Forecaster

ArpsHyperbolic

Categorical in XInsamplePred intPred int insample

Arps hyperbolic decline curve forecaster.

Models production decline as:

\[\begin{split}q(t) = \\frac{q_i}{(1 + b D_i t)^{1/b}}\end{split}\]

where \(q_i\) is the initial rate, \(D_i\) is the nominal decline rate, and \(b\) is the hyperbolic exponent (0 < b < 2 for physical decline). The exponential (b → 0) and harmonic (b = 1) cases are limiting forms. Parameters are estimated via nonlinear least squares (scipy.optimize.curve_fit). Probabilistic forecasts are produced by Monte Carlo sampling from the multivariate normal distribution over the fitted parameters using the covariance matrix from the curve fit.

Quickstart

python

from sktime.forecasting.arps_dca import ArpsHyperbolic

estimator = ArpsHyperbolic(qi_init=None, di_init=0.1, b_init=0.5, n_samples=1000, random_state=None, output='rate', anchor=False, base_np=0.0, max_fit_retries=3)

Parameters(9)

qi_initfloat or None, default=None: Initial rate guess. If None, the first observed value is used.
di_initfloat, default=0.1: Initial nominal decline rate guess.
b_initfloat, default=0.5: Initial b-exponent guess.
n_samplesint, default=1000: Number of Monte Carlo samples for probabilistic forecasts.
random_stateint, RandomState instance or None, default=None: Seed for reproducible probabilistic forecasts.
outputstr, default=”rate”: "rate" for instantaneous rate, "cumulative" for cumulative production.
anchorstr or False, default=False: Last-observation anchoring: "multiplicative", "additive", or False.
base_npfloat, default=0.0: Cumulative production offset added when output="cumulative".
max_fit_retriesint, default=3: Number of additional fitting attempts with perturbed initial parameters if the first attempt fails to converge. Set to 0 to disable retries. If all attempts fail, naive (degenerate) prediction intervals are returned with a warning.

Examples

>>> import pandas as pd
>>> import numpy as np
>>> from sktime.forecasting.arps_dca import ArpsHyperbolic
>>> t = np. arange (10)
>>> q = 1000 / (1 + 0.5 * 0.1 * t) ** (1 / 0.5)
>>> y = pd. Series (q, index = t)
>>> forecaster = ArpsHyperbolic ()
>>> forecaster. fit (y, fh = [1, 2, 3 ]) ArpsHyperbolic(
... )