StuartGordonReid

#' @title A more efficient estimator for the value of sigma. Sigma is the 
#' standard deviation of the random component of returns in the Geometric 
#' Brownian Motion model. This estimate can be calculated in an unbiased manner.
#' 
#' @description Given a log price process and a parameter, q, which specifies 
#' the sampling intervel this function estimates the value of Sigma. Sigma 
#' represents the standarddeviation of the random disturbance component of 
#' daily  returns. This estimate can be annualized and can be computed in 
#' a biased or unbiased manner.
#' 

StuartGordonReid

#' @title Estimator for the value of sigma. Sigma is the standard deviation of 
#' the random component of returns in the Geometric Brownian Motion model. This 
#' estimate can be calculated in a biased or unbiased manner.
#' 
#' @description Given a log price process and a parameter, q, which specifies 
#' the sampling intervel this function estimates the value of Sigma. Sigma 
#' represents the standarddeviation of the random disturbance component of daily 
#' returns. This estimate can be annualized and can be computed in a biased or 
#' unbiased manner.
#' 

StuartGordonReid

#' @title Estimator for the value of mu. Mu is the drift component in the 
#' Geometric Brownian Motion model.
#' 
#' @description Given a log price process, this function estimates the value of 
#' mu. Mu is the daily component of the returns which is attributable to upward, 
#' or downward, drift. This estimate can be annualized.
#' 
#' @param X vector :: A log price process.
#' @param annualize logical :: Annualize the parameter estimate.
#' @return mu.est double :: The estimated value of mu.

StuartGordonReid

# Plot fifteen asset price paths without stochastic volatility.
charts.PerformanceSummary(returnProcesses(15, t = (252*5), 
                                          stochastic.volatility = FALSE), 
                          colorset = seq(1,15))

# Plot fifteen asset price paths with stochastic volatility.
charts.PerformanceSummary(returnProcesses(15, t = (252*5), 
                                          stochastic.volatility = TRUE), 
                          colorset = seq(1,15))

StuartGordonReid

# Load the required packages.
library(PerformanceAnalytics)
library(xts)


#' @title Sample a random disturbance from either a normal distribution with a 
#' constant standard deviation (Geometric Brownian Motion model) or from a 
#' distribution with a stochastic standard deviation (Stochastic Volatility GBM)
#' 
#' @description Given a long run random disturbance mean, mu, and a standard 

StuartGordonReid

def random_excursions_variant(self, bin_data):
    """
    Note that this description is taken from the NIST documentation [1]
    [1] http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf

    The focus of this test is the total number of times that a particular state is visited (i.e., occurs) in a
    cumulative sum random walk. The purpose of this test is to detect deviations from the expected number of visits
    to various states in the random walk. This test is actually a series of eighteen tests (and conclusions), one
    test and conclusion for each of the states: -9, -8, …, -1 and +1, +2, …, +9.

StuartGordonReid

def random_excursions(self, bin_data):
    """
    Note that this description is taken from the NIST documentation [1]
    [1] http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf

    The focus of this test is the number of cycles having exactly K visits in a cumulative sum random walk. The
    cumulative sum random walk is derived from partial sums after the (0,1) sequence is transferred to the
    appropriate (-1, +1) sequence. A cycle of a random walk consists of a sequence of steps of unit length taken at
    random that begin at and return to the origin. The purpose of this test is to determine if the number of visits
    to a particular state within a cycle deviates from what one would expect for a random sequence. This test is

StuartGordonReid

def cumulative_sums(self, bin_data: str, method="forward"):
    """
    Note that this description is taken from the NIST documentation [1]
    [1] http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf

    The focus of this test is the maximal excursion (from zero) of the random walk defined by the cumulative sum of
    adjusted (-1, +1) digits in the sequence. The purpose of the test is to determine whether the cumulative sum of
    the partial sequences occurring in the tested sequence is too large or too small relative to the expected
    behavior of that cumulative sum for random sequences. This cumulative sum may be considered as a random walk.
    For a random sequence, the excursions of the random walk should be near zero. For certain types of non-random

StuartGordonReid

def approximate_entropy(self, bin_data: str, pattern_length=10):
    """
    Note that this description is taken from the NIST documentation [1]
    [1] http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf

    As with the Serial test of Section 2.11, the focus of this test is the frequency of all possible overlapping
    m-bit patterns across the entire sequence. The purpose of the test is to compare the frequency of overlapping
    blocks of two consecutive/adjacent lengths (m and m+1) against the expected result for a random sequence.

    :param bin_data: a binary string

StuartGordonReid

def serial(self, bin_data, pattern_length=16, method="first"):
    """
    Note that this description is taken from the NIST documentation [1]
    [1] http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf

    The focus of this test is the frequency of all possible overlapping m-bit patterns across the entire
    sequence. The purpose of this test is to determine whether the number of occurrences of the 2m m-bit
    overlapping patterns is approximately the same as would be expected for a random sequence. Random
    sequences have uniformity; that is, every m-bit pattern has the same chance of appearing as every other
    m-bit pattern. Note that for m = 1, the Serial test is equivalent to the Frequency test of Section 2.1.