> ## Documentation Index > Fetch the complete documentation index at: https://systematica.mintlify.site/llms.txt > Use this file to discover all available pages before exploring further. # Arbitrage Index > systematica.api.analytics.arbitrage_index ## `ArbitrageIndexCV` ```python theme={null} ArbitrageIndexCV( id: str = None, loader_or_data: Callable = , timeframe: str = '1d', start: str = None, end: str = None, s1: str = 'BTCUSDT', s2: str = 'ETHUSDT', suffix: str = 'h5', use_close: bool = True, freq: str = None, signal_model: str = None, long_entries: float = nan, long_exits: float = nan, short_entries: float = nan, short_exits: float = nan, clean: bool = True, select_symbols: str | int | List[str | int] = None, portfolio_config: Dict[str, Any] = _Nothing.NOTHING, model_params: Dict[str, Any] = _Nothing.NOTHING, metrics: str | List[str] = None, metrics_kwargs: Dict[str, Any] = _Nothing.NOTHING, use_rolling: bool = False, storage: str | optuna.storages._base.BaseStorage = None, pruner: optuna.pruners._base.BasePruner = , sampler: optuna.samplers._base.BaseSampler = , study_name: str = None, direction: str | List[str] = 'maximize', load_if_exists: bool = False, n_trials: int = 100, n_completed_trials: int = None, timeout: float = None, n_jobs: int = 1, catch: Iterable[Type[Exception]] | Type[Exception] = _Nothing.NOTHING, callbacks: Iterable[Callable[[optuna.study.study.Study, optuna.trial._frozen.FrozenTrial], None]] | None = None, gc_after_trial: bool = False, show_progress_bar: bool = False, verbose: bool = True, tracker: Type = None, model: Any = None, preprocess_func: Callable = None, ) ``` Breakdown analysis for arbitrage index models, extending `WalkForwardCV`. Includes methods to compute Kendall's Tau, determine the best copula, and extract copula parameters. Method generated by attrs for class WalkForwardCV. ### Ancestors * `systematica.walk_forward.cv.WalkForwardCV` * `systematica.walk_forward.base.BaseWalkForward` * `abc.ABC` * `systematica.generic.base.Model` * `systematica.generic.base.Feature` ### Methods #### `get_kendall_tau` ```python theme={null} get_kendall_tau( self, key: str = 'train', raw_output: bool = True, set_datetime_index: bool = True, ) ‑> pandas.core.series.Series ``` Compute Kendall's Tau correlation coefficient in each split. **Parameters**: | Name | Type | Default | Description | | -------------------- | ------ | ------- | ----------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `raw_output` | `bool` | `True` | If `True`, returns raw results. Default is `True`, which returns processed results. | | `set_datetime_index` | `bool` | `True` | If `True`, set end-test datetime index. Ignored otherwise. Defaults to `True`. | **Returns**: | Type | Description | | ----------- | --------------------------------------- | | `pd.Series` | Series containing Kendall's Tau values. | #### `get_ecdf` ```python theme={null} get_ecdf( self, key: str = 'test', raw_output: bool = True, set_datetime_index: bool = True, ) ‑> pandas.core.frame.DataFrame ``` Compute ECDF object in each set. Retrieves processed data splits based on the cross-validation splitter. **Parameters**: | Name | Type | Default | Description | | -------------------- | ------ | ------- | ----------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `raw_output` | `bool` | `True` | If `True`, returns raw results. Default is `True`, which returns processed results. | | `set_datetime_index` | `bool` | `True` | If `True`, set end-test datetime index. Ignored otherwise. Defaults to `True`. | **Returns**: | Type | Description | | -------------- | ----------------------------------------------------------------- | | `pd.DataFrame` | DataFrame containing ECDF objects, indexed by the test set index. | #### `get_copula` ```python theme={null} get_copula( self, key: str = 'train', raw_output: bool = True, set_datetime_index: bool = True, ) ‑> pandas.core.series.Series ``` Identify the best-fitting copula. **Parameters**: | Name | Type | Default | Description | | -------------------- | ------ | ------- | ----------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `raw_output` | `bool` | `True` | If `True`, returns raw results. Default is `True`, which returns processed results. | | `set_datetime_index` | `bool` | `True` | If `True`, set end-test datetime index. Ignored otherwise. Defaults to `True`. | **Returns**: | Type | Description | | ----------- | -------------------------------------------------------------- | | `pd.Series` | Series containing the names of the best-fitting copula models. | #### `get_dependence` ```python theme={null} get_dependence( self, key: str = 'train', raw_output: bool = True, set_datetime_index: bool = True, ) ‑> pandas.core.series.Series ``` Compute the dependence parameter) for the best-fitting copula in each set. **Parameters**: | Name | Type | Default | Description | | -------------------- | ------ | ------- | ----------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `raw_output` | `bool` | `True` | If `True`, returns raw results. Default is `True`, which returns processed results. | | `set_datetime_index` | `bool` | `True` | If `True`, set end-test datetime index. Ignored otherwise. Defaults to `True`. | **Returns**: | Type | Description | | ----------- | ------------------------------------------- | | `pd.Series` | Series containing the dependence parameter. | #### `iter_transform_output` ```python theme={null} iter_transform_output( self, key: str = 'train', apply_transform: bool = False, reset_stacked_by_set: bool = False, to_numpy: bool = False, ) ‑> pandas.core.frame.DataFrame | numpy.ndarray ``` Get model output, either transformed or as partial derivatives. **Parameters**: | Name | Type | Default | Description | | ---------------------- | ------ | ------- | -------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `apply_transform` | `bool` | `False` | If `True`, applies the model transformation to the output. Defaults to `False`. | | `reset_stacked_by_set` | `bool` | `False` | If `True`, resets the index stacked by set. Defaults to `False`. | | `to_numpy` | `bool` | `False` | If `True`, returns a NumPy array instead of a DataFrame. Defaults to `False`. | **Returns**: | Type | Description | | -------------- | ----------------- | | `pd.DataFrame` | The model output. | #### `get_marginals` ```python theme={null} get_marginals( self, key: str = 'train', reset_stacked_by_set: bool = False, to_numpy: bool = False, ) ‑> pandas.core.frame.DataFrame | numpy.ndarray ``` Get model marginals. **Parameters**: | Name | Type | Default | Description | | ---------------------- | ------ | ------- | -------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `reset_stacked_by_set` | `bool` | `False` | If `True`, resets the index stacked by set. Defaults to `False`. | | `to_numpy` | `bool` | `False` | If `True`, returns a NumPy array instead of a DataFrame. Defaults to `False`. | **Returns**: | Type | Description | | -------------- | -------------------- | | `pd.DataFrame` | The model marginals. | #### `get_partial_derivative` ```python theme={null} get_partial_derivative( self, key: str = 'train', reset_stacked_by_set: bool = False, to_numpy: bool = False, ) ‑> pandas.core.frame.DataFrame | numpy.ndarray ``` Get model partial derivatives. **Parameters**: | Name | Type | Default | Description | | ---------------------- | ------ | ------- | -------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `reset_stacked_by_set` | `bool` | `False` | If `True`, resets the index stacked by set. Defaults to `False`. | | `to_numpy` | `bool` | `False` | If `True`, returns a NumPy array instead of a DataFrame. Defaults to `False`. | **Returns**: | Type | Description | | -------------- | ------------------------------ | | `pd.DataFrame` | The model partial derivatives. | #### `get_transform` ```python theme={null} get_transform( self, key: str = 'train', reset_stacked_by_set: bool = False, to_numpy: bool = False, ) ‑> pandas.core.frame.DataFrame | numpy.ndarray ``` Get model output after applying the transformation. **Parameters**: | Name | Type | Default | Description | | ---------------------- | ------ | ------- | -------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `reset_stacked_by_set` | `bool` | `False` | If `True`, resets the index stacked by set. Defaults to `False`. | | `to_numpy` | `bool` | `False` | If `True`, returns a NumPy array instead of a DataFrame. Defaults to `False`. | **Returns**: | Type | Description | | -------------- | --------------------------------------------------- | | `pd.DataFrame` | The model output after applying the transformation. | #### `get_all_metrics` ```python theme={null} get_all_metrics( self, key: str, level_names: List[str] = None, reset_stacked_by_set: bool = False, to_numpy: bool = False, ) ‑> Dict[str, pandas.core.frame.DataFrame] ``` Get all metrics in a single iteration through splits. This method performs one iteration through all walk-forward splits, computing all required metrics simultaneously. This avoids redundant copula fitting that occurs when calling get\_kendall\_tau(), get\_dependence(), get\_copula(), get\_transform(), etc. separately. **Parameters**: | Name | Type | Default | Description | | ---------------------- | ------------------------------------- | ------- | ----------------------------------------------------------------------------------------------------------------------- | | `key` | `str` | `--` | Dataset to use, either 'train' or 'test'. | | `level_names` | `tp.List[str, str], default `None\`\` | `--` | Names for the levels in the resulting hierarchical index. if `None` defaults to `['field', 'symbol']`. Defaults to None | | `reset_stacked_by_set` | `bool` | `False` | If `True`, resets the index stacked by set. Defaults to `False`. | | `to_numpy` | `bool` | `False` | If `True`, returns a NumPy array instead of a DataFrame. Defaults to `False`. | **Returns**: | Type | Description | | -------------- | ----------- | | `pd.DataFrame` | All metrics | **Notes**: This is the performance-critical method. By computing all metrics in one pass, we reduce complexity from `O(6n)` to `O(n)` where `n` is the number of splits. #### `run_portfolio` ```python theme={null} run_portfolio( self, key: str = 'train', validate_model: bool = True, ) ‑> vectorbtpro.portfolio.base.Portfolio ``` Generate a `vectobtpro` portfolio object. **Parameters**: | Name | Type | Default | Description | | ---------------- | ---------------- | ------- | ---------------------------------------------------------------------- | | `key` | `str, optional` | `--` | Dataset to use, either 'train' or 'test'. Default is 'train'. | | `validate_model` | `bool, optional` | `--` | If True, validate model parameters before processing. Default is True. | **Returns**: | Type | Description | | --------------- | ----------------------- | | `vbt.Portfolio` | A vbt portfolio object. | #### `run_report` ```python theme={null} run_report( self, key: str = 'train', validate_model: bool = True, ) ‑> pandas.core.frame.DataFrame ``` Generate a report DataFrame with model inputs, outputs, and metrics. This optimized version computes all metrics in a single pass through the walk-forward splits, reducing redundant copula fitting. **Parameters**: | Name | Type | Default | Description | | ---------------- | ------ | --------- | ----------------------------------------------------- | | `key` | `str` | `'train'` | Dataset to use, either 'train' or 'test'. | | `validate_model` | `bool` | `True` | If True, validate model parameters before processing. | **Returns**: | Type | Description | | -------------- | ------------------------------------------------------------------------------------------------ | | `pd.DataFrame` | A DataFrame containing model metrics, signals, and trade history, all aligned on a common index. | **Notes**: Performance optimization: This method performs a single iteration through all splits, computing all metrics simultaneously to avoid redundant copula fitting operations. #### `plot_kendall_tau` ```python theme={null} plot_kendall_tau( self, key: str = 'train', fig: vectorbtpro.utils.figure.FigureWidget = None, **layout_kwargs, ) ‑> vectorbtpro.utils.figure.FigureWidget ``` Plot Kendall's Tau values. **Parameters**: | Name | Type | Default | Description | | --------------- | ------------------ | ------- | -------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `fig` | `vbt.FigureWidget` | `None` | Existing figure to update, by default `None`. | | `layout_kwargs` | `tp.Kwargs` | `--` | Additional layout keyword arguments for customization. | **Returns**: | Type | Description | | ------------------ | ------------------------------------------- | | `vbt.FigureWidget` | The figure displaying Kendall's Tau values. | #### `plot_copula` ```python theme={null} plot_copula( self, key: str = 'train', fig: vectorbtpro.utils.figure.FigureWidget = None, **layout_kwargs, ) ‑> vectorbtpro.utils.figure.FigureWidget ``` Plot the best-fitting copula models. **Parameters**: | Name | Type | Default | Description | | --------------- | ------------------ | ------- | -------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `fig` | `vbt.FigureWidget` | `None` | Existing figure to update, by default `None`. | | `layout_kwargs` | `tp.Kwargs` | `--` | Additional layout keyword arguments for customization. | **Returns**: | Type | Description | | ------------------ | ----------------------------------------------------- | | `vbt.FigureWidget` | The figure displaying the best-fitting copula models. | #### `plot_dependence` ```python theme={null} plot_dependence( self, key: str = 'train', fig: vectorbtpro.utils.figure.FigureWidget = None, **layout_kwargs, ) ‑> vectorbtpro.utils.figure.FigureWidget ``` Plot the dependence parameter values. **Parameters**: | Name | Type | Default | Description | | --------------- | ------------------ | ------- | -------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `fig` | `vbt.FigureWidget` | `None` | Existing figure to update, by default `None`. | | `layout_kwargs` | `tp.Kwargs` | `--` | Additional layout keyword arguments for customization. | **Returns**: | Type | Description | | ------------------ | ---------------------------------------- | | `vbt.FigureWidget` | The figure displaying dependence values. | #### `plot_tail_concentration` ```python theme={null} plot_tail_concentration( self, key: str = 'train', set_datetime_index: bool = True, title: str | None = None, smoothing: float | None = 1.3, ) ‑> pandas.core.series.Series ``` Container with copula tail concentration figure object. **Parameters**: | Name | Type | Default | Description | | -------------------- | ------- | ------- | ---------------------------------------------------------------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `set_datetime_index` | `bool` | `True` | It `True`, set output datetime index. Note that it is indexed by the test set index inferred from `get_best_copula`. Defaults to `True`. | | `title` | `str` | `None` | The title for the plot. If not provided, a default title based on the fitted copula's representation is used. | | `smoothing` | `float` | `1.3` | Smoothing parameter for the spline line shape. If provided, the curves will be smoothed using a spline interpolation. | **Returns**: | Type | Description | | ----------- | --------------------------------- | | `pd.Series` | Copula ail concentration figures. | #### `plot_heatmap` ```python theme={null} plot_heatmap( self, key: str = 'train', set_datetime_index: bool = True, title: str | None = None, ) ‑> pandas.core.series.Series ``` Container with copula heatmap figure object. **Parameters**: | Name | Type | Default | Description | | -------------------- | ------ | ------- | ---------------------------------------------------------------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `set_datetime_index` | `bool` | `True` | It `True`, set output datetime index. Note that it is indexed by the test set index inferred from `get_best_copula`. Defaults to `True`. | | `title` | `str` | `None` | The title for the plot. If not provided, a default title based on the fitted copula's representation is used. | **Returns**: | Type | Description | | ----------- | ----------------------- | | `pd.Series` | Copula heatmap figures. | #### `plot_surface` ```python theme={null} plot_surface( self, key: str = True, set_datetime_index: bool = True, title: str | None = None, ) ‑> pandas.core.series.Series ``` Container with copula surface figure object. **Parameters**: | Name | Type | Default | Description | | -------------------- | ------ | ------- | ---------------------------------------------------------------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `set_datetime_index` | `bool` | `True` | It `True`, set output datetime index. Note that it is indexed by the test set index inferred from `get_best_copula`. Defaults to `True`. | | `title` | `str` | `None` | The title for the plot. If not provided, a default title based on the fitted copula's representation is used. | **Returns**: | Type | Description | | ----------- | ----------------------- | | `pd.Series` | Copula surface figures. | #### `plot_contour` ```python theme={null} plot_contour( self, key: str = 'train', set_datetime_index: bool = True, show_latest_point: bool = False, alpha: float = 0.5, opacity: float = 0.2, title: str | None = None, showlegend: bool = True, fig: plotly.basedatatypes.BaseFigure = None, **layout_kwargs, ) ‑> pandas.core.series.Series ``` Container with copula contour figure object. **Parameters**: | Name | Type | Default | Description | | -------------------- | ------------------------ | ------- | ---------------------------------------------------------------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `set_datetime_index` | `bool` | `True` | It `True`, set output datetime index. Note that it is indexed by the test set index inferred from `get_best_copula`. Defaults to `True`. | | `show_latest_point` | `bool, Default `True\`\` | `--` | If True, show latest values as red dot. Defaults to True. | | `alpha` | `float` | `0.5` | Contour alpha size. Defaults to `0.5`. | | `opacity` | `float` | `0.2` | Point opacity. Defaults to `0.2`. | | `title` | `str` | `None` | The title for the plot. If not provided, a default title based on the fitted copula's representation is used. | | `showlegend` | `bool` | `True` | Show legend. Defaults to `True`. | | `fig` | `tp.BaseFigure` | `None` | Existing figure to update. If None, a new figure is created. Defaults to `None`. | | `layout_kwargs` | `tp.Kwargs` | `--` | Additional keyword arguments for customizing the layout. | **Returns**: | Type | Description | | ----------- | ----------------------- | | `pd.Series` | Copula surface figures. | #### `plot_all` ```python theme={null} plot_all( self, key: str = 'train', in_outputs: str | List[str] | None = None, select_signals: Literal[{'short_exits', 'short_entries', 'long_entries', 'long_exits'}] = None, set_datetime_index: bool = True, show_latest_point: bool = False, show_contour: bool = True, alpha: float = 0.5, opacity: float = 0.2, title: str | None = None, showlegend: bool = True, fig: plotly.basedatatypes.BaseFigure = None, **layout_kwargs, ) ‑> pandas.core.series.Series ``` Container with copula contour, marginal and signals figure object. **Parameters**: | Name | Type | Default | Description | | -------------------- | --------------------------- | ------- | ---------------------------------------------------------------------------------------------------------------------------------------- | | `key` | `str` | `train` | If `train`, extract train-set. If `test`, extract test-set. Defaults to `train`. | | `in_outputs` | `None` | `--` | \| str \| tp.List\[str], default `None` Report data. Defaults to `None`. | | `select_signals` | `tp.Literal[VALID_SIGNALS]` | `None` | Filter `Signals` by a signal (e.g. `long_entries`). If None, It is ignored. Defaults to `None`. | | `set_datetime_index` | `bool` | `True` | It `True`, set output datetime index. Note that it is indexed by the test set index inferred from `get_best_copula`. Defaults to `True`. | | `show_contour` | `bool` | `True` | Show contour if `True`. Defaults to `True`. | | `show_latest_point` | `bool, Default `True\`\` | `--` | If True, show latest values as red dot. Defaults to True. | | `alpha` | `float` | `0.5` | Contour alpha size. Defaults to `0.5`. | | `opacity` | `float` | `0.2` | Point opacity. Defaults to `0.2`. | | `title` | `str` | `None` | The title for the plot. If not provided, a default title based on the fitted copula's representation is used. | | `showlegend` | `bool` | `True` | Show legend. Defaults to `True`. | | `fig` | `tp.BaseFigure` | `None` | Existing figure to update. If None, a new figure is created. Defaults to `None`. | | `layout_kwargs` | `tp.Kwargs` | `--` | Additional keyword arguments for customizing the layout. | **Returns**: | Type | Description | | ----------- | ----------------------- | | `pd.Series` | Copula surface figures. | ## `ArbitrageIndexRolling` ```python theme={null} ArbitrageIndexRolling( id: str = None, loader_or_data: Callable = , timeframe: str = '1d', start: str = None, end: str = None, s1: str = 'BTCUSDT', s2: str = 'ETHUSDT', suffix: str = 'h5', use_close: bool = True, freq: str = None, signal_model: str = None, long_entries: float = nan, long_exits: float = nan, short_entries: float = nan, short_exits: float = nan, clean: bool = True, select_symbols: str | int | List[str | int] = None, portfolio_config: Dict[str, Any] = _Nothing.NOTHING, model_params: Dict[str, Any] = _Nothing.NOTHING, metrics: str | List[str] = None, metrics_kwargs: Dict[str, Any] = _Nothing.NOTHING, use_rolling: bool = False, storage: str | optuna.storages._base.BaseStorage = None, pruner: optuna.pruners._base.BasePruner = , sampler: optuna.samplers._base.BaseSampler = , study_name: str = None, direction: str | List[str] = 'maximize', load_if_exists: bool = False, n_trials: int = 100, n_completed_trials: int = None, timeout: float = None, n_jobs: int = 1, catch: Iterable[Type[Exception]] | Type[Exception] = _Nothing.NOTHING, callbacks: Iterable[Callable[[optuna.study.study.Study, optuna.trial._frozen.FrozenTrial], None]] | None = None, gc_after_trial: bool = False, show_progress_bar: bool = False, verbose: bool = True, tracker: Type = None, model: Any = None, preprocess_func: Callable = None, ) ``` Breakdown analysis for arbitrage index models, extending `BaseRollingWalkForward`. Includes methods to compute Kendall's Tau, determine the best copula, and extract copula parameters. Method generated by attrs for class ArbitrageIndexRolling. ### Ancestors * `systematica.walk_forward.rolling.RollingWalkForward` * `systematica.walk_forward.base.BaseWalkForward` * `abc.ABC` * `systematica.generic.base.Model` * `systematica.generic.base.Feature`