public:courses:finance:computational_finance:descriptive_statistics

Week5 - Descriptive Statistics

  • Recall:
    • \(E[X_t] = \mu\) indep of t.
    • \(var(X_t) = \sigma^2\) indep of t.
    • \(cov(X_t,X_{t-j}) = \gamma_j\) indep of t.
    • \(cor(X_t,X_{t-j}) = \rho_j\) indep of t.
  • In SP500, the capitalization of each company is used to compute the weight for that company in the “SP500 portfolio”: \(w_i = \frac{cap_i}{\sum\limits_j cap_j}\)
  • The volativity of SP500 is also called market volatility.
  • Descriptive statistics = data summaries (we try to compute some features from the data).
  • We can build blockly histograms or smoothed histograms.
  • We can infer the mean, deviation, skewness and kurtosis from the histograms.
  • Sample quantile is often called empirical quantile or percentile.
  • q.25 is the first quartile
  • q.50 is the second quartile (or median)
  • q.75 is the third quartile
  • q.75 - q.25 is the interquartile range (IQR)
  • eg. value at risk computed from the data (eg. from empirical quantiles).
  • We can compute Sample mean, variance, std deviation, skewness, kurtosis and excess kurtosis.
  • public/courses/finance/computational_finance/descriptive_statistics.txt
  • Last modified: 2020/07/10 12:11
  • (external edit)