.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_ch9\ch9_additive.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_ch9_ch9_additive.py: ==================================== 9.06 Additive noise map ==================================== We reproduce here the figure 9.6 of the book. Utilitary functions can be found next to this file. Here, we only define codpy-related functions. .. GENERATED FROM PYTHON SOURCE LINES 10-12 Necessary Imports ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 12-34 .. code-block:: Python import os import sys import matplotlib.pyplot as plt import numpy as np from codpy.kernel import Sampler try: CURRENT_DIR = os.path.dirname(os.path.abspath(__file__)) except NameError: CURRENT_DIR = os.getcwd() data_path = os.path.join(CURRENT_DIR, "data") PARENT_DIR = os.path.abspath(os.path.join(CURRENT_DIR, "..")) sys.path.insert(0, PARENT_DIR) import utils.ch9.mapping as maps from utils.ch9.data_utils import stats_df from utils.ch9.market_data import retrieve_market_data from utils.ch9.path_generation import generate_paths from utils.ch9.plot_utils import display_historical_vs_generated_distribution .. GENERATED FROM PYTHON SOURCE LINES 35-37 Parameter definition ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 37-53 .. code-block:: Python def get_cdpres_param(): return { "rescale_kernel": {"max": 2000, "seed": None}, "rescale": True, "grid_projection": True, "reproductibility": False, "date_format": "%d/%m/%Y", "begin_date": "01/06/2020", "end_date": "01/06/2022", "today_date": "01/06/2022", "symbols": ["AAPL", "GOOGL", "AMZN"], } .. GENERATED FROM PYTHON SOURCE LINES 54-56 Get the market data ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 56-58 .. code-block:: Python params = retrieve_market_data() .. GENERATED FROM PYTHON SOURCE LINES 59-65 Defining the map ------------------------ The additive noise map is defined as: $$\eta_Y(\varepsilon) = \varepsilon - f(Y), \qquad \varepsilon = \eta_Y^{-1}(\eta) = \eta + f(Y),$$ Where, $\eta_Y$ is a white noise, that is an independent random variable, and $f : \mathbb{R}^{D_Y} \to \mathbb{R}^{D_{\varepsilon}}$ is a smooth function modeling the dependence of $\varepsilon$ on $Y$. If unknown, $f$ can be estimated from historical data using the denoising algorithm .. GENERATED FROM PYTHON SOURCE LINES 65-71 .. code-block:: Python params["map"] = maps.composition_map( [maps.additive_noise_map(), maps.log_map, maps.remove_time()] ) params = maps.apply_map(params) .. GENERATED FROM PYTHON SOURCE LINES 72-76 We define our sampler on the mapped data using codpy's Sampler ------------------------------------------------------------------------ You can define your own latent generator function, here we use a simple uniform distribution. But if not provided, a default one will be used by the Sampler class. .. GENERATED FROM PYTHON SOURCE LINES 76-81 .. code-block:: Python mapped_data = params["transform_h"].values generator = lambda n: np.random.uniform(size=(n, mapped_data.shape[1])) sampler = Sampler(mapped_data, latent_generator=generator) params["sampler"] = sampler .. GENERATED FROM PYTHON SOURCE LINES 82-84 We plot the original distribution vs the generated one ------------------------------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 84-88 .. code-block:: Python params = display_historical_vs_generated_distribution(params) params["graphic"](params) plt.show() .. image-sg:: /auto_ch9/images/sphx_glr_ch9_additive_001.png :alt: ch9 additive :srcset: /auto_ch9/images/sphx_glr_ch9_additive_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 89-93 Reproductibility test ------------------------------------------------ We regenerate the same path by generating from the latent representation We make sure we get the original data back. .. GENERATED FROM PYTHON SOURCE LINES 93-98 .. code-block:: Python params["reproductibility"] = True params = generate_paths(params) params["graphic"](params) plt.show() .. image-sg:: /auto_ch9/images/sphx_glr_ch9_additive_002.png :alt: ch9 additive :srcset: /auto_ch9/images/sphx_glr_ch9_additive_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 99-101 We now generate a new set of 10 paths ------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 101-109 .. code-block:: Python params["reproductibility"] = False params["Nz"] = 100 params = generate_paths(params) params["graphic"](params) plt.show() stats = stats_df(params["transform_h"], params["transform_g"]).T print(stats) .. image-sg:: /auto_ch9/images/sphx_glr_ch9_additive_003.png :alt: ch9 additive :srcset: /auto_ch9/images/sphx_glr_ch9_additive_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none 0 1 2 Mean -2.4e-06(0.0011) -4.8e-06(0.0009) 1.3e-06(0.00052) Variance 0.19(0.039) -0.36(-0.19) -0.1(-0.16) Skewness 0.0003(0.0003) 0.00034(0.00033) 0.00025(0.00023) Kurtosis 2.1(0.62) 3.4(0.72) 1.3(0.058) KS test 0.11(0.05) 0.36(0.05) 0.58(0.05) .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 4.208 seconds) .. _sphx_glr_download_auto_ch9_ch9_additive.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: ch9_additive.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: ch9_additive.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: ch9_additive.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_