T = 1
## Generate coupled Gaussian Random Walks
DF = coupled_random_walks( S1 = S1, S2 = S2, T = T,
N = N, mu1 = mu1, mu2 = mu2,
sigma1 = sigma1, sigma2 = sigma2,
alpha = SIMILARITY, epsilon = 0,
lag = LAG, seed = None)
## Difference data using % change (Gaussian transition probability distribution)
DF = DF.pct_change().iloc[1:]
## Calculate Linear TE using Geweke-Granger Causality Formula
PC = TransferEntropy(DF = DF,
endog = 'S2',
exog = 'S1',
lag = LAG)
PC.linear_TE(n_shuffles=N_SHUFFLES)
## Update results with linear TE from X->Y and from Y->X
(lTE[i,j,0], lTE[i,j,1]) = (PC.results['TE_linear_XY'], PC.results['TE_linear_YX'])
(lZ[i,j,0], lZ[i,j,1]) = (PC.results['z_score_linear_XY'], PC.results['z_score_linear_YX'])
## Note equiprobable bins is a misnomer; these bins are a marginal-equiprobable partition
AB = AutoBins(DF,LAG)
equal_bins = AB.equiprobable_bins(N_BINS)
## Calculate TE using information-theoretic method
PC.nonlinear_TE(pdf_estimator = 'histogram',
bins = equal_bins,
n_shuffles = N_SHUFFLES)
sigma1=0.5,
sigma2=0.25,
alpha=alpha,
epsilon=AUTOSIMILARITY,
lag=LAG,
seed=None)
## To get data which is Gaussian distributed, we use a scaled %-change with mu = 0
DF = DF.pct_change().iloc[1:]
#plot_pdf(DF,show=True)
## Initialise TE object
causality = TransferEntropy(
DF=DF,
endog='S2', # Dependent Variable
exog='S1', # Independent Variable
lag=LAG)
## Generate histogram bins
auto = AutoBins(DF[['S1', 'S2']], lag=LAG)
edges = auto.sigma_bins(max_bins=5)
## Calculate TE using Histogram
TE_Hists[observation,
i, :] = causality.nonlinear_TE(pdf_estimator='histogram',
bins=edges,
n_shuffles=N_SHUFFLES)
Z_Hists[observation, i, :] = (causality.results['z_score_XY'].iloc[0],
causality.results['z_score_YX'].iloc[0])
## Randomise initial conditions
S1 = np.random.rand()
S2 = np.random.rand()
DF = coupled_logistic_map(S1=S1,
S2=S2,
T=1,
N=N,
alpha=0.4,
epsilon=1,
r=4)
## Initialise TE object
causality = TransferEntropy(
DF=DF,
endog='S2', # Dependent Variable
exog='S1', # Independent Variable
lag=1)
## Calculate NonLinear TE
(TE_XY, TE_YX) = causality.nonlinear_TE(pdf_estimator='histogram',
bins=bins,
n_shuffles=N_SHUFFLES)
observations.append((TE_XY, TE_XY))
## Store average over multiple observations
observations = np.array(observations).reshape(N_OBSERVATIONS, 2)
TE_XYs.append(np.average(observations[:, 0]))
errors.append(np.std(observations[:, 0]))
DF.index = pd.to_datetime(DF.index, unit='s')
## Forward-Fill Missing Data
DF = DF[[SM,Return]].replace(0, np.nan).fillna(method='ffill')
## Difference the data using log-returns
DF[SM] = np.log(DF[SM]).diff()
DF[Return] = np.log(DF[Return]).diff()
DF = DF[1:-1]
## Initialise TE Objects
linearPC = TransferEntropy(DF = DF,
endog = Return,
exog = SM,
lag = LAG,
window_size = WINDOW_SIZE,
window_stride = WINDOWS_STRIDE)
nonlinearPC = TransferEntropy(DF = DF,
endog = Return,
exog = SM,
lag = LAG,
window_size = WINDOW_SIZE,
window_stride = WINDOWS_STRIDE)
## Calculate marginal equipartion
DF = LaggedTimeSeries(DF, LAG).df
auto = AutoBins(DF, LAG)
equal_bins = auto.equiprobable_bins(n_bins)
TEs_YX = []
z_scoresXY = []
z_scoresYX = []
##------------------------------ Compare TE at Different Lags ------------------------------##
for LAG in LAGs:
print('LAG', LAG)
## Create Lagged Time Series
DF = LaggedTimeSeries(walks, LAG).df
## Initialise TE object
linear_causality = TransferEntropy(
DF=DF,
endog='S2', # Dependent Variable
exog='S1', # Independent Variable
lag=LAG)
causality = TransferEntropy(
DF=DF,
endog='S2', # Dependent Variable
exog='S1', # Independent Variable
lag=LAG)
## Define Bins
bins = {
'S1': [-5, -2.5, -1, -0.5, 0, 0.5, 1, 2.5, 5],
'S1_lag' + str(LAG): [-5, -2.5, -1, -0.5, 0, 0.5, 1, 2.5, 5],
'S2': [-5, -2.5, -1, -0.5, 0, 0.5, 1, 2.5, 5],
'S2_lag' + str(LAG): [-5, -2.5, -1, -0.5, 0, 0.5, 1, 2.5, 5]
}
sigma1=0.05,
sigma2=0.05,
alpha=SIMILARITY,
epsilon=AUTOSIMILARITY,
lag=LAG,
seed=SEED)
## For Gaussian-Distributed data, a scaled %-change with mu = 0
DF = DF.pct_change().iloc[1:]
## Calculate TE for different bins
for j, n_bins in enumerate(N_BINS):
print('bins:', n_bins)
## Initialise TE objects
causality_equal = TransferEntropy(DF=DF,
endog='S2',
exog='S1',
lag=LAG)
causality_MIC = TransferEntropy(DF=DF,
endog='S2',
exog='S1',
lag=LAG)
causality_Sigma = TransferEntropy(DF=DF,
endog='S2',
exog='S1',
lag=LAG)
## Initialise bins
equal_bins = {
'S1':
list(np.linspace(DF['S1'].min(), DF['S1'].max(), n_bins + 1)),
'S1_lag' + str(LAG):