Length Of Available Time Series Research Articles

Centennial relationships between ocean temperature and Atlantic puffin production reveal shifting decennial trends.

The current warming of the oceans has been shown to have detrimental effects for a number of species. An understanding of the underlying mechanisms may be hampered by the non-linearity and non-stationarity of the relationships between temperature and demography, and by the insufficient length of available time series. Most demographic time series are too short to study the effects of climate on wildlife in the classical sense of meteorological patterns over at least 30years. Here we present a harvest time series of Atlantic puffins (Fratercula arctica) that goes back as far as 1880. It originates in the world's largest puffin colony, in southwest Iceland, which has recently experienced a strong decline. By estimating an annual chick production index for 128years, we found prolonged periods of strong correlations between local sea surface temperature (SST) and chick production. The sign of decennial correlations switches three times during this period, where the phases of strong negative correlations between puffin productivity and SST correspond to the early 20th century Arctic warming period and to the most recent decades. Most of the variation (72%) in chick production is explained by a model in which productivity peaks at an SST of 7.1°C, clearly rejecting the assumption of a linear relationship. There is also evidence supporting non-stationarity: The SST at which puffins production peaked has increased by 0.24°C during the 20th century, although the increase in average SST during the same period has been more than three times faster. The best supported models indicate that the population's decline is at least partially caused by the increasing SST around Iceland.

Analytic Solution to Variance Optimization with No Short-Selling

A large portfolio of independent, but not identically distributed, returns is optimized under the variance risk measure with a ban on short positions. To the best of our knowledge, this is the first time such a constrained optimization is carried out analytically, which is made possible by the application of methods borrowed from the theory of disordered systems. The no-short selling constraint acts as an asymmetric l1 regularizer, setting some of the portfolio weights to zero and keeping the estimation error bounded, avoiding the divergence present in the non-regularized case. However, the susceptibility, i.e. the sensitivity of the optimal portfolio weights to changes in the returns, diverges at a critical value 2 of the ratio N/T, where N is the number of different assets in the portfolio and T is the sample size (the length of available time series). This means that a ban on short positions does not prevent the phase transition in the optimization problem, it merely shifts the critical point from its nonregularized value of N/T = 1 to 2. It is shown that this critical value is universal, independent of the distribution of the returns. Beyond this critical value, the variance of the portfolio identically vanishes for any portfolio weight vector constructed as a linear combination of the eigenvectors from the null space of the covariance matrix, but these linear combinations are not legitimate solutions of the optimization problem, as they are infinitely sensitive to any change in the input parameters, in particular they will wildly fluctuate from sample to sample. With some narrative license we may say that the regularizer takes care of the longitudinal fluctuations of the optimal weight vector, but does not eliminate the divergent transverse fluctuations. We also calculate the distribution of the optimal weights over the random samples and show that the regularizer preferentially removes the assets with large variances, in accord with one’s natural expectation. The analytic calculations are supported by numerical simulations. The analytic and numerical results are in perfect agreement for N/T N/T > 2, where we know from exact linear algebraic considerations that no meaningful solution exits. The resolution of this paradox is that there are regularizers built into these solvers that stabilize the otherwise freely fluctuating, meaningless solutions. This should serve as a warning against the use of ready-made solver programs in empirical work without a good understanding of the theoretical structure of the problem at hand and the details of the tool used to solve it, and where the fundamental instability of the numerics may be masked by the stabilization due to the solver rather than the data.

Convergence Revisited: A Multi-Definition, Multi-Method Analysis of the UCR and the NCVS Crime Series (1973-2008)

Inter-study discrepancies in the length of available time series, definition of convergence, rate calculation adjustment, and application of statistical techniques have contributed to confusions in understanding the relationship between the uniform crime reports (UCR) and the national crime victimization survey (NCVS). This study tests and compares the outcomes of UCR–NCVS crime rate convergence in a 36-year time series (1973-2008) using multiple definitions and an assortment of methods. With adjusted crime rates, our graphic analysis shows strong evidence of convergence between the two series in all crime categories. High correlation coefficients (.80+) are obtained in Robbery, Burglary and MV Theft categories using nondetrended data and the full 36-year time series. Split-series correlation analyses based on 18 equal-sized (half) series yield not only very high coefficients (.90+) in the more recent split-series but also a clear pattern in support of the UCR–NCVS convergence (as “correlated rates”) conclusion in all crime categories examined. Similarly, rate deviation regression analyses confirm that the differences between the UCR and the NCVS crime rates in all tested categories are decreasing significantly over time and that the two crime series are in the process of converging. Outcomes derived from the Engle-Granger test of cointegration, in contrast, are the most modest, indicating that the two crime series have only cointegrated in the Burglary category. We suggest that conclusions on the UCR–NCVS convergence are partly contingent on the definitional and methodological contexts. Convergence studies should be conducted periodically not only to monitor the validity of the dual national crime measures but also to identify questions deserving attentions from both researchers and policy- makers.

The role of coal consumption in the economic growth of the Polish economy in transition

The main goal of this paper is an analysis of the causal links between quarterly coal consumption in the Polish economy and GDP. For the sake of accurate computation an additional variable – employment – was also taken into account. Computations conducted for the period Q1 2000 to Q4 2009 by means of recent causality techniques confirmed the neutrality of hard coal usage with respect to economic growth. On the other hand, calculations for the pairs lignite-GDP and total coal consumption-GDP showed the existence of a significant nonlinear causality from coal usage to economic growth. This is clear evidence for claiming that lignite plays an important role in the economic growth of the Polish economy. Furthermore, each coal-related variable was found to have a nonlinear causal impact on employment. Because of the relatively short length of available time series we additionally applied bootstrap critical values. The empirical results computed by both methods did not exhibit significant differences. These results have important policy implications. In general, our findings support the hypothesis that closing hard coal mines in Poland should have no significant repercussions on economic growth. However, this does not seem to be true for lignite mines.

Cross-Platform Microarray Data Normalisation for Regulatory Network Inference

BackgroundInferring Gene Regulatory Networks (GRNs) from time course microarray data suffers from the dimensionality problem created by the short length of available time series compared to the large number of genes in the network. To overcome this, data integration from diverse sources is mandatory. Microarray data from different sources and platforms are publicly available, but integration is not straightforward, due to platform and experimental differences.MethodsWe analyse here different normalisation approaches for microarray data integration, in the context of reverse engineering of GRN quantitative models. We introduce two preprocessing approaches based on existing normalisation techniques and provide a comprehensive comparison of normalised datasets.ConclusionsResults identify a method based on a combination of Loess normalisation and iterative K-means as best for time series normalisation for this problem.

Detection of coupling between oscillators from their short time series: Condition of applicability of the method of phase dynamics modeling

One of the most sensitive methods for determining the presence and character of coupling between two oscillators is based on the modeling of their phase dynamics. This method is applicable if the observed oscillations are not synchronous and the length of available time series is no less than 50 characteristic periods. Now it is established that the method can be applied to still shorter time series with a length of 20 to 50 periods, provided that the estimated phase coherence coefficient (measuring the degree of synchronization) does not exceed a certain threshold dependent on the time series length and the frequency detuning. This result expands the possibilities of detecting the coupling between oscillatory systems under conditions of nonstationary signals and deficient data.

Global autocorrelation scales of the partial pressure of oceanic CO2

A global database of approximately 1.7 million observations of the partial pressure of carbon dioxide in surface ocean waters (pCO2) collected between 1970 and 2003 is used to estimate its spatial autocorrelation structure. The patterns of the lag distance where the autocorrelation exceeds 0.8 is similar to patterns in the spatial distribution of the first baroclinic Rossby radius of deformation indicating that ocean circulation processes play a significant role in determining the spatial variability of pCO2. Separate calculations for times when the Sun is north and south of the equator revealed no obvious seasonal dependence of the spatial autocorrelation scales. The pCO2 measurements at Ocean Weather Station (OWS) “P” in the eastern subarctic Pacific (50°N, 145°W) is the only fixed location where an uninterrupted time series of sufficient length exists to calculate a meaningful temporal autocorrelation function for lags greater than a few days. The estimated temporal autocorrelation function at OWS “P” is highly variable. A spectral analysis of the longest four pCO2 time series indicates a high level of variability occurring over periods from the atmospheric synoptic to the maximum length of the time series, in this case 42 days. It is likely that a relative peak in variability with a period of 3–6 days is related to atmospheric synoptic period variability and ocean mixing events due to wind stirring. However, the short length of available time series makes identifying temporal relationships between pCO2 and atmospheric or ocean processes problematic.

Noisy covariance matrices and portfolio optimization II

Recent studies inspired by results from random matrix theory (Galluccio et al.: Physica A 259 (1998) 449; Laloux et al.: Phys. Rev. Lett. 83 (1999) 1467; Risk 12 (3) (1999) 69; Plerou et al.: Phys. Rev. Lett. 83 (1999) 1471) found that covariance matrices determined from empirical financial time series appear to contain such a high amount of noise that their structure can essentially be regarded as random. This seems, however, to be in contradiction with the fundamental role played by covariance matrices in finance, which constitute the pillars of modern investment theory and have also gained industry-wide applications in risk management. Our paper is an attempt to resolve this embarrassing paradox. The key observation is that the effect of noise strongly depends on the ratio r= n/ T, where n is the size of the portfolio and T the length of the available time series. On the basis of numerical experiments and analytic results for some toy portfolio models we show that for relatively large values of r (e.g. 0.6) noise does, indeed, have the pronounced effect suggested by Galluccio et al. (1998), Laloux et al. (1999) and Plerou et al. (1999) and illustrated later by Laloux et al. (Int. J. Theor. Appl. Finance 3 (2000) 391), Plerou et al. (Phys. Rev. E, e-print cond-mat/0108023) and Rosenow et al. (Europhys. Lett., e-print cond-mat/0111537) in a portfolio optimization context, while for smaller r (around 0.2 or below), the error due to noise drops to acceptable levels. Since the length of available time series is for obvious reasons limited in any practical application, any bound imposed on the noise-induced error translates into a bound on the size of the portfolio. In a related set of experiments we find that the effect of noise depends also on whether the problem arises in asset allocation or in a risk measurement context: if covariance matrices are used simply for measuring the risk of portfolios with a fixed composition rather than as inputs to optimization, the effect of noise on the measured risk may become very small.

Stability of water masses‐impact on cod recruitment off West Greenland

ABSTRACTBased upon the hypothesis of Meyer (1968: Hansa, 16:2–4) that periods of low stability of the water column in autumn should parallel good cod year‐classes in the following year, the paper analyzes available time series of cod recruitment, subsurface oceanographic stability data and wind stress data off West Greenland. No significant correlations were found between stability, wind stress and recruitment when considering the entire. length of available time series. However, splitting the autumn‐based oceanographic data set into a pre‐ 1970s part (when warm climatic conditions and high recruitment prevailed), and a recent part (for the past 20 years of cooling climate) yields significant coherence of recruitment and environmental conditions for the cold climate period. For the warm climate period, only occasional consistency is shown. The possible influence of the Great Salinity Anomaly on recruitment of cod is discussed. It is suggested that during the past 20 years a new correlation mechanism, an advective coupling instead of low stability coupling, may explain the variability of recruitment.