# stationary_bootstrap_calibrate#

Functions

 `OptimalLength`(data) Function calculates the optimal parameter value when using a stationary bootstraping algorithm. Returns the value at points x of the Trapezoidal function. `mlag`(x, n) Returns a numpy array in which the k-th column is the series x pushed down (lagged) by k places.
OptimalLength(data: ndarray)[source]#

Function calculates the optimal parameter value when using a stationary bootstraping algorithm. The method is based on the 2004 paper by Politis & White: Dimitris N. Politis & Halbert White (2004) Automatic Block-Length Selection for the Dependent Bootstrap, Econometric Reviews, 23:1, 53-70, DOI: 10.1081/ETC-120028836

The code was modified compared to Patton’s implementation in that it takes as input a one dimensional time-series and returns the optimalblock size only for the stationary bootstrap algorithm.

Warning! The minimal size of the time series is 9 elements.

Example

```>>> import numpy as np
>>> data = np.array([0.4,0.2,0.1,0.4,0.3,0.1,0.3,0.4,0.2,0.5,0.1,0.2])
>>> OptimalLength(data)
4.0
```
Parameters:

data – ndarray array containing the time-series that we wish to bootstrap. Ex. np.array([-1,0.2,0.3,0.7,0.5,0.1,0.4,0.3,0.5])

Returns:

optimal value of the parameter m Ex. 1

Return type:

Bstar

Original Matlab version written by: James P. LeSage, Dept of Economics University of Toledo 2801 W. Bancroft St, Toledo, OH 43606 jpl@jpl.econ.utoledo.edu

This Python implementation is based on Andrew J. Patton’s Matlab code avalible at: http://public.econ.duke.edu/~ap172/

Implemented by Gregor Fabjan from Qnity Consultants on 12/11/2021.

mlag(x: ndarray, n) ndarray[source]#

Returns a numpy array in which the k-th column is the series x pushed down (lagged) by k places.

Example:

```>>> import numpy as np
>>> x = np.array([1,2,3,4])
>>> n = 2
>>> mlag(x,n)
array([[0, 0],
[1, 0],
[2, 1],
[3, 2]])
```

The function was tested passing a numpy array (ndarray) as input and requires numpy to run.

Parameters:
• x – ndarray array for which the lagged matrix is calculated. np.array([1,2,3,4])

• n

integer specifying how many lags does the function consider

Returns:

xlag: ndarray contining the k-th lagged values in the k-th column of the matrix

Original Matlab version written by: James P. LeSage, Dept of Economics University of Toledo 2801 W. Bancroft St, Toledo, OH 43606 jpl@jpl.econ.utoledo.edu

This Python implementation is based on Andrew J. Patton’s Matlab code avalible at: http://public.econ.duke.edu/~ap172/

Implemented by Gregor Fabjan from Qnity Consultants on 12/11/2021

lam(x: ndarray) ndarray[source]#

Returns the value at points x of the Trapezoidal function.

Trapezoidal funcion maps all numbers bigger than 1 or smaller than -1 to zero. Values between -1/2 to 1/2 to 1 and the rest either on the line connecting (-1,0) to (-1/2,1) or (1/2,1) to (1,0).

Example

```>>> import numpy as np
>>> x = np.array([0.55])
>>> lam(x)
array([0.9])
```
Parameters:

x – ndarray array of points on which we wish to apply the trapezoidal mapping. Ex. np.array([-1,0.2,0.3,0.7])

Returns:

ndarray of mapped points Ex. array([0. , 1. , 1. , 0.6])

Original Matlab version written by: James P. LeSage, Dept of Economics University of Toledo 2801 W. Bancroft St, Toledo, OH 43606 jpl@jpl.econ.utoledo.edu

This Python implementation is based on Andrew J. Patton’s Matlab code avalible at: http://public.econ.duke.edu/~ap172/

Implemented by Gregor Fabjan from Qnity Consultants on 12/11/2021.