. The empirical results suggest that the US unemployment rate can be specified in terms of a fractionally integrated process, which interacts with some non-linear functions of labour demand variables such as real oil prices and real interest rates. We also find evidence of a long-memory component. Our results are consistent with a hysteresis model with path dependency rather than a NAIRU model with an underlying unemployment equilibrium rate, thereby giving support to more activist stabilisation policies. However, any suitable model should also include business cycle asymmetries, with implications for both forecasting and policy-making.

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

Tourism in Azores Islands: Persistence in the Monthly Arrivals

This study analyses the persistence in the international monthly arrivals to the Azores Islands using a model based on fractional integration and seasonal autoregressions. The estimated fractional differencing parameter gives an indication of the long run evolution of the series. We use both aggregate data and disaggregate monthly data by location of origin and island destination. The results show that the aggregate series corresponding to the total number of arrivals is a nonstationary I(d) process with d above 1, and the most persistent ones are those travelling to Säo Miguel, especially from Holland, Finland, Norway, Germany, Denmark and the UK.Monthly arrivals; Seasonal fractional integration; Persistence; Azores Islands.

Non-destructive testing evaluation of low velocity impact damage in carbon fiber-reinforced laminated composites

Fiber-reinforced laminated composite materials are widely used in aircraft, modern vehicles and light-weight structures. With their high elastic modulus, high strength, and capability of being tailored for a several applications, these materials offer definite advantages compared to more traditional structural materials. However, their behavior under impact is of concern since those events may occur during manufacturing, normal operation or maintenance. The situation is critical for impacts that induce significant internal damage undetectable by visual inspection, which causes large reductions on the strength and stability of the structure. New standardized tests to assess the impact tolerance (ASTM D7136 and D7137) lose some of its appeal by its destructive nature as well as costs involved. Non-destructive techniques such as ultrasonic phased array or experimental modal analysis can be complementary in the evaluation of damage and structural integrity. The results of both destructive and non-destructive experiments carried out on forty-eight composite specimens are presented. A good correlation between incident impact energy and delaminated area as well as variation of eigenfrequencies is noticed. This study does not only provide a better understanding of the impact phenomenon but can also help in design and implementation of new test procedures for structural assessment

Multiple cyclical fractional structures in financial time series

This paper analyses multiple cyclical structures in financial time series. In particular, we focus on the monthly structure of the Nasdaq, the Dow Jones and the Standard&Poor stock market indices. The three series are modelled as long-memory processes with poles in the spectrum at multiple frequencies, including the long-run or zero frequency

Al/Fe-, Al/Cu- and Al/(Fe-Cu)-pillared clays: Structural features at low Atomic Active Metal Ratios (AMR)

A set of Al/Fe-, Al/Cu- and Al/(Fe-Cu)-pillared clays were prepared from a Colombian bentonite in sodium or natural (Ca/Mg) form as starting materials. The effect of the loading of the second metal(s) (Fe and/or Cu) related to Al (AMR) in the intercalating solutions at low range of values ≤ 10%, on the main physicochemical properties was investigated. The insertion of the active metals rose almost linearly with AMR for both binary, Al/Fe- and Al/Cu- mixed metal systems. For the three-metal Al/(Fe-Cu)- mixed system, the stabilization of copper behaved randomly as a function of AMR, while the stabilization of Fe was almost not affected by the presence of Cu. On the basis of the ionic radii of the metals involved, a possible competition of the two active metals for the octahedral sites available in the Al13 polycationic structure is proposed for the three-metal system (ionic radii values: Al3+ = 0.68 Å; Fe3+ = 0.67 Å; Cu2+ = 0.73 Å), but also as a good explanation for the efficiency of stabilization for iron around 15 times higher than copper in the binary metal systems. A clear dependence of the compensation of the cationic exchange capacity by polycations with the AMR value was found only for the system Al/Fe-, which was explained in terms of the opposite changes in the final pH obtained in the intercalating solutions, induced by the active metals in the Keggin-like polycations. The change in the basal spacings obtained in the XRD patterns from oriented glasses as a function of AMR was interpreted in terms of the opposite effect expected on the molecular size of the polycations as higher amounts of Fe or Cu would isomorphically substitute Al into the Al13 framework, allowing to propose that both, iron and copper are able to carry out such a substitution, although in different extent. The hydrogen consumption in the H2-TPR analysis of the materials was mainly distributed between two broad peaks: one from about 250ºC to 580ºC, and a second one from about 750ºC to 950ºC. Despite the several metal oxide species that are possible to form, the first signal in samples modified with the Al/Fe- system may correspond with the sequential overlapped reduction of Fe2O3 in up to three steps: (1) Fe2O3 → Fe3O4; (2) Fe3O4 → FeO; and (3) FeO → Fe, and to two sequential reduction effects in the range of 210-260 ºC for Cu2+→ Cu+ and Cu+→ Cu0 at higher temperatures of ca. 400 ºC to 700 ºC. In the Al/Fe- system two shoulders were observed at around 600ºC and 850ºC, whose intensity grow as the active metal loading increases, seem to be related to two kinds of metal sites repeatedly claimed in the literature as responsible for the high catalytic activity displayed by these materials in Fenton-like reactions; Fe “decorating” Al pillars and true mixed Al/Fe pillars, respectively. The textural analysis of the natural modified samples suggest that at AMR below 5.0 %, a discrete maximum exist for the systems Al/Fe- and Al/Cu- over which the sorption capacity starts to be significantly affected. Simultaneous thermal analysis (DSC/TGA) demonstrated that the addition of a second metal in the intercalating system enhanced more the fraction of physisorbed water and decreased the maximum temperature for such a thermal event than intercalation with simple Al- polycations. SEM micrographs showed significant changes in morphology of the particles as AMR increased from 2.0 to 5.0%; as the amount of iron and/or copper added to the system increased, a greater amount of tiny particles deposited on the clay surface was seen, may be corresponding with external oxide aggregates. Likewise, the ratio Fe/Al obtained from the semi-quantitative surface chemical EDX analysis of the samples modified with the system Al/Fe- indicated that the AMR increasing also leads to higher fraction of the iron inserted represented in intercalated, possibly less aggregated mixed species in the materials. Acknowledgements: Financial support from MEC and FEDER funds (Ref. MAT2007-66439-C02)

Fractional integration and data frequency

This paper examines the robustness of fractional integration estimates to different data frequencies. We show by means of Monte Carlo experiments that if the number of differences is an integer value (e.g., 0 or 1) there is no distortion when data are collected at wider intervals; however, if it is a fractional value, the distortion increases as the number of periods between the observations increases, which results in lower orders of integration than those of the true DGP. An empirical application using the S&P500 index is also carried out.