pyamr.core.stats package

Submodules

pyamr.core.stats.adfuller module

Classes:

ADFWrapper([estimator, evaluate])

The Augmented Dickey-Fuller test can be used to test for a unit root in a univariate process in the presence of serial correlation.

class pyamr.core.stats.adfuller.ADFWrapper(estimator=None, evaluate=True)

Bases: BaseWrapper

The Augmented Dickey-Fuller test can be used to test for a unit root in a univariate process in the presence of serial correlation. It tests the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity. The more negative the statistic, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence.

H	Hypothesis	Stationarity
H0	The series has a unit root	Non-stationary
H1	The series has no unit root	Stationary / Trend-Stationary

If p-value > 0.05: Failed to reject H0.

If p-value <= 0.05: Reject H0.

The absence of unit root is not a proof of non-stationarity. As such, it is also possible to use the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test to identify the existence of an underlying trend which can also be removed to obtain a stationary process. These are called trend-stationary processes.

In both, unit-root and trend-stationary processes, the mean can be increasing or decreasing over time; however, in the presence of a shock, trend-stationary processes revert to this mean tendency in the long run (deterministic trend) while unit-root processes have a permanent impact (stochastic trend).

Methods:

as_summary([alpha, verbose])	This method creates the summary to display.
evaluate(**kwargs)	Evaluates the model.
is_stationary([alpha])	This method returns a boolean with the stationarity outocme.
stationarity([alpha])	This method returns the stationarity outcome.

as_summary(alpha=0.05, verbose=1, **kwargs)

This method creates the summary to display.

evaluate(**kwargs)

Evaluates the model.

is_stationary(alpha=0.05)

This method returns a boolean with the stationarity outocme.

Parameters:

alpha (float) – The statistical significance

stationarity(alpha=0.05)

This method returns the stationarity outcome.

Parameters:

alpha (float) – The stastistical significance

pyamr.core.stats.correlation module

Classes:

CorrelationWrapper([estimator, evaluate])

The Pearson Correlation Coefficient measures the linear correlation between two variables with a value within the range [-1,1].

class pyamr.core.stats.correlation.CorrelationWrapper(estimator=None, evaluate=True)

Bases: BaseWrapper

The Pearson Correlation Coefficient measures the linear correlation between two variables with a value within the range [-1,1]. Coefficient values of -1, 0 and 1 indicate total negative linear correlation, no inear correlation and total positive correlation respectively. In this study, the coefficient is used to assess whether or not there is a linear correlation between the number of observations (susceptibility test records) and the computed resistance index.

The Spearman Correlation Coefficient…

The Cross-Correlation ….

Methods:

as_summary([alpha])	This method displays the summary.
evaluate([alpha])	This method sets all the variables into this class.
fit(x1, x2, **kwargs)	This method computes kendall for monotonic increase

as_summary(alpha=0.05)

This method displays the summary.

evaluate(alpha=0.05)

This method sets all the variables into this class.

fit(x1, x2, **kwargs)

This method computes kendall for monotonic increase

Note

the pvalues produced by scipy are not reliable if less than 500 observations.

Parameters:

• x1 (np.array) – Variable x1

• y2 (np.array) – Variable y2

Returns:

object

Return type:

A CorrelationWrapper objects.

pyamr.core.stats.kendall module

Classes:

KendallWrapper([estimator, evaluate])

The Kendall statistical test, also known as Kendall's rank correlation test or Kendall's tau test, is a nonparametric statistical test used to assess the strength and direction of association between two variables.

Functions:

kendall(x)

Computes the kendall statistical test

class pyamr.core.stats.kendall.KendallWrapper(estimator=None, evaluate=True)

Bases: BaseWrapper

The Kendall statistical test, also known as Kendall’s rank correlation test or Kendall’s tau test, is a nonparametric statistical test used to assess the strength and direction of association between two variables. It is particularly suited for analyzing ranked or ordinal data, where the values of the variables are ranked or ordered but not necessarily quantitatively measurable. The coefficient ranges from -1 to +1, where a value of +1 indicates a perfect positive rank correlation, -1 indicates a perfect negative rank correlation, and 0 indicates no rank correlation.

Methods:

as_summary([alpha])	This method displays the summary.
evaluate([alpha])	Evaluates the model for the specified alpha.
trend_direction(alpha)	This method returns the trend direction.
trend_exists(alpha)	This method returns a boolean with the stationarity outocme.

as_summary(alpha=0.05)

This method displays the summary.

evaluate(alpha=0.05, **kwargs)

Evaluates the model for the specified alpha.

trend_direction(alpha)

This method returns the trend direction.

Parameters:

alpha (float) – The significance level

trend_exists(alpha)

This method returns a boolean with the stationarity outocme.

Parameters:

alpha (float) – The significance level

pyamr.core.stats.kendall.kendall(x)

Computes the kendall statistical test

Parameters:

• x (a vector of data)

• alpha (significance level (0.05 default))

Returns:

• trend (tells the trend (increasing, decreasing or no trend))

• h (True (if trend is present) or False (if trend is absence))

• p (p value of the significance test)

• z (normalized test statistics)

pyamr.core.stats.kpss module

Classes:

KPSSWrapper([estimator, evaluate])

The Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test is used to identify whether a time series is stationary around a deterministic trend (thus trend stationary) against the alternative of a unit root.

class pyamr.core.stats.kpss.KPSSWrapper(estimator=None, evaluate=True)

Bases: BaseWrapper

The Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test is used to identify whether a time series is stationary around a deterministic trend (thus trend stationary) against the alternative of a unit root.

In the KPSS test, the absence of a unit root is not a proof of stationarity but, by design, of trend stationarity. This is an important distinction since it is possible for a time series to be non-stationary, have no unit root yet be trend-stationary.

In both, unit-root and trend-stationary processes, the mean can be increasing or decreasing over time; however, in the presence of a shock, trend-stationary processes revert to this mean tendency in the long run (deterministic trend) while unit-root processes have a permanent impact (stochastic trend).

H	Hypothesis	Stationarity
H0	The series has no unit root	Trend-stationary
H1	The series has a unit root	No Trend-Stationary

If p-value > alpha: Failed to reject H0

If p-value <= alpha: Reject H0

pyamr.core.stats.stationarity module

Classes:

StationarityWrapper([estimator, evaluate])

In time series analysis, "stationarity" refers to a key assumption about the behavior of a time series over time.

class pyamr.core.stats.stationarity.StationarityWrapper(estimator=None, evaluate=True)

Bases: BaseWrapper

In time series analysis, “stationarity” refers to a key assumption about the behavior of a time series over time. A stationary time series is one in which statistical properties, such as mean, variance, and autocorrelation, remain constant over time. Stationarity is an important concept because many time series analysis techniques rely on this assumption for their validity. There are different types of stationarity that can be observed in time series data.

The augmented Dickey–Fuller test or ADF can be used to determine the presence of a unit root. When the other roots of the characteristic function lie inside the unit circle the first difference of the process is stationary. Due to this property, these are also called difference-stationary processes. Since the absence of unit root is not a proof of non-stationarity, the Kwiatkowski–Phillips–Schmidt–Shin or KPSS test can be used to identify the existence of an underlying trend which can also be removed to obtain a stationary process. These are called trend-stationary processes. In both, unit-root and trend-stationary processes, the mean can be increasing or decreasing over time; however, in the presence of a shock, trend-stationary processes (blue) revert to this mean tendency in the long run (deterministic trend) while unit-root processes (green) have a permanent impact (stochastic trend). The significance level of the tests is usually set to 0.05.

ADF	KPSS	Outcome	Note
Non-Stationary	Non-Stationary	Non-Stationary
Stationary	Stationary	Stationary
Non-Stationary	Stationary	Trend-Stationary	Check the de-trended series
Stationary	Non-Stationary	Difference-Stationary	Check the differenced-series

Methods:

as_summary([alpha])	This method creates the summary to display.
evaluate([alpha])	This method initialises the series.
fit(x[, adf_kwargs, kpss_kwargs])	This method studies the stationarity of a given time-series.

as_summary(alpha=0.05)

This method creates the summary to display.

evaluate(alpha=0.05, **kwargs)

This method initialises the series.

fit(x, adf_kwargs={}, kpss_kwargs={}, **kwargs)

This method studies the stationarity of a given time-series.

The parameters which can be passed to the adfuller and kpss methods are listed below:

• adfuller_kwargs = {x, maxlag, regression, autolag, store, regresults}

• kpss_kwargs = {x, regression, lags, store}

@see statsmodels.tsa.stattools.adfuller @see statsmodels.tsa.stattoosl.kpss

Parameters:

• x (array-like) – The time series

• adf_kwargs (dict-like) – The parameters to pass to the adfuller function

• kpss_kwargs (dict-like) – The parameters to apss to the kpss function

Returns:

object

Return type:

An StationarityWrapper objects.

pyamr.core.stats.wbase module

Classes:

BaseWrapper([estimator, evaluate])

Base Wrapper

Functions:

fargs(function, kwargs)	Finds parameters in kwargs tho use in function.
getargspecdict(instance, funcname)	This method creates a dictionary with pairs name and value.

class pyamr.core.stats.wbase.BaseWrapper(estimator=None, evaluate=True)

Bases: object

Base Wrapper

Methods:

as_series([flabel, label])	This method returns a series with all the information.
as_summary()	This method displays the final summary.
evaluate(**kwargs)
fit(**kwargs)	This method performs the fit.
from_list_dataframe(wrapper_list, **kwargs)	This methods creates a dataframe summary from a list.
grid_search(grid_params[, verbose])	This method computes grid search.
load(fname)	This method loads the wrapper.
save(fname)	This method saves the wrapper.

as_series(flabel=True, label=None)

This method returns a series with all the information.

Parameters:

• flabel (boolean) – Wether to include a label before the attributes.

• label (string) – The label to include before the attributes. By default it includes the value of the attribute self._name in lowercase.

Returns:

series

Return type:

pandas series with the results, configuration and model.

as_summary()

This method displays the final summary.

evaluate(**kwargs)

fit(**kwargs)

This method performs the fit.

Parameters:

kwargs (dict-like) – The arguments that will be passed to the method.

from_list_dataframe(wrapper_list, **kwargs)

This methods creates a dataframe summary from a list.

Parameters:

• wrapper_list (array-like) – The list with wrapper objects.

• flabel (boolean) – Wether to include a label before the attributes.

• label (string) – The label to include before the attributes. By default it includes the value of the attribute self._name in lowercase.

Returns:

summary

Return type:

pandas dataframe.

grid_search(grid_params, verbose=0)

This method computes grid search.

Parameters:

• grid_params (array-like) – The grid of parameters to search.

• verbose (int) – Wether to show the progress of the search.

Returns:

summary

Return type:

summary with all the elements.

load(fname)

This method loads the wrapper.

save(fname)

This method saves the wrapper.

pyamr.core.stats.wbase.fargs(function, kwargs)

Finds parameters in kwargs tho use in function.

Parameters:

• function (callable) – The function

• kwargs (dict-like) – The parameters and corresponding values.

pyamr.core.stats.wbase.getargspecdict(instance, funcname)

This method creates a dictionary with pairs name and value.

Parameters:

• instance (object with values)

• funcname (function which parameters name will be looked for.)

Returns:

tpls

Return type:

dictionary with argument name and value.

Module contents