{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Statistical Moments - Skewness and Kurtosis\n",
"## Bonus: Jarque-Bera Normality Test\n",
"By Evgenia \"Jenny\" Nitishinskaya, Maxwell Margenot, and Delaney Granizo-Mackenzie.\n",
"\n",
"Part of the Quantopian Lecture Series:\n",
"\n",
"* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n",
"* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n",
"\n",
"Notebook released under the Creative Commons Attribution 4.0 License."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import scipy.stats as stats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sometimes mean and variance are not enough to describe a distribution. When we calculate variance, we square the deviations around the mean. In the case of large deviations, we do not know whether they are likely to be positive or negative. This is where the skewness and symmetry of a distribution come in. A distribution is symmetric if the parts on either side of the mean are mirror images of each other. For example, the normal distribution is symmetric. The normal distribution with mean $\\mu$ and standard deviation $\\sigma$ is defined as\n",
"$$ f(x) = \\frac{1}{\\sigma \\sqrt{2 \\pi}} e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}} $$\n",
"We can plot it to confirm that it is symmetric:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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smga3VhewPBEA5mraknPixAk1NjbqwIEDcrlcevnll3XgwIGp9//4xz/Wm2++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\nAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot a normal distribution with mean = 0 and standard deviation = 2\n",
"xs = np.linspace(-6,6, 300)\n",
"normal = stats.norm.pdf(xs)\n",
"plt.plot(xs, normal);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A distribution which is not symmetric is called skewed. For instance, a distribution can have many small positive and a few large negative values (negatively skewed) or vice versa (positively skewed), and still have a mean of 0. A symmetric distribution has skewness 0. Positively skewed unimodal (one mode) distributions have the property that mean > median > mode. Negatively skewed unimodal distributions are the reverse, with mean < median < mode. All three are equal for a symmetric unimodal distribution.\n",
"\n",
"The explicit formula for skewness is:\n",
"$$ S_K = \\frac{n}{(n-1)(n-2)} \\frac{\\sum_{i=1}^n (X_i - \\mu)^3}{\\sigma^3} $$\n",
"\n",
"Where $n$ is the number of observations, $\\mu$ is the arithmetic mean, and $\\sigma$ is the standard deviation. The sign of this quantity describes the direction of the skew as described above. We can plot a positively skewed and a negatively skewed distribution to see what they look like. For unimodal distributions, a negative skew typically indicates that the tail is fatter on the left, while a positive skew indicates that the tail is fatter on the right."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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KJU446L4ZFjMCtHX2o6ymHVOi/aB2dey1nheTJAkPLxveyLbuW8f86wIRERFd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vgBW7Zswcsvv4yxsTG89NJLePTRR6s9LWoAH330EZqbm6s9DWoADz74ID788MOyxlYszJw4cQI9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\nnAAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate x-values for which we will plot the distribution\n",
"xs2 = np.linspace(stats.lognorm.ppf(0.01, .7, loc=-.1), stats.lognorm.ppf(0.99, .7, loc=-.1), 150)\n",
"\n",
"# Negatively skewed distribution\n",
"lognormal = stats.lognorm.pdf(xs2, .7)\n",
"plt.plot(xs2, lognormal, label='Skew > 0')\n",
"\n",
"# Positively skewed distribution\n",
"plt.plot(xs2, lognormal[::-1], label='Skew < 0')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Although skew is less obvious when graphing discrete data sets, we can still compute it. For example, below are the skew, mean, and median for S&P 500 returns 2012-2014. Note that the skew is negative, and so the mean is less than the median."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Skew: -0.208327061229\n",
"Mean: 0.000732549262327\n",
"Median: 0.000805529770079\n"
]
},
{
"data": {
"image/png": 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T8+abb/7S25O3vrHdvXv3odsuv/zy3HPPPbnhhhtavSot1Ow5mDRpUqZOnZok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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"start = '2012-01-01'\n",
"end = '2015-01-01'\n",
"pricing = get_pricing('SPY', fields='price', start_date=start, end_date=end)\n",
"returns = pricing.pct_change()[1:]\n",
"\n",
"print 'Skew:', stats.skew(returns)\n",
"print 'Mean:', np.mean(returns)\n",
"print 'Median:', np.median(returns)\n",
"\n",
"plt.hist(returns, 30);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Kurtosis\n",
"\n",
"Kurtosis attempts to measure the shape of the deviation from the mean. Generally, it describes how peaked a distribution is compared the the normal distribution, called mesokurtic. All normal distributions, regardless of mean and variance, have a kurtosis of 3. A leptokurtic distribution (kurtosis > 3) is highly peaked and has fat tails, while a platykurtic distribution (kurtosis < 3) is broad. Sometimes, however, kurtosis in excess of the normal distribution (kurtosis - 3) is used, and this is the default in `scipy`. A leptokurtic distribution has more frequent large jumps away from the mean than a normal distribution does while a platykurtic distribution has fewer."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Excess kurtosis of leptokurtic distribution: 3.0\n",
"Excess kurtosis of mesokurtic distribution: 0.0\n",
"Excess kurtosis of platykurtic distribution: -0.593762875598\n"
]
},
{
"data": {
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a5yBzskmRqfzy0vuZFpXG1sJd/OLTp6lrqe94z86OZjnaPFNEZFRSmBERkX6z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\nCCGEEEKILkmSGSGEEEIIIUSX9P/SxzzhlH+L4wAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot some example distributions\n",
"plt.plot(xs,stats.laplace.pdf(xs), label='Leptokurtic')\n",
"print 'Excess kurtosis of leptokurtic distribution:', (stats.laplace.stats(moments='k'))\n",
"plt.plot(xs, normal, label='Mesokurtic (normal)')\n",
"print 'Excess kurtosis of mesokurtic distribution:', (stats.norm.stats(moments='k'))\n",
"plt.plot(xs,stats.cosine.pdf(xs), label='Platykurtic')\n",
"print 'Excess kurtosis of platykurtic distribution:', (stats.cosine.stats(moments='k'))\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"The formula for kurtosis is\n",
"$$ K = \\left ( \\frac{n(n+1)}{(n-1)(n-2)(n-3)} \\frac{\\sum_{i=1}^n (X_i - \\mu)^4}{\\sigma^4} \\right ) $$\n",
"\n",
"while excess kurtosis is given by\n",
"$$ K_E = \\left ( \\frac{n(n+1)}{(n-1)(n-2)(n-3)} \\frac{\\sum_{i=1}^n (X_i - \\mu)^4}{\\sigma^4} \\right ) - \\frac{3(n-1)^2}{(n-2)(n-3)} $$\n",
"\n",
"For a large number of samples, the excess kurtosis becomes approximately\n",
"\n",
"$$ K_E \\approx \\frac{1}{n} \\frac{\\sum_{i=1}^n (X_i - \\mu)^4}{\\sigma^4} - 3 $$\n",
"\n",
"Since above we were considering perfect, continuous distributions, this was the form that kurtosis took. However, for a set of samples drawn for the normal distribution, we would use the first definition, and (excess) kurtosis would only be approximately 0.\n",
"\n",
"We can use `scipy` to find the excess kurtosis of the S&P 500 returns from before."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Excess kurtosis of returns: 1.21431979997\n"
]
}
],
"source": [
"print \"Excess kurtosis of returns: \", stats.kurtosis(returns)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The histogram of the returns shows significant observations beyond 3 standard deviations away from the mean, multiple large spikes, so we shouldn't be surprised that the kurtosis is indicating a leptokurtic distribution."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Other standardized moments\n",
"\n",
"It's no coincidence that the variance, skewness, and kurtosis take similar forms. They are the first and most important standardized moments, of which the $k$th has the form\n",
"$$ \\frac{E[(X - E[X])^k]}{\\sigma^k} $$\n",
"\n",
"The first standardized moment is always 0 $(E[X - E[X]] = E[X] - E[E[X]] = 0)$, so we only care about the second through fourth. All of the standardized moments are dimensionless numbers which describe the distribution, and in particular can be used to quantify how close to normal (having standardized moments $0, \\sigma, 0, \\sigma^2$) a distribution is."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Normality Testing Using Jarque-Bera\n",
"\n",
"The Jarque-Bera test is a common statistical test that compares whether sample data has skewness and kurtosis similar to a normal distribution. We can run it here on the S&P 500 returns to find the p-value for them coming from a normal distribution.\n",
"\n",
"The Jarque Bera test's null hypothesis is that the data came from a normal distribution. Because of this it can err on the side of not catching a non-normal process if you have a low p-value. To be safe it can be good to increase your cutoff when using the test.\n",
"\n",
"Remember to treat p-values as binary and not try to read into them or compare them. We'll use a cutoff of 0.05 for our p-value.\n",
"\n",
"## Test Calibration\n",
"\n",
"Remember that each test is written a little differently across different programming languages. You might not know if it's the null or alternative hypothesis that the tested data come from a normal distribution. It is recommended that you use the `?` notation plus online searching to find documentation on the test; plus it is often a good idea to calibrate a test by checking it on simulated data and making sure it gives the right answer. Let's do that now."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.054\n"
]
}
],
"source": [
"from statsmodels.stats.stattools import jarque_bera\n",
"\n",
"N = 1000\n",
"M = 1000\n",
"\n",
"pvalues = np.ndarray((N))\n",
"\n",
"for i in range(N):\n",
" # Draw M samples from a normal distribution \n",
" X = np.random.normal(0, 1, M);\n",
" _, pvalue, _, _ = jarque_bera(X)\n",
" pvalues[i] = pvalue\n",
" \n",
"# count number of pvalues below our default 0.05 cutoff\n",
"num_significant = len(pvalues[pvalues < 0.05])\n",
"\n",
"print float(num_significant) / N"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Great, if properly calibrated we should expect to be wrong $5\\%$ of the time at a 0.05 significance level, and this is pretty close. This means that the test is working as we expect."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The returns are likely not normal.\n"
]
}
],
"source": [
"_, pvalue, _, _ = jarque_bera(returns)\n",
"\n",
"if pvalue > 0.05:\n",
" print 'The returns are likely normal.'\n",
"else:\n",
" print 'The returns are likely not normal.'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This tells us that the S&P 500 returns likely do not follow a normal distribution."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*"
]
}
],
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