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