Working GARCH model.

Sinbad-The-Sailor · Aug 4, 2023 · b822941 · b822941
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Showing 9 changed files with 409 additions and 145 deletions.
diff --git a/src2/autograd.ipynb b/src2/autograd.ipynb
@@ -89,7 +89,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -98,6 +98,43 @@
     "                                method=\"BFGS\",\n",
     "                                jac=True) # NB: we will compute the jacobian"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "      fun: -72.71104166630812\n",
+       " hess_inv: array([[3.43587575e-06, 4.82986207e-12],\n",
+       "       [4.82986207e-12, 9.07303824e-05]])\n",
+       "      jac: array([2.63101469e-08, 3.41229494e-06])\n",
+       "  message: 'Optimization terminated successfully.'\n",
+       "     nfev: 21\n",
+       "      nit: 9\n",
+       "     njev: 21\n",
+       "   status: 0\n",
+       "  success: True\n",
+       "        x: array([-0.02342842,  0.93132647])"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "res"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {

diff --git a/src2/models/ar.py b/src2/models/ar.py
@@ -7,7 +7,7 @@
 
 from models.model import Model
 from utils.config import MAXIMUM_AR_ORDER
-from utils.exceptions import ParameterError, StationarityError
+from utils.exceptions import StationarityError
 
 
 class AR(Model):
@@ -32,7 +32,9 @@ class AR(Model):
         * Model signifiance can be ascertained through regression like F-test.
 
     REFERENCES:
-        *
+        * Time Series Analysis by Hamilton.
+        * PACF Statistical Cutoff:
+          http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/xegbohtmlnode39.html
     """
 
     def __init__(self, time_series: pd.Series):
@@ -69,7 +71,7 @@ def _log_likelihood(self) -> torch.Tensor:
         variance = torch.square(self._sigma)
         pi = torch.tensor(torch.pi)
 
-        return - (self._number_of_observations - self._order) * (torch.log(pi) + torch.log(variance)) - 1 / (2 * variance) * torch.sum(squared_difference)
+        return - (self._number_of_observations - self._order) / 2 * (torch.log(pi) + torch.log(variance)) - 1 / (2 * variance) * torch.sum(squared_difference)
 
 
     def calibrate(self):

diff --git a/src2/models/garch.py b/src2/models/garch.py
@@ -4,47 +4,69 @@
 import pandas as pd
 
 from scipy.optimize import minimize
+from torch.distributions import Normal
 
 from models.model import Model
 from utils.config import INITIAL_VARIANCE_GARCH_OBSERVATIONS, INITIAL_GARCH_PARAMETERS
+from utils.exceptions import ParameterError
 
 class GARCH(Model):
 
     def __init__(self, time_series: pd.Series):
         super().__init__(time_series)
 
+    @property
+    def parameters(self) -> tuple[float, 3]:
+        self._check_calibration()
+
+        optimal_parameters = self._optimal_parameters
+        alpha = optimal_parameters[0]
+        beta = optimal_parameters[1]
+        long_run_variance = self._long_run_variance
+
+        return alpha, beta, long_run_variance
+
+    @property
+    def _number_of_parameters(self) -> int:
+        return len(self.parameters)
+
+    @property
+    def _optimal_parameters(self) -> np.array:
+        return self._uncondition_parameters(parameters=torch.tensor(self._solution.x)).numpy()
+
+    @property
+    def _inital_solution(self) -> np.array:
+        return np.array(self._precondition_parameters(parameters=torch.tensor(INITIAL_GARCH_PARAMETERS)))
+
+    @property
+    def _log_likelihood(self) -> torch.tensor:
+        optimal_cost = torch.tensor(self._solution.fun)
+        pi = torch.tensor(torch.pi)
+        number_of_observations = torch.tensor(self._number_of_observations)
+        return -(1 / 2) * (number_of_observations * torch.log(2 * pi) + optimal_cost)
+
     def calibrate(self):
         self._initiate_parameters()
-        self._inital_solution = np.array(self._precondition_parameters(parameters=torch.tensor(INITIAL_GARCH_PARAMETERS)))
-        solution = minimize(self._cost_function,
-                            self._inital_solution,
-                            method="BFGS",
-                            jac=True)
-        self._solution = solution
+        self._solve_maximum_likelihood()
+        self._sanity_check()
         self._calibrated = True
 
     def transform_to_true(self, uniform_sample: torch.Tensor) -> torch.Tensor:
-        ...
+        self._check_calibration()
 
     def transform_to_uniform(self):
-        ...
+        self._check_calibration()
+
+        parameters = torch.Tensor(self._solution.x)
+        variance = self._compute_variance(parameters=parameters)
+        volatility = torch.sqrt(variance)
+        returns = self._data
+        residuals = returns / volatility
+
+        return Normal(0, 1).cdf(residuals)
 
-    def _compute_variance(self, parameters: torch.Tensor) -> torch.Tensor:
-        initial_variance = self._initial_variance
-        variance = np.zeros(self._number_of_observations)
-        mu_corr = torch.exp(-torch.exp(-parameters[0]))
-        mu_ewma = torch.exp(-torch.exp(-parameters[1]))
 
-        for i in range(self._number_of_observations):
-            if i == 0:
-                variance[i] = initial_variance
-            else:
-                variance[i] = self._long_run_variance + mu_corr * (mu_ewma * variance[i - 1]
-                                                                   + (1 - mu_ewma) * self._squared_returns[i - 1]
-                                                                   - self._long_run_variance
-                                                                   )
 
-        return torch.tensor(variance)
 
     def _cost_function(self, parameters: np.array) -> tuple[float, 2]:
         """
@@ -57,11 +79,22 @@ def _cost_function(self, parameters: np.array) -> tuple[float, 2]:
             tuple(float, float): log loss value and the corresponding gradient.
         """
         parameters = torch.tensor(parameters, requires_grad=True)
-        variance = self._compute_variance(parameters=parameters)
-        log_loss = torch.sum(torch.log(variance) + self._squared_returns / variance)
-        log_loss.backward()
-        print(log_loss, parameters.grad)
+        mu = torch.exp(-torch.exp(-parameters))
+        mu_corr = mu[0]
+        mu_ewma = mu[1]
 
+        log_loss = torch.tensor(0.0)
+        for i in range(self._number_of_observations):
+            if i == 0:
+                variance = self._initial_variance
+            else:
+                variance = self._long_run_variance + mu_corr * (mu_ewma * variance
+                                                                   + (1 - mu_ewma) * self._squared_returns[i - 1].detach()
+                                                                   - self._long_run_variance
+                                                                   )
+            log_loss = log_loss + torch.log(variance) + self._squared_returns[i].detach() / variance
+
+        log_loss.backward()
         return log_loss.data.cpu().numpy(), parameters.grad.data.cpu().numpy()
 
     def _initiate_parameters(self):
@@ -70,18 +103,54 @@ def _initiate_parameters(self):
         self._initial_variance = self._compute_inital_variance()
         self._long_run_variance = torch.square(torch.std(self._data))
 
+    def _solve_maximum_likelihood(self):
+        solution = minimize(self._cost_function,
+                                    self._inital_solution,
+                                    method="L-BFGS-B",
+                                    jac=True)
+        self._solution = solution
+
     def _compute_inital_variance(self) -> torch.Tensor:
         if self._number_of_observations > INITIAL_VARIANCE_GARCH_OBSERVATIONS:
             return torch.square(torch.std(self._data[:INITIAL_VARIANCE_GARCH_OBSERVATIONS]))
         return self._initial_squared_returns
 
-    @property
-    def _number_of_parameters(self):
-        return super()._number_of_parameters
+    def _compute_variance(self, parameters: torch.Tensor) -> torch.Tensor:
+        initial_variance = self._initial_variance
+        variance = torch.zeros(self._number_of_observations)
+        mu_corr = torch.exp(-torch.exp(-parameters[0]))
+        mu_ewma = torch.exp(-torch.exp(-parameters[1]))
 
-    @property
-    def _log_likelihood(self):
-        return super()._log_likelihood
+        for i in range(self._number_of_observations):
+            if i == 0:
+                variance[i] = initial_variance
+            else:
+                variance[i] = self._long_run_variance + mu_corr * (mu_ewma * variance[i - 1]
+                                                                   + (1 - mu_ewma) * self._squared_returns[i - 1]
+                                                                   - self._long_run_variance
+                                                                   )
+        return variance
+
+    def _sanity_check(self):
+        parameter_check = self._check_parameters()
+        solution_check = self._check_solution()
+
+        if not parameter_check:
+            # log.
+            ...
+
+        if not solution_check:
+            # log.
+            ...
+
+        if not parameter_check or not solution_check:
+            raise ParameterError("Parameters could not be asceratined succesfully.")
+
+    def _check_parameters(self) -> bool:
+        return self._solution.success
+
+    def _check_solution(self) -> bool:
+        return np.sum(self._optimal_parameters) < 1
 
     @staticmethod
     def _precondition_parameters(parameters: torch.Tensor) -> torch.Tensor:
@@ -103,7 +172,7 @@ def _precondition_parameters(parameters: torch.Tensor) -> torch.Tensor:
         return torch.tensor([z_corr, z_ewma])
 
     @staticmethod
-    def _uncondition_parameters(params: torch.Tensor) -> torch.Tensor:
+    def _uncondition_parameters(parameters: torch.Tensor) -> torch.Tensor:
         """
         Unconditioning to obtain more original parameters from transformed parameters.
 
@@ -113,8 +182,8 @@ def _uncondition_parameters(params: torch.Tensor) -> torch.Tensor:
         Returns:
             torch.Tensor: GARCH parameters.
         """
-        mu_corr = torch.exp(-torch.exp(-params[0]))
-        mu_ewma = torch.exp(-torch.exp(-params[1]))
+        mu_corr = torch.exp(-torch.exp(-parameters[0]))
+        mu_ewma = torch.exp(-torch.exp(-parameters[1]))
 
         alpha = mu_corr * (1 - mu_ewma)
         beta = mu_corr * mu_ewma

diff --git a/src2/models/model.py b/src2/models/model.py
@@ -80,10 +80,10 @@ def bic(self) -> torch.Tensor:
         log_likelihood = self._log_likelihood
         number_of_parameters = torch.tensor(self._number_of_parameters)
         number_of_observations = torch.tensor(self._number_of_observations)
-        pi = torch.tensor(torch.pi)
 
         return number_of_parameters * torch.log(number_of_observations) - 2 * log_likelihood
 
+
     def _check_calibration(self):
         """
         Checks if successful calibration has been made.

diff --git a/src2/models/model_factory.py b/src2/models/model_factory.py
diff --git a/src2/run.ipynb b/src2/run.ipynb
@@ -2,22 +2,9 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 1,
    "metadata": {},
-   "outputs": [
-    {
-     "ename": "ImportError",
-     "evalue": "cannot import name 'INITIAL_VARIANCE_GARCH_OBSERVATIONS' from 'utils.config' (/Users/axelnilsson/Desktop/Abacus/src2/utils/config.py)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
-      "\u001b[0;32m/var/folders/d7/rpl_88f12ln2z1s2h4m9ybjm0000gn/T/ipykernel_43843/1386310877.py\u001b[0m in \u001b[0;36m<cell line: 11>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mutils\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata_handler\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mYahooDataHandler\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmodels\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mar\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mAR\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mmodels\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgarch\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mGARCH\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/Desktop/Abacus/src2/models/garch.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmodels\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mModel\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mutils\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconfig\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mINITIAL_VARIANCE_GARCH_OBSERVATIONS\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mINITIAL_GARCH_PARAMETERS\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;32mclass\u001b[0m \u001b[0mGARCH\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mModel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mImportError\u001b[0m: cannot import name 'INITIAL_VARIANCE_GARCH_OBSERVATIONS' from 'utils.config' (/Users/axelnilsson/Desktop/Abacus/src2/utils/config.py)"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import torch\n",
     "import pandas as pd\n",
@@ -36,14 +23,9 @@
     "plt.style.use(['science', 'notebook', 'grid'])"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": []
-  },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -52,7 +34,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -91,7 +73,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -100,6 +82,13 @@
     "        data = risk_factor.price_history.log_returns"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": 8,