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    "## Method of Moment Estimation\n",
    "\n",
    "**Functions**\n",
    "\n",
    "`DataFrame.mean`, `DatFrame.sum`, `plt.subplots`, `plt.plot`, `stats.kurtosis`, `stats.skewness`\n",
    "\n",
    "### Exercise 16\n",
    "Estimate the mean, variance, skewness and kurtosis of the S&P 500 and Hang Seng using\n",
    "the method of moments using monthly data."
   ]
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    "### Exercise 17\n",
    "Estimate the asymptotic covariance of the mean and variance of the two series (separately,\n",
    "but not the skewness and kurtosis). "
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    "### Exercise 18\n",
    "Estimate the Sharpe ratio of the two series and compute the asymptotic variance of\n",
    "the Sharpe ratio. See Chapter 2 of the notes for more on this problem.\n",
    "\n",
    "\n",
    "The asymptotic variance is computed as \n",
    "\n",
    "$$ D \\Sigma D^\\prime$$\n",
    "\n",
    "where\n",
    "\n",
    "$$ D = [\\sigma^{-1}, -1/2 \\mu \\sigma^{-3} ] $$\n",
    "\n",
    "and $\\Sigma$ is the asymptotic covariance of the mean and variance. Finally, we\n",
    "divide by $n$ the sample size when computing the statistic variance. "
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    "\n",
    "### Exercise 19\n",
    "Plot rolling estimates of the four moments using 120 months of consecutive data using a\n",
    "4 by 1 subplot against the dates.\n",
    "\n",
    "The simple approach to this problem uses a loop across 120, 121, ..., $n$ and computes\n",
    "the statistics using 120 observations. The figure is then created with a call to `plt.subplots`\n",
    "and the series can be directly plotted by calling `ax.plot`.\n",
    "\n",
    "The pandas-centric approach uses teh `rolling` method to compute rolling statistics and\n",
    "then uses `.plot.line` with `subplots=True` to produce the plot."
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