Testing I(1) against I(d) alternatives in the presence of deteministic components

This paper discusses the role of deterministic components in the DGP and in the auxiliary regression model which underlies the implementation of the Fractional Dickey-Fuller (FDF) test for I(1) against I(d) processes with d ∈ [0, 1). This is an important test in many economic applications because I(d) processess with d & 1 are mean-reverting although, when 0.5 ≤ d & 1,, like I(1) processes, they are nonstationary. We show how simple is the implementation of the FDF in these situations, and argue that it has better properties than LM tests. A simple testing strategy entailing only asymptotically normally distributed tests is also proposed. Finally, an empirical application is provided where the FDF test allowing for deterministic components is used to test for long-memory in the per capita GDP of several OECD countries, an issue that has important consequences to discriminate between growth theories, and on which there is some controversy.

The Persistence of Inflation in OECDCountries: a Fractionally Integrated Approach

The statistical properties of inflation and, in particular, its degree of persistence and stability over time is a subject of intense debate and no consensus has been achieved yet. The goal of this paper is to analyze this controversy using a general approach, with the aim of providing a plausible explanation for the existing contradictory results. We consider the inflation rates of 21 OECD countries which are modelled as fractionally integrated (FI) processes. First, we show analytically that FI can appear in inflation rates after aggregating individual prices from firms that face different costs of adjusting their prices. Then, we provide robust empirical evidence supporting the FI hypothesis using both classical and Bayesian techniques. Next, we estimate impulse response functions and other scalar measures of persistence, achieving an accurate picture of this property and its variation across countries. It is shown that the application of some popular tools for measuring persistence, such as the sum of the AR coefficients, could lead to erroneous conclusions if fractional integration is present. Finally, we explore the existence of changes in inflation inertia using a novel approach. We conclude that the persistence of inflation is very high (although non-permanent) in most post-industrial countries and that it has remained basically unchanged over the last four decades.

Testing I(1) against I(d) alternatives in the presence of deteministic components

This paper discusses the role of deterministic components in the DGP and in the auxiliaryregression model which underlies the implementation of the Fractional Dickey-Fuller (FDF) test for I(1) against I(d) processes with d [0, 1). This is an important test in many economic applications because I(d) processess with d < 1 are mean-reverting although, when 0.5 = d < 1, like I(1) processes, they are nonstationary. We show how simple is the implementation of the FDF in these situations, and argue that it has better properties than LM tests. A simple testing strategy entailing only asymptotically normally distributedtests is also proposed. Finally, an empirical application is provided where the FDF test allowing for deterministic components is used to test for long-memory in the per capita GDP of several OECD countries, an issue that has important consequences to discriminate between growth theories, and on which there is some controversy.

Further evidence on the statistical properties of real GNP

The well-known lack of power of unit root tests has often been attributed to the shortlength of macroeconomic variables and also to DGP s that depart from the I(1)-I(0)alternatives. This paper shows that by using long spans of annual real GNP and GNPper capita (133 years) high power can be achieved, leading to the rejection of both theunit root and the trend-stationary hypothesis. This suggests that possibly neither modelprovides a good characterization of these data. Next, more flexible representations areconsidered, namely, processes containing structural breaks (SB) and fractional ordersof integration (FI). Economic justification for the presence of these features in GNP isprovided. It is shown that the latter models (FI and SB) are in general preferred to theARIMA (I(1) or I(0)) ones. As a novelty in this literature, new techniques are appliedto discriminate between FI and SB models. It turns out that the FI specification ispreferred, implying that GNP and GNP per capita are non-stationary, highly persistentbut mean-reverting series. Finally, it is shown that the results are robust when breaksin the deterministic component are allowed for in the FI model. Some macroeconomicimplications of these findings are also discussed.

The persistence of inflation in OECD countries: A fractionally integrated approach

The statistical properties of inflation and, in particular, its degree of persistence and stability over time is a subject of intense debate and no consensus has been achieved yet. The goal of this paper is to analyze this controversy using a general approach, with the aim of providing a plausible explanation for the existing contradictory results. We consider the inflation rates of 21 OECD countries which are modelled as fractionally integrated (FI) processes. First, we show analytically that FI can appear in inflation rates after aggregating individual prices from firms that face different costs of adjusting their prices. Then, we provide robust empirical evidence supporting the FI hypothesis using both classical and Bayesian techniques. Next, we estimate impulse response functions and other scalar measures of persistence, achieving an accurate picture of this property and its variation across countries. It is shown that the application of some popular tools for measuring persistence, such as the sum of the AR coefficients, could lead to erroneous conclusions if fractional integration is present. Finally, we explore the existence of changes in inflation inertia using a novel approach. We conclude that the persistence of inflation is very high (although non-permanent) in most post-industrial countries and that it has remained basically unchanged over the last four decades.

Minimum distance estimation of stationary and non-stationary ARFIMA processes

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator iseasy to compute and is consistent and asymptotically normally distributed for fractionallyintegrated (FI) processes with an integration order d strictly greater than -0.75. Therefore, it can be applied to both stationary and non-stationary processes. Deterministic components are also allowed in the DGP. Furthermore, as a by-product, the estimation procedure provides an immediate check on the adequacy of the specified model. This is so because the criterion function, when evaluated at the estimated values, coincides with the Box-Pierce goodness of fit statistic. Empirical applications and Monte-Carlo simulations supporting the analytical results and showing the good performance of the estimator in finite samples are also provided.

What is what?: A simple time-domain test of long-memory vs. structural breaks

This paper proposes a new time-domain test of a process being I(d), 0 < d = 1, under the null, against the alternative of being I(0) with deterministic components subject to structural breaks at known or unknown dates, with the goal of disentangling the existing identification issue between long-memory and structural breaks. Denoting by AB(t) the different types of structural breaks in the deterministic components of a time series considered by Perron (1989), the test statistic proposed here is based on the t-ratio (or the infimum of a sequence of t-ratios) of the estimated coefficient on yt-1 in an OLS regression of ?dyt on a simple transformation of the above-mentioned deterministic components and yt-1, possibly augmented by a suitable number of lags of ?dyt to account for serial correlation in the error terms. The case where d = 1 coincides with the Perron (1989) or the Zivot and Andrews (1992) approaches if the break date is known or unknown, respectively. The statistic is labelled as the SB-FDF (Structural Break-Fractional Dickey- Fuller) test, since it is based on the same principles as the well-known Dickey-Fuller unit root test. Both its asymptotic behavior and finite sample properties are analyzed, and two empirical applications are provided.

Enhanced radar precipitation estimates using a combined clutter and beam blockage correction technique

Weather radar observations are currently the most reliable method for remote sensing of precipitation. However, a number of factors affect the quality of radar observations and may limit seriously automated quantitative applications of radar precipitation estimates such as those required in Numerical Weather Prediction (NWP) data assimilation or in hydrological models. In this paper, a technique to correct two different problems typically present in radar data is presented and evaluated. The aspects dealt with are non-precipitating echoes - caused either by permanent ground clutter or by anomalous propagation of the radar beam (anaprop echoes) - and also topographical beam blockage. The correction technique is based in the computation of realistic beam propagation trajectories based upon recent radiosonde observations instead of assuming standard radio propagation conditions. The correction consists of three different steps: 1) calculation of a Dynamic Elevation Map which provides the minimum clutter-free antenna elevation for each pixel within the radar coverage; 2) correction for residual anaprop, checking the vertical reflectivity gradients within the radar volume; and 3) topographical beam blockage estimation and correction using a geometric optics approach. The technique is evaluated with four case studies in the region of the Po Valley (N Italy) using a C-band Doppler radar and a network of raingauges providing hourly precipitation measurements. The case studies cover different seasons, different radio propagation conditions and also stratiform and convective precipitation type events. After applying the proposed correction, a comparison of the radar precipitation estimates with raingauges indicates a general reduction in both the root mean squared error and the fractional error variance indicating the efficiency and robustness of the procedure. Moreover, the technique presented is not computationally expensive so it seems well suited to be implemented in an operational environment.

Tumor necrosis factor-alpha mediates changes in tissue protein turnover in a rat cancer cachexia model.

Rats bearing the Yoshida AH-130 ascites hepatoma showed enhanced fractional rates of protein degradation in gastrocnemius muscle, heart, and liver, while fractional synthesis rates were similar to those in non-tumor bearing rats. This hypercatabolic pattern was associated with marked perturbations of the hormonal homeostasis and presence of tumor necrosis factor in the circulation. The daily administration of a goat anti-murine TNF IgG to tumor-bearing rats decreased protein degradation rates in skeletal muscle, heart, and liver as compared with tumor-bearing rats receiving a nonimmune goat IgG. The anti-TNF treatment was also effective in attenuating early perturbations in insulin and corticosterone homeostasis. Although these results suggest that tumor necrosis factor plays a significant role in mediating the changes in protein turnover and hormone levels elicited by tumor growth, the inability of such treatment to prevent a reduction in body weight implies that other mediators or tumor-related events were also involved.

Una extensión de la regresión propuesta por Geweke y Porter-Hudak para la estimación del orden de diferenciación en modelos ARFIMA

Recientemente, ha aumentado mucho el interés por la aplicación de los modelos de memoria larga a variables económicas, sobre todo los modelos ARFIMA. Sin duda , el método más usado para la estimación de estos modelos en el ámbito del análisis económico es el propuesto por Geweke y Portero-Hudak (GPH) aun cuando en trabajos recientes se ha demostrado que, en ciertos casos, este estimador presenta un sesgo muy importante. De ahí que, se propone una extensión de este estimador a partir del modelo exponencial propuesto por Bloomfield, y que permite corregir este sesgo.A continuación, se analiza y compara el comportamiento de ambos estimadores en muestras no muy grandes y se comprueba como el estimador propuesto presenta un error cuadrático medio menor que el estimador GPH

A comparative long-memory Analysis between Spanish, Mexican and U.S. interest rates

Evidence exists that many natural facts are described better as a fractal. Although fractals are very useful for describing nature, it is also appropiate to review the concept of random fractal in finance. Due to the extraordinary importance of Brownian motion in physics, chemistry or biology, we will consider the generalization that supposes fractional Brownian motion introduced by Mandelbrot.The main goal of this work is to analyse the existence of long range dependence in instantaneous forward rates of different financial markets. Concretelly, we perform an empirical analysis on the Spanish, Mexican and U.S. interbanking interest rate. We work with three time series of daily data corresponding to 1 day operations from 28th March 1996 to 21st May 2002. From among all the existing tests on this matter we apply the methodology proposed in Taqqu, Teverovsky and Willinger (1995).

Una extensión de la regresión propuesta por Geweke y Porter-Hudak para la estimación del orden de diferenciación en modelos ARFIMA

Recientemente, ha aumentado mucho el interés por la aplicación de los modelos de memoria larga a variables económicas, sobre todo los modelos ARFIMA. Sin duda , el método más usado para la estimación de estos modelos en el ámbito del análisis económico es el propuesto por Geweke y Portero-Hudak (GPH) aun cuando en trabajos recientes se ha demostrado que, en ciertos casos, este estimador presenta un sesgo muy importante. De ahí que, se propone una extensión de este estimador a partir del modelo exponencial propuesto por Bloomfield, y que permite corregir este sesgo.A continuación, se analiza y compara el comportamiento de ambos estimadores en muestras no muy grandes y se comprueba como el estimador propuesto presenta un error cuadrático medio menor que el estimador GPH

Multipole modes and spin features in the Raman spectrum of nanoscopic quantum rings

We present a systematic study of ground state and spectroscopic properties of many-electron nanoscopic quantum rings. Addition energies at zero magnetic field (B) and electrochemical potentials as a function of B are given for a ring hosting up to 24 electrons. We find discontinuities in the excitation energies of multipole spin and charge density modes, and a coupling between the charge and spin density responses that allow to identify the formation of ferromagnetic ground states in narrow magnetic field regions. These effects can be observed in Raman experiments, and are related to the fractional Aharonov-Bohm oscillations of the energy and of the persistent current in the ring

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

A comparative long-memory Analysis between Spanish, Mexican and U.S. interest rates

Evidence exists that many natural facts are described better as a fractal. Although fractals are very useful for describing nature, it is also appropiate to review the concept of random fractal in finance. Due to the extraordinary importance of Brownian motion in physics, chemistry or biology, we will consider the generalization that supposes fractional Brownian motion introduced by Mandelbrot.The main goal of this work is to analyse the existence of long range dependence in instantaneous forward rates of different financial markets. Concretelly, we perform an empirical analysis on the Spanish, Mexican and U.S. interbanking interest rate. We work with three time series of daily data corresponding to 1 day operations from 28th March 1996 to 21st May 2002. From among all the existing tests on this matter we apply the methodology proposed in Taqqu, Teverovsky and Willinger (1995).