Convert Out-of-Sample Signature to Predicted Values

This function predicts future values for a time series starting from the last known predicted value. It uses a series of predicted signature changes to extrapolate future values, assuming that changes continue in a similar manner to the signatures provided. This is particularly useful in scenarios where short-term predictions are made in complex systems based on embedded dynamic structures as described in the associated literature.

Usage

convertSignatureToValueOutOfSample(
  E,
  tau,
  Y_pred_last,
  i,
  h,
  predictedSignatureY
)

Arguments

E

Integer, the number of future values to predict.

tau

Integer, the time delay used in the system dynamics; while not used directly in this function, it is relevant in the broader context of the methodology for embedding time series data.

Y_pred_last

Numeric, the last predicted value from which future values will be extrapolated.

i

Integer, the starting index for the prediction; not used in this function but generally important in the broader algorithm.

h

Integer, the horizon step from the last known actual value to the first prediction point; not used directly in this function but part of the overall predictive framework.

predictedSignatureY

Numeric vector, the predicted incremental changes (signature) at each step used for extrapolation of the series.

Value

Numeric vector containing the extrapolated future values of the series, starting from Y_pred_last and extending for E steps, adjusted by the predicted signature changes.

Examples

# Suppose Y_pred_last is the last known predicted value of a financial time series
Y_pred_last <- 120
# Assume predicted signature changes based on a model's output
predictedSignatureY <- c(2, 3, 4, 5, 6)
# Number of future points to predict
E <- 5
# Example values for tau and i, h not used in this function directly
tau <- 1
i <- 1
h <- 1

# Generate future predictions
futureValues <- convertSignatureToValueOutOfSample(E, tau, Y_pred_last, i, h, predictedSignatureY)
print(futureValues)
#> [1] 120 122 125 129 134