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MeanReversionTutorial.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "MeanReversionTutorial.ipynb",
"version": "0.3.2",
"provenance": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"[View in Colaboratory](https://colab.research.google.com/gist/gjlr2000/6c1b4e63e233bdff9b235fc2fb81e77f/meanreversiontutorial.ipynb)"
]
},
{
"metadata": {
"id": "EVVS23TJyeDW",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# Mean Reversion: Intuition and Background.\n",
"\n",
"## What is Mean Reversion ?\n",
"\n",
"Instead of starting with a deep scientific (either mathematical or psychological) definition of Mean Reversion, I prefer to appeal to the 'guts' of a trader who is looking for them. For a trader, a mean-reverting signal is the time series of prices of an asset or a portfolio of assets that kind of moves upwards and downwards around a constant mean. When this mythical signal is discovered, the trader will simply 'buy low, sell high'.\n",
"\n",
"Using the magic of jupyter books, I can show some real examples on code that anyone can run. Let me show you a typical signal used in Fixed Income: the Treasury Rates 2-5-10 butterfly (but keep in mind that you can change the parameters below to do your own exploring).\n",
"\n",
"First, I show how to download and plot the whole term structure:"
]
},
{
"metadata": {
"id": "YRS7HOt8ydPG",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 302
},
"outputId": "18f8a519-f61f-4dca-d7c4-c77745969047"
},
"cell_type": "code",
"source": [
"# -*- coding: utf-8 -*-\n",
"\n",
"# In this section I add the initial libraries required for this tutorial\n",
"# 'requests': allow HTTP-post API calls\n",
"import requests\n",
"# 'json': to format as json calls to API\n",
"import json \n",
"# 'pandas': to plot the timeseries\n",
"import pandas as pd\n",
"# 'datetime': to convert different date formats\n",
"import datetime as dt\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"import time\n",
"\n",
"# defining the api-endpoint \n",
"# API_ENDPOINT = \"https://markovsimulator.azurewebsites.net/api/MarkovCalibrator_01?code=UFYL9CcFRERnVbZJ3ELdRRY7u59vD3BgONzaGLNEOekTfKf0Ug9Bfw==\"\n",
"API_ENDPOINT = \"https://gmaatest.azurewebsites.net/api/HttpTriggerCSharp1?code=COXmk9ou6Mr8/dUCYj045SaeNm6jCkPzJ3ilU/dCiTvNcFNQax4BMQ==\"\n",
"\n",
"# Treasury rates: we can download them from Quandl\n",
"QUAND_TS = \"https://www.quandl.com/api/v3/datasets/USTREASURY/YIELD.json?api_key=o6YKGjyDcseE3LFKrSK3\"\n",
"\n",
"\n",
"# Call Quandl to get all the data\n",
"q = requests.get(url = QUAND_TS)\n",
"q_json = q.json() \n",
"q_data = q_json['dataset']['data']\n",
"\n",
"# Compute derived series from Quandl Data\n",
"dates = []\n",
"values = []\n",
"q_len = len(q_data)\n",
"column_len = len(q_data[0])\n",
"column = column_len-1\n",
"columns = q_json['dataset']['column_names']\n",
"print (columns)\n",
"\n",
"\n",
"# The following could be easily done using Quandl's\n",
"# python API - but I keep it the 'hard way' to allow\n",
"# compatibility with Google Colaboratory\n",
"df_rates = pd.DataFrame.from_records(q_data, columns = columns)\n",
"df_rates['Date'] = pd.to_datetime(df_rates['Date'])\n",
"df_rates.set_index('Date', inplace=True)\n",
"df_rates.plot()\n"
],
"execution_count": 10,
"outputs": [
{
"output_type": "stream",
"text": [
"['Date', '1 MO', '3 MO', '6 MO', '1 YR', '2 YR', '3 YR', '5 YR', '7 YR', '10 YR', '20 YR', '30 YR']\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f54bb364978>"
]
},
"metadata": {
"tags": []
},
"execution_count": 10
},
{
"output_type": "display_data",
"data": {
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v+YMy3i7V7HFgtCZszf5E9hWqx44Jk3SXMPUI8ZTUyOsLAQVF1LffaNIit8w9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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f54bdd65358>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "ZGc4wk6A32qA",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"Below, I will pick only the rate history corresponding to the 2-5-10 butterfly, and then compute its time series using the 1-2-1 weights (also known as 50:50 as the weights of the 2s and 10s 'wings' are half of the 5s 'body').\n",
"\n",
"The plot will result (hopefully) in a time series that moves around zero and goes from -0.6 to +0.8: this is usually one of 'typical' mean reverting signals found by practiotioners."
]
},
{
"metadata": {
"id": "ByC83D4E3HwP",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 353
},
"outputId": "5b918dc2-98bb-41fd-ff6f-364f882d43ae"
},
"cell_type": "code",
"source": [
"\n",
"\n",
"\n",
"# columns names: [\"Date\",\"1 MO\",\"3 MO\",\"6 MO\",\"1 YR\",\"2 YR\",\"3 YR\",\"5 YR\",\"7 YR\",\"10 YR\",\"20 YR\",\"30 YR\"]\n",
"# as the index start from 0, columns 2,5 and 10 are:\n",
"cols = [5, 7, 9]\n",
"\n",
"columns_fly = [columns[i] for i in cols]\n",
"TimeSeries = df_rates[columns_fly]\n",
"\n",
"# I use this line to keep each weight linked to the name of the maturity\n",
"Weights = pd.DataFrame([-1, 2, -1], index = TimeSeries.columns)\n",
"print (Weights)\n",
"\n",
"# Now all I have to is the 'dot' product of Weights and TimeSeries\n",
"butterfly_ts = (TimeSeries.dot(Weights)).dropna()\n",
"butterfly_ts.plot()\n"
],
"execution_count": 11,
"outputs": [
{
"output_type": "stream",
"text": [
" 0\n",
"2 YR -1\n",
"5 YR 2\n",
"10 YR -1\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f54bd88d518>"
]
},
"metadata": {
"tags": []
},
"execution_count": 11
},
{
"output_type": "display_data",
"data": {
"image/png": 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0buZLozUzd0LMcsGhOPhIQ2CtoRGzRUJtkyegK0S74aDH9rG+nzOlBo1RDGO4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\neknPRvQEKCYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f54bd92b710>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "9I20sctA9dPa",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"Now that we can *see* what a mean reverting timeseries looks like, a practicioner can visually identify what the mean looks like (zero) and the bands where the signal spend most of the time (-0.6 and +0.6). \n",
"Here is where quants started providing value - by properly modeling the Time Series we could add more useful information: \n",
" \n",
"* how long could it take it to revert to the mean ? \n",
"* how probable is that it will be around (or far away from) the mean in the next days ?\n",
"* is this signal _really_ mean reverting ? (a seasoned practicioner will notice the different behaviours in 1990 to 1996, 1996 to 2001, 2001 to 2006, etc., but for the sake of illustration just keep an open mind for the moment.)\n",
"\n",
"**Note:** If you are reading this from the github source, some of the formulas below will be scrambled. Try the Google Colaboratory [original version](https://colab.research.google.com/drive/1dEjjPPpJ6FVzgZaqp1EjYENSwE7Q9TU8#scrollTo=9I20sctA9dPa).\n",
"\n",
"To answer this questions quants introduced mathematical modeling using stochastic processes, and defined Mean Reversion as:\n",
"\n",
">The simple Ornstein-Uhlenbeck mean reverting (OUMR) process given by the stochastic differential\n",
"equation (SDE)\n",
"$$d x(t) = \\theta(\\mu - x(t)) dt + \\sigma dB(t),$$ \n",
"$$x(0) = x_0$$\n",
"for constants $\\mu$, $\\theta$, $\\sigma$ and $x_0$ and where $B(t)$ is standard Brownian motion.\n",
"In this model the process $x(t)$ fluctuates randomly, but tends to revert to some fundamental\n",
"level $\\mu$. The behavior of this 'reversion' depends on both the short term standard deviation $\\sigma$ and\n",
"the speed of reversion parameter $\\theta$\n",
"\n",
"Using the definition above, and with *known* values of $\\theta$ and $\\sigma$ we are now able to answer the questions we posed above. For readers that are mathematically inclined, we refer them to the [Wikipedia entry](https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process) where it is shown the full derivation of the stochastic process.\n",
"\n",
"While the math seems nice, we start to lose the intuition. On the example above we visually noticed the (-0.6, 0.6) band, a mean of 0, and oscillations that take a couple of years for it to return to the mean - where is that information in the formulas ? \n",
"\n",
"The mean seems simple enough - it looks (and it is) the 'fundamental level' $\\mu$. \n",
"\n",
"Practitioners used to the [68-95-99.7](https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule) rule (a 2 standard deviation band roughly comprises 95% of observations) and who 'eyeball' the (-0.6, 0.6) band as 2 std around the mean of 0 would think $\\sigma$ is roughly 0.3. But $\\sigma$ *does not* correspond to the width of the band, instead it has to scaled by the mean reversion speed $\\theta$:\n",
"$$\\operatorname {var} (x(t))={{\\sigma ^{2}} \\over {2\\theta} }.\\,$$\n",
"$$\\operatorname {std band} = \\sqrt { {{\\sigma ^{2}} \\over {2\\theta} } }$$\n",
"Practitioners tend to use [Bollinger Bands](https://en.wikipedia.org/wiki/Bollinger_Bands) to \"guesstimate\" the standard deviation band and trade whenenever the signal reaches a certain multiple (usually 2) - see my [last notebook](https://colab.research.google.com/drive/11i2hkrrxC9msa4YqFr6NF9SZ7QpOELvj).\n",
"\n",
"We need to know $\\theta$ (the mean reversion speed) to get the correct $\\operatorname {var} (x(t))$. This extra complexity brings the advantage of being able to compute the amount of time required for the series to go from any level to half way closer to the mean:\n",
"$$\\operatorname {half life} = {{ \\operatorname{ln}(2)} \\over {\\theta}}$$\n",
"\n",
"\n",
"\n"
]
},
{
"metadata": {
"id": "mdmXJLZbXanS",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"### Expected Forward Path\n",
"\n",
"The formulas for the forward path are:\n",
"$$E[x(t) | x_0] = \\bar{x} + (x_o - \\bar{x}) e^{-\\theta t}$$\n",
"and\n",
"$$\\operatorname {Var}[ x(t) | x_0] = \\frac{\\sigma ^2}{2 \\theta} \\left(1 - e^{-2 \\theta t} \\right)$$ \n",
"\n",
"In python:\n"
]
},
{
"metadata": {
"id": "B3j3nwVuZbQp",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"# Using the formulas to compute the forward expected mean and standard devition at some time\n",
"# t in the future (today being time '0', and expressed in terms of a year being one unit)\n",
"def OUmu_t(currentValue, mu, theta, t):\n",
" return mu + (currentValue - mu)*np.exp(-theta * t)\n",
"\n",
"def OUsigma_t(sigma, theta, t):\n",
" return np.sqrt ( ( 1 - np.exp(-2 * theta * t)) * sigma * sigma / (2 * theta) )"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "WWnQCtWxIDOZ",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# Calibrating Mean Reverting parameters\n",
"\n",
"A practitioner will have some intuitive 'sense' (or 'gut feeling') of the mean reverting parameters, but if someone is analysing many signals it is better to automate the process. One method used to compute the parameters is 'Maximum Likelihood Expectation'; using Markov's API we can compute it and verify our intuition: "
]
},
{
"metadata": {
"id": "zakgUyuVJBGo",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 122
},
"outputId": "5a293d42-ed60-4d30-d6b1-39ffb29cc8ef"
},
"cell_type": "code",
"source": [
"# Time Series API format\n",
"json_ts = {\n",
" \"calType\" : \"\",\n",
" \"seriesName\" : \"butterfly\",\n",
" \"colName\" : \"Value\",\n",
" \"dates\": [], \n",
" \"vals\" : []\n",
"}\n",
"\n",
"# Preprocessing for API (from pandas TS)\n",
"butterfly_ts = butterfly_ts.dropna()\n",
"butterfly_ts.sort_index(inplace = True)\n",
"json_ts['vals'] = butterfly_ts[0].tolist() \n",
"butterfly_ts['dates_'] = butterfly_ts.index\n",
"json_ts['dates'] = butterfly_ts['dates_'].apply(lambda x: x.strftime('%Y-%m-%d')).tolist()\n",
"\n",
"# Calling the Azure function API:\n",
"r = requests.post(url = API_ENDPOINT, json = json_ts)\n",
"r_json = r.json()\n",
"print (r_json)\n",
"\n",
"# Converting results to 'intuitive' numbers:\n",
"mean = r_json['calibrationResult']['Mu']\n",
"print ('Mean:',mean)\n",
"sigma = r_json['calibrationResult']['Sigma']\n",
"# the API has a nomenclature difference;\n",
"# what I defined as theta in the text is called Lambda in the API\n",
"theta = r_json['calibrationResult']['Lambda']\n",
"\n",
"# Using the formulas in the text to get the intuitive statistics\n",
"half_life = np.log(2)/ theta\n",
"print('Half life: (in years)', half_life)\n",
"std_band = np.sqrt( sigma * sigma / (2 * theta))\n",
"print('2 std band:', std_band*2)\n",
"\n",
"\n"
],
"execution_count": 7,
"outputs": [
{
"output_type": "stream",
"text": [
"{'calibrationResult': {'Mu': 0.08243615378404112, 'Sigma': 0.5692197267153007, 'Lambda': 2.0803132455726336, 'LogLikelihood': -14023.902136306633, 'ProcessType': 'Mean Reverting', 'LastPrice': 0.15000000000000036, 'DaysPerYear': 365.25}, 'timeSeries': {}, 'ts_string': None, 'time_ser_dates': None, 'time_ser_values': None}\n",
"Mean: 0.08243615378404112\n",
"Half life: (in years) 0.3331936582315743\n",
"2 std band: 0.5581238394218108\n",
"https://gmaatest.azurewebsites.net/api/HttpTriggerCSharp1?code=COXmk9ou6Mr8/dUCYj045SaeNm6jCkPzJ3ilU/dCiTvNcFNQax4BMQ==\n"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "CqGruY8V0taG",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"The results are close to our initial 'eyeballing': mean is close to zero (at 8bps), half life of 0.33 years (3.6 months) visually fits with the 2 year cycles we identified to go from one side of the band to the other (one year to fully mean revert - roughly 6 times the half life), and finally the 2 standard deviation band of 0.55 is close to the visual range of (-0.6, 0.6) we identified."
]
},
{
"metadata": {
"id": "dz4mcP_1iRcH",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 351
},
"outputId": "5da00ffa-4227-486d-fecd-7936b7aaf1ff"
},
"cell_type": "code",
"source": [
"fly_augmented = butterfly_ts[0].to_frame('fly').dropna()\n",
"fly_augmented['mu'] = mean\n",
"fly_augmented['+2std'] = mean + std_band*2\n",
"fly_augmented['-2std'] = mean - std_band*2\n",
"fly_augmented['+3std'] = mean + std_band*3\n",
"fly_augmented['-3std'] = mean - std_band*3\n",
"\n",
"last_row = (fly_augmented.last('D'))\n",
"lt_date = last_row.index[0]\n",
"#lt_value = last_row['fly'][0]\n",
"\n",
"# what happens if the last value is close to the\n",
"# 2 std band ?\n",
"lt_value = std_band*2+mean\n",
"\n",
"# what happens at the maximum level\n",
"lt_value = fly_augmented['fly'].max()\n",
"print ('the maximum fly level is:', lt_value)\n",
"\n",
"ax = fly_augmented.plot(style = ['-', 'y--', 'g--', 'g--', 'r--', 'r--'],\n",
" figsize = (9,5), legend ='reverse')\n",
"\n",
"# Draw the forward path 6 x half life as mentioned above\n",
"rng = pd.date_range(last_row.index[0], \n",
" periods=int(half_life*365.25*6), \n",
" freq='D')\n",
"rng_days = (rng - last_row.index[0])\n",
"fwd = pd.Series(rng).to_frame('fwd')\n",
"fwd['fwd_mu'] = fwd['fwd'].apply(lambda x: OUmu_t(lt_value, mean, theta, (x - lt_date).days/365.25 ))\n",
"fwd['fwd_std'] = fwd['fwd'].apply(lambda x: OUsigma_t(sigma, theta, (x - lt_date).days/365.25 ))\n",
"fwd['fwd_2p_std'] = fwd['fwd_mu'] + 2 * fwd['fwd_std']\n",
"fwd['fwd_2m_std'] = fwd['fwd_mu'] - 2 * fwd['fwd_std']\n",
"fwd = fwd.set_index('fwd')\n",
"fwd[['fwd_mu', 'fwd_2p_std', 'fwd_2m_std']].plot(ax = ax, style = ['y-.', 'g-.', 'g-.'])\n",
"\n"
],
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"text": [
"the maximum fly level is: 0.8200000000000003\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f54bdd77320>"
]
},
"metadata": {
"tags": []
},
"execution_count": 9
},
{
"output_type": "display_data",
"data": {
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ieZrAB2VtWsVNe6qYsyI+7ckCgcDFTUdP5Z3zl9Oz6wMhrTcgeyCPjH+ciuZybvl5MhZr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rsPvx65gs9+vWD8+9m7BmJwnwir12seZfXfdw7Ai1vYObFiQrxRUEKXsWhyCjb/cI4lwxehlaIo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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f54bb3bd748>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "hOUotm8CQt4P",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"In our example we used the maximum historical level of the time series as the 'starting point' of the forward Expected path. \n",
"\n",
"Note that even when the trade starts above the 2std band, the path can still go quite above it - traders have to keep this in mind when setting up stop losses - in this example the 2std forward standard deviation conditional on starting at 0.82 (the maximum historical level) reaches 1.00 at some point.\n",
"\n",
"The calibration returned values similar to the ones we were expecting, _but_ if the trader has a strong belief that the values should be something different she can reverse the functions to input her own parameters:\n",
"\n",
"$$ \\sigma =\\sqrt{2\\theta \\operatorname {var} (x(t)) }$$\n",
"$$ \\theta = {{\\operatorname {ln}(2)} \\over {\\operatorname{half life}}}$$\n",
"\n",
"With an automated way of computing parameters a trader can 'augment' his opportunity set.\n",
"\n",
"## Quick note on Profit and Stop Loss targets\n",
"Profit-taking targets are quite simple -- the target is usually a number on the way to the mean (and we can simulate many times).\n",
"\n",
"On the other hand, there is a counter-intuitive meaning to the forward expected paths **given** that we start at a level above the 2 standard deviation band: see the expected forward 2 standard deviation graph, and notice how it goes **higher** that the 3 standard (in this case roughly 90bps). Some traders will put the stop loss somewhat lower than the 3 standard deviation band with the belief that there is less than a 0.18% probability of it ever arriving there - and if it were to happen, then they would think the mean reversion was broken.\n",
"\n",
"By looking at the conditional path **given** we start from a high level, at one moment in time the probability of the trade going above 90bps will only be a 2 standard deviation event (roughly 2.3% - see [the 68-95-99.7 rule](https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule)) - so still 'unlucky', but **not** a black swan. \n",
"\n"
]
},
{
"metadata": {
"id": "tAZWTH53RraS",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"I get a few questions like the ones below: \n",
"\n",
"## Why are you using the API ? I thought python had loads of libraries already.\n",
"Markov's API uses numerical methods to compute the parameters; until very recently a few researchers used simplyfing assumptions to obtain an analytical formula, but by using a numerical optimization method and the current computing power available we can obtain results that remove the biases introduced by the simplifications, like:\n",
"\n",
"### Substituting the Ornstein-Uhlenbeck process with the discrete time AR(1) process\n",
"Because financial data is stored at discrete intervals, research was developed to find [analogues](https://math.stackexchange.com/questions/345773/how-the-ornstein-uhlenbeck-process-can-be-considered-as-the-continuous-time-anal) between the continuous process and the discrete time process. \n",
"\n",
"> In the case of Ornstein-Uhlenbeck (OU) the equivalent in discrete time is the 'AR(1) process' (Autoregressive 1st Order, a discrete model where the latest variable depends linearly on its previous value):\n",
"$$x_{k+1}=c + a x_{k}+ b \\varepsilon_k$$\n",
"where $x_k = x(k\\Delta t)$ ***assuming*** a discretization of OU at times $(k \\Delta t)_{k \\in N_0}$, $\\varepsilon_k$ is white noise and $a$, $b$ and $c$ are constant parameters. If you put $c=\\theta \\mu \\Delta t$, $a= - \\theta \\Delta t$ and $b=\\sigma \\sqrt{\\Delta t}$ you get\n",
"$$x_{k+1}=\\theta (\\mu - x_k) \\Delta t+\\sigma \\varepsilon_k \\sqrt{\\Delta t}$$\n",
" \n",
"Note the assumption implication that the price of the asset will be taken always at the same time interval.\n",
"\n",
"This assumption is quite important; some academic papers try to wave it away by mentioning 'weekly', monthly or another regular sampling of the underlying timeseries. In real life, traders like to see intraday and daily data and clearly understand that the news that impact the price can come at any time (overnight, and over the weekends).\n",
"\n",
"By claiming that the year can be divided by 252 business days in order to fit AR(1) methods, some researchers are throwing away valuable weekend and holiday information. The API used in the python example does not assume a constant sampling rate. \n",
"\n",
"Still, lots of derived research has been done using this discretized AR(1) process:\n",
"\n",
"* Analytic calibration methods, (useful if your only tool is Excel)\n",
"* Tests of mean reversion (if you want to know if the series is or not mean reverting),\n",
"* Tests to figure out if linear combinations of 2 or more series are mean reverting,\n",
"\n",
"and in the [next tutorial](https://colab.research.google.com/drive/1a1zFFd4MwZ8ljXtEE16JXyO8W4SWcS4P) we can use it to find out answer to the next FAQ:\n",
"\n",
"\n",
"\n"
]
},
{
"metadata": {
"id": "OmDHx1r4tHjf",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"## How can I find Mean Reverting tradeable signals ?\n",
"\n",
"(to be continued: [\"Mean Reversion: How to find it ?\"](https://colab.research.google.com/drive/1a1zFFd4MwZ8ljXtEE16JXyO8W4SWcS4P))"
]
}
]
}
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