# Utility Functions¶

The utility functions help in adjusting the simulated data cube. There are some assumptions about the cube. Namely, assuming that we are running a Monte-Carlo simulation of asset returns, the axis will be 3 dimensional where each axis represents the time, trials and asset class respectively.

## Calibrate Data¶

muarch.calibrate.calibrate_data(data: numpy.ndarray, mean: Optional[Iterable[float]] = None, sd: Optional[Iterable[float]] = None, time_unit: Union[int, str] = 'month', inplace=False, tol=1e-06) → numpy.ndarray[source]

Calibrates the data given the target mean and standard deviation.

Parameters
• data (ndarray) – Data tensor to calibrate

• mean (iterable float, optional) – The target annual mean vector

• sd (iterable float, optional) – The target annual standard deviation (volatility) vector

• time_unit (int or str) – Specifies how many units (first axis) is required to represent a year. For example, if each time period represents a month, set this to 12. If quarterly, set to 4. Defaults to 12 which means 1 period represents a month. Alternatively, you could put in a string name of the time_unit. Accepted values are weekly, monthly, quarterly, semi-annually and yearly

• inplace (bool) – If True, calibration will modify the original data. Otherwise, a deep copy of the original data will be made before calibration. Deep copy can be time consuming if data is big.

• tol (float) – Tolerance used to determine if calibrate should be called. For example, if the cube’s target annualized mean is similar to the actual tolerance, function will skip the mean adjustment.

Returns

An instance of the adjusted numpy tensor

Return type

ndarray

## Truncate Outliers¶

muarch.calibrate.truncate_outliers(data: numpy.ndarray, *, bounds: List[Tuple[float, float]] = None, sd=0, replacement='mean', inplace=False)[source]

Truncates outliers by replacing it with the mean, median or a specified value.

Outlier is determined by the number of standard deviations past the mean within the asset group.

Parameters
• data (ndarray) – The tensor (data cube) where the axis represents time, trials and number of asset classes respectively

• bounds (List of numbers) – A list containing the lower and upper bound for each asset class. If specified, this takes precedence over the sd parameter. If sd is set to 0 and bounds are not specified, no changes will be made

• sd (float) – The number of standard deviations to consider a point an outlier. If sd is set to 0 and bounds are not specified, no changes will be made

• replacement ({float, 'mean', 'median'}) – The value to replace outliers with. Valid values are ‘mean’, ‘median’ or a number.

• inplace (bool) – If True, calibration will modify the original data. Otherwise, a deep copy of the original data will be made before calibration. Deep copy can be time consuming if data is big.

Returns

A data cube with the outliers replaced

Return type

ndarray

## Basic Statistics¶

muarch.funcs.moments.get_annualized_mean(data: numpy.ndarray, time_unit: Union[int, str] = 'monthly') → Union[float, numpy.ndarray][source]

Gets the annualized mean for each asset class in the data cube

Parameters
• data – Data matrix or tensor. The axis must represent time, trials and assets respectively where the assets axis is valid only if the data is a tensor.

• time_unit (int or str) – Specifies how many units (first axis) is required to represent a year. For example, if each time period represents a month, set this to 12. If quarterly, set to 4. Defaults to 12 which means 1 period represents a month. Alternatively, you could put in a string name of the time_unit. Accepted values are weekly, monthly, quarterly, semi-annually and yearly

Returns

The annualized mean for the asset class or an array containing the annualized mean for each asset class.

Return type

float or ndarray

muarch.funcs.moments.get_annualized_sd(data: numpy.ndarray, time_unit: Union[int, str] = 'monthly') → Union[float, numpy.ndarray][source]

Gets the annualized standard deviation for each asset class in the data cube

Parameters
• data – Data matrix or tensor. The axis must represent time, trials and assets respectively where the assets axis is valid only if the data is a tensor.

• time_unit (int or str) – Specifies how many units (first axis) is required to represent a year. For example, if each time period represents a month, set this to 12. If quarterly, set to 4. Defaults to 12 which means 1 period represents a month. Alternatively, you could put in a string name of the time_unit. Accepted values are weekly, monthly, quarterly, semi-annually and yearly

Returns

The annualized standard deviation (volatility) for the asset class or an array containing the annualized standard deviation for each asset class.

Return type

float ndarray

muarch.funcs.moments.get_annualized_skew(data: numpy.ndarray, time_unit: Union[int, str] = 'monthly') → Union[float, numpy.ndarray][source]

Gets the annualized skew for each asset class in the data cube

Parameters
• data – Data matrix or tensor. The axis must represent time, trials and assets respectively where the assets axis is valid only if the data is a tensor.

• time_unit (int or str) – Specifies how many units (first axis) is required to represent a year. For example, if each time period represents a month, set this to 12. If quarterly, set to 4. Defaults to 12 which means 1 period represents a month. Alternatively, you could put in a string name of the time_unit. Accepted values are weekly, monthly, quarterly, semi-annually and yearly

Returns

The annualized skew for the asset class or an array containing the annualized skew for each asset class.

Return type

float or ndarray

muarch.funcs.moments.get_annualized_kurtosis(data: numpy.ndarray, time_unit: Union[int, str] = 'monthly') → Union[float, numpy.ndarray][source]

Gets the annualized kurtosis for each asset class in the data cube

Parameters
• data – Data matrix or tensor. The axis must represent time, trials and assets respectively where the assets axis is valid only if the data is a tensor.

• time_unit (int or str) – Specifies how many units (first axis) is required to represent a year. For example, if each time period represents a month, set this to 12. If quarterly, set to 4. Defaults to 12 which means 1 period represents a month. Alternatively, you could put in a string name of the time_unit. Accepted values are weekly, monthly, quarterly, semi-annually and yearly

Returns

The annualized kurtosis for the asset class or an array containing the annualized kurtosis for each

asset class.

Return type

ndarray