ARFIMA model for log stock prices:

• Fractionally differences a stock price (uses a fixed window)
• Fits an ARMA model on it (using the Hannan–Rissanen algorithm)
• Tests the residual autocorrelation, whether there are ARCH effects, and coefficient significance

Hidden Markov Model (observed data distributed according to Gaussian) - fit with Gibbs Sampler

• Fits a hidden markov model (2 hidden states, observed data is normally distributed) to time series data using a gibbs sampler
• Within the gibbs sampler used Metropolis-Hastings jumps
• Finds the optimal parameters (besides the hidden states) by finding the mean of the samples
• Finds the optimal hidden states using the Viterbi Algoirthm (implemented so that probabilities are also returned)

Beta:

• find a relationship coefficient between different time series (takes into account the need to difference the time series if the residuals are not stationary)

Implements:

• Dickey-Fuller test (unit-root test / stationarity test)
• Ljung-Box test (significant autocorrelation test)
• ARCH test (conditionally heteroskedasticity test)
• Lo-modified Rescaled Range (long term memory test)
• Multi-Regression coefficient p-test
• autocorrelation calculation
• multiple distributions