theta_method – Theta method (Assimakopoulos-Nikolopoulos 2000) – M3-competition winning baseline.#

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Operational op under axis family, sub-layer L4_A_model_selection, layer l4. Standalone callable: mf.functions.theta_fit.

Function signature#

mf.functions.theta_fit(
    X: np.ndarray | pd.DataFrame,
    y: np.ndarray | pd.Series,
) -> ThetaFitResult

Parameters#

name

type

default

constraint

description

X

`np.ndarray

pd.DataFrame`

—

—

y

`np.ndarray

pd.Series`

—

—

Returns#

ThetaFitResult — frozen dataclass with fit results.

Attribute

Type

Description

.theta

float

Theta parameter (default 2.0 = M3 winner).

.alpha_

float

Fitted SES smoothing parameter.

.n_obs

int

Number of observations.

.predict(X)

np.ndarray

Forecast, len(X) steps ahead.

.summary()

str

Table: theta, alpha, observation count.

Behavior#

Hand-coded Theta(2) closed-form forecast: blends a long-run linear-trend regression with a short-run simple-exponential-smoothing (SES) level. For θ = 2 (M3 winner), the h-step-ahead forecast is ŷ_{T+h} = 0.5 · (a + b · (T+h)) + 0.5 · ℓ_T, where (a, b) are the OLS trend slope/intercept on time index and ℓ_T is the SES level at time T (smoothing parameter α selected via scipy.optimize.minimize_scalar minimising the in-sample 1-step MSE).

Defaults: theta = 2.0 (M3 winner), seasonal = False, seasonal_periods = 12. The constructor exposes theta for forward compatibility; only the θ=2 closed form is exercised in v0.9.0 – general θ requires a θ-line decomposition out of scope for this run.

When to use

M3 / M4-style univariate baselines; quick reference forecast against more elaborate models.

When NOT to use

Strongly seasonal series (use holt_winters or seasonally-adjusted target); covariate-driven forecasting.

In recipe context#

Set params.family = "theta_method" in the relevant layer to activate this op within a recipe:

# Layer L4 recipe fragment
params:
  family: theta_method

References#

  • macroforecast design Part 2, L4: ‘forecasting model is the layer where every authoring iteration ends – pick family, tune, repeat.’

  • Assimakopoulos & Nikolopoulos (2000) ‘The theta model: a decomposition approach to forecasting’, International Journal of Forecasting 16(4): 521-530.

  • Hyndman & Billah (2003) ‘Unmasking the Theta method’, International Journal of Forecasting 19(2): 287-290.

  • Petropoulos et al. (2022) ‘Forecasting: theory and practice’, International Journal of Forecasting 38(3): 705-871.