Close

# Linear Regression Lines

Overview Linear regression is a statistical tool used to predict future values from past values. In the case of security prices, it is commonly used to determine when prices are overextended. A Linear Regression trendline uses the least squares method to plot a straight line through prices so as to […]

# Linear Regression

This tutorial written and reproduced with permission from Peter Ponzo We assume that some set of variables, y1, y2, … yK, is dependent upon variables xk1, xk2, … xkn (for k = 1 to K). We assume the relationship betwen the ys and xs is “almost” linear, like so: [1] y1 = ß0 + ß1×11 + ß2×12 + … +ßnx1n + e1 y2 = ß0 + ß1×21 + ß2×22 + … +ßnx2n + e2 …….. yK = ß0 + ß1xK1 + ß2xK2 + … […]

# Kurtosis

This tutorial written and reproduced with permission from Peter Ponzo I want to talk about a total Portfolio gain, over N years (or days or months), and how it depends upon the MEAN return and the distribution of returns and … Like Normal of Lognormal stuff? Yes. Suppose that the […]

# Johnson Curves

This tutorial written and reproduced with permission from Peter Ponzo I’ve never been enthusiastic about the common assumptions that stock returns are distributed normally or lognormally or … whatever. For example, the normal and lognormal distributions look like Figure 1a. The normal density distribution is described by:   [1]   […]

# Ito Calculus

This tutorial written and reproduced with permission from Peter Ponzo   Kiyosi Ito studied mathematics in the Faculty of Science of the Imperial University of Tokyo, graduating in 1938. In the 1940s he wrote several papers on Stochastic Processes and, in particular, developed what is now called Ito Calculus. I haven’t […]