Adds test for collinearity to the `econometrics` menu (#5018)

* Add `vif` command to the ecomometrics menu

Adds `vif` command, which tests collinearity by calculating the variance inflation factor.

* Fix spelling

* Fix ruff

* Fix ruff

* Fix mypy + add sdk example

* Fix mypy

* Fix pylint

* Fix input + error handling

* Remove rouge print + error handling for one column

* fix linting

8 files changed, 194 insertions, 13 deletions

diff --git a/openbb_terminal/core/sdk/models/econometrics_sdk_model.py b/openbb_terminal/core/sdk/models/econometrics_sdk_model.py
index 690dd7ca2d3..018d5de9fcf 100644
--- a/openbb_terminal/core/sdk/models/econometrics_sdk_model.py
+++ b/openbb_terminal/core/sdk/models/econometrics_sdk_model.py
@@ -39,6 +39,7 @@ class EconometricsRoot(Category):
         `re`: The random effects model is virtually identical to the pooled OLS model except that is accounts for the\n
         `root`: Calculate test statistics for unit roots\n
         `root_chart`: Determine the normality of a timeseries.\n
+        `vif`: Determine the vif, which tests for collinearity.\n
     """
 
     _location_path = "econometrics"
@@ -75,3 +76,4 @@ class EconometricsRoot(Category):
         self.re = lib.econometrics_regression_model.get_re
         self.root = lib.econometrics_model.get_root
         self.root_chart = lib.econometrics_view.display_root
+        self.vif = lib.econometrics_model.get_vif
diff --git a/openbb_terminal/core/sdk/trail_map.csv b/openbb_terminal/core/sdk/trail_map.csv
index eb85b6579d6..e339b496bbf 100644
--- a/openbb_terminal/core/sdk/trail_map.csv
+++ b/openbb_terminal/core/sdk/trail_map.csv
@@ -183,6 +183,7 @@ econometrics.panel,econometrics_regression_model.get_regressions_results,econome
 econometrics.pols,econometrics_regression_model.get_pols,
 econometrics.re,econometrics_regression_model.get_re,
 econometrics.root,econometrics_model.get_root,econometrics_view.display_root
+econometrics.vif,econometrics_model.get_vif,
 econometrics.garch,econometrics_model.get_garch,econometrics_view.display_garch
 economy.available_indices,economy_yfinance_model.get_available_indices,
 economy.balance,economy_oecd_model.get_balance,economy_oecd_view.plot_balance
diff --git a/openbb_terminal/econometrics/econometrics_controller.py b/openbb_terminal/econometrics/econometrics_controller.py
index 8602eeabec2..03b1a9a538d 100644
--- a/openbb_terminal/econometrics/econometrics_controller.py
+++ b/openbb_terminal/econometrics/econometrics_controller.py
@@ -77,6 +77,7 @@ class EconometricsController(BaseController):
         "garch",
         "granger",
         "coint",
+        "vif",
     ]
     CHOICES_MENUS: List[str] = [
         "qa",
@@ -189,6 +190,7 @@ class EconometricsController(BaseController):
                 "corr",
                 "season",
                 "lag",
+                "vif",
             ]:
                 choices[feature] = dict()
 
@@ -235,12 +237,14 @@ class EconometricsController(BaseController):
             ]:
                 self.choices[feature] = {c: {} for c in self.files}
 
-            self.choices["type"] = {
-                c: {} for c in self.files + list(dataset_columns.keys())
-            }
-            self.choices["desc"] = {
-                c: {} for c in self.files + list(dataset_columns.keys())
-            }
+            for feature in ["type", "desc", "vif"]:
+                self.choices[feature] = {
+                    c: {} for c in self.files + list(dataset_columns.keys())
+                }
+            self.choices["vif"] = dict(
+                self.choices["vif"],
+                **{"-d": self.choices["vif"], "--data": self.choices["vif"]},
+            )
 
             pairs_timeseries = list()
             for dataset_col in list(dataset_columns.keys()):
@@ -286,20 +290,21 @@ class EconometricsController(BaseController):
         mt.add_cmd("lag", self.files)
         mt.add_cmd("ret", self.files)
         mt.add_cmd("export", self.files)
-        mt.add_info("time_series_")
+        mt.add_info("_assumption_testing_")
         mt.add_cmd("norm", self.files)
-        mt.add_cmd("ols", self.files)
         mt.add_cmd("granger", self.files)
         mt.add_cmd("root", self.files)
         mt.add_cmd("coint", self.files)
+        mt.add_cmd("vif", self.files)
+        mt.add_cmd("dwat", self.files and self.regression["OLS"]["model"])
+        mt.add_cmd("bgod", self.files and self.regression["OLS"]["model"])
+        mt.add_cmd("bpag", self.files and self.regression["OLS"]["model"])
+        mt.add_info("_time_series_")
+        mt.add_cmd("ols", self.files)
         mt.add_cmd("garch", self.files)
         mt.add_info("_panel_")
         mt.add_cmd("panel", self.files)
         mt.add_cmd("compare", self.files)
-        mt.add_info("_residuals_")
-        mt.add_cmd("dwat", self.files and self.regression["OLS"]["model"])
-        mt.add_cmd("bgod", self.files and self.regression["OLS"]["model"])
-        mt.add_cmd("bpag", self.files and self.regression["OLS"]["model"])
 
         console.print(text=mt.menu_text, menu="Econometrics")
         console.print()
@@ -1884,7 +1889,7 @@ class EconometricsController(BaseController):
             formatter_class=argparse.ArgumentDefaultsHelpFormatter,
             prog="bgod",
             description=(
-                "Show Breusch-Godfrey autocorrelation test results."
+                "Show Breusch-Godfrey autocorrelation test results. "
                 "Needs OLS to be run in advance with independent and dependent variables"
             ),
         )
@@ -2182,3 +2187,78 @@ class EconometricsController(BaseController):
                 console.print(
                     "[red]More than one dataset.column must be provided.\n[/red]"
                 )
+
+    @log_start_end(log=logger)
+    def call_vif(self, other_args: List[str]):
+        """Process vif command"""
+        parser = argparse.ArgumentParser(
+            add_help=False,
+            formatter_class=argparse.ArgumentDefaultsHelpFormatter,
+            prog="vif",
+            description=r"""Calculates VIF (variance inflation factor), which tests collinearity.
+
+            It quantifies the severity of multicollinearity in an ordinary least squares regression analysis. The square
+            root of the variance inflation factor indicates how much larger the standard error increases compared to if
+            that variable had 0 correlation to other predictor variables in the model.
+
+            It is defined as:
+
+            $ VIF_i = 1 / (1 - R_i^2) $
+            where $ R_i $ is the coefficient of determination of the regression equation with the column i being the
+            result from the i:th series being the exogenous variable.
+
+            A VIF over 5 indicates a high collinearity and correlation. Values over 10 indicates causes problems,
+            while a value of 1 indicates no correlation. Thus VIF values between 1 and 5 are most commonly considered
+            acceptable. In order to improve the results one can often remove a column with high VIF.
+
+            For further information see: https://en.wikipedia.org/wiki/Variance_inflation_factor""",
+        )
+        parser.add_argument(
+            "-d",
+            "--data",
+            help="The datasets and columns we want to add <dataset>,<dataset2.column>,<dataset2.column2>",
+            dest="data",
+            type=check_list_values(self.choices["vif"]),
+            default=None,
+        )
+        if other_args and "-" not in other_args[0][0]:
+            other_args.insert(0, "-d")
+        ns_parser = self.parse_known_args_and_warn(
+            parser, other_args, EXPORT_ONLY_RAW_DATA_ALLOWED
+        )
+
+        data = pd.DataFrame()
+        if ns_parser:
+            if ns_parser.data is None:
+                console.print("[red]Please enter a dataset to calculate vif for.[/red]")
+                return
+            if len(ns_parser.data) == 1 and "." in ns_parser.data[0]:
+                console.print(
+                    "[red]Please enter at least a dataset or two columns to calculate vif for."
+                    "vif can only be calculated for at least two columns.[/red]"
+                )
+            for option in ns_parser.data:
+                if "." in option:
+                    dataset, column = option.split(".")
+                else:
+                    dataset = option
+                    column = None
+
+                if dataset not in self.datasets:
+                    console.print(
+                        f"[red]Not able to find the dataset {dataset}. Please choose one of "
+                        f"the following: {', '.join(self.datasets)}[/red]"
+                    )
+                elif column is not None:
+                    if column not in self.datasets[dataset]:
+                        console.print(
+                            f"[red]Not able to find the column {column}. Please choose one of "
+                            f"the following: {', '.join(self.datasets[dataset].data)}[/red]"
+                        )
+                    else:
+                        data[f"{dataset}_{column}"] = self.datasets[dataset][column]
+                else:
+                    for column in list(self.datasets[dataset].columns):
+                        data[f"{dataset}_{column}"] = self.datasets[dataset][column]
+
+            econometrics_view.display_vif(data)
diff --git a/openbb_terminal/econometrics/econometrics_model.py b/openbb_terminal/econometrics/econometrics_model.py
index fdcabb4c68e..b1c6dde473a 100644
--- a/openbb_terminal/econometrics/econometrics_model.py
+++ b/openbb_terminal/econometrics/econometrics_model.py
@@ -13,6 +13,8 @@ import pandas as pd
 import statsmodels.api as sm
 from arch import arch_model
 from scipy import stats
+from statsmodels.stats.outliers_influence import variance_inflation_factor
+from statsmodels.tools.tools import add_constant
 from statsmodels.tsa.stattools import adfuller, grangercausalitytests, kpss
 
 from openbb_terminal.rich_config import console
@@ -482,3 +484,51 @@ def get_engle_granger_two_step_cointegration_test(
     adfstat, pvalue, _, _, _ = adfuller(z, maxlag=1, autolag=None)
 
     return c, gamma, alpha, z, adfstat, pvalue
+
+
+def get_vif(dataset: pd.DataFrame, columns: Optional[list] = None) -> pd.DataFrame:
+    r"""Calculates VIF (variance inflation factor), which tests collinearity.
+
+    It quantifies the severity of multicollinearity in an ordinary least squares regression analysis. The square
+    root of the variance inflation factor indicates how much larger the standard error increases compared to if
+    that variable had 0 correlation to other predictor variables in the model.
+
+    It is defined as:
+
+    $ VIF_i = 1 / (1 - R_i^2) $
+    where $ R_i $ is the coefficient of determination of the regression equation with the column i being the result
+    from the i:th series being the exogenous variable.
+
+    A VIF over 5 indicates a high collinearity and correlation. Values over 10 indicates causes problems, while a
+    value of 1 indicates no correlation. Thus VIF values between 1 and 5 are most commonly considered acceptable.
+    In order to improve the results one can often remove a column with high VIF.
+
+    For further information see: https://en.wikipedia.org/wiki/Variance_inflation_factor
+
+    Parameters
+    ----------
+    dataset: pd.Series
+        Dataset to calculate VIF on
+    columns: Optional[list]
+        The columns to calculate to test for collinearity
+
+    Returns
+    -------
+    pd.DataFrame
+        Dataframe with the resulting VIF values for the selected columns
+    Examples
+    --------
+    >>> from openbb_terminal.sdk import openbb
+    >>> longley = openbb.econometrics.load("longley")
+    >>> openbb.econometrics.vif(longley, ["TOTEMP","UNEMP","ARMED"])
+    """
+    df = add_constant(dataset if columns is None else dataset[columns])
+    vif = pd.DataFrame(
+        {
+            "VIF Values": [
+                variance_inflation_factor(df.values, i) for i in range(df.shape[1])
+            ][1:]
+        },
+        index=df.columns[1:],
+    )
+    return vif
diff --git a/openbb_terminal/econometrics/econometrics_view.py b/openbb_terminal/econometrics/econometrics_view.py
index c13342c8944..6bebc81065a 100644
--- a/openbb_terminal/econometrics/econometrics_view.py
+++ b/openbb_terminal/econometrics/econometrics_view.py
@@ -621,3 +621,47 @@ def display_cointegration_test(
         return fig.show(external=external_axes)
 
     return None
+
+
+@log_start_end(log=logger)
+def display_vif(
+    dataset: pd.DataFrame,
+    columns: Optional[list] = None,
+    export: str = "",
+    sheet_name: Optional[str] = None,
+):
+    """Displays the VIF (variance inflation factor), which tests for collinearity, values for each column.
+
+    Parameters
+    ----------
+    dataset: pd.Series
+        Dataset to calculate VIF on
+    columns: Optional[list]
+        The columns to calculate to test for collinearity
+    sheet_name: Optional[str]
+        Optionally specify the name of the sheet the data is exported to.
+    export: str
+        Format to export data.
+    """
+    columns = dataset.columns if columns is None else columns
+    if any(dataset[column].dtype not in [int, float] for column in columns):
+        console.print(
+            "All column types must be numeric. Consider using the command 'type' to change this.\n"
+        )
+    else:
+        results = econometrics_model.get_vif(dataset, columns)
+
+        print_rich_table(
+            results,
+            headers=list(results.columns),
+            show_index=True,
+            title="Collinearity Test",
+        )
+
+        export_data(
+            export,
+            os.path.dirname(os.path.abspath(__file__)),
+            f"{dataset}_{','.join(columns)}_vif",
+            results,
+            sheet_name,
+        )
diff --git a/openbb_terminal/miscellaneous/i18n/en.yml b/openbb_terminal/miscellaneous/i18n/en.yml
index f06570a2d4f..71633e8f9ce 100644
--- a/openbb_terminal/miscellaneous/i18n/en.yml
+++ b/openbb_terminal/miscellaneous/i18n/en.yml
@@ -981,6 +981,8 @@ en:
   econometrics/coint: co-integration test on a multitude of columns
   econometrics/garch: estimate future volatility with GARCH
   econometrics/ret: calculate returns for the given time series
+  econometrics/vif: perform collinearity test (VIF)
+  econometrics/_assumption_testing_: Assumption Testing
   portfolio/bro: brokers holdings    supports robinhood, ally, degiro, coinbase
   portfolio/po: portfolio optimization   optimize your portfolio weights efficiently
   portfolio/load: load transactions into the portfolio (use load --example for an example)
diff --git a/openbb_terminal/miscellaneous/integration_tests_scripts/econometrics/test_econometrics.openbb b/openbb_terminal/miscellaneous/integration_tests_scripts/econometrics/test_econometrics.openbb
index 2e0ae729b31..6f9bbd6d662 100644
--- a/openbb_terminal/miscellaneous/integration_tests_scripts/econometrics/test_econometrics.openbb
+++ b/openbb_terminal/miscellaneous/integration_tests_scripts/econometrics/test_econometrics.openbb
@@ -51,6 +51,7 @@ panel -d wp.lwage -i wp.black,wp.hisp,wp.exper,wp.married,wp.educ,wp.union -r bo
 
 load longley -a ll
 ols -d ll.totemp -i ll.gnpdefl,ll.gnp,ll.unemp,ll.armed,ll.pop,ll.year
+vif ll.totemp,ll.unemp,ll.armed
 
 ## Regression Tests
 
diff --git a/openbb_terminal/sdk.py b/openbb_terminal/sdk.py
index d41133a5b38..74bb632fa43 100644
--- a/openbb_terminal/sdk.py
+++ b/openbb_terminal/sdk.py
@@ -140,6 +140,7 @@ class OpenBBSDK:
             `re`: The random effects model is virtually identical to the pooled OLS model except that is accounts for the\n
             `root`: Calculate test statistics for unit roots\n
             `root_chart`: Determine the normality of a timeseries.\n
+            `vif`: Determine the vif, which tests for collinearity.\n
         """
 
         return model.EconometricsRoot()