ts_norm_an: Adaptive Normalization

In tspredit: Time Series Prediction with Integrated Tuning

Adaptive Normalization

Description

Transform data to a common scale while adapting to changes in distribution over time (optionally over a trailing window).

Usage

ts_norm_an(
  outliers = outliers_boxplot(),
  nw = 0,
  average = c("mean", "ema"),
  operation = c("divide", "subtract", "softdivide", "asinh"),
  scale = c("sd", "mad", "none"),
  lambda = 1,
  epsilon = 1e-08
)

Arguments

outliers	Indicate outliers transformation class. NULL can avoid outliers removal.
nw	integer: window size.
average	Character. Adaptive reference statistic: "mean" or "ema".
operation	Character. Adaptive normalization operator: "divide", "subtract", "softdivide", or "asinh".
scale	Character. Local scale estimator used by the hybrid operators: "sd", "mad", or "none".
lambda	Numeric. Weight assigned to the adaptive level term inside the hybrid reference scale.
epsilon	Numeric. Positive floor used to stabilize near-zero denominators and local scales.

Details

ts_norm_an() supports a family of adaptive window-wise transformations:

• "divide" rescales a window by its adaptive reference level.

• "subtract" recenters the window by subtracting the adaptive reference level.

• "softdivide" computes a stabilized relative deviation: (x - \mu) / \sqrt{s^2 + (\lambda \mu)^2 + \epsilon^2}.

• "asinh" applies an inverse-hyperbolic-sine contrast around the adaptive reference level using the same stabilized scale.

The concrete operators are implemented in tsanutils(), while ts_norm_an() focuses on estimating the adaptive references and applying the chosen transformation consistently during fit, transform, and inverse transform.

The adaptive reference \mu is estimated either by a simple mean or by an exponentially weighted mean (average = "ema"). The hybrid operators additionally use a local scale estimate s based on either the standard deviation or the MAD.

Value

A ts_norm_an object.

References

Ogasawara, E., Martinez, L. C., De Oliveira, D., Zimbrão, G., Pappa, G. L., Mattoso, M. (2010). Adaptive Normalization: A novel data normalization approach for non-stationary time series. Proceedings of the International Joint Conference on Neural Networks (IJCNN). doi:10.1109/IJCNN.2010.5596746

Huber PJ (1964). Robust Estimation of a Location Parameter. Annals of Mathematical Statistics, 35(1), 73-101. doi:10.1214/aoms/1177703732

Burbidge JB, Magee L, Robb AL (1988). Alternative Transformations to Handle Extreme Values of the Dependent Variable. Journal of the American Statistical Association, 83(401), 123-127.

Bellemare MF, Wichman CJ (2020). Elasticities and the Inverse Hyperbolic Sine Transformation. Oxford Bulletin of Economics and Statistics, 82(1), 50-61. doi:10.1111/obes.12325

Examples

# time series to normalize
library(daltoolbox)
library(tspredit)
data(tsd)

# convert to sliding windows
ts <- ts_data(tsd$y, 10)
ts_head(ts, 3)
summary(ts[,10])

# divisive adaptive normalization (default)
preproc <- ts_norm_an()
preproc <- fit(preproc, ts)
tst <- transform(preproc, ts)
ts_head(tst, 3)

# subtractive adaptive normalization
preproc <- ts_norm_an(operation = "subtract")
preproc <- fit(preproc, ts)
tst <- transform(preproc, ts)
ts_head(tst, 3)

# EMA-based soft division
preproc <- ts_norm_an(average = "ema", operation = "softdivide", scale = "mad")
preproc <- fit(preproc, ts)
tst <- transform(preproc, ts)
ts_head(tst, 3)

tspredit documentation built on May 15, 2026, 1:07 a.m.