arbitragelab.cointegration_approach.coint_sim

This module allows simulation of cointegrated time series pairs.

Module Contents

Classes

CointegrationSimulation

This is a class that can be used to simulate cointegrated price series pairs.
class CointegrationSimulation(ts_num: int, ts_length: int)

This is a class that can be used to simulate cointegrated price series pairs.

The class will generate a price first-order difference time series defined by an AR(1) process, a cointegration error series defined by an AR(1) process, and calculate the other price series based on the cointegration equation.

static initialize_params() → Tuple[dict, dict]

Initialize the default parameters for the first-order difference of share S2 price series and cointegration error.

Returns:

(dict, dict) Necessary parameters for share S2 price simulation; necessary parameters for cointegration error simulation.

get_price_params() → dict

Getter for price simulation parameters.

Returns:

price_params: (dict) Necessary parameters for share S2 price simulation.

get_coint_params() → dict

Getter for cointegration error simulation parameters.

Returns:

coint_params: (dict) Necessary parameters for cointegration error simulation.

set_price_params(param: str, value: float)

Setter for price simulation parameters.

Change one specific parameter to a designated value. Possible parameters are [“ar_coeff”, “white_noise_var”, “constant_trend”].

Parameters:

  • param – (str) Parameter dictionary key.

  • value – (float) Parameter value.

set_coint_params(param: str, value: float)

Setter for cointegration error simulation parameters.

Change one specific parameter to a designated value. Possible parameters are [“ar_coeff”, “white_noise_var”, “constant_trend”, “beta”].

Parameters:

  • param – (str) Parameter dictionary key.

  • value – (float) Parameter value.

load_params(params: dict, target: str = 'price')

Setter for simulation parameters.

Change the entire parameter sets by loading the dictionary.

Parameters:

  • params – (dict) Parameter dictionary.

  • target – (str) Indicate which parameter to load. Possible values are “price” and “coint”.

simulate_ar(params: dict, burn_in: int = 50, use_statsmodels: bool = True) → numpy.array

Simulate an AR(1) process without using the statsmodels package. The AR(1) process is defined as the following recurrence relation.

\[y_t = \mu + \phi y_{t-1} + e_t, \quad e_t \sim N(0, \sigma^2) \qquad \mathrm{i.i.d}\]
Parameters:

  • params – (dict) A parameter dictionary containing AR(1) coefficient, constant trend, and white noise variance.

  • burn_in – (int) The amount of data used to burn in the process.

  • use_statsmodel – (bool) If True, use statsmodels; otherwise, directly calculate recurrence.

Returns:

(np.array) ts_num simulated series generated.

simulate_coint(initial_price: float, use_statsmodels: bool = False) → Tuple[numpy.array, numpy.array, numpy.array]

Generate cointegrated price series and cointegration error series.

Parameters:

  • initial_price – (float) Starting price of share S2.

  • use_statsmodels – (bool) Use statsmodels API or use raw method. If True, then statsmodels API will be used.

Returns:

(np.array, np.array, np.array) Price series of share S1, price series of share S2, and cointegration error.

verify_ar(price_matrix: numpy.array) → Tuple[float, float | None]

Test function to confirm that the simulated price series is an AR(1) process.

Parameters:

price_matrix – (np.array) A matrix where each column is a hypothetical AR(1) process.

Returns:

(float, float) The mean AR(1) coefficient of the process; the standard deviation of AR(1) coefficient of the process.

verify_coint(price_series_x: numpy.array, price_series_y: numpy.array, x_name: str = 'Share S1', y_name: str = 'Share S2') → Tuple[float, float | None]

Use the Engle-Granger test to verify if the simulated series are cointegrated.

Parameters:

  • price_series_x – (np.array) A matrix where each column is a simulated price series of share S1.

  • price_series_y – (np.array) A matrix where each column is a simulated price series of share S2.

  • x_name – (str) Column name for share S1 column of Engle-Granger input dataframe.

  • y_name – (str) Column name for share S2 column of Engle-Granger input dataframe.

Returns:

(float, float) Mean of hedge ratio; standard deviation of hedge ratio.

plot_coint_series(series_x: numpy.array, series_y: numpy.array, coint_error: numpy.array, figw: float = 15.0, figh: float = 10.0) → matplotlib.pyplot.Figure

Plot the simulated cointegrated series.

Parameters:

  • series_x – (np.array) Price series of share S1

  • series_y – (np.array) price series of share S2

  • coint_error – (np.array) Cointegration error.

  • figw – (float) Figure width.

  • figh – (float) Figure height.

Returns:

(plt.Figure) Figure with the simulated cointegrated series.