> For the complete documentation index, see [llms.txt](https://market-quant.gitbook.io/home/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://market-quant.gitbook.io/home/api-reference/tools/cointegration/hursthalflifecointegration.md). # HurstHalfLifeCointegration() Analyzes stock pairs based on cointegration, Hurst exponent, half-life, and mean crossings. The `HurstHalfLifeCointegration` class is designed to analyze stock pairs by fetching their historical price data and applying a series of statistical tests. The class uses the Engle-Granger cointegration test, calculates the Hurst exponent, estimates the half-life of the spread between the pairs, and counts the number of mean crossings, based on configurable thresholds. *** ## **Class: `HurstHalfLifeCointegration()`** A tool for identifying mean-reverting pairs of stocks using statistical methods. Generates a list of eligible pairs based on: * Cointegration test * Hurst exponent (for mean reversion check) * Half-life of the spread * Mean crossings Supports customizable thresholds for the selection of eligible stock pairs based on user-defined parameters. *** ## **Constructor: `__init__()`** Initializes the `HurstHalfLifeCointegration` object and configures thresholds for analysis. ### **Arguments:** * **tickers** (`list`): List of stock tickers to analyze. * **start** (`str`): Start date for fetching historical stock data in the format 'YYYY-MM-DD'. * **end** (`str`): End date for fetching historical stock data in the format 'YYYY-MM-DD'. * **p\_value\_threshold** (`float`, optional): Maximum acceptable p-value for the cointegration test. Default is `0.05`. * **hurst\_threshold** (`float`, optional): Maximum acceptable Hurst exponent value (less than `0.5` for mean-reversion). Default is `0.5`. * **min\_half\_life** (`int`, optional): Minimum half-life of the spread in days. Default is `1`. * **max\_half\_life** (`int`, optional): Maximum half-life of the spread in days. Default is `365`. * **min\_crossings** (`int`, optional): Minimum number of mean crossings per year. Default is `12`. ### **Attributes Initialized:** * **tickers**: The list of stock tickers to analyze. * **start**: The start date for downloading stock data. * **end**: The end date for downloading stock data. * **p\_value\_threshold**: The maximum p-value for the cointegration test. * **hurst\_threshold**: The maximum Hurst exponent value to filter mean-reverting pairs. * **min\_half\_life**: The minimum half-life of the spread. * **max\_half\_life**: The maximum half-life of the spread. * **min\_crossings**: The minimum number of mean crossings required. * **data**: Holds the fetched stock data. *** ## **Method: `download_data()`** Downloads historical stock data for the specified tickers using the Yahoo Finance API (`yfinance`). ### **Arguments:** None ### **Returns:** None (Stock data is stored in the `self.data` attribute) *** ## **Method: `calculate_cointegration()`** Performs the Engle-Granger cointegration test on a pair of stocks. ### **Arguments:** * **pair** (`tuple`): A tuple containing two stock tickers. ### **Returns:** * A tuple of the two tickers and their p-value if the p-value is below the `p_value_threshold`. * `None` if the p-value is above the threshold or an error occurs. *** ## **Method: `calculate_hurst()`** Calculates the Hurst exponent to determine if a stock pair exhibits mean-reverting behavior. ### **Arguments:** * **series** (`pd.Series`): A time series of the spread between two stocks. ### **Returns:** * The Hurst exponent (`float`) if the series is valid and meets the criteria. * `None` if the calculation fails due to invalid data or an error. *** ## **Method: `calculate_half_life()`** Calculates the half-life of mean reversion for a stock pair spread using an Ordinary Least Squares (OLS) regression. ### **Arguments:** * **spread** (`pd.Series`): The spread between two stock prices. ### **Returns:** * The half-life of the spread (`float`). *** ## **Method: `calculate_mean_crossings()`** Counts how many times the spread crosses its mean, which helps identify whether the pair exhibits frequent mean reversion. ### **Arguments:** * **spread** (`pd.Series`): The spread between two stock prices. ### **Returns:** * The number of mean crossings (`int`). *** ## **Method: `process_pair()`** Processes each pair of stocks by: 1. Checking cointegration. 2. Calculating the Hurst exponent. 3. Estimating the half-life of the spread. 4. Counting the mean crossings. ### **Arguments:** * **pair** (`tuple`): A tuple of two stock tickers. ### **Returns:** * A tuple of the two tickers and their statistical properties (p-value, Hurst exponent, half-life, mean crossings) if they meet all the thresholds. * `None` if the pair fails any of the tests or thresholds. *** ## **Method: `find_eligible_pairs()`** Applies the `process_pair` method to all possible combinations of the stock tickers to find eligible pairs using parallel processing. ### **Arguments:** None ### **Returns:** * A list of eligible stock pairs that meet all the statistical criteria. *** ## **Method: `run_analysis()`** Downloads the stock data and processes all pairs to find eligible pairs. ### **Arguments:** None ### **Returns:** None *** ## **Example Usage** ```python tickers_csv_path = 'tickers.csv' tickers = load_tickers_from_csv(tickers_csv_path) # Initialize the analyzer with customizable parameters analyzer = HurstHalfLifeCointegration( tickers=tickers, start='2022-01-01', end='2024-01-01', p_value_threshold=0.05, hurst_threshold=0.4, min_half_life=5, max_half_life=250, min_crossings=10 ) # Run the analysis analyzer.run_analysis() ``` ### **Customization Options** * **Thresholds for Statistical Tests**: Users can set custom thresholds for cointegration p-value, Hurst exponent, half-life of mean reversion, and mean crossings to fine-tune the analysis. * **Stock Tickers**: The class accepts any combination of tickers supported by Yahoo Finance. * **Date Range**: Allows specifying a date range (`start` and `end`) for historical data analysis.