psytest.sadftest module

psytest.sadftest module#

psytest.sadftest#

This module contains the functions related to the Sup ADF test and the Backward Sup ADF test. The functions allow us to calculate both the test statistic and the asymptotic distribution of the test statistic

See psytest.adfstat for the basic Augmented Dickey-Fuller test.

psytest.sadftest.bsadf_stat(y: ndarray[tuple[int, ...], dtype[float64]], r0: float, r2: float, kmax: int) → float[source]#

Calculates the Backward Sup ADF test statistic.

Parameters:

  • y (NDArray[float64]) – Time series values.

  • r0 (float) – Minimum index.

  • r2 (float) – End index.

  • kmax (int) – Max lag.

Returns:

teststat – BSADF statistic.

Return type:

float

Notes

The Backward Sup ADF statistic is calculated as: .. math:

\text{BSADF}(r_2) = \max_{r_1 \in [0, r_2 - r_0]} \text{ADF}(y_{r_1:r_2})

where \(\text{ADF}(y_{r_1:r_2})\) is the Augmented Dickey-Fuller test statistic for the series \(y_{r_1:r_2}\) (see psytest.adfstat.rolling_adfuller_stat()).

psytest.sadftest.bsadf_stat_all_series(y: ndarray[tuple[int, ...], dtype[float64]], r0: float, rstep: float, kmax: int) → ndarray[tuple[int, ...], dtype[float64]][source]#

Calculates BSADF statistics over all possible (r1, r2) combinations.

Parameters:

  • y (NDArray[float64]) – Time series values.

  • r0 (float) – Minimum index.

  • rstep (float) – Step size.

  • kmax (int) – Max lag.

Returns:

teststat_array – Array of test statistics.

Return type:

NDArray[float64]

psytest.sadftest.r2_index(r2: float, r0: float, rstep: float) → int[source]#

Get the index of r2 in the grid from r0 to 1 with step size rstep

psytest.sadftest.make_r2_grid(r0: float, rstep: float) → ndarray[tuple[int, ...], dtype[float64]][source]#

Creates the grid of all possible r2 values.

psytest.sadftest.make_r1_grid(r2: float, r0: float, rstep: float) → ndarray[tuple[int, ...], dtype[float64]][source]#

Creates the grid of all possible r1 values given r2.

psytest.sadftest.make_r1r2_combinations(r0: float, rstep: float) → ndarray[tuple[int, ...], dtype[float64]][source]#

Creates a grid of all (r1, r2) index pairs to evaluate BSADF.

Parameters:
Returns:

Grid of (r1, r2) pairs.

Return type:

[float64]

Notes

The grid is defined as: .. math:

\text{grid} = \{(r_1, r_2) : r_0 \leq r_2 \leq 1, \quad r_0 \leq r_1 \leq r_2 - r_0, \\
\quad rstep = (r_2 - r_0)/n, \\
\quad n = \lfloor (1 - r_0)/rstep \rfloor + 1\}

with \(r_0\) being the minimum index, \(r_2\) being the end index, and \(r_1\) being the start index. The values of \(r_1\) and \(r_2\) are created from a grid with increments of rstep.

psytest.sadftest.bsadfuller_critval(r0: float, rstep: float, nreps: int, nobs: int, alpha: Iterable | float, kmax: int) → ndarray[tuple[int, ...], dtype[float64]][source]#

Calculates critical values of BSADF statistics from Monte Carlo simulations.

Parameters:

  • r0 (float) – Minimum index.

  • rstep (float) – Step size.

  • nreps (int) – Number of replications.

  • nobs (int | None) – Number of observations.

  • alpha (Iterable | float) – Significance levels.

Returns:

critval – Critical values matrix.

Return type:

NDArray[float64]

Notes

The critical values are calculated as: .. math:

\text{CV}_{i,\alpha} = \text{Quantile}_{1 - \alpha}(\text{BSADF}_i)

where \(\text{BSADF}_i\) is the \(i\)-th simulated BSADF statistic (see psytest.adfstat.bsadf_stat()) and \(\text{Quantile}_{1 - \alpha}\) is the quantile function for the distribution of the BSADF statistic.

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