ab kf

ab_kf.py

def fit_ab_kf(single_cumulative_returns,dex_cumulative_returns):
    n_steps = len(dex_cumulative_returns)

    A = np.matrix([[1,0],[0,1]])
    # Transition matrix is dependent on previous B0/B1 with no inherent cross dependency
    
    C = map(lambda x: np.matrix(np.append(1,x[0])),np.reshape(dex_cumulative_returns,(n_steps,1,1)))
    # Observation matrix is tensor of [1,x_t] (of length equal to our observations)
    
    # Initial hidden state means are 0 for intercept and 1 for slope
    
    # Initial coverariance estimates aren't terribly critical, I've picked just two small numbers
    
    # Transition covariance describes the B0 and B1 variances -- these can be estimated from 
    # inverse of covariance matrix (preicison matrix)
    
    kf = pykalman.KalmanFilter(transition_matrices=[A for i in xrange(n_steps)],
                      observation_matrices=C,
                      observation_covariance=np.eye(1)*1e-3,
                      transition_covariance = np.eye(2)*1e-5,
                      initial_state_mean=np.array([0,1]),
                      initial_state_covariance = np.eye(2)*1e-5)
    (filtered_state_means, filtered_state_covariances)=kf.filter(np.reshape(single_cumulative_returns,(n_steps,1)))
    kf_theos = (filtered_state_means[:,1]*dex_cumulative_returns+filtered_state_means[:,0])
    return kf_theos