05_moving_averages.ipynb

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    "# Moving Average\n",
    "\n",
    "_Moving Average_ (MA) is an indicator that constantly describes the average price over a period. It's also called _rolling average_. The mean over the last $k$ data points can be calculated as:\n",
    "\n",
    "$\\displaystyle {\\begin{aligned}{\\textit {SMA}}_{k}={\\frac {p_{n-k+1}+p_{n-k+2}\\cdots +p_{n}}{k}}={\\frac {1}{k}}\\sum _{i=n-k+1}^{n}p_{i}\\end{aligned}}$\n",
    "\n",
    "Intuitively, the value for a 3 days moving average in a given date $t$ is computed by simply calculating the average of the previous 3 values: $(t + t_{-1} + t_{-2}) / 3$.\n",
    "\n",
    "Luckily, Pandas comes with batteries included, offering us the `.rolling()` function, that accepts the number of days to use:"
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    "import pandas as pd\n",
    "from sample_data import stock_prices\n",
    "\n",
    "msft = stock_prices('msft')\n",
    "ma50 = msft.Close.rolling(50).mean()\n",
    "ma200 = msft.Close.rolling(200).mean()"
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    "`ma50` is a Series with all the computed moving average values"
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       "Date\n",
       "2022-06-28    266.840599\n",
       "2022-06-29    266.435399\n",
       "2022-06-30    265.865999\n",
       "2022-07-01    265.330399\n",
       "Name: Close, dtype: float64"
      ]
     },
     "execution_count": 2,
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   "source": [
    "ma50.tail(4)"
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    "Using `ma50` and `ma200`, we can plot them to observe the trends over time. Lines should follow the main price values, but you should observe a more _soft_ reactions to price changes."
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       "<Figure size 1000x600 with 1 Axes>"
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   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "matplotlib.rcParams['font.family'] = \"IBM Plex Mono\"\n",
    "\n",
    "ig, ax = plt.subplots(figsize=(10,6))\n",
    "\n",
    "msft.Close['2019':].plot(color='#D1D5DB', label=\"Price\")\n",
    "ma50['2019':].plot(color='#3B82F6', label=\"MA50\")\n",
    "ma200['2019':].plot(color='#1E3A8A', label=\"MA200\")\n",
    "plt.legend()\n",
    "plt.show()"
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   "cell_type": "markdown",
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    "### Exercise 5.1\n",
    "\n",
    "Read 2019 data for `aapl` and compute the moving average for the last 50 days using Spark.\n",
    "\n",
    "### Exercise 5.2\n",
    "\n",
    "Compute the same MA20, but this time by using [the new Pandas API for Spark](https://databricks.com/blog/2021/10/04/pandas-api-on-upcoming-apache-spark-3-2.html). \n",
    "\n",
    "There could be a warning message like this one: _No Partition Defined for Window operation_. What does it mean?"
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    "## Exponential Moving Average (EMA)\n",
    "\n",
    "A variation of this is to use the _Exponential Moving Average (EMA)_, that gives more weight to recent prices. SMA represent the average of prices in a timespan, and are better suited to identify \"resistance\" levels. In contrast, EMA has less lag and is therefore more sensitive to recent prices.\n",
    "\n",
    "${ewm}(α)=(1−α)⋅{emw}_{t-1}+α⋅x_t$\n",
    "\n",
    "Where $x_t$ is the price value as of today and ${emw}_{t-1}$ the EMA value from yesterday.\n",
    "\n",
    "EMA is calculated using a smoothing or decat factor $\\alpha$ that determines the weight given to the current period's value. The smoothing factor is a value between 0 and 1. A smaller smoothing factor gives more weight to recent data, making the EMA more responsive to recent price changes. Conversely, a larger smoothing factor places more weight on older data, resulting in a smoother and slower-moving EMA.\n",
    "\n",
    "$\\alpha$ is typically calculated as $\\alpha = 2 / (N + 1)$, where $N$ represents the number of periods or time intervals used in the EMA calculation.\n",
    "\n",
    "Pandas offers us the [ewm](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.ewm.html) function to calculate the exponentially weighted windows:"
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   "execution_count": 4,
   "id": "787be591-146c-402c-a3a6-820b39e50e76",
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       "<Figure size 1000x600 with 1 Axes>"
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   "source": [
    "msft_2016 = msft['2016':'2017']\n",
    "ema10 = msft_2016.Close.ewm(span=10, adjust=False).mean()\n",
    "sma50 = msft_2016.Close.rolling(50).mean()\n",
    "sma100 = msft_2016.Close.rolling(100).mean()\n",
    "\n",
    "ig, ax = plt.subplots(figsize=(10,6))\n",
    "\n",
    "msft_2016.Close.plot(ax=ax, color='#D1D5DB', label=\"price\")\n",
    "ema10.plot(ax=ax, color='#EF4444', linestyle=\"--\", label=\"ema10\")\n",
    "sma50.plot(ax=ax, color='#3B82F6', label=\"sma50\")\n",
    "sma100.plot(ax=ax, color='#1E3A8A', label=\"sma100\")\n",
    "plt.legend()\n",
    "plt.show()"
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   "source": [
    "One interesting thing about `ewm` is that it supports incremental updates. To use it, you have to call the `online` method right after `ewm` and that would return an object that allows to update the data with new data points."
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   "cell_type": "code",
   "execution_count": 5,
   "id": "cd8a5dd1-add7-474a-9a0a-d7cfde0ce33b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Luis.Belloch/src/master/pandas_notebooks/.direnv/python-3.11/lib/python3.11/site-packages/pandas/core/window/online.py:57: NumbaExperimentalFeatureWarning: Use of isinstance() detected. This is an experimental feature.\n",
      "  result[0] = np.where(nobs >= minimum_periods, weighted_avg, np.nan)\n"
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    {
     "data": {
      "text/plain": [
       "Date\n",
       "2017-12-28    85.460432\n",
       "2017-12-29    85.474899\n",
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    "online_ema10 = msft_2016.Close.ewm(span=10, adjust=False).online()\n",
    "online_ema10.mean().tail(2)"
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  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "46057e0f-a2f3-49cf-a69d-85bfc33a26b4",
   "metadata": {},
   "outputs": [
    {
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       "dtype: float64"
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     "execution_count": 6,
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    "online_ema10.mean(update=pd.Series([86.0]))"
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   "source": [
    "## MACD\n",
    "\n",
    "There's another indicator called _Moving Average Convergence/Divergence oscillator (MACD)_. It's calculated by getting two moving averages and substracting the longer moving average by the sorter one. In the calculated MCDA below, negative MACD values indicate that the 12-day EMA is below the 26-day EMA."
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   "execution_count": 7,
   "id": "8a5dac24-41dc-43b5-99c0-7449c41b52be",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "Date\n",
       "2016-01-04    0.000000\n",
       "2016-01-05    0.019943\n",
       "2016-01-06   -0.044431\n",
       "2016-01-07   -0.244333\n",
       "2016-01-08   -0.385402\n",
       "                ...   \n",
       "2017-12-22    0.918154\n",
       "2017-12-26    0.867302\n",
       "2017-12-27    0.842306\n",
       "2017-12-28    0.813922\n",
       "2017-12-29    0.768049\n",
       "Name: Close, Length: 503, dtype: float64"
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     "metadata": {},
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    "ema12 = msft_2016.Close.ewm(span=12, adjust=False).mean()\n",
    "ema26 = msft_2016.Close.ewm(span=26, adjust=False).mean()\n",
    "macd = ema12 - ema26\n",
    "macd"
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  {
   "cell_type": "markdown",
   "id": "66e76baa-c455-4429-8199-8d8f5c584d53",
   "metadata": {},
   "source": [
    "Additionally, we can calculate a _signal line_ that would identify events on the MACD when both lines cross. When signal line is below the MACD, things are improving over time."
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   "execution_count": 8,
   "id": "bcaaf876-5ea1-41e5-826a-a913c06348b8",
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   ],
   "source": [
    "signal = macd.ewm(span=9, adjust=False).mean()\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "msft_2016.Close.plot(ax=ax, color='#374151', alpha=0.2, secondary_y=True)\n",
    "macd.plot(ax=ax, color='#2563EB')\n",
    "signal.plot(ax=ax, color='#EF4444')"
   ]
  }
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