Components of multifractality in the Central England Temperature anomaly series

We study the multifractal nature of the Central England Temperature (CET) anomaly, a time series that spans more than 200 years. The series is analyzed as a complete data set and considering a sliding window of 11 years. In both cases, we quantify the broadness of the multifractal spectrum as well as its components defined by the deviations from the Gaussian distribution and the influence of the dependence between measurements. The results show that the chief contribution to the multifractal structure comes from the dynamical dependencies, mainly the weak ones, followed by a residual contribution of the deviations from Gaussianity. However, using the sliding window, we verify that the spikes in the non-Gaussian contribution occur at very close dates associated with climate changes determined in previous works by component analysis methods. Moreover, the strong non-Gaussian contribution found in the multifractal measures from the 1960s onwards is in agreement with global results very recently proposed in the literature.Comment: 21 pages, 10 figure

Minding impacting events in a model of stochastic variance

We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold and another one when the local standard deviation outnumbers it. In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterised by large values of the Hurst exponent is greater than 0.8, which are ubiquitous features in complex systems.Comment: 18 pages, 5 figures, 1 table. To published in PLoS on

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

Multiple shifts and fractional integration in the us and uk unemployment rates

This paper analyses the long-run behaviour of the US and UK unemployment rates by testing for possibly fractional orders of integration and multiple shifts using a sample of over 100 annual observations. The results show that the orders of integration are higher than 0 in both series, which implies long memory. If we assume that the underlying disturbances are white noise, the values are higher than 0.5, i.e., nonstationary. However, if the disturbances are autocorrelated, the orders of integration are in the interval (0, 0.5), implying stationarity and mean-reverting behaviour. Moreover, when multiple shifts are taken into account, unemployment is more persistent in the US than in the UK, implying the need for stronger policy action in the former to bring unemployment back to its original level

China’s market economy, shadow banking and the frequency of growth slowdown

The activity of the Shadow Banks in China has been the subject of considerable interest in recent years. Total shadow banking lending has reached over 60% of GDP and has grown faster than regular bank lending. It has been argued that unregulated shadow banking has fuelled a credit boom that poses a risk to the stability of the financial system. This paper estimates a model of the Chinese economy using a DSGE framework that accommodates a banking sector that isolates the effects of lending to the private sector including shadow bank lending. A refinement of the model allows for bank lending including lending by the shadow banks to affect the credit premium on private investment. The main finding is that while financial shocks are significant, it is real shocks that dominate. The model is used to simulate the frequency of growth slowdowns in China and concludes that these are more likely to be driven by real sector shocks rather than financial sector, including shadow bank shocks. This paper differs from other applications in its use of indirect inference to test the fitted model against a threeequation VAR of inflation, output gap and interest rate