In this paper, the waveforms measured by the strain gauge in the tapping test on a number of healthy subjects and patients with Parkinson's disease are analyzed with the objective of reaching a quantitatively evaluation of the associated symptom. It has been observed that the waveform of a patient with Parkinson's disease becomes more irregular as the symptom is getting more serious, while the waveform of a healthy subject is rather regular. In this study, the regularity of the waveform is evaluated by the so-called trajectory parallel measure. The results show a large difference in the trajectory parallel measure of the waveforms of healthy subjects vs. those of the Parkinson's disease patients. Furthermore, the trajectory parallel measure of Parkinson's disease patients can be quantitatively ranked to correlate to the degree of the symptom. This paper begins with a brief description about Parkinson's disease. The trajectory parallel measure is then introduced and applied to analysis of the waveforms of both healthy subjects and patients with Parkinson's disease. Illustrative results are shown to demonstrate the applicability of the proposed analysis methodology.

It is now known that a seemingly random irregular time series can be deterministic chaos (hereafter, chaos). However, there can be various kind of noise superimposed into signals from real systems. Other factors affecting a signal include sampling intervals and finite length of observation. Perhaps, there may be cases in which a chaotic time series is considered as noise. J. Theiler proposed a method of surrogating data to address these problems. The proposed method is one of a number of approaches for testing a statistical hypothesis. The method can identify the deterministic characteristics of a time series. In this approach, a surrogate data is formed to have stochastic characteristics with the statistic value associated with the original data. When the characteristics of the original data differs from that of a surrogate data, the null hypothesis is no longer valid. In other words, the original data is deterministic. In comparing the characteristics of an original time series data and that of a surrogate data, the maximum Lyapunov exponents, correlation dimensions and prediction accuracy are utilized. These techniques, however, can not calculate the structure in local subspaces on the attractor and the flow of trajectories. In deal with these issues, we propose the trajectory parallel measure (TPM) method to determine whether the null hypothesis should be rejected. In this paper, we apply the TPM method and the method of surrogate data to test a chaotic time series and a random time series. We also examine whether a practical time series has a deterministic property or not. The results demonstrate that the TPM method is useful for judging whether the original and the surrogate data sets are different. For illustration, the TPM method is applied to a practical time series, tap water demand data.