Statnote 32 : the partial correlation coefficient

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. The most important statistic used to measure the degree of correlation between two variables is Pearson’s ‘product moment correlation coefficient’ (‘r’). The correlation between two variables may be due to their common relation to other variables. Hence, investigators using correlation studies need to be alert to the possibilities of spurious correlation and the methods of ‘partial correlation’ are one method of taking this into account. This statnote applies the methods of partial correlation to three scenarios. First, to a fairly obvious example of a spurious correlation resulting from the ‘size effect’ involving the relationship between the number of general practitioners (GP) and the number of deaths of patients in a town. Second, to the relationship between the abundance of the nitrogen-fixing bacterium Azotobacter in soil and three soil variables, and finally, to a more complex scenario, first introduced in Statnote 24involving the relationship between the growth of lichens in the field and climate.

Statnote 33:the intra-class correlation coefficient

The intra-class correlation coefficient (ICC or ri) is a method of measuring correlation when the data are paired and therefore, should be used when experimental units are organised into groups. A useful analogy is with the unpaired or paired ‘t’ test to compare the differences between the means of two groups. In studies of reproducibility, there may actually be little difference between the ICC and Pearson’s ‘r’ for ‘true’ repeated measurements. If, however, there is a systematic change in the measurements made on the first compared with the second occasion, then the ICC will be significantly less than ‘r’, and less confidence would be placed in the reproducibility of the results.

New negative temperature coefficient thermistor ceramics in Mn-doped CaCu3-xMnxTi4O12 (0≤x≤1) system

New negative temperature coefficient (NTC) ceramics based on CaCu 3-xMnxTi4O12 (0≤x≤1) compositions have been investigated. The grain size of the CaCu 3-xMnxTi4O12 samples decreases at first and then increases with increasing Mn content. The X-ray photoelectron spectroscopy analysis corroborates the presence of Mn3+ and Mn 4+ in Mn-doped samples, which results in a decrease in the activation energy. All the NTC thermistors prepared show a linear relationship between the natural logarithm of the resistivity and the reciprocal temperature, indicative of NTC characteristics. The Mn-doped CaCu3-xMnxTi 4O12 NTC thermistors provide various electrical properties, depending on Mn content. The values of ρ25, B constant and activation energy of the NTC thermistors are in the range of 2.22×106-3.22×108 Ω cm, 5488-8031 K, and 0.473-0.692 eV, respectively. © 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Modelling stock volatilities during financial crises:a time varying coefficient approach

We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two decades in the volatility dynamics, including the underlying volatility persistence and volatility spillover structure. Using daily data from several key stock market indices, the results of our bivariate GARCH models show the existence of time varying correlations as well as time varying shock and volatility spillovers between the returns of FTSE and DAX, and those of NIKKEI and Hang Seng, which became more prominent during the recent financial crisis. Our theoretical considerations on the time varying model which provides the platform upon which we integrate our multifaceted empirical approaches are also of independent interest. In particular, we provide the general solution for time varying asymmetric GARCH specifications, which is a long standing research topic. This enables us to characterize these models by deriving, first, their multistep ahead predictors, second, the first two time varying unconditional moments, and third, their covariance structure.