{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Markov Variance Switching\n",
    "\n",
    "Kim, C., Nelson, C., and Startz, R. (1998). Testing for mean reversion in heteroskedastic data based on Gibbs-sampling-augmented randomization. Journal of Empirical Finance, (5)2, pp.131-154.\n",
    "\n",
    "**Author:** shittles\n",
    "\n",
    "**Created:** 2024-09-18\n",
    "\n",
    "**Modified:** 2024-09-19\n",
    "\n",
    "## Changelog\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ray\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import plotly.express as px\n",
    "import plotly.graph_objects as go\n",
    "import statsmodels.api as sm\n",
    "\n",
    "from sklearn.compose import make_column_transformer\n",
    "from sklearn.preprocessing import RobustScaler\n",
    "\n",
    "from vectorbtpro import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ray.init()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "vbt.settings.set_theme(\"dark\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ingestion\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "symbol = \"^GSPC\"  # the S&P 500 ticker"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = vbt.YFData.pull(\n",
    "    symbol, start=\"50 years ago\", end=\"today\", timeframe=\"daily\", tz=\"UTC\"\n",
    ")  # 50 years of data\n",
    "\n",
    "data.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.data[symbol]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.data[symbol].index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The opens are corrupt...\n",
    "data.plot(yaxis=dict(type=\"log\")).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# but the closes are fine.\n",
    "data.data[\"^GSPC\"][\"Close\"].vbt.plot(yaxis=dict(type=\"log\")).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cleaning\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.data[symbol][\"Dividends\"].any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.data[symbol][\"Stock Splits\"].any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data.remove_features([\"Dividends\", \"Stock Splits\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data = data.transform(lambda df: df.loc[\"April 19th 1982\" < df.index])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data.plot(yaxis=dict(type=\"log\")).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# len(data.index) / 365.25  # 30 years of data remaining"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modelling\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sr_open = data.get(\"Open\")\n",
    "# sr_high = data.get(\"High\")\n",
    "# sr_low = data.get(\"Low\")\n",
    "sr_close = data.get(\"Close\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sr_log_open = np.log(sr_open)\n",
    "# sr_log_high = np.log(sr_high)\n",
    "# sr_log_low = np.log(sr_low)\n",
    "sr_log_close = np.log(sr_close)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "sr_log_returns = data.log_returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sr_log_returns.vbt.plot().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "column_transformer = make_column_transformer(\n",
    "    (RobustScaler(), [symbol]),\n",
    ")\n",
    "\n",
    "sr_log_returns_scaled = pd.Series(\n",
    "    data=column_transformer.fit_transform(pd.DataFrame(sr_log_returns)).ravel(),\n",
    "    index=sr_log_returns.index,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sr_log_returns_scaled.vbt.plot().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "k_regimes_kns = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "kns = sm.tsa.MarkovRegression(\n",
    "    sr_log_returns_scaled, k_regimes=k_regimes_kns, trend=\"n\", switching_variance=True\n",
    ")\n",
    "results_kns = kns.fit()\n",
    "\n",
    "results_kns.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "results_kns.filtered_marginal_probabilities  # using data until time t (excluding time t+1, ..., T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "results_kns.smoothed_marginal_probabilities  # using data until time T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = vbt.make_subplots(\n",
    "    rows=k_regimes_kns,\n",
    "    cols=1,\n",
    "    y_title=\"Smoothed Marginal Variance Regime Probabilities\",\n",
    "    shared_xaxes=True,\n",
    "    subplot_titles=[\n",
    "        \"Medium-variance\",\n",
    "        \"Low-variance\",\n",
    "        \"High-variance\",\n",
    "    ],  # order changes dependent on fit\n",
    ")\n",
    "\n",
    "for i in range(k_regimes_kns):\n",
    "    fig = results_kns.smoothed_marginal_probabilities[i].vbt.plot(\n",
    "        add_trace_kwargs=dict(row=i + 1, col=1), fig=fig\n",
    "    )\n",
    "\n",
    "\n",
    "fig.update_layout(showlegend=False)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_annotated_line(\n",
    "    fig: go.Figure,\n",
    "    x: pd.Series,\n",
    "    y: pd.Series,\n",
    "    classes: pd.Series,\n",
    "    dict_class_colours: dict,\n",
    "    dict_class_labels: dict,\n",
    ") -> go.Figure:\n",
    "    \"\"\"Plot a line chart where each trace is coloured based on its class.\n",
    "\n",
    "    Yes, plotly really doesn't support this out of the box.\n",
    "\n",
    "    Args:\n",
    "        fig: Figure.\n",
    "        x: Indices.\n",
    "        y: Close prices.\n",
    "        classes: Regimes.\n",
    "        dict_class_colours: In the format {class: colour}\n",
    "        dict_class_labels: In the format {class: label}\n",
    "\n",
    "    Returns:\n",
    "        fig: The figure.\n",
    "    \"\"\"\n",
    "    # Plot each segment in its corresponding color.\n",
    "    for i in range(len(x) - 1):\n",
    "        fig.add_trace(\n",
    "            go.Scatter(\n",
    "                x=x[i : i + 2],\n",
    "                y=y[i : i + 2],\n",
    "                mode=\"lines\",\n",
    "                line=dict(color=dict_class_colours[classes[i]], width=2),\n",
    "                showlegend=False,  # added manually\n",
    "            )\n",
    "        )\n",
    "\n",
    "    # Label each regime.\n",
    "    for regime, colour in dict_class_colours.items():\n",
    "        fig.add_trace(\n",
    "            go.Scatter(\n",
    "                x=[None],\n",
    "                y=[None],\n",
    "                mode=\"lines\",\n",
    "                line=dict(color=colour, width=2),\n",
    "                name=dict_class_labels[regime],\n",
    "            )\n",
    "        )\n",
    "\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "sr_variance_regime_forecasts = results_kns.filtered_marginal_probabilities.idxmax(\n",
    "    axis=1\n",
    ")\n",
    "\n",
    "sr_variance_regime_predictions = results_kns.smoothed_marginal_probabilities.idxmax(\n",
    "    axis=1\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sr_variance_regime_forecasts.vbt.plot().show()\n",
    "sr_variance_regime_predictions.vbt.plot().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# order changes dependent on fit\n",
    "dict_variance_regime_labels = {\n",
    "    0: \"Medium\",\n",
    "    1: \"Low\",\n",
    "    2: \"High\",\n",
    "}\n",
    "\n",
    "dict_variance_regime_colours = {\n",
    "    0: \"orange\",\n",
    "    1: \"green\",\n",
    "    2: \"red\",\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = vbt.make_figure()\n",
    "\n",
    "fig = plot_annotated_line(\n",
    "    fig,\n",
    "    data.index,\n",
    "    sr_log_close,\n",
    "    # sr_variance_regime_forecasts.rolling(5).mean().fillna(0).round(0),\n",
    "    sr_variance_regime_forecasts,\n",
    "    # sr_variance_regime_predictions,\n",
    "    dict_variance_regime_colours,\n",
    "    dict_variance_regime_labels,\n",
    ")\n",
    "\n",
    "fig.update_layout(\n",
    "    title=\"Filtered Variance Regime Labels\",\n",
    "    # title=\"Smoothed Variance Regime Labels\",\n",
    "    xaxis_title=\"Date\",\n",
    "    yaxis_title=\"Log Close\",\n",
    "    showlegend=True,\n",
    ")\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backtest\n",
    "### Filtered marginal probabilities\n",
    "A backtest using filtered marginal probabilities.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO - Double check me!\n",
    "# Assuming that you sell today if yesterday was in the high-variance regime.\n",
    "# entries = (sr_variance_regime_forecasts != 2).vbt.signals.fshift()\n",
    "# exits = (sr_variance_regime_forecasts == 2).vbt.signals.fshift()\n",
    "\n",
    "# Assuming that you sell today (at the close) if today was in the high-variance regime.\n",
    "entries = (sr_variance_regime_forecasts != 2)\n",
    "exits = (sr_variance_regime_forecasts == 2)\n",
    "\n",
    "# I haven't tested any additional logic.\n",
    "# entries = (sr_variance_regime_forecasts.rolling(5).mean().fillna(0).round(0) != 2)\n",
    "\n",
    "clean_entries, clean_exits = entries.vbt.signals.clean(exits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = sr_variance_regime_forecasts.vbt.plot()\n",
    "\n",
    "clean_entries.vbt.signals.plot_as_entries(sr_variance_regime_forecasts, fig=fig)\n",
    "clean_exits.vbt.signals.plot_as_exits(sr_variance_regime_forecasts, fig=fig)\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf = vbt.Portfolio.from_signals(\n",
    "    close=sr_close,\n",
    "    entries=clean_entries,\n",
    "    exits=clean_exits,\n",
    "    direction=\"both\",\n",
    "    fees=0.001,\n",
    "    size=1.0,\n",
    "    size_type=vbt.pf_enums.SizeType.ValuePercent,\n",
    ")\n",
    "\n",
    "pf.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf.plot(yaxis=dict(type=\"log\")).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf.drawdowns.plot(yaxis=dict(type=\"log\")).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf.plot_underwater(pct_scale=True).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Re-fitting Every Day\n",
    "A backtest with a single training and validation set, that's refit every day"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_days_validation = int(365.25 * 2)  # 2 years of data held back for the validation set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# slices_sr = vbt.Splitter.split_range(slice(None), new_split=-n_days_validation, index=data.index)\n",
    "splitter_fr = vbt.Splitter.from_rolling(\n",
    "    data.index, length=len(data.index), split=len(data.index) - n_days_validation\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "splitter_fr.plot().show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a Ray remote function for parallelization.\n",
    "@ray.remote\n",
    "def compute_smoothed_marginal_probabilities(sr):\n",
    "    kns = sm.tsa.MarkovRegression(\n",
    "        sr,\n",
    "        k_regimes=k_regimes_kns,\n",
    "        trend=\"n\",\n",
    "        switching_variance=True,\n",
    "    )\n",
    "    results_kns = kns.fit()\n",
    "\n",
    "    # the smoothing might not work properly out of sample\n",
    "    return results_kns.smoothed_marginal_probabilities.iloc[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The predict method doesn't support out of sample forecasts...\n",
    "# kns = sm.tsa.MarkovRegression(\n",
    "#     sr_log_returns[splitter_fr.get_mask()[\"set_0\"]],\n",
    "#     k_regimes=k_regimes_kns,\n",
    "#     trend=\"n\",\n",
    "#     switching_variance=True,\n",
    "# )\n",
    "# results_kns = kns.fit()\n",
    "\n",
    "# results_kns.summary()\n",
    "\n",
    "# results_kns.predict(sr_log_returns[splitter_fr.get_mask()[\"set_1\"]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://github.com/statsmodels/statsmodels/issues/7982"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "sr_train = sr_log_returns[splitter_fr.get_mask()[\"set_0\"]]\n",
    "sr_validate = sr_log_returns[splitter_fr.get_mask()[\"set_1\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ...so re-fit the model every timestep.\n",
    "futures = []\n",
    "\n",
    "sr_log_returns_to_date = sr_train.copy()\n",
    "\n",
    "# launch parallel tasks\n",
    "for i in range(len(sr_validate)):\n",
    "    sr_log_returns_to_date = pd.concat(\n",
    "        [\n",
    "            sr_log_returns_to_date,\n",
    "            pd.Series(sr_validate.iloc[i], index=[sr_validate.index[i]]),\n",
    "        ]\n",
    "    )\n",
    "\n",
    "    futures.append(\n",
    "        compute_smoothed_marginal_probabilities.remote(sr_log_returns_to_date)\n",
    "    )\n",
    "\n",
    "# collect results\n",
    "smoothed_marginal_probabilities = ray.get(futures)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "smoothed_marginal_probabilities = pd.concat(smoothed_marginal_probabilities, axis=1).T\n",
    "\n",
    "smoothed_marginal_probabilities.index.name = \"Date\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "sr_variance_regime_predictions = smoothed_marginal_probabilities.idxmax(\n",
    "    axis=1\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sr_close_validate = sr_close[splitter_fr.get_mask()[\"set_1\"]]\n",
    "\n",
    "sr_log_close_validate = sr_log_close[splitter_fr.get_mask()[\"set_1\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = vbt.make_figure()\n",
    "\n",
    "fig = plot_annotated_line(\n",
    "    fig,\n",
    "    data.index[splitter_fr.get_mask()[\"set_1\"]],\n",
    "    sr_log_close_validate,\n",
    "    sr_variance_regime_predictions,\n",
    "    dict_variance_regime_colours,\n",
    "    dict_variance_regime_labels,\n",
    ")\n",
    "\n",
    "fig.update_layout(\n",
    "    title=\"Variance Regime Forecasts\",\n",
    "    xaxis_title=\"Date\",\n",
    "    yaxis_title=\"Log Close\",\n",
    "    showlegend=True,\n",
    ")\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO - Double check me!\n",
    "# Assuming that you sell today if yesterday was in the high-variance regime.\n",
    "# entries = (sr_variance_regime_forecasts != 2).vbt.signals.fshift()\n",
    "# exits = (sr_variance_regime_forecasts == 2).vbt.signals.fshift()\n",
    "\n",
    "# Assuming that you sell today (at the close) if today was in the high-variance regime.\n",
    "entries = (sr_variance_regime_forecasts != 2)\n",
    "exits = (sr_variance_regime_forecasts == 2)\n",
    "\n",
    "# I haven't tested any additional logic.\n",
    "# entries = (sr_variance_regime_forecasts.rolling(5).mean().fillna(0).round(0) != 2)\n",
    "\n",
    "clean_entries, clean_exits = entries.vbt.signals.clean(exits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = sr_variance_regime_forecasts.vbt.plot()\n",
    "\n",
    "clean_entries.vbt.signals.plot_as_entries(sr_variance_regime_forecasts, fig=fig)\n",
    "clean_exits.vbt.signals.plot_as_exits(sr_variance_regime_forecasts, fig=fig)\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf = vbt.Portfolio.from_signals(\n",
    "    close=sr_close_validate,\n",
    "    entries=clean_entries,\n",
    "    exits=clean_exits,\n",
    "    direction=\"both\",\n",
    "    fees=0.001,\n",
    "    size=1.0,\n",
    "    size_type=vbt.pf_enums.SizeType.ValuePercent,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf.plot(yaxis=dict(type=\"log\")).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf.drawdowns.plot(yaxis=dict(type=\"log\")).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pf.plot_underwater(pct_scale=True).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Observations\n",
    "- For this implementation you have to use the filtered probabilities to not introduce look-ahead bias.\n",
    "- If you backtest the smoothed probilities (which smoothes using all of the data) it only performs well after the great financial crisis. Why? No clue.\n",
    "- It looks like its better for labelling than it is as a strategy in its current state.\n",
    "- After slow recessions like the dot-com bubble, there can be a medium-variance decline which this simple strategy doesn't capture.\n",
    "- After fast recessions like covid-19, there can be a high-variance rebound which this simple strategy doesn't capture.\n",
    "- **It looks like you can safely leverage up during low-variance regimes.**\n",
    "- Maybe you could combine this strategy with other recession-leading indicators (e.g. manufacturing/services pmi, federal funds rate, 10y-2y yield curve, 1y-3mo yield curve) to help time the tops?\n",
    "- Maybe you could combine this strategy with another trend-following strategy (e.g. VWAP, EMA, BBANDS, ADX) to help time the bottoms?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "ray.shutdown()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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