vastorbit.machine_learning.model_selection.statistical_tests.tsa.cochrane_orcutt

vastorbit.machine_learning.model_selection.statistical_tests.tsa.cochrane_orcutt(model: LinearModel, input_relation: Annotated[str | VastFrame, ''], ts: str, prais_winsten: bool = False, drop_tmp_model: bool = True) → LinearModel

Performs a Cochrane-Orcutt estimation.

Parameters:

• model (LinearModel) – Linear regression object.

• input_relation (SQLRelation) – Input relation.

• ts (str) – VastColumn of numeric or date-like type (date, datetime, timestamp, etc.) used as the timeline and to order the data.

• prais_winsten (bool, optional) – If True, retains the first observation of the time series, increasing precision and efficiency. This configuration is called the Prais–Winsten estimation.

• drop_tmp_model (bool, optional) – If true, drops the temporary model.

Returns:

A Linear Model with the different information stored as attributes:

• intercept_:

  Model’s intercept.

• coef_:

  Model’s coefficients.

• pho_:

  Cochrane-Orcutt pho.

• anova_table_:

  ANOVA table.

• r2_:

  R2 score.

Return type:

model_tmp

Examples

Initialization

Let’s try this test on a dummy dataset that has the following elements:

• A value of interest that has noise related to time

• Time-stamp data

Before we begin we can import the necessary libraries:

import vastorbit as vo
import numpy as np

Example 1: Trend

Now we can create the dummy dataset:

# Initialization
N = 30 # Number of Rows.
days = list(range(N))
y_val = [2 * x + np.random.normal(scale = 4 * x) for x in days]

# VastFrame
vdf = vo.VastFrame(
    {
        "day": days,
        "y1": y_val,
    }
)

We can visually inspect the trend by drawing the appropriate graph:

vdf.scatter(["day", "y1"])

Model Fitting

Next, we can fit a Linear Model. To do that we need to first import the model and intialize:

from vastorbit.machine_learning.vast.linear_model import LinearRegression

model = LinearRegression()

Next we can fit the model:

model.fit(vdf, X = "day", y = "y1")

Now we can apply the Cochrane-Orcutt estimation to get the new modified model:

from vastorbit.machine_learning.model_selection.statistical_tests import cochrane_orcutt

new_model = cochrane_orcutt(model = model, input_relation = vdf, ts = "day")

Now we can compare the coefficients of both the models to see the difference.

model.coef_

new_model.coef_

We can see that the new model has slightly different coefficients to cater for the autocorrelated noise.