.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_ch9\ch9_random_walk_log_normal.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_random_walk_log_normal.py: ========================== 9.02 Random walks ========================== We reproduce here the figure 9.2 and 9.3 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 map is defined as: $$\epsilon = (\delta_0 \circ \text{Log })(X) = \Big(\ln(X^{k+1})-\ln(X^{k})\Big)_{k=0,\ldots}$$ With $\delta_0$ being the difference map $$\delta_0(X) := X^{k+1}-X^{k}$$ .. GENERATED FROM PYTHON SOURCE LINES 65-68 .. code-block:: Python params["map"] = maps.composition_map([maps.diff(), maps.log_map, maps.remove_time()]) params = maps.apply_map(params) .. GENERATED FROM PYTHON SOURCE LINES 69-73 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 73-78 .. 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 79-81 We plot the original distribution vs the generated one ------------------------------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 81-85 .. code-block:: Python params = display_historical_vs_generated_distribution(params) params["graphic"](params) plt.show() .. image-sg:: /auto_ch9/images/sphx_glr_ch9_random_walk_log_normal_001.png :alt: ch9 random walk log normal :srcset: /auto_ch9/images/sphx_glr_ch9_random_walk_log_normal_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 86-90 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 90-95 .. code-block:: Python params["reproductibility"] = True params = generate_paths(params) params["graphic"](params) plt.show() .. image-sg:: /auto_ch9/images/sphx_glr_ch9_random_walk_log_normal_002.png :alt: ch9 random walk log normal :srcset: /auto_ch9/images/sphx_glr_ch9_random_walk_log_normal_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 96-98 We now generate a new set of 10 paths ------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 98-106 .. code-block:: Python params["reproductibility"] = False params["Nz"] = 10 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_random_walk_log_normal_003.png :alt: ch9 random walk log normal :srcset: /auto_ch9/images/sphx_glr_ch9_random_walk_log_normal_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none 0 1 2 Mean 0.0012(0.0019) -3e-05(0.0012) 0.00091(0.0021) Variance -0.069(-0.34) -0.44(-0.31) -0.09(-0.18) Skewness 0.0004(0.00035) 0.0005(0.00037) 0.00033(0.0003) Kurtosis 2(0.46) 6.7(1.7) 1.4(0.5) KS test 0.6(0.05) 0.18(0.05) 0.26(0.05) .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 3.260 seconds) .. _sphx_glr_download_auto_ch9_ch9_random_walk_log_normal.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: ch9_random_walk_log_normal.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: ch9_random_walk_log_normal.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: ch9_random_walk_log_normal.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_