Source code for tensortrade.stochastic.processes.ornstein_uhlenbeck

# Copyright 2020 The TensorTrade Authors.
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# Licensed under the Apache License, Version 2.0 (the "License");
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#     http://www.apache.org/licenses/LICENSE-2.0
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import numpy as np
import pandas as pd

from stochastic.processes.noise import GaussianNoise

from tensortrade.stochastic.processes.brownian_motion import brownian_motion_log_returns
from tensortrade.stochastic.utils.helpers import get_delta, scale_times_to_generate
from tensortrade.stochastic.utils.parameters import ModelParameters, default


[docs]def ornstein_uhlenbeck_levels(params: 'ModelParameters') -> 'np.array': """Constructs the rate levels of a mean-reverting Ornstein-Uhlenbeck process. Parameters ---------- params : ModelParameters The parameters for the stochastic model. Returns ------- `np.array` The interest rate levels for the Ornstein Uhlenbeck process """ ou_levels = [params.all_r0] brownian_motion_returns = brownian_motion_log_returns(params) for i in range(1, params.all_time): drift = params.ou_a * (params.ou_mu - ou_levels[i - 1]) * params.all_delta randomness = brownian_motion_returns[i - 1] ou_levels.append(ou_levels[i - 1] + drift + randomness) return np.array(ou_levels)
[docs]def ornstein(base_price: int = 1, base_volume: int = 1, start_date: str = '2010-01-01', start_date_format: str = '%Y-%m-%d', times_to_generate: int = 1000, time_frame: str = '1h', params: 'ModelParameters' = None) -> 'pd.DataFrame': """Generates price data from the OU process. Parameters ---------- base_price : int, default 1 The base price to use for price generation. base_volume : int, default 1 The base volume to use for volume generation. start_date : str, default '2010-01-01' The start date of the generated data start_date_format : str, default '%Y-%m-%d' The format for the start date of the generated data. times_to_generate : int, default 1000 The number of bars to make. time_frame : str, default '1h' The time frame. params : `ModelParameters`, optional The model parameters. Returns ------- `pd.DataFrame` The generated data frame containing the OHLCV bars. References ---------- [1] https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process """ delta = get_delta(time_frame) times_to_generate = scale_times_to_generate(times_to_generate, time_frame) params = params or default(base_price, times_to_generate, delta) prices = ornstein_uhlenbeck_levels(params) volume_gen = GaussianNoise(t=times_to_generate) volumes = volume_gen.sample(times_to_generate) + base_volume start_date = pd.to_datetime(start_date, format=start_date_format) price_frame = pd.DataFrame([], columns=['date', 'price'], dtype=float) volume_frame = pd.DataFrame([], columns=['date', 'volume'], dtype=float) price_frame['date'] = pd.date_range(start=start_date, periods=times_to_generate, freq="1min") price_frame['price'] = abs(prices) volume_frame['date'] = price_frame['date'].copy() volume_frame['volume'] = abs(volumes) price_frame.set_index('date') price_frame.index = pd.to_datetime(price_frame.index, unit='m', origin=start_date) volume_frame.set_index('date') volume_frame.index = pd.to_datetime(volume_frame.index, unit='m', origin=start_date) data_frame = price_frame['price'].resample(time_frame).ohlc() data_frame['volume'] = volume_frame['volume'].resample(time_frame).sum() return data_frame