Toolkit.py

import numpy as np

def Wiener(dt=1,X0=0,num_steps=10000, mu=0, sigma=1):
    '''
    dt: Time step
    X0: Starting Point
    num_steps: Number of steps
    mu: Mean of Gaussian
    sigma: STD of Gaussian
    '''
    # create result array
    res = np.zeros(num_steps)
    # initialize start value
    res[0] = X0
    # calculate and store time series
    for t in range(1,num_steps):
        res[t] = res[t-1] + np.random.normal(mu,sigma)*dt

    # return time series
    return res
    
def OU(dt=1, X0=0, num_steps= 10000, alpha=0.5, mu=0, sigma=0.5):
    '''
    dt: Time step
    X0: Starting Point
    num_steps: Number of steps
    alpha: oscillation parameter
    mu: Mean of Gaussian
    sigma: STD of Gaussian
    '''
    res = np.zeros(num_steps)
    res[0] = X0
    for t in range(1,num_steps):
        res[t] = alpha*res[t-1]*dt + sigma*np.random.normal(mu,sigma)
    return res

def WhiteNoise(X0=0,num_steps=1000, mu=0, sigma=1,a=1.):
    '''
    X0: Starting Point
    num_steps: Number of steps
    mu: Mean of Gaussian
    sigma: STD of Gaussian
    a: amplification parameter
    '''
    # create result array
    res = np.zeros(num_steps)
    # initialize start value
    res[0] = X0
    # calculate and store time series
    for t in range(1,num_steps):
        res[t] = a*np.random.normal(mu,sigma)

    # return time series
    return res

def AutocorrelationFunction(x, lag=20):
    '''
    x: Input Data
    lag: Time lag
    '''
    return np.array([1]+[np.corrcoef(x[:-i], x[i:])[0,1] for i in range(1, lag)])


def MovingAverage(timeseries,lag=3):
    '''
        Calculates The Simple Moving Average (SMA) of a timeseries with a certain lag.
        timeseries: The timeseries data to impliment the Simple Moving Average (SMA).
        lag: The lag to use for the Simple Moving Average (SMA).
    '''
    ma = np.empty(len(timeseries))
    ma[:] = np.nan
    for i in range(lag,len(timeseries) - lag):
        ma[i] = np.mean(timeseries[i-lag//2:i+lag//2+1])
    return ma

def VarianceFunction(x, lag):
    return [np.var((np.cumsum(np.insert(x, 0, 0))[i:] - np.cumsum(np.insert(x, 0, 0))[:-i] )/ float(i))/np.var(x)
            for i in range(1, lag + 1)]


def sin(t,T=2*np.pi,A=1):
    '''
    A: Amplitude
    T: Period
    t: time-steps
    '''
    return A*np.sin(2*np.pi/T*t)