def mc_ar1_spectrum(self,
data=None,
N=1000,
filter_type=None,
filter_cutoff=None,
spectrum='mtm'):
""" calculates the Monte-Carlo spectrum
with 1, 2.5, 5, 95, 97.5, 99 percentiles
input:
x .. time series
spectrum .. spectral density estimation function
N .. number of MC simulations
filter_type ..
filter_cutoff ..
spectrum .. 'mtm': multi-taper method, 'per': periodogram, 'Welch'
output:
mc_spectrum ..
"""
if data is None: data = np.array(self.ts)
assert type(data) == np.ndarray
AM = ARMA(endog=data, order=(1, 0)).fit()
phi, std = AM.arparams[0], np.sqrt(AM.sigma2)
mc = self.mc_ar1_ARMA(phi=phi, std=std, n=len(data), N=N)
if filter_type is not None:
assert filter_type in ['lowpass', 'chebychev']
assert type(filter_cutoff) == int
assert filter_cutoff > 1
n = int(
filter_cutoff / 2
) + 1 # datapoints to remove from either end due to filter edge effects
mc = mc[:, n:-n]
if filter_type == 'lowpass': mc = lowpass(mc.T, filter_cutoff).T
elif filter_type == 'chebychev':
mc = chebychev(mc.T, filter_cutoff).T
if spectrum == 'mtm': freq, _ = self.mtspectrum()
elif spectrum == 'per': freq, _ = self.periodogram()
elif spectrum == 'Welch': freq, _ = self.Welch()
mc_spectra = np.zeros((N, len(freq)))
# mc_spectra = np.zeros((N, int(len(mc[0,:])/2)+1))#int(self.len/2)+1))
for i in range(N):
if spectrum == 'mtm':
freq, mc_spectra[i, :] = self.mtspectrum(data=mc[i, :])
elif spectrum == 'per':
freq, mc_spectra[i, :] = self.periodogram(data=mc[i, :])
elif spectrum == 'Welch':
freq, mc_spectra[i, :] = self.Welch(data=mc[i, :])
mc_spectrum = {}
mc_spectrum['median'] = np.median(mc_spectra, axis=0)
mc_spectrum['freq'] = freq
for p in [1, 2.5, 5, 95, 97.5, 99]:
mc_spectrum[str(p)] = np.percentile(mc_spectra, p, axis=0)
return mc_spectrum
def filter_timeseries(self, data, filter_type, filter_cutoff):
assert filter_type in ['lowpass', 'chebychev']
assert type(filter_cutoff) == int
assert filter_cutoff > 1
n = int(
filter_cutoff / 2
) + 1 # datapoints to remove from either end due to filter edge effects
if filter_type == 'lowpass': data = lowpass(data, filter_cutoff)[n:-n]
elif filter_type == 'chebychev':
data = chebychev(data, filter_cutoff)[n:-n]
return data