Probability plot correlation detection

When experimental data are collected over time or distance there is always a chance of having autocorrelated residuals. Box et al. (1994) provide an extensive treatment of correlated disturbances in discrete time models. The structure of the disturbance term is often moving average or autoregressive models. Detection of autocorrelation in the residuals can be established either from a time series plot of the residuals versus time (or experiment number) or from a lag plot. If we can see a pattern in the residuals over time, it probably means that there is correlation between the disturbances. 

A comparison of the dependence of the improvement factor on the salt concentration for the ammonium bromide-ethanol-water system at x = 0.246 (Figure 3) and that observed by Jaques and Furter (3) for ammonium chloride-ethanol-water at x = 0.223 reveals many similarities between these two systems. Their k values are similar, they both yield good correlation with Equation 1, and in both systems an inflection can be detected in the experimental plot of improvement factor vs. salt concentration at 0.05 mole fraction salt. The inflection probably can be attributed to a change in the solvent structure owing to the presence of salt. 

In Fig. 15, we plot the correlation functions for the same parameters as in Fig. 14, but now A/0. We first observe that the behavior of the correlation functions is qualitatively different to the case where A = 0. For correlated dipole moments with p = 0.99, the values of g (xj and y (x) remain below unity for all times. This shows that for any x the probability of emission of two photons from levels 1) or 3) is very small. We can interpret this as extended simultaneous periods of darkness in the fluorescence from the two atomic transitions after detection of a photon at time x = 0, detection of another photon at time x > 0, emitted from levels 1) or 3), is very unlikely. We point out that the simultaneous periods of darkness appear only for correlated transitions with p 0. Dark periods of fluorescence have been predicted by Cook and Kimble [60] and Pegg et al. [61] for a V-type atom with orthogonal dipole moments of the transitions and significantly different decay rates T and... 

---