CalculateEmbeddingDim: Estimate the proper embedding dimension for the RR time series

Description

This function determines the minimum embedding dimension from a scalar time series using the algorithm proposed by L. Cao (see references).

Usage

CalculateEmbeddingDim(
  HRVData,
  numberPoints = 5000,
  timeLag = 1,
  maxEmbeddingDim = 15,
  threshold = 0.95,
  maxRelativeChange = 0.05,
  doPlot = TRUE
)

Arguments

HRVData: Data structure that stores the beats register and information related to it
numberPoints: Number of points from the time series that will be used to estimate the embedding dimension. By default, 5000 points are used.
timeLag: Time lag used to build the Takens' vectors needed to estimate the embedding dimension (see buildTakens). Default: 1.
maxEmbeddingDim: Maximum possible embedding dimension for the time series. Default: 15.
threshold: Numerical value between 0 and 1. The embedding dimension is estimated using the E1(d) function. E1(d) stops changing when d is greater than or equal to embedding dimension, staying close to 1. This value establishes a threshold for considering that E1(d) is close to 1. Default: 0.95
maxRelativeChange: Maximum relative change in E1(d) with respect to E1(d-1) in order to consider that the E1 function has been stabilized and it will stop changing. Default: 0.05.
doPlot: Logical value. If TRUE (default value), a plot of E1(d) and E2(d) is shown.

Details

The Cao's algorithm uses 2 functions in order to estimate the embedding dimension from a time series: the E1(d) and the E2(d) functions, where d denotes the dimension.

E1(d) stops changing when d is greater than or equal to the embedding dimension, staying close to 1. On the other hand, E2(d) is used to distinguish deterministic signals from stochastic signals. For deterministic signals, there exists some d such that E2(d)!=1. For stochastic signals, E2(d) is approximately 1 for all the values.

References

Cao, L. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenomena, 110,1, pp. 43-50 (1997).

Examples

Run this code

if (FALSE) {
data(HRVProcessedData)
HRVData = HRVProcessedData
HRVData = SetVerbose(HRVData,T)
timeLag = CalculateTimeLag(HRVData,technique = "ami")
embeddingDim = CalculateEmbeddingDim(HRVData,
                                     timeLag = timeLag,
                                     maxEmbeddingDim = 15)
}