Nonparametric inferences for kurtosis and conditional kurtosis

Under the assumption of strictly stationary process, this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series. We apply this method to the daily returns of S＆P500 index and the Shanghai Composite Index, and simulate GARCH data for verifying the efficiency of the presented model. Our results indicate that the risk series distribution is heavily tailed, but the historical information can make its future distribution light-tailed. However the far future distribution＇s tails are little affected by the historical data.

NEW METHOD TO OBTAIN THE POWER SPECTRA OF HIDDEN VARIABLES AND ITS APPLICATION TO OCEAN DATA

A novel method is proposed to obtain the power spectra of hidden variables in a chaotic time series. By embedding the data in phase space , and recording the conditional probability density of points that the trajectory encounters as it evolves in the reconstructed phase space, it is possible to recover the power spectra of hidden variables in chaotic time series through a spectral analysis over the conditional probability density time series. The method is robust in the application to Lorenz system, 4 dimension Rssler system and rigid body motion by linear feedback system (LFRBM). Applying the method to the time series of sea surface temperature (SST) of the South China Sea, we obtained the power spectra of the wind speed (WS) from SST data. Furthermore, the results showed that there exists an important nonlinear interaction between the SST and the WS.

DIAGNOSIS AND IDENTIFICATION OF DYNAMIC CORRELATION FACTORS BETWEEN WEST-PACIFIC SUBTROPICAL HIGH AND EAST ASIA MONSOON SYSTEM INDEXES

Based on the daily reanalysis data of NCEP / NCAR and by using the method of phase space reconstruction, the point conditional probability density of the subtropical high ridge index are determined and then used, together with their power spectra, to seek the correlation between them and individual monsoon-affecting factors and their power spectra. Through diagnosis, six indexes are discovered that have the most important effects on the subtropical high index. The results of the diagnosis indicate that the technique can identify the factors which are dynamically correlated. It can offer the basis in determining and choosing dynamic conceptual factors.

A new inverse method and application to ocean data

A new method is proposed to inverse normalization data of hidden variables in a dynamical system by embedding a time series in multidimensional spaces and applying a normalization analysis to the conditional probability density of points in the reconstructed phase spaces. The method is robust in the application to Lorenz system and 4-dimensional R?ssler system by testing quantitatively and qualitatively the correlation coefficient between inverse data and original data in time domain and in frequency domain, respectively. By applying the method to analyzing the South China Sea data, the normalization data of wind speed is extracted from the sea surface temperatu-re time series.

Generalized fixed-effects and mixed-effects parameters height-diameter models with diffusion processes

Statistical models using stochastic differential equations （SDEs） to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. In this study, the SDE mixed-effects parameter models based on a Vasicek non-homogeneous diffusion process are formulated. The breast height diameter- dependent drift function additionally depends on deterministic function that describes the dynamic of certain exogenous stand variables （crown height, eh, crown width Cw, mean breast height diameter, do, mean height, ho, age, A, soil fertility index SFI, stocking level, S） versus breast height diameter. The mixed-effects parameters SDE models included a random parameter that affected the models asymptote. The parameter estimators are evaluated by maximum likelihood procedure. The objective of the research was to develop a generalized mixed-effects parameters SDE heightdiameter models and to illustrate issues using dataset of Scots pine trees （Pinus sylvestris L.） in Lithuania with the breast height diameter outside the bark larger than 0cm. The parameters of all used models were estimated using an estimation dataset and were evaluated using a validation dataset. The new developed height diameter models are an improvement over exogenous stand variables, in that it can be calibrated to a new stand with observed height-diameter pairs, thus improving height prediction.