finish stylized facts

requirements.txt

@@ -4,4 +4,5 @@ requests
 yfinance
 cufflinks
 plotly
-seaborn
+seaborn
+scipy

standa.ipynb

@@ -1118,7 +1118,7 @@
     "    sigma = df[\"log_rtn\"].std()\n",
     "    norm_pdf = scs.norm.pdf(r_range, loc=mu, scale=sigma)\n",
     "\n",
-    "    fig, ax = plt.subplots(1, 2, figsize=(16, 8))\n",
+    "    fig, ax = plt.subplots(1, 2)\n",
     "\n",
     "    # histogram\n",
     "    sns.distplot(df.log_rtn, kde=False, norm_hist=True, ax=ax[0])\n",
@@ -1145,17 +1145,11 @@
     "    df : DataFrame\n",
     "        DataFrame with returns\n",
     "    \"\"\"\n",
-    "    fig, ax = plt.subplots(1, 2, figsize=(16, 8))\n",
     "\n",
-    "    # squared returns\n",
-    "    df[\"sq_rtn\"] = df[\"log_rtn\"] ** 2\n",
-    "    df[\"sq_rtn\"].plot(ax=ax[0])\n",
-    "    ax[0].set_title(\"Volatility clustering\", fontsize=16)\n",
+    "    # create new figure\n",
+    "    fig, ax = plt.subplots(1, 1)\n",
     "\n",
-    "    # absolute returns\n",
-    "    df[\"abs_rtn\"] = df[\"log_rtn\"].abs()\n",
-    "    df[\"abs_rtn\"].plot(ax=ax[1])\n",
-    "    ax[1].set_title(\"Volatility clustering\", fontsize=16)\n",
+    "    df[\"log_rtn\"].plot(title=\"Daily returns\", ax=ax)\n",
     "\n",
     "    sns.despine()\n",
     "    plt.tight_layout()\n",
@@ -1199,6 +1193,94 @@
     "    return pn.widgets.Tabulator(stats_df, show_index=True)\n",
     "\n",
     "\n",
+    "def plot_abscense_of_autocorrelation(df):\n",
+    "    \"\"\"\n",
+    "    Plot absence of autocorrelation\n",
+    "\n",
+    "    Parameters\n",
+    "    ----------\n",
+    "    df : DataFrame\n",
+    "        DataFrame with returns\n",
+    "    \"\"\"\n",
+    "\n",
+    "    N_LAGS = 50\n",
+    "    SIGNIFICANCE_LEVEL = 0.05\n",
+    "\n",
+    "    # create new figure\n",
+    "    fig, ax = plt.subplots(1, 1)\n",
+    "\n",
+    "    acf = smt.graphics.plot_acf(\n",
+    "        df[\"log_rtn\"], lags=N_LAGS, alpha=SIGNIFICANCE_LEVEL, ax=ax\n",
+    "    )\n",
+    "\n",
+    "    sns.despine()\n",
+    "    plt.tight_layout()\n",
+    "\n",
+    "    return fig\n",
+    "\n",
+    "\n",
+    "def plot_small_and_decreasing_autocorrelations(df):\n",
+    "    \"\"\"\n",
+    "    Plot small and decreasing autocorrelations\n",
+    "\n",
+    "    Parameters\n",
+    "    ----------\n",
+    "    df : DataFrame\n",
+    "        DataFrame with returns\n",
+    "    \"\"\"\n",
+    "\n",
+    "    fig, ax = plt.subplots(2, 1)\n",
+    "    SIGNIFICANCE_LEVEL = 0.05\n",
+    "    N_LAGS = 50\n",
+    "\n",
+    "    smt.graphics.plot_acf(\n",
+    "        df[\"log_rtn\"] ** 2, lags=N_LAGS, alpha=SIGNIFICANCE_LEVEL, ax=ax[0]\n",
+    "    )\n",
+    "    ax[0].set(title=\"Autocorrelation Plots\", ylabel=\"Squared Returns\")\n",
+    "\n",
+    "    smt.graphics.plot_acf(\n",
+    "        np.abs(df[\"log_rtn\"]), lags=N_LAGS, alpha=SIGNIFICANCE_LEVEL, ax=ax[1]\n",
+    "    )\n",
+    "    ax[1].set(ylabel=\"Absolute Returns\", xlabel=\"Lag\")\n",
+    "\n",
+    "    sns.despine()\n",
+    "    plt.tight_layout()\n",
+    "\n",
+    "    return fig\n",
+    "\n",
+    "\n",
+    "def plot_leverage_effect(df):\n",
+    "    \"\"\"\n",
+    "    Plot leverage effect\n",
+    "\n",
+    "    Parameters\n",
+    "    ----------\n",
+    "    df : DataFrame\n",
+    "        DataFrame with returns\n",
+    "    \"\"\"\n",
+    "\n",
+    "    df[\"rolling_std_252\"] = df[[\"log_rtn\"]].rolling(window=252).std()\n",
+    "    df[\"rolling_std_21\"] = df[[\"log_rtn\"]].rolling(window=21).std()\n",
+    "\n",
+    "    fig, ax = plt.subplots(3, 1, figsize=(18, 15), sharex=True)\n",
+    "\n",
+    "    df[\"Close\"].plot(ax=ax[0])\n",
+    "    ax[0].set(title=\"Price time series\", ylabel=\"Price ($)\")\n",
+    "\n",
+    "    df[\"log_rtn\"].plot(ax=ax[1])\n",
+    "    ax[1].set(ylabel=\"Log returns\")\n",
+    "\n",
+    "    df[\"rolling_std_252\"].plot(ax=ax[2], color=\"r\", label=\"Rolling Volatility 252d\")\n",
+    "    df[\"rolling_std_21\"].plot(ax=ax[2], color=\"g\", label=\"Rolling Volatility 21d\")\n",
+    "    ax[2].set(ylabel=\"Moving Volatility\", xlabel=\"Date\")\n",
+    "    ax[2].legend()\n",
+    "\n",
+    "    sns.despine()\n",
+    "    plt.tight_layout()\n",
+    "\n",
+    "    return fig\n",
+    "\n",
+    "\n",
     "def get_stylized_facts_charts(ticker: str = TICKER_DEFAULT):\n",
     "    \"\"\"\n",
     "    Create panel with stylized facts charts. The stylized facts are:\n",
@@ -1225,79 +1307,14 @@
     "    # Volatility clustering\n",
     "    fig3 = plot_volatility_clustering(df)\n",
     "\n",
-    "    fig, ax = plt.subplots(3, 2, figsize=(15, 10))\n",
-    "\n",
-    "    # plot returns distribution\n",
-    "    sns.histplot(\n",
-    "        df[\"log_rtn\"],\n",
-    "        ax=ax[0, 0],\n",
-    "        kde=True,\n",
-    "        stat=\"density\",\n",
-    "        color=\"darkblue\",\n",
-    "        alpha=0.5,\n",
-    "        bins=50,\n",
-    "    )\n",
-    "    ax[0, 0].set_title(\"Returns distribution\")\n",
-    "\n",
-    "    # plot returns distribution\n",
-    "    sns.histplot(\n",
-    "        df[\"log_rtn\"],\n",
-    "        ax=ax[0, 1],\n",
-    "        kde=True,\n",
-    "        stat=\"density\",\n",
-    "        color=\"darkblue\",\n",
-    "        alpha=0.5,\n",
-    "        bins=50,\n",
-    "    )\n",
-    "    ax[0, 1].set_title(\"Returns distribution\")\n",
-    "\n",
-    "    # plot returns distribution\n",
-    "    sns.histplot(\n",
-    "        df[\"log_rtn\"],\n",
-    "        ax=ax[0, 1],\n",
-    "        kde=True,\n",
-    "        stat=\"density\",\n",
-    "        color=\"darkblue\",\n",
-    "        alpha=0.5,\n",
-    "        bins=50,\n",
-    "    )\n",
-    "    ax[0, 1].set_title(\"Returns distribution\")\n",
-    "\n",
-    "    # plot returns distribution\n",
-    "    sns.histplot(\n",
-    "        df[\"log_rtn\"],\n",
-    "        ax=ax[0, 1],\n",
-    "        kde=True,\n",
-    "        stat=\"density\",\n",
-    "        color=\"darkblue\",\n",
-    "        alpha=0.5,\n",
-    "        bins=50,\n",
-    "    )\n",
-    "    ax[0, 1].set_title(\"Returns distribution\")\n",
-    "\n",
-    "    # plot returns distribution\n",
-    "    sns.histplot(\n",
-    "        df[\"log_rtn\"],\n",
-    "        ax=ax[0, 1],\n",
-    "        kde=True,\n",
-    "        stat=\"density\",\n",
-    "        color=\"darkblue\",\n",
-    "        alpha=0.5,\n",
-    "        bins=50,\n",
-    "    )\n",
-    "    ax[0, 1].set_title(\"Returns distribution\")\n",
-    "\n",
-    "    # plot returns distribution\n",
-    "    sns.histplot(\n",
-    "        df[\"log_rtn\"],\n",
-    "        ax=ax[0, 1],\n",
-    "        kde=True,\n",
-    "        stat=\"density\",\n",
-    "        color=\"darkblue\",\n",
-    "        alpha=0.5,\n",
-    "        bins=50,\n",
-    "    )\n",
-    "    ax[0, 1].set_title(\"Returns distribution\")\n",
+    "    # Absence of autocorrelation\n",
+    "    fig4 = plot_abscense_of_autocorrelation(df)\n",
+    "\n",
+    "    # Small and decreasing autocorrelations of squared and absolute returns\n",
+    "    fig5 = plot_small_and_decreasing_autocorrelations(df)\n",
+    "\n",
+    "    # Leverage effect\n",
+    "    fig6 = plot_leverage_effect(df)\n",
     "\n",
     "    return pn.Column(\n",
     "        pn.pane.Markdown(\"## 1. Non-Gaussian distribution of returns\"),\n",
@@ -1307,7 +1324,13 @@
     "        pn.pane.Markdown(\"## 2. Volatility clustering\"),\n",
     "        fig3,\n",
     "        pn.pane.Markdown(\"## 3. Absence of autocorrelation\"),\n",
-    "        fig,\n",
+    "        fig4,\n",
+    "        pn.pane.Markdown(\n",
+    "            \"## 4. Small and decreasing autocorrelations of squared and absolute returns\"\n",
+    "        ),\n",
+    "        fig5,\n",
+    "        pn.pane.Markdown(\"## 5. Leverage effect\"),\n",
+    "        fig6,\n",
     "    )"
    ]
   },