Estimate RQA parameters

Find optimal parameters for constructing a Recurrence Matrix. A wrapper for various algorithms used to find optimal values for the embedding delay and the number of embedding dimensions.

est_parameters(
  y,
  lagMethods = c("first.minimum", "global.minimum", "max.lag"),
  estimateDimensions = "preferSmallestInLargestHood",
  maxDim = 10,
  emLag = NULL,
  maxLag = NA,
  minVecLength = 20,
  nnSize = NA,
  nnRadius = NA,
  nnThres = 10,
  theiler = 0,
  doPlot = TRUE,
  silent = TRUE,
  ...
)

Arguments

y

A numeric vector or time series

lagMethods

A character vector with one or more of the following strings: "first.minimum","global.minimum","max.lag". If emLag represents a valid lag this value will be reported as "user.lag" (default = c("first.minimum","global.minimum","max.lag"))

estimateDimensions

Decide on an optimal embedding dimension relative to the values in maxDim and lagMethods, according to a number of preferences passed as a character vector. The order in which the preferences appear in the vector affects the selection procedure, with index 1 being most important preference. The following options are available:

• preferNone - No optimal number will be picked all other preferences will be ignored

• preferSmallestDim - Pick smallest number of dimensions associated with a percentage NN below nnThres

• preferSmallestNN - Pick the number of dimensions that is associated with the smallest percentage NN below nnThres

• preferSmallestLag - If the value of nnThres does not lead to a unique preference for a pair of dimension and lag values, use the pair with the smallest lag

• preferSmallestInLargestHood - The default option: If no unique pair can be found, prefer pairs with smallest values for lag, dimensions, percentage NN for the largest NN size

maxDim

Maximum number of embedding dimensions to consider (default = 10)

emLag

Optimal embedding lag (delay), e.g., provided by an optimising algorithm. If NULL the lags based on the mutual information in lagMethods will be reported. If a numeric value representing a valid lag is passed, this value will be used to estimate the number of dimensions (default = NULL)

maxLag

Maximum embedding lag to consider. If NA then the value is caclulated as floor(length(y)/(maxDim+1)) (default = NA)

minVecLength

The minimum length of state space vectors after delay-embedding. For short time series, this will affect the possible values of maxDim that can be used to evaluate the drop in nearest neighbours. In general it is not recommended to evaluate high dimensional state spaces, based on a small number of state soace coordinates, the default is an absolute minimum and possibly even lower than that. (default = 20)

nnSize

Neighbourhood diameter (integer, the number.boxes parameter of tseriesChaos::false.nearest()) used to speed up neighbour search. (default = NA)

nnRadius

Points smaller than the radius are considered neighbours. If NA the value will be sd(y)/10 (default = NA)

nnThres

Threshold value (in percentage 0-100) representing the percentage of Nearest Neighbours that would be acceptable when using N surrogate dimensions. The smallest number of surrogate dimensions that yield a value below the threshold will be considered optimal (default = 10)

theiler

Theiler window on distance matrix (default = 0)

doPlot

Produce a diagnostic plot the results (default = TRUE)

silent

Silent-ish mode

...

Other parameters passed to nonlinearTseries::timeLag()

Value

A list object containing the optimal values (as indicated by the user) and iteration history.

Details

A number of functions are called to determine optimal parameters for delay embedding a time series:

• Embedding lag (emLag): The default is to call est_emLag(), which is a wrapper around nonlinearTseries::timeLag() with technique=ami to get lags based on the mutual information function.

• Embedding dimension (m, emDim): The default is to call est_emDim(), which is a wrapper around tseriesChaos::false.nearest()

See also

Other Estimate Recurrence Parameters: est_emDim(), est_emLag(), est_parameters_roc(), est_radius(), est_radius_rqa()

Examples

set.seed(4321)
est_parameters(y=rnorm(100))
#> Changed value of maxDim to 8