Detects the number of information layers present in trade-data using the algorithms in Ersan (2016) , Ersan and Ghachem (2022a) , and Ghachem and Ersan (2022a) .

## Usage

detectlayers_e(data, confidence = 0.995, correction = TRUE)

detectlayers_eg(data, confidence = 0.995)

detectlayers_ecm(data, hyperparams = list())

## Arguments

data

confidence

A number from (0.5,1), corresponding to the range of the confidence interval used to determine whether a given cluster is compact, and therefore can be considered an information layer. If all values of absolute order imbalances (AOI) within a given cluster are within the confidence interval of a Skellam distribution with level equal to 'confidence', and centered on the mean of AOI, then the cluster is considered compact, and, therefore, an information layer. If some observations are outside the confidence interval, then the data is clustered further. The default value is 0.995. [i] This is an argument of the functions detectlayers_e(), and detectlayers_eg().

correction

A binary variable that determines whether the data will be adjusted prior to implementing the algorithm of Ersan (2016) . The default value is TRUE.

hyperparams

A list containing the hyperparameters of the ECM algorithm. When not empty, it contains one or more of the following elements: maxeval, tolerance, maxinit, and maxlayers. More about these elements are found in the Details section. [i] This is an argument of the function detectlayers_ecm().

## Value

Returns an integer corresponding to the number of layers detected in the data.

## Details

The argument 'data' should be a numeric dataframe, and contain at least two variables. Only the first two variables will be considered: The first variable is assumed to correspond to the total number of buyer-initiated trades, while the second variable is assumed to correspond to the total number of seller-initiated trades. Each row or observation correspond to a trading day. NA values will be ignored.

The argument hyperparams contains the hyperparameters of the ECM algorithm. It is either empty or contains one or more of the following elements:

• maxeval: (integer) It stands for maximum number of iterations of the ECM for each initial parameter set. When missing, maxeval takes the default value of 100.

• tolerance (numeric) The ECM algorithm is stopped when the (relative) change of log-likelihood is smaller than tolerance. When missing, tolerance takes the default value of 0.001.

• maxinit: (integer) It is the maximum number of initial parameter sets used for the ECM estimation per layer. When missing, maxinit takes the default value of 20.

• maxlayers (integer) It is the upper limit of number of layers used in the ECM algorithm. To find the optimal number of layers, the ECM algorithm will estimate a model for each value of the number of layers between 1 and maxlayers, and then picks the model that has the lowest Bayes information criterion (BIC). When missing, maxlayers takes the default value of 8.

## References

Ersan O (2016). “Multilayer Probability of Informed Trading.” Available at SSRN 2874420.

Ersan O, Ghachem M (2022a). “Identifying information types in probability of informed trading (PIN) models: An improved algorithm.” Available at SSRN 4117956.

Ghachem M, Ersan O (2022a). “Estimation of the probability of informed trading models via an expectation-conditional maximization algorithm.” Available at SSRN 4117952.

## Examples

# There is a preloaded quarterly dataset called 'dailytrades' with 60
# observations. Each observation corresponds to a day and contains the