compotime.models.LocalTrendForecaster

class compotime.models.LocalTrendForecaster

Bases: object

Local trend state-space forecaster.

Notes

The local trend model is described by the following equations:

\[\begin{split}\boldsymbol y_t &= \boldsymbol l_{t-1} + \boldsymbol b_{t-1} + \boldsymbol \epsilon_t \\ \boldsymbol l_t &= \boldsymbol l_{t-1} + \boldsymbol b_{t-1} + \alpha \boldsymbol \epsilon_t \\ \boldsymbol b_t &= \boldsymbol b_{t-1} + \beta \boldsymbol \epsilon_t\end{split}\]

where \(\boldsymbol y_t\) represents the unbounded time series observations at timestep \(t\) that result from applying the log-ratio transform. \(\boldsymbol l_t\) and \(\boldsymbol b_t\) represent the level and the trend, respectively.

An equivalent expression is as follows

\[\begin{split}\boldsymbol y_t' &= \boldsymbol w' \boldsymbol X_{t-1} + \boldsymbol \epsilon_t' \\ \boldsymbol X_t &= \boldsymbol F \boldsymbol X_{t-1} + \boldsymbol g \boldsymbol \epsilon_t'\end{split}\]

where

\(\boldsymbol X_t = \begin{bmatrix} \boldsymbol l^{'}_{t} \\ \boldsymbol b^{'}_{t} \end{bmatrix}\), \(\boldsymbol w = \begin{bmatrix} 1 \\ 1 \end{bmatrix}\), \(\boldsymbol F = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}\) and \(\boldsymbol g = \begin{bmatrix} \alpha \\ \beta \end{bmatrix}\).

__init__()

Methods

__init__()
fit(y)	Fit the model.
predict(horizon)	Predict future values of the time series.

Attributes

optim_params_
opt_success_
X_
fitted_curve_
colnames_
time_idx_
idx_freq_
base_col_idx_

fit(y: DataFrame) → Self

Fit the model.

Parameters:

y – Time series dataframe, where rows represent the timestamps and columns the different shares series.

Returns:

Fitted instance of the model.

Return type:

Self

predict(horizon: int) → DataFrame

Predict future values of the time series.

Parameters:

horizon – Number of steps into the future to be predicted.

Returns:

Predicted time series.

Return type:

pd.DataFrame