The determinism test, which is based on a correct reconstruction of the attractor, enables us to measure average directional vectors in the coarse-grained embedding space [19]. The embedding space should be coarse-grained into equally sized boxes. Each pass of the trajectory through the th box can be regarded as a unit vector , and their directions are approximated by the points where the particular pass enters and leaves the box. Their average directional vector of the unit vector through the th box is defined by
= 1 ∑ =1 ,(7)
where is the total of all passes in box . Therefore, an approximate direction for the vector field can be obtained by all occupied boxes. If the **data** set sources from a deterministic dynamic process as well as a fine enough coarse-grained partitioning, the vector inside one box would nearly not cross. Since each crossing will decrease the size of the average vector , the average length of all directional vectors will be 1 for a deterministic process, while for a random process it will be 0. In order to verify whether the studied sway is from a stationarity process, stationarity test is evaluated [16,20]. To perform this method, the time series (20000 points) is divided into ℎ (ℎ = 100) short nonoverlapping segments; therefore, a cross-prediction error ( ) statistic is calculated for ℎ 2 possible combinations. We obtain a very sensitive statistic capable of detecting minute changes in dynamics and thus a very powerful probe for stationarity. If of each combination is not much larger than the average, the examined time series can be considered to be from a stationary system.