Heterogeneous dynamics, aggregation and the persistence of economic shocks.

It has been recently emphasized that, if individuals have heterogeneous dynamics, estimates of shock persistence based on aggregate data are significatively higher than those derived from its disaggregate counterpart. However, a careful examination of the implications of this statement on the various tools routinely employed to measure persistence is missing in the literature. This paper formally examines this issue. We consider a disaggregate linear model with heterogeneous dynamics and compare the values of several measures of persistence across aggregation levels. Interestingly, we show that the average persistence of aggregate shocks, as measured by the impulse response function (IRF) of the aggregate model or by the average of the individual IRFs, is identical on all horizons. This result remains true even in situations where the units are (short-memory) stationary but the aggregate process is long-memory or even nonstationary. In contrast, other popular persistence measures, such as the sum of the autoregressive coefficients or the largest autoregressive root, tend to be higher the higher the aggregation level. We argue, however, that this should be seen more as an undesirable property of these measures than as evidence of different average persistence across aggregation levels. The results are illustrated in an application using U.S. inflation data.Heterogeneous dynamics, aggregation, persistence, impulse response function, sum of the autoregressive coefficients, U.S. inflation persistence.

Is the observed persistence spurious? A test for fractional integration versus short memory and structural breaks

Although it is commonly accepted that most macroeconomic variables are nonstationary, it is often difficult to identify the source of the non-stationarity. In particular, it is well-known that integrated and short memory models containing trending components that may display sudden changes in their parameters share some statistical properties that make their identification a hard task. The goal of this paper is to extend the classical testing framework for I(1) versus I(0)+ breaks by considering a a more general class of models under the null hypothesis: non-stationary fractionally integrated (FI) processes. A similar identification problem holds in this broader setting which is shown to be a relevant issue from both a statistical and an economic perspective. The proposed test is developed in the time domain and is very simple to compute. The asymptotic properties of the new technique are derived and it is shown by simulation that it is very well-behaved in finite samples. To illustrate the usefulness of the proposed technique, an application using inflation data is also provided.Fractional integration, structural breaks, unit roots, trends

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 short length 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 GNP per capita (133 years) high power can be achieved, leading to the rejection of both the unit root and the trend-stationary hypothesis. This suggests that possibly neither model provides a good characterization of these data. Next, more flexible representations are considered, namely, processes containing structural breaks (SB) and fractional orders of integration (FI). Economic justification for the presence of these features in GNP is provided. It is shown that the latter models (FI and SB) are in general preferred to the ARIMA (I(1) or I(0)) ones. As a novelty in this literature, new techniques are applied to discriminate between FI and SB models. It turns out that the FI specification is preferred, implying that GNP and GNP per capita are non-stationary, highly persistent but mean-reverting series. Finally, it is shown that the results are robust when breaks in the deterministic component are allowed for in the FI model. Some macroeconomic implications of these findings are also discussed.GNP, unit roots, fractional integration, structural change, long memory, exogenous growth models

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 is easy to compute and is consistent and asymptotically normally distributed for fractionally integrated (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.Fractional integration, nonstationary long-memory time series, minimum distance estimation

Bioerosive structures of sclerozoan foraminifera from the lower pliocene of southern Spain: a contribution to the palaeoecology of marine hard substrate communities

A palaeoecological study of sclerozoan foraminifera of the families Saccamminidae (aff. Sagenina), Lituolidae (Placopsilina), Cibicididae (Cibicides, Dyocibicides, Cibicidella) and Planorbulinidae (Planorbulina and Planorbulinella) that colonized epifaunal bivalves (ostreids and pectinids) during the early Pliocene in southern Spain has led to the recognition of two new boring ichnogenera: Camarichnus ichnogen. nov., with two ichnospecies, C. subrectangularis ichnosp. nov. and C. arcuatus ichnosp. nov., and Canalichnus ichnogen. nov., with one ichnospecies, C. tenuis ichnosp. nov. The first two ichnospecies were produced by adnate lituolids and cibicidids, the last by saccamminids. Their recognition is very important when quantifying populations of these organisms. Colonisation took place after death of the host bivalves, when they acted as very stable substrates whose topography probably controlled the initial settlement pattern of the foraminifera. The colonisation sequence started with the foraminifera (lituolids-saccamminids-cibicidids-planorbulinids) and was followed by vermetid gastropods, serpulids, spirorbids, cheilostome bryozoans and/or ostreids. Preferred orientations and over-growth relationships between cheilostome bryozoans and serpulids have been detected in this material.info:eu-repo/semantics/publishedVersio

Two stories outside Boltzmann-Gibbs statistics: Mori's q-phase transitions and glassy dynamics at the onset of chaos

First, we analyze trajectories inside the Feigenbaum attractor and obtain the atypical weak sensitivity to initial conditions and loss of information associated to their dynamics. We identify the Mori singularities in its Lyapunov spectrum with the appearance of a special value for the entropic index q of the Tsallis statistics. Secondly, the dynamics of iterates at the noise-perturbed transition to chaos is shown to exhibit the characteristic elements of the glass transition, e.g. two-step relaxation, aging, subdiffusion and arrest. The properties of the bifurcation gap induced by the noise are seen to be comparable to those of a supercooled liquid above a glass transition temperature.Comment: Proceedings of: 31st Workshop of the International School of Solid State Physics, Complexity, Metastability and Nonextensivity, Erice (Sicily) 20-26 July 2004 World Scientific in the special series of the E. Majorana conferences, in pres