Random Walk
In this chapter, we discuss some statistical properties used in Econophysics. Econophysics explore how socio-economic systems can be studied from a physicist’s perspective. This course presents the approach adopted by physicists to analyze and model financial markets.
- 1D Random Walk
- Gaussian Process
- Speed of Convergence
- Berry - Essen Theorem 1,2
Stochastic Processes
This section, we discuss types of stable distribution. A specific type of distribution encountered in the sum of n IID random variables that has the property that it does not change its functional form for different values of n.
- Lorentzian and Gaussian Distributions
- Characteristic function of stable process
- Scaling and Self-similarity
- Power Laws
Scales in financial data
This section, we discuss nature of financial data and statistical analyses to understand market dynamics. Also, applied reasons related to the key problems of option pricing and portfolio management.
- Rate of Return
Stationarity and time correlation
In this chapter we consider the degree of stationarity observed in time series of price changes in finacial markets. We take a similar approach concerning time correlation, classes of correlation of short-range and long-range correlated stochastic processes.
- Correlation
- Long and short range correlation
- Autocorrelation function and spectral density