analysis

class pydaddy.analysis.AutoCorrelation(**kwargs)

Bases: object

This class defines methods to calculate the _autocorrelation function of time series, fit an exponential curve to it and calculate the _autocorrealtion time.

Parameters: fft : bool If True, use fft method (wiener khinchin theorem) to calculate acf.

_acf(data, t_lag)

Get auto correaltion function for given data and lag t_lag

Parameters

  • data (array) – timeseries data

  • t_lag (int) – maxmium lag

Returns

  • x (array) – lags

  • c (array) – correlation values

Notes

If fft flag is set True and no valid fft points are found, the method uses standard formula method to calculate the autocorrealtion function

_acf_fft(data, t_lag)

Calculates autocorrelation using wiener khinchin theorem.

_act(X, t_lag=1000)

Get autocorrelation time of X.

_ccf(x, y, t_lag)

” Returns the cross-correlation function between x and y.

_fit_exp(x, y)

Fits an exponential function of the form a*exp((-1/b)*t) + c

Parameters

  • x (array) – x data

  • y (array) – y data

Returns

  • params (Tuple (a, b, c) containing the fitted parameters.)

  • cov (Covariance matrix of errors)

Notes

Reference : scipy.optimize.curve_fit

_get_autocorr_time(X, t_lag=1000, update=True)

Get the autocorrelation time of data X, for the analysis.

_nan_acf(data, t_lag)

Calculates autocorrealtion using the correaltion formula, ignoring all points with nan’s

_nan_ccf(data_x, data_y, t_lag)

Calculates cross-correlation using the correaltion formula, ignoring all points with nan’s

class pydaddy.analysis.GaussianTest(**kwargs)

Bases: pydaddy.analysis.UnderlyingNoise, pydaddy.metrics.Metrics, pydaddy.analysis.AutoCorrelation

Used to check if the noise is gaussian in nature

_get_critical_values(kl_dist)

Get critical values of null hypothesis, i.e values at the boundries of 2.5% and 97.5% of null hypothesis

_noise_analysis(X, Dt, dt, t_int, inc, point=0, **kwargs)

Check if noise is gaussian

Parameters

  • X (array) – timeseries data

  • Dt (int) – drift timescale

  • inc (float) – increment in order parameter of X

  • point (int) – point at which noise is to be extracted

Returns

  • gaussian_noise (bool) : True is the noise is gaussian

  • noise (array) : extracted noise

  • kl_dist (array) : null hypothesis uses

  • k (float) : test statistics used for test of hypothesis

  • l_lim (float) : lower critical limit

  • h_lim (float) : upper critical limit

  • noise_correlation (array) : noise autocorrelation

Return type

tuple

class pydaddy.analysis.UnderlyingNoise(**kwargs)

Bases: pydaddy.sde.SDE

Extract noise from time series

_noise(X, bins, avg_drift, inc, t_int, point=0)

Get noise from X at a paticular point

Parameters

  • X (array) – time series

  • inc (float) – binning increments

  • point (float) – point at which noise is to be extracted

  • Dt (int) – drift time scale

  • t_int (int) – time difference between consecutive observations

Returns

noise extracted from data at given point

Return type

array

_noise_vector(X, Y, bins_x, bins_y, avg_drift_x, avg_drift_y, inc_x, inc_y, t_int, point_x=0, point_y=0)
_residual_timeseries(X, bins, avg_drift, t_int)
_residual_timeseries_vector(X, Y, bins_x, bins_y, avg_drift_x, avg_drift_y, t_int)