{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "code", "source": [ "import numpy as np\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns" ], "metadata": { "id": "ryCg7tFh1Vaz" }, "execution_count": 3, "outputs": [] }, { "cell_type": "code", "source": [ "!pip install fredapi" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "aQhXSA07fm5t", "outputId": "5cdc3117-689a-48eb-820d-45da3551cb5b" }, "execution_count": 2, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Collecting fredapi\n", " Downloading fredapi-0.5.2-py3-none-any.whl.metadata (5.0 kB)\n", "Requirement already satisfied: pandas in /usr/local/lib/python3.12/dist-packages (from fredapi) (2.2.2)\n", "Requirement already satisfied: numpy>=1.26.0 in /usr/local/lib/python3.12/dist-packages (from pandas->fredapi) (2.0.2)\n", "Requirement already satisfied: python-dateutil>=2.8.2 in /usr/local/lib/python3.12/dist-packages (from pandas->fredapi) (2.9.0.post0)\n", "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.12/dist-packages (from pandas->fredapi) (2025.2)\n", "Requirement already satisfied: tzdata>=2022.7 in /usr/local/lib/python3.12/dist-packages (from pandas->fredapi) (2025.2)\n", "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.12/dist-packages (from python-dateutil>=2.8.2->pandas->fredapi) (1.17.0)\n", "Downloading fredapi-0.5.2-py3-none-any.whl (11 kB)\n", "Installing collected packages: fredapi\n", "Successfully installed fredapi-0.5.2\n" ] } ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "id": "xFCX71rZmSEj", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "6c7ba128-6c4b-481b-87c6-8f51d92b6522" }, "outputs": [ { "output_type": "stream", "name": "stderr", "text": [ "/tmp/ipython-input-1312669008.py:30: FutureWarning: YF.download() has changed argument auto_adjust default to True\n", " usd_index = yf.download('DX-Y.NYB', start='2010-01-01')\n", "[*********************100%***********************] 1 of 1 completed\n" ] }, { "output_type": "stream", "name": "stdout", "text": [ "\n", "Combined data shape: (167, 6)\n", " Copper_Spot_Price Copper_Spot_Price_lb (USD_Index, DX-Y.NYB) \\\n", "2010-01-01 7367.375000 3.341789 77.840526 \n", "2010-02-01 6867.675000 3.115129 80.155789 \n", "2010-03-01 7466.934783 3.386949 80.671304 \n", "2010-04-01 7729.837500 3.506199 81.232857 \n", "2010-05-01 6843.157895 3.104008 85.361501 \n", "\n", " Fed_Funds_Rate CPI Oil_Price_WTI \n", "2010-01-01 0.11 217.488 78.325789 \n", "2010-02-01 0.13 217.281 76.387368 \n", "2010-03-01 0.16 217.353 81.203478 \n", "2010-04-01 0.20 217.403 84.292857 \n", "2010-05-01 0.20 217.290 73.743500 \n" ] } ], "source": [ "import yfinance as yf\n", "import pandas_datareader as pdr\n", "from fredapi import Fred\n", "import pandas as pd\n", "\n", "\n", "fred = Fred(api_key='2b89a22a93a46a84fb958d90e54465cc')\n", "\n", "\n", "\n", "def filter_dates(df):\n", " df = df[df.index >= '2010-01-01']\n", " df = df[~((df.index >= '2020-01-01') & (df.index < '2022-01-01'))]\n", " return df\n", "\n", "\n", "start_date = '2010-01-01'\n", "end_date = '2019-12-31'\n", "start_date_2 = '2022-01-01'\n", "\n", "# Get copper prices (从yfinance)\n", "copper = fred.get_series('PCOPPUSDM', observation_start='2010-01-01')\n", "copper = copper.to_frame(name='Copper_Spot_Price')\n", "#copper_monthly = copper.resample('MS').mean().dropna()\n", "copper_monthly = filter_dates(copper)\n", "copper_monthly['Copper_Spot_Price_lb'] = copper_monthly['Copper_Spot_Price'] / 2204.62\n", "\n", "# 2. Get USD Index\n", "usd_index = yf.download('DX-Y.NYB', start='2010-01-01')\n", "usd_index = usd_index[['Close']].rename(columns={'Close': 'USD_Index'})\n", "usd_index_monthly = usd_index.resample('MS').mean().dropna()\n", "usd_index_monthly = filter_dates(usd_index_monthly)\n", "\n", "# Get Fed Funds Rate\n", "fed_funds = fred.get_series('FEDFUNDS').to_frame(name='Fed_Funds_Rate')\n", "\n", "# Get CPI\n", "cpi = fred.get_series('CPIAUCSL').to_frame(name='CPI')\n", "\n", "# Get oil prices\n", "oil = fred.get_series('DCOILWTICO').to_frame(name='Oil_Price_WTI')\n", "oil_monthly = oil.resample('MS').mean().dropna()\n", "oil_monthly = filter_dates(oil_monthly)\n", "\n", "\n", "\n", "fed_funds = filter_dates(fed_funds)\n", "cpi = filter_dates(cpi)\n", "\n", "\n", "\n", "\n", "\n", "df_combined = copper_monthly.join([usd_index_monthly, fed_funds, cpi, oil_monthly], how='outer')\n", "print(\"\\nCombined data shape:\", df_combined.shape)\n", "print(df_combined.head())" ] }, { "cell_type": "code", "source": [ "copper" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 423 }, "id": "r7UgQE1TxLhl", "outputId": "4b80bc9b-43e7-45d5-b49c-3e7c0e079dcd" }, "execution_count": 19, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " Copper_Spot_Price\n", "2010-01-01 7367.375000\n", "2010-02-01 6867.675000\n", "2010-03-01 7466.934783\n", "2010-04-01 7729.837500\n", "2010-05-01 6843.157895\n", "... ...\n", "2025-02-01 9330.975000\n", "2025-03-01 9735.823333\n", "2025-04-01 9172.695909\n", "2025-05-01 9531.200909\n", "2025-06-01 9835.068095\n", "\n", "[186 rows x 1 columns]" ], "text/html": [ "\n", "
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\n" ], "application/vnd.google.colaboratory.intrinsic+json": { "type": "dataframe", "variable_name": "copper", "summary": "{\n \"name\": \"copper\",\n \"rows\": 186,\n \"fields\": [\n {\n \"column\": \"Copper_Spot_Price\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 1508.9292256484046,\n \"min\": 4471.7875,\n \"max\": 10230.8939130435,\n \"num_unique_values\": 186,\n \"samples\": [\n 5882.225,\n 8276.71380952381,\n 8304.95047619048\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n }\n ]\n}" } }, "metadata": {}, "execution_count": 19 } ] }, { "cell_type": "code", "source": [ "df_combined.columns = ['Copper_Spot_Price', 'Copper_Spot_Price_lb', 'USD_Index',\n", " 'Fed_Funds_Rate', 'CPI', 'Oil_Price_WTI']\n", "y = df_combined['Copper_Spot_Price_lb']\n", "X = df_combined[['USD_Index', 'Fed_Funds_Rate', 'CPI', 'Oil_Price_WTI']]" ], "metadata": { "id": "VRsvEv742YEa" }, "execution_count": 11, "outputs": [] }, { "cell_type": "code", "source": [ "df_clean = df_combined.dropna()\n", "y = df_clean['Copper_Spot_Price_lb']\n", "X = df_clean[['USD_Index', 'Fed_Funds_Rate', 'CPI', 'Oil_Price_WTI']]\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n", "\n", "\n", "model = LinearRegression()\n", "model.fit(X_train, y_train)\n", "\n", "\n", "y_train_pred = model.predict(X_train)\n", "y_test_pred = model.predict(X_test)\n" ], "metadata": { "id": "IwkqEJp6221t" }, "execution_count": 12, "outputs": [] }, { "cell_type": "code", "source": [ "print(\"\\nTraining Set:\")\n", "print(f\" R²: {r2_score(y_train, y_train_pred):.4f}\")\n", "print(f\" RMSE: {np.sqrt(mean_squared_error(y_train, y_train_pred)):.4f}\")\n", "\n", "print(\"\\nTest Set:\")\n", "print(f\" R²: {r2_score(y_test, y_test_pred):.4f}\")\n", "print(f\" RMSE: {np.sqrt(mean_squared_error(y_test, y_test_pred)):.4f}\")" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "SMiJu85A4KXa", "outputId": "fe8eb692-6baa-4ed7-cc21-4f1591afa7c6" }, "execution_count": 13, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "\n", "Training Set:\n", " R²: 0.7910\n", " RMSE: 0.3057\n", "\n", "Test Set:\n", " R²: 0.7063\n", " RMSE: 0.3441\n" ] } ] }, { "cell_type": "code", "source": [ "import statsmodels.api as sm\n", "X_train_with_const = sm.add_constant(X_train)\n", "model_sm = sm.OLS(y_train, X_train_with_const).fit()\n", "print(model_sm.summary())" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "wT2WhbWtfbCy", "outputId": "f0c17375-7884-4468-d30d-f520a737c2c2" }, "execution_count": 10, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ " OLS Regression Results \n", "================================================================================\n", "Dep. Variable: Copper_Spot_Price_lb R-squared: 0.791\n", "Model: OLS Adj. R-squared: 0.784\n", "Method: Least Squares F-statistic: 117.3\n", "Date: Sat, 15 Nov 2025 Prob (F-statistic): 3.53e-41\n", "Time: 03:11:20 Log-Likelihood: -30.173\n", "No. Observations: 129 AIC: 70.35\n", "Df Residuals: 124 BIC: 84.65\n", "Df Model: 4 \n", "Covariance Type: nonrobust \n", "==================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "----------------------------------------------------------------------------------\n", "const 0.8370 0.490 1.708 0.090 -0.133 1.807\n", "USD_Index -0.0498 0.008 -6.546 0.000 -0.065 -0.035\n", "Fed_Funds_Rate -0.0400 0.037 -1.092 0.277 -0.113 0.033\n", "CPI 0.0251 0.003 7.821 0.000 0.019 0.031\n", "Oil_Price_WTI 0.0099 0.002 4.367 0.000 0.005 0.014\n", "==============================================================================\n", "Omnibus: 6.274 Durbin-Watson: 2.118\n", "Prob(Omnibus): 0.043 Jarque-Bera (JB): 6.857\n", "Skew: 0.335 Prob(JB): 0.0324\n", "Kurtosis: 3.910 Cond. No. 5.07e+03\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 5.07e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ] }, { "cell_type": "code", "source": [ "import numpy as np\n", "\n", "\n", "def directional_accuracy(y_true, y_pred):\n", " actual_direction = np.diff(y_true) > 0\n", " predicted_direction = np.diff(y_pred) > 0\n", " return (actual_direction == predicted_direction).mean()\n", "\n", "\n", "dir_acc_test = directional_accuracy(y_test.values, y_test_pred)\n", "print(f\"Directional Accuracy (Test): {dir_acc_test:.4f} ({dir_acc_test*100:.2f}%)\")\n", "\n", "\n", "dir_acc_train = directional_accuracy(y_train.values, y_train_pred)\n", "print(f\"Directional Accuracy (Train): {dir_acc_train:.4f} ({dir_acc_train*100:.2f}%)\")" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "aD_qZe1W4gsi", "outputId": "b37ddcfe-01e1-44fe-c532-18ad53e4235e" }, "execution_count": 11, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Directional Accuracy (Test): 0.8438 (84.38%)\n", "Directional Accuracy (Train): 0.8672 (86.72%)\n" ] } ] }, { "cell_type": "code", "source": [ "import pandas as pd\n", "import numpy as np\n", "\n", "\n", "coefficients = pd.DataFrame({\n", " 'Feature': X.columns,\n", " 'Coefficient': model.coef_,\n", " 'Abs_Coefficient': np.abs(model.coef_)\n", "}).sort_values('Abs_Coefficient', ascending=False)\n", "\n", "print(\"Feature Importance (by coefficient magnitude):\")\n", "print(coefficients)\n", "\n", "\n", "X_std = X.std()\n", "standardized_coef = model.coef_ * X_std\n", "\n", "feature_importance = pd.DataFrame({\n", " 'Feature': X.columns,\n", " 'Standardized_Coefficient': standardized_coef,\n", " 'Abs_Std_Coefficient': np.abs(standardized_coef)\n", "}).sort_values('Abs_Std_Coefficient', ascending=False)\n", "\n", "print(\"\\nFeature Importance (standardized):\")\n", "print(feature_importance)\n", "\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "plt.figure(figsize=(10, 6))\n", "plt.barh(feature_importance['Feature'], feature_importance['Abs_Std_Coefficient'])\n", "plt.xlabel('Absolute Standardized Coefficient')\n", "plt.title('Feature Importance')\n", "plt.tight_layout()\n", "plt.show()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 833 }, "id": "3ddSdFr54uGU", "outputId": "1b14f28a-ebdd-4d0f-8145-3e1653f30a07" }, "execution_count": 12, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Feature Importance (by coefficient magnitude):\n", " Feature Coefficient Abs_Coefficient\n", "0 USD_Index -0.049830 0.049830\n", "1 Fed_Funds_Rate -0.040009 0.040009\n", "2 CPI 0.025056 0.025056\n", "3 Oil_Price_WTI 0.009924 0.009924\n", "\n", "Feature Importance (standardized):\n", " Feature Standardized_Coefficient Abs_Std_Coefficient\n", "CPI CPI 0.806765 0.806765\n", "USD_Index USD_Index -0.500887 0.500887\n", "Oil_Price_WTI Oil_Price_WTI 0.200027 0.200027\n", "Fed_Funds_Rate Fed_Funds_Rate -0.073685 0.073685\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ] }, { "cell_type": "code", "source": [ "import statsmodels.api as sm\n", "\n", "\n", "X_train_with_const = sm.add_constant(X_train)\n", "\n", "\n", "model_sm = sm.OLS(y_train, X_train_with_const).fit()\n", "\n", "\n", "print(model_sm.summary())\n", "\n", "\n", "\n", "print(\"=\"*60)\n", "print(f\"{'Variable':<20} {'Coefficient':<15} {'t-statistic':<15} {'p-value':<15}\")\n", "print(\"=\"*60)\n", "\n", "for var, coef, t_stat, p_val in zip(model_sm.params.index,\n", " model_sm.params.values,\n", " model_sm.tvalues.values,\n", " model_sm.pvalues.values):\n", " significance = \"***\" if p_val < 0.001 else \"**\" if p_val < 0.01 else \"*\" if p_val < 0.05 else \"\"\n", " print(f\"{var:<20} {coef:>12.6f} {t_stat:>12.4f} {p_val:>12.6f} {significance}\")\n", "\n", "print(\"\\n*** p<0.001, ** p<0.01, * p<0.05\")" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "nQncS0QxgOsU", "outputId": "3b7d4b54-526c-4294-aed5-f594e99a1953" }, "execution_count": 13, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ " OLS Regression Results \n", "================================================================================\n", "Dep. Variable: Copper_Spot_Price_lb R-squared: 0.791\n", "Model: OLS Adj. R-squared: 0.784\n", "Method: Least Squares F-statistic: 117.3\n", "Date: Sat, 15 Nov 2025 Prob (F-statistic): 3.53e-41\n", "Time: 03:13:32 Log-Likelihood: -30.173\n", "No. Observations: 129 AIC: 70.35\n", "Df Residuals: 124 BIC: 84.65\n", "Df Model: 4 \n", "Covariance Type: nonrobust \n", "==================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "----------------------------------------------------------------------------------\n", "const 0.8370 0.490 1.708 0.090 -0.133 1.807\n", "USD_Index -0.0498 0.008 -6.546 0.000 -0.065 -0.035\n", "Fed_Funds_Rate -0.0400 0.037 -1.092 0.277 -0.113 0.033\n", "CPI 0.0251 0.003 7.821 0.000 0.019 0.031\n", "Oil_Price_WTI 0.0099 0.002 4.367 0.000 0.005 0.014\n", "==============================================================================\n", "Omnibus: 6.274 Durbin-Watson: 2.118\n", "Prob(Omnibus): 0.043 Jarque-Bera (JB): 6.857\n", "Skew: 0.335 Prob(JB): 0.0324\n", "Kurtosis: 3.910 Cond. No. 5.07e+03\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 5.07e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\n", "变量的统计显著性:\n", "============================================================\n", "Variable Coefficient t-statistic p-value \n", "============================================================\n", "const 0.837025 1.7082 0.090094 \n", "USD_Index -0.049830 -6.5464 0.000000 ***\n", "Fed_Funds_Rate -0.040009 -1.0917 0.277062 \n", "CPI 0.025056 7.8205 0.000000 ***\n", "Oil_Price_WTI 0.009924 4.3671 0.000026 ***\n", "\n", "*** p<0.001, ** p<0.01, * p<0.05\n" ] } ] }, { "cell_type": "code", "source": [ "import pandas as pd\n", "import numpy as np\n", "import statsmodels.api as sm\n", "\n", "\n", "X_train_with_const = sm.add_constant(X_train)\n", "model_sm = sm.OLS(y_train, X_train_with_const).fit()\n", "\n", "\n", "feature_stats = pd.DataFrame({\n", " 'Feature': X.columns,\n", " 'Coefficient': model.coef_,\n", " 'Abs_Coefficient': np.abs(model.coef_),\n", " 't_statistic': model_sm.tvalues[1:].values,\n", " 'p_value': model_sm.pvalues[1:].values,\n", " 'Significance': ['***' if p < 0.001 else '**' if p < 0.01 else '*' if p < 0.05 else ''\n", " for p in model_sm.pvalues[1:].values]\n", "}).sort_values('Abs_Coefficient', ascending=False)\n", "\n", "print(\"\\nFeature Importance with Statistical Significance:\")\n", "print(\"=\"*80)\n", "print(feature_stats.to_string(index=False))\n", "print(\"\\n*** p<0.001, ** p<0.01, * p<0.05\")" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "1y9PQm_Sgffa", "outputId": "58f9a627-3c84-47bc-c276-06622ecc1f00" }, "execution_count": 14, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "\n", "Feature Importance with Statistical Significance:\n", "================================================================================\n", " Feature Coefficient Abs_Coefficient t_statistic p_value Significance\n", " USD_Index -0.049830 0.049830 -6.546406 1.403136e-09 ***\n", "Fed_Funds_Rate -0.040009 0.040009 -1.091745 2.770620e-01 \n", " CPI 0.025056 0.025056 7.820530 1.960103e-12 ***\n", " Oil_Price_WTI 0.009924 0.009924 4.367067 2.628657e-05 ***\n", "\n", "*** p<0.001, ** p<0.01, * p<0.05\n" ] } ] }, { "cell_type": "markdown", "source": [ "New Model\n" ], "metadata": { "id": "PYt6kPVoSS_U" } }, { "cell_type": "code", "source": [ "china_gdp = fred.get_series('CHNGDPNQDSMEI', observation_start='2010-01-01')\n", "china_gdp = china_gdp.to_frame(name='China_GDP_Growth')" ], "metadata": { "id": "RHckimXXSUVm" }, "execution_count": 5, "outputs": [] }, { "cell_type": "code", "source": [ "china_gdp = filter_dates(china_gdp)\n", "df_combined_new = df_combined.join(china_gdp, how='left')\n", "df_combined_new = df_combined_new.dropna()" ], "metadata": { "id": "XhrAAAa8SjJf" }, "execution_count": 18, "outputs": [] }, { "cell_type": "code", "source": [ "df_combined_new" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 1000 }, "id": "WLyvM0SAS5Kx", "outputId": "cc50379c-6481-4144-9d41-699bad6718e3" }, "execution_count": 22, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " Copper_Spot_Price Copper_Spot_Price_lb USD_Index \\\n", "2010-01-01 7367.375000 3.341789 77.840526 \n", "2010-04-01 7729.837500 3.506199 81.232857 \n", "2010-07-01 6750.568182 3.062010 83.070476 \n", "2010-10-01 8289.761905 3.760177 77.459999 \n", "2011-01-01 9533.200000 4.324192 79.146000 \n", "2011-04-01 9482.750000 4.301308 74.724500 \n", "2011-07-01 9650.464286 4.377382 74.757000 \n", "2011-10-01 7394.190476 3.353952 77.154285 \n", "2012-01-01 8061.916667 3.656828 80.268000 \n", "2012-04-01 8285.526316 3.758256 79.401500 \n", "2012-07-01 7584.261364 3.440167 83.067619 \n", "2012-10-01 8062.032609 3.656881 79.708095 \n", "2013-01-01 8053.738636 3.653119 79.873333 \n", "2013-04-01 7221.161905 3.275468 82.525000 \n", "2013-07-01 6906.641304 3.132804 82.789546 \n", "2013-10-01 7203.021739 3.267240 79.866522 \n", "2014-01-01 7291.465909 3.307357 80.809524 \n", "2014-04-01 6673.562500 3.027081 79.853334 \n", "2014-07-01 7113.380435 3.226579 80.547726 \n", "2014-10-01 6737.478261 3.056072 85.670435 \n", "2015-01-01 5830.535714 2.644690 92.977000 \n", "2015-04-01 6042.087500 2.740648 97.591905 \n", "2015-07-01 5456.750000 2.475143 96.962273 \n", "2015-10-01 5216.090909 2.365982 95.714091 \n", "2016-01-01 4471.787500 2.028371 99.023000 \n", "2016-04-01 4872.738095 2.210239 94.403809 \n", "2016-07-01 4864.904762 2.206686 96.572501 \n", "2016-10-01 4731.261905 2.146067 97.738999 \n", "2017-01-01 5754.559524 2.610227 101.122000 \n", "2017-04-01 5683.902778 2.578178 100.045263 \n", "2017-07-01 5985.119048 2.714808 94.861001 \n", "2017-10-01 6807.602273 3.087880 93.719545 \n", "2018-01-01 7065.852273 3.205020 90.744762 \n", "2018-04-01 6851.512500 3.107797 90.293333 \n", "2018-07-01 6250.750000 2.835296 94.597619 \n", "2018-10-01 6219.586957 2.821161 95.852609 \n", "2019-01-01 5939.102273 2.693935 95.937619 \n", "2019-04-01 6438.362500 2.920396 97.358572 \n", "2019-07-01 5941.195652 2.694884 97.365909 \n", "2019-10-01 5757.297826 2.611469 98.173044 \n", "2022-01-01 9782.337500 4.437199 95.966500 \n", "2022-04-01 10174.347619 4.615012 100.708500 \n", "2022-07-01 7544.809524 3.422272 107.033500 \n", "2022-10-01 7651.082857 3.470477 111.941428 \n", "2023-01-01 9007.346364 4.085668 102.711999 \n", "2023-04-01 8809.157500 3.995771 101.764210 \n", "2023-07-01 8476.679048 3.844962 101.327499 \n", "\n", " Fed_Funds_Rate CPI Oil_Price_WTI China_GDP_Growth \n", "2010-01-01 0.11 217.488 78.325789 8.750130e+12 \n", "2010-04-01 0.20 217.403 84.292857 9.934740e+12 \n", "2010-07-01 0.18 217.605 76.319524 1.059637e+13 \n", "2010-10-01 0.19 219.035 81.892857 1.193068e+13 \n", "2011-01-01 0.17 221.187 89.170500 1.044699e+13 \n", "2011-04-01 0.10 224.093 109.532500 1.188959e+13 \n", "2011-07-01 0.07 225.395 97.303500 1.265622e+13 \n", "2011-10-01 0.07 226.750 86.322381 1.380121e+13 \n", "2012-01-01 0.08 227.842 100.273500 1.173576e+13 \n", "2012-04-01 0.14 229.187 103.321000 1.313206e+13 \n", "2012-07-01 0.16 228.590 87.895238 1.380896e+13 \n", "2012-10-01 0.16 231.638 89.491304 1.518120e+13 \n", "2013-01-01 0.14 231.679 94.756667 1.294496e+13 \n", "2013-04-01 0.15 231.797 92.021364 1.435187e+13 \n", "2013-07-01 0.09 232.900 104.670909 1.522227e+13 \n", "2013-10-01 0.09 233.669 100.538261 1.677723e+13 \n", "2014-01-01 0.07 235.288 94.617143 1.407598e+13 \n", "2014-04-01 0.09 236.468 102.069048 1.564896e+13 \n", "2014-07-01 0.09 237.498 103.588636 1.654847e+13 \n", "2014-10-01 0.09 237.430 84.396957 1.808289e+13 \n", "2015-01-01 0.11 234.747 47.219000 1.511379e+13 \n", "2015-04-01 0.12 236.222 54.452857 1.685497e+13 \n", "2015-07-01 0.13 238.034 50.900909 1.765977e+13 \n", "2015-10-01 0.12 237.733 46.223636 1.925729e+13 \n", "2016-01-01 0.34 237.652 31.683158 1.624100e+13 \n", "2016-04-01 0.37 238.992 40.755238 1.814082e+13 \n", "2016-07-01 0.39 240.101 44.651500 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Copper_Spot_PriceCopper_Spot_Price_lbUSD_IndexFed_Funds_RateCPIOil_Price_WTIChina_GDP_Growth
2010-01-017367.3750003.34178977.8405260.11217.48878.3257898.750130e+12
2010-04-017729.8375003.50619981.2328570.20217.40384.2928579.934740e+12
2010-07-016750.5681823.06201083.0704760.18217.60576.3195241.059637e+13
2010-10-018289.7619053.76017777.4599990.19219.03581.8928571.193068e+13
2011-01-019533.2000004.32419279.1460000.17221.18789.1705001.044699e+13
2011-04-019482.7500004.30130874.7245000.10224.093109.5325001.188959e+13
2011-07-019650.4642864.37738274.7570000.07225.39597.3035001.265622e+13
2011-10-017394.1904763.35395277.1542850.07226.75086.3223811.380121e+13
2012-01-018061.9166673.65682880.2680000.08227.842100.2735001.173576e+13
2012-04-018285.5263163.75825679.4015000.14229.187103.3210001.313206e+13
2012-07-017584.2613643.44016783.0676190.16228.59087.8952381.380896e+13
2012-10-018062.0326093.65688179.7080950.16231.63889.4913041.518120e+13
2013-01-018053.7386363.65311979.8733330.14231.67994.7566671.294496e+13
2013-04-017221.1619053.27546882.5250000.15231.79792.0213641.435187e+13
2013-07-016906.6413043.13280482.7895460.09232.900104.6709091.522227e+13
2013-10-017203.0217393.26724079.8665220.09233.669100.5382611.677723e+13
2014-01-017291.4659093.30735780.8095240.07235.28894.6171431.407598e+13
2014-04-016673.5625003.02708179.8533340.09236.468102.0690481.564896e+13
2014-07-017113.3804353.22657980.5477260.09237.498103.5886361.654847e+13
2014-10-016737.4782613.05607285.6704350.09237.43084.3969571.808289e+13
2015-01-015830.5357142.64469092.9770000.11234.74747.2190001.511379e+13
2015-04-016042.0875002.74064897.5919050.12236.22254.4528571.685497e+13
2015-07-015456.7500002.47514396.9622730.13238.03450.9009091.765977e+13
2015-10-015216.0909092.36598295.7140910.12237.73346.2236361.925729e+13
2016-01-014471.7875002.02837199.0230000.34237.65231.6831581.624100e+13
2016-04-014872.7380952.21023994.4038090.37238.99240.7552381.814082e+13
2016-07-014864.9047622.20668696.5725010.39240.10144.6515001.910106e+13
2016-10-014731.2619052.14606797.7389990.40241.74149.7752382.115662e+13
2017-01-015754.5595242.610227101.1220000.65243.61852.5040001.818677e+13
2017-04-015683.9027782.578178100.0452630.90244.19351.0605262.019503e+13
2017-07-015985.1190482.71480894.8610011.15244.24346.6305262.127893e+13
2017-10-016807.6022733.08788093.7195451.15246.62651.5777272.354287e+13
2018-01-017065.8522733.20502090.7447621.41248.85963.6985712.020357e+13
2018-04-016851.5125003.10779790.2933331.69250.22766.2538102.239622e+13
2018-07-016250.7500002.83529694.5976191.91251.21470.9814292.344743e+13
2018-10-016219.5869572.82116195.8526092.19252.77270.7486962.588089e+13
2019-01-015939.1022732.69393595.9376192.40252.56151.3757142.171683e+13
2019-04-016438.3625002.92039697.3585722.42255.23363.8623812.415026e+13
2019-07-015941.1956522.69488497.3659092.40255.80257.3580952.510463e+13
2019-10-015757.2978262.61146998.1730441.83257.15553.9630432.767980e+13
2022-01-019782.3375004.43719995.9665000.08282.54283.2220002.715092e+13
2022-04-0110174.3476194.615012100.7085000.33288.582101.7775002.939195e+13
2022-07-017544.8095243.422272107.0335001.68294.940101.6190003.092706e+13
2022-10-017651.0828573.470477111.9414283.08297.97987.5547623.355079e+13
2023-01-019007.3463644.085668102.7119994.33300.45678.1230002.849966e+13
2023-04-018809.1575003.995771101.7642104.83302.85879.4463163.080376e+13
2023-07-018476.6790483.844962101.3274995.12304.61576.0695003.199923e+13
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\n" ], "application/vnd.google.colaboratory.intrinsic+json": { "type": "dataframe", "variable_name": "df_combined_new", "summary": "{\n \"name\": \"df_combined_new\",\n \"rows\": 47,\n \"fields\": [\n {\n \"column\": \"Copper_Spot_Price\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 1427.1459718395677,\n \"min\": 4471.7875,\n \"max\": 10174.3476190476,\n \"num_unique_values\": 47,\n \"samples\": [\n 4731.2619047619,\n 5757.29782608696,\n 4864.90476190476\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Copper_Spot_Price_lb\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0.6473432935560631,\n \"min\": 2.028371102502926,\n \"max\": 4.6150119381333745,\n \"num_unique_values\": 47,\n \"samples\": [\n 2.146066852682957,\n 2.611469471422268,\n 2.206686305079678\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"USD_Index\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 9.752536321389126,\n \"min\": 74.72449989318848,\n \"max\": 111.94142804827008,\n \"num_unique_values\": 47,\n \"samples\": [\n 97.73899917602539,\n 98.1730436242145,\n 96.57250061035157\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Fed_Funds_Rate\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 1.30574451277995,\n \"min\": 0.07,\n \"max\": 5.12,\n \"num_unique_values\": 34,\n \"samples\": [\n 0.37,\n 0.9,\n 1.83\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"CPI\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 23.82728924117877,\n \"min\": 217.403,\n \"max\": 304.615,\n \"num_unique_values\": 47,\n \"samples\": [\n 241.741,\n 257.155,\n 240.101\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Oil_Price_WTI\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 21.475137473172758,\n \"min\": 31.683157894736844,\n \"max\": 109.5325,\n \"num_unique_values\": 47,\n \"samples\": [\n 49.775238095238095,\n 53.96304347826087,\n 44.6515\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"China_GDP_Growth\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 6532648465222.127,\n \"min\": 8750129999999.999,\n \"max\": 33550790000000.0,\n \"num_unique_values\": 47,\n \"samples\": [\n 21156620000000.0,\n 27679800000000.0,\n 19101060000000.0\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n }\n ]\n}" } }, "metadata": {}, "execution_count": 22 } ] }, { "cell_type": "markdown", "source": [ "without the Fed funds rate" ], "metadata": { "id": "6PU-i0HVS4PA" } }, { "cell_type": "code", "source": [ "y = df_clean['Copper_Spot_Price_lb']\n", "X = df_clean[['USD_Index', 'CPI', 'Oil_Price_WTI']]\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n", "\n", "\n", "model = LinearRegression()\n", "model.fit(X_train, y_train)\n", "\n", "\n", "y_train_pred = model.predict(X_train)\n", "y_test_pred = model.predict(X_test)\n", "\n", "import statsmodels.api as sm\n", "X_train_with_const = sm.add_constant(X_train)\n", "model_sm = sm.OLS(y_train, X_train_with_const).fit()\n", "print(model_sm.summary())" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "_586GanLTZg9", "outputId": "af9eb9b5-82b3-47f4-ffe8-ff68ba4f0cb3" }, "execution_count": 21, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ " OLS Regression Results \n", "================================================================================\n", "Dep. Variable: Copper_Spot_Price_lb R-squared: 0.789\n", "Model: OLS Adj. R-squared: 0.784\n", "Method: Least Squares F-statistic: 155.8\n", "Date: Sun, 16 Nov 2025 Prob (F-statistic): 4.69e-42\n", "Time: 20:15:10 Log-Likelihood: -30.790\n", "No. Observations: 129 AIC: 69.58\n", "Df Residuals: 125 BIC: 81.02\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "=================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "---------------------------------------------------------------------------------\n", "const 1.1445 0.401 2.852 0.005 0.350 1.939\n", "USD_Index -0.0470 0.007 -6.557 0.000 -0.061 -0.033\n", "CPI 0.0223 0.002 11.203 0.000 0.018 0.026\n", "Oil_Price_WTI 0.0109 0.002 5.245 0.000 0.007 0.015\n", "==============================================================================\n", "Omnibus: 6.284 Durbin-Watson: 2.132\n", "Prob(Omnibus): 0.043 Jarque-Bera (JB): 6.371\n", "Skew: 0.377 Prob(JB): 0.0414\n", "Kurtosis: 3.786 Cond. No. 4.15e+03\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 4.15e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ] }, { "cell_type": "markdown", "source": [ "without CPI\n" ], "metadata": { "id": "e0YwnLDPUjQh" } }, { "cell_type": "code", "source": [ "y = df_clean['Copper_Spot_Price_lb']\n", "X = df_clean[['USD_Index', 'Oil_Price_WTI']]\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n", "\n", "\n", "model = LinearRegression()\n", "model.fit(X_train, y_train)\n", "\n", "\n", "y_train_pred = model.predict(X_train)\n", "y_test_pred = model.predict(X_test)\n", "\n", "import statsmodels.api as sm\n", "X_train_with_const = sm.add_constant(X_train)\n", "model_sm = sm.OLS(y_train, X_train_with_const).fit()\n", "print(model_sm.summary())" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "fuhfSLjpUlGb", "outputId": "5f5aa253-8c5b-436c-ddb1-493fe5531007" }, "execution_count": 24, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ " OLS Regression Results \n", "================================================================================\n", "Dep. Variable: Copper_Spot_Price_lb R-squared: 0.577\n", "Model: OLS Adj. R-squared: 0.570\n", "Method: Least Squares F-statistic: 85.98\n", "Date: Sun, 16 Nov 2025 Prob (F-statistic): 2.82e-24\n", "Time: 20:19:26 Log-Likelihood: -75.628\n", "No. Observations: 129 AIC: 157.3\n", "Df Residuals: 126 BIC: 165.8\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "=================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "---------------------------------------------------------------------------------\n", "const -1.1183 0.489 -2.287 0.024 -2.086 -0.151\n", "USD_Index 0.0257 0.004 5.955 0.000 0.017 0.034\n", "Oil_Price_WTI 0.0273 0.002 13.110 0.000 0.023 0.031\n", "==============================================================================\n", "Omnibus: 6.104 Durbin-Watson: 1.807\n", "Prob(Omnibus): 0.047 Jarque-Bera (JB): 6.104\n", "Skew: 0.533 Prob(JB): 0.0473\n", "Kurtosis: 2.969 Cond. No. 1.51e+03\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 1.51e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ] }, { "cell_type": "markdown", "source": [ " without CPI and then add China’s GDP growth rate" ], "metadata": { "id": "IMhKZKW1T5-q" } }, { "cell_type": "code", "source": [ "y = df_combined_new['Copper_Spot_Price_lb']\n", "X = df_combined_new[['USD_Index', 'China_GDP_Growth', 'Oil_Price_WTI']]\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n", "\n", "\n", "model = LinearRegression()\n", "model.fit(X_train, y_train)\n", "\n", "\n", "y_train_pred = model.predict(X_train)\n", "y_test_pred = model.predict(X_test)\n", "\n", "import statsmodels.api as sm\n", "X_train_with_const = sm.add_constant(X_train)\n", "model_sm = sm.OLS(y_train, X_train_with_const).fit()\n", "print(model_sm.summary())" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "sNaqgE-8T_XG", "outputId": "b1678bbe-8a74-4aa7-eb11-5d013821f0ae" }, "execution_count": 23, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ " OLS Regression Results \n", "================================================================================\n", "Dep. Variable: Copper_Spot_Price_lb R-squared: 0.545\n", "Model: OLS Adj. R-squared: 0.503\n", "Method: Least Squares F-statistic: 13.15\n", "Date: Sun, 16 Nov 2025 Prob (F-statistic): 8.20e-06\n", "Time: 20:17:38 Log-Likelihood: -17.399\n", "No. Observations: 37 AIC: 42.80\n", "Df Residuals: 33 BIC: 49.24\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "====================================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------------\n", "const 2.9665 1.648 1.800 0.081 -0.387 6.320\n", "USD_Index -0.0217 0.019 -1.125 0.269 -0.061 0.018\n", "China_GDP_Growth 4.85e-14 2.4e-14 2.019 0.052 -3.69e-16 9.74e-14\n", "Oil_Price_WTI 0.0175 0.005 3.447 0.002 0.007 0.028\n", "==============================================================================\n", "Omnibus: 0.598 Durbin-Watson: 1.634\n", "Prob(Omnibus): 0.741 Jarque-Bera (JB): 0.666\n", "Skew: 0.070 Prob(JB): 0.717\n", "Kurtosis: 2.358 Cond. No. 4.88e+14\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 4.88e+14. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ] } ] }