Convert Signature to Predicted Values

This function calculates predicted values of a series based on its previous value and predicted signature changes. It starts with an initial value from a historical series and sequentially adds predicted signature changes to generate a sequence of predicted values.

Usage

convertSignatureToValue(E, tau, Y, i, h, predictedSignatureY)

Arguments

E

Integer, the length of the series for which predictions are needed.

tau

Integer, the time delay used in the system dynamics (not used in this function but typically relevant in the broader context of time series prediction).

Y

Numeric vector, the original series from which the prediction starts.

i

Integer, the starting index in the vector Y from which the prediction should commence.

h

Integer, the horizon step for which the initial predicted value is directly obtained from Y.

predictedSignatureY

Numeric vector, the predicted changes (signature) at each step used for prediction.

Value

Numeric vector containing the predicted values of the series starting from index i+h in Y and extending for E steps, adjusted by the predicted signature.

Examples

Y <- c(1, 2, 3, 5, 8, 13, 21)
E <- 5
tau <- 1 # Example value, not used in the function
i <- 2
h <- 3
predictedSignatureY <- c(0.5, 1.5, 2.5, 3.5, 4.5)
predictedValues <- convertSignatureToValue(E, tau, Y, i, h, predictedSignatureY)
print(predictedValues)
#> [1]  8.0  8.5 10.0 12.5 16.0