> ## 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.reports.arbitrage_index

## `ArbitrageIndexReport`

```python theme={null}
ArbitrageIndexReport(
    data: vectorbtpro.data.base.Data,
    s1: str,
    s2: str,
    model: ~BaseStatArb,
    use_close: bool = True,
    freq: str = 'auto',
)
```

Breakdown analysis for arbitrage index models, extending `BaseModelBreakdownCV`.
Includes methods to compute Kendall's Tau, determine the best copula, and
extract copula parameters.

Method generated by attrs for class BaseReportCV.

### Ancestors

* `systematica.api.base.BaseReportCV`
* `systematica.api.base.BaseReportMixin`
* `abc.ABC`

### Methods

#### `get_kendall_tau`

```python theme={null}
get_kendall_tau(
    self,
) ‑> pandas.core.series.Series
```

Compute Kendall's Tau correlation coefficient for the training data in
each split.

**Returns**:

| Type        | Description                                                           |
| ----------- | --------------------------------------------------------------------- |
| `pd.Series` | Series containing Kendall's Tau values indexed by the test set index. |

#### `get_best_copula`

```python theme={null}
get_best_copula(
    self,
) ‑> pandas.core.series.Series
```

Identify the best-fitting copula for each training dataset in the splits.

**Returns**:

| Type        | Description                                                                                   |
| ----------- | --------------------------------------------------------------------------------------------- |
| `pd.Series` | Series containing the names of the best-fitting copula models, indexed by the test set index. |

#### `get_theta`

```python theme={null}
get_theta(
    self,
) ‑> pandas.core.series.Series
```

Compute the copula parameter (theta) for the best-fitting copula in
each training dataset.

**Returns**:

| Type        | Description                                                                                |
| ----------- | ------------------------------------------------------------------------------------------ |
| `pd.Series` | Series containing the theta parameter values divided by 10, indexed by the test set index. |

#### `plot_kendall_tau`

```python theme={null}
plot_kendall_tau(
    self,
    fig: vectorbtpro.utils.figure.FigureWidget = None,
    **layout_kwargs,
) ‑> vectorbtpro.utils.figure.FigureWidget
```

Plot Kendall's Tau values.

**Parameters**:

| Name            | Type               | Default | Description                                            |
| --------------- | ------------------ | ------- | ------------------------------------------------------ |
| `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_best_copula`

```python theme={null}
plot_best_copula(
    self,
    fig: vectorbtpro.utils.figure.FigureWidget = None,
    **layout_kwargs,
) ‑> vectorbtpro.utils.figure.FigureWidget
```

Plot the best-fitting copula models.

**Parameters**:

| Name            | Type               | Default | Description                                            |
| --------------- | ------------------ | ------- | ------------------------------------------------------ |
| `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_theta`

```python theme={null}
plot_theta(
    self,
    fig: vectorbtpro.utils.figure.FigureWidget = None,
    **layout_kwargs,
) ‑> vectorbtpro.utils.figure.FigureWidget
```

Plot the theta parameter values divided by `10`.

**Parameters**:

| Name            | Type               | Default | Description                                            |
| --------------- | ------------------ | ------- | ------------------------------------------------------ |
| `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 theta values. |