gp_binance_demo/kappa/data_processing.py

import json
import pandas as pd
import threading
from collections import deque
from scipy.integrate import trapz
import numpy as np
from logger_config import logger

# 假设我们有一个数据流，订单簿和成交数据
order_book_snapshots = deque(maxlen=600)        # 存储过去600个订单簿快照
trade_snapshots = deque(maxlen=6000)            # 存储过去6000个成交数据

stop_event = threading.Event()

# 初始参数
k_initial = 0.5
A_initial = 1.0

# 假设S0是初始的参考价格
S0 = -1


def on_message_trade(_ws, message):
    global trade_snapshots
    json_message = json.loads(message)
    trade = {
        'price': float(json_message['data']['p']),
        'qty': float(json_message['data']['q']),
        'timestamp': pd.to_datetime(json_message['data']['T'], unit='ms'),
        'side': 'sell' if json_message['data']['m'] else 'buy'
    }
    trade_snapshots.append(trade)
    process_depth_data()


def on_message_depth(_ws, message):
    global order_book_snapshots
    json_message = json.loads(message)
    bids = [[float(price), float(quantity)] for price, quantity in json_message['data']['b'][:10]]
    asks = [[float(price), float(quantity)] for price, quantity in json_message['data']['a'][:10]]
    timestamp = pd.to_datetime(json_message['data']['E'], unit='ms')
    order_book_snapshots.append({
        'bids': bids,
        'asks': asks,
        'timestamp': timestamp
    })
    process_depth_data()


def calculate_phi(prices, k, S0):
    """
    计算 φ(k, ξ) 的值
    :param prices: 时间序列的价格数据
    :param k: 参数 k
    :param S0: 初始价格
    :return: φ(k, ξ) 的值
    """
    price_changes = np.array(prices) - S0
    exponentials = np.exp(k * price_changes)
    phi = np.mean(exponentials)
    return phi


def calculate_integral_phi(prices, k, S0, time_points):
    """
    计算 ∫ φ(k, ξ) dξ 的值，越大说明波动率也越大（价格波动）。
    :param prices: 时间序列的价格数据
    :param k: 参数 k
    :param S0: 初始价格
    :param time_points: 时间点数组
    :return: ∫ φ(k, ξ) dξ 的值
    """
    # 计算每个时间点的 φ(k, ξ) 值
    phi_values = [calculate_phi(prices[:i + 1], k, S0) for i in range(len(prices))]

    # 使用梯形法计算积分
    integral_phi = trapz(phi_values, time_points)

    return integral_phi


def estimate_lambda(waiting_times, T):
    """
    通过等待时间估计 λ(δ)
    :param waiting_times: 等待时间的数组
    :param T: 时间窗口的大小
    :return: λ(δ) 的估计值
    """
    # 将 waiting_times 转换为 NumPy 数组
    waiting_times = np.array(waiting_times)

    sum_indicator = np.sum(waiting_times < T)
    sum_waiting_times = int(np.sum(waiting_times).total_seconds() * 1000)
    lambda_hat = sum_indicator / sum_waiting_times
    return lambda_hat


def process_depth_data():
    global order_book_snapshots, trade_snapshots

    # 数据预热，至少10条深度数据以及100条成交数据才能用于计算
    if len(order_book_snapshots) < 10 and len(trade_snapshots) < 100:
        return

    global k_initial, A_initial, S0
    S_values = [((snapshot['bids'][0][0] + snapshot['asks'][0][0]) / 2) for snapshot in order_book_snapshots]

    if S0 < 0:
        S0 = S_values[0]

    # ========================= 计算 log(∫ φ(k, ξ) dξ) ==================
    # 提取时间戳并计算时间间隔
    order_book_timestamps = [snapshot['timestamp'] for snapshot in order_book_snapshots]
    order_book_time_points = [(timestamp - order_book_timestamps[0]).total_seconds() for timestamp in order_book_timestamps]

    # 计算 ∫ φ(k, ξ) dξ
    integral_phi_value = calculate_integral_phi(S_values, k_initial, S0, order_book_time_points)

    # 计算 log(∫ φ(k, ξ) dξ)
    log_integral_phi_value = np.log(integral_phi_value)

    # ========================== 估计 λ(δ) ==============================
    # 计算等待时间
    trade_timestamps = [snapshot['timestamp'] for snapshot in trade_snapshots]
    waiting_times = [trade_timestamps[i] - trade_timestamps[i - 1] for i in range(1, len(trade_timestamps))]
    # 时间窗口的大小
    T = pd.to_datetime(100, unit='ms') - pd.to_datetime(0, unit='ms')

    lambda_hat = estimate_lambda(waiting_times, T)
    # logger.info("λ(δ) 的值: " + str(lambda_hat) + "log(∫ φ(k, ξ) dξ) 的值: " + str(log_integral_phi_value))
    log_lambda_hat_value = np.log(lambda_hat)
    logger.info("log(λ(δ)) 的值: " + str(log_lambda_hat_value) + "log(∫ φ(k, ξ) dξ) 的值: " + str(log_integral_phi_value))