We present the symmetric thermal optimal path (TOPS) method to determine the time-dependent lead-lag relationship between two stochastic time series. This novel version of the previously introduced TOP method alleviates some inconsistencies by imposi
ng that the lead-lag relationship should be invariant with respect to a time reversal of the time series after a change of sign. This means that, if `$X$ comes before $Y$, this transforms into `$Y$ comes before $X$ under a time reversal. We show that previously proposed bootstrap test lacks power and leads too often to a lack of rejection of the null that there is no lead-lag correlation when it is present. We introduce instead two novel tests. The first the free energy p-value $rho$ criterion quantifies the probability that a given lead-lag structure could be obtained from random time series with similar characteristics except for the lead-lag information. The second self-consistent test embodies the idea that, for the lead-lag path to be significant, synchronizing the two time series using the time varying lead-lag path should lead to a statistically significant correlation. We perform intensive synthetic tests to demonstrate their performance and limitations. Finally, we apply the TOPS method with the two new tests to the time dependent lead-lag structures of house price and monetary policy of the United Kingdom (UK) and United States (US) from 1991 to 2011. The TOPS approach stresses the importance of accounting for change of regimes, so that similar pieces of information or policies may have drastically different impacts and developments, conditional on the economic, financial and geopolitical conditions. This study reinforces the view that the hypothesis of statistical stationarity is highly questionable.
Using a recently introduced method to quantify the time varying lead-lag dependencies between pairs of economic time series (the thermal optimal path method), we test two fundamental tenets of the theory of fixed income: (i) the stock market variatio
ns and the yield changes should be anti-correlated; (ii) the change in central bank rates, as a proxy of the monetary policy of the central bank, should be a predictor of the future stock market direction. Using both monthly and weekly data, we found very similar lead-lag dependence between the S&P500 stock market index and the yields of bonds inside two groups: bond yields of short-term maturities (Federal funds rate (FFR), 3M, 6M, 1Y, 2Y, and 3Y) and bond yields of long-term maturities (5Y, 7Y, 10Y, and 20Y). In all cases, we observe the opposite of (i) and (ii). First, the stock market and yields move in the same direction. Second, the stock market leads the yields, including and especially the FFR. Moreover, we find that the short-term yields in the first group lead the long-term yields in the second group before the financial crisis that started mid-2007 and the inverse relationship holds afterwards. These results suggest that the Federal Reserve is increasingly mindful of the stock market behavior, seen at key to the recovery and health of the economy. Long-term investors seem also to have been more reactive and mindful of the signals provided by the financial stock markets than the Federal Reserve itself after the start of the financial crisis. The lead of the S&P500 stock market index over the bond yields of all maturities is confirmed by the traditional lagged cross-correlation analysis.
Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes. In recent years, quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the process c
an be understood by investigating the topological properties of the network. We study the topological properties of horizontal visibility graphs constructed from fractional Brownian motions with different Hurst index $Hin(0,1)$. Special attention has been paid to the impact of Hurst index on the topological properties. It is found that the clustering coefficient $C$ decreases when $H$ increases. We also found that the mean length $L$ of the shortest paths increases exponentially with $H$ for fixed length $N$ of the original time series. In addition, $L$ increases linearly with respect to $N$ when $H$ is close to 1 and in a logarithmic form when $H$ is close to 0. Although the occurrence of different motifs changes with $H$, the motif rank pattern remains unchanged for different $H$. Adopting the node-covering box-counting method, the horizontal visibility graphs are found to be fractals and the fractal dimension $d_B$ decreases with $H$. Furthermore, the Pearson coefficients of the networks are positive and the degree-degree correlations increase with the degree, which indicate that the horizontal visibility graphs are assortative. With the increase of $H$, the Pearson coefficient decreases first and then increases, in which the turning point is around $H=0.6$. The presence of both fractality and assortativity in the horizontal visibility graphs converted from fractional Brownian motions is different from many cases where fractal networks are usually disassortative.
We perform rescaled range analysis upon the signals measured by Dual Particle Dynamical Analyzer in gas-liquid two-phase turbulent jets. A novel rescaled range analysis is proposed to investigate these unevenly sampled signals. The Hurst exponents of
velocity and other passive scalars in the bulk of spray are obtained to be 0.59$pm $0.02 and the fractal dimension is hence 1.41$pm $ 0.02, which are in remarkable agreement with and much more precise than previous results. These scaling exponents are found to be independent of the configuration and dimensions of the nozzle and the fluid flows. Therefore, such type of systems form a universality class with invariant scaling properties.
This paper has been withdrawn by the authors due to a fatal error in the analysis. The manuscript was submitted to Chemical Engineering Science. To clarify the situation, we copy the main comment from an anonymous referee here: To my understanding, t
he authors analyze i = 1 ... 63 time series and calculate their mean and standard deviation. These time series correspond to individual, single ignition processes. Is this correct? If yes, these processes, as Fig. 3 shows very clearly, are not stationary, and the pressure difference (i.e., the signal) quickly decays to zero. In this case both the mean and the standard deviation are poorly defined, for example because both depend in a trivial fashion on the observation period T. I am not aware of any study (including those cited by the authors) which allows for any conclusion from such non-stationary signals. The results of Menezes and Barabasi are strictly only valid for stationary time series, and they cannot be applied at all in this case. We agree with this insightful comment that our data are not stationary and the method adopted in our manuscript does not apply. We do not see any possibility to correct this error and decide to withdraw it. We would like to thank gratefully the referee and apologize for any inconvenience caused by our oversight.
On a laboratory-scale testing platform of impinging entrained-flow gasifier with four opposed burners, the flame images for diesel combustion and gasification process were measured with a single charge coupled device (CCD) camera. The two-dimensional
multifractal detrended fluctuation analysis was employed to investigate the multifractal nature of the flame images. Sound power-law scaling in the annealed average of detrended fluctuations was unveiled when the order $q>0$ and the multifractal feature of flame images were confirmed. Further analyses identified two multifractal parameters, the minimum and maximum singularity $alpha_{min}$ and $alpha_{max}$, serving as characteristic parameters of the multifractal flames. These two characteristic multifractal parameters vary with respect to different experimental conditions.
