Theta

The Theta method decomposes a time series into two "theta lines" and combines their forecasts.

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Theta

from durbyn import Theta

model = Theta(model_type="OTM").fit(y, m=12)
fc = model.forecast(h=12, level=[80, 95])

Parameters

Parameter	Type	Default	Description
model_type	str	"OTM"	Model type: "OTM" (optimised), "STM" (simple), "DSTM", "DOTM"
alpha	float \| None	None	Smoothing parameter
theta_param	float \| None	None	Theta parameter value
initial_level	float \| None	None	Initial level value
nmse	int	3	Steps for multi-step MSE evaluation

Model Types

Type	Description
"STM"	Simple Theta Method
"OTM"	Optimised Theta Method
"DSTM"	Dynamic Simple Theta Method
"DOTM"	Dynamic Optimised Theta Method

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AutoTheta

Automatically selects the best Theta model type.

from durbyn import AutoTheta

model = AutoTheta().fit(y, m=12)
fc = model.forecast(h=12, level=[80, 95])

# With specific decomposition
model = AutoTheta(
    decomposition_type="multiplicative",
    nmse=5,
).fit(y, m=12)

Parameters

Parameter	Type	Default	Description
model	str \| None	None	Specific model type. None to try all
decomposition_type	str	"multiplicative"	Seasonal decomposition: "multiplicative" or "additive"
alpha	float \| None	None	Smoothing parameter
theta_param	float \| None	None	Theta parameter
initial_level	float \| None	None	Initial level value
nmse	int	3	Steps for multi-step MSE

---

Example

from durbyn import Theta, AutoTheta, compare

y_train = y[:24]
y_test = y[24:]

result = compare(
    models={
        "STM": Theta(model_type="STM"),
        "OTM": Theta(model_type="OTM"),
        "DOTM": Theta(model_type="DOTM"),
        "AutoTheta": AutoTheta(),
    },
    y_train=y_train,
    y_test=y_test,
    m=12,
)

print(result.to_dataframe())