如何计算和绘制时间序列的多个线性趋势？

Question

将线性趋势拟合到一组数据是直截了当的。但是，如何将多个趋势线拟合到一个时间序列？我将趋势定义为高于或低于指数移动平均线的价格。当价格高于EMA时，我需要适应一个积极的趋势，当趋势变为负值时，新的负趋势线等等。在我的下面的代码中，我的pandas数据框中的market_data['Signal']告诉我趋势是上升+1还是下降-1。

我猜我需要某种循环，但我无法弄清楚逻辑......

import pandas as pd
import pandas_datareader.data as web
import datetime as dt
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
import matplotlib.dates as mdates

#Colecting data
market = '^DJI'
end = dt.datetime(2016, 12, 31)
start = dt.date(end.year-10, end.month, end.day)
market_data = web.DataReader(market, 'yahoo', start, end)

#Calculating EMA and difference
market_data['ema'] = market_data['Close'].ewm(200).mean()
market_data['diff_pc'] = (market_data['Close'] / market_data['ema']) - 1

#Defining bull/bear signal
TH = 0
market_data['Signal'] = np.where(market_data['diff_pc'] > TH, 1, 0)
market_data['Signal'] = np.where(market_data['diff_pc'] < -TH, -1, market_data['Signal'])

为了适应趋势线，我想使用numpy polyfit

x = np.array(mdates.date2num(market_data.index.to_pydatetime()))
fit = np.polyfit(x, market_data['Close'], 1)

理想情况下，我只想绘制信号持续时间超过n个周期的趋势。

结果应如下所示：

Answer 1

这是一个解决方案。 min_signal是连续变换趋势所需的连续信号数。我导入Seaborn以获得更好看的情节，但如果没有该行，它的工作原理完全相同：

import pandas as pd
import pandas_datareader.data as web
import datetime as dt
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
import matplotlib.dates as mdates

#Colecting data
market = '^DJI'
end = dt.datetime(2016, 12, 31)
start = dt.date(end.year-10, end.month, end.day)
market_data = web.DataReader(market, 'yahoo', start, end)

#Calculating EMA and difference
market_data['ema'] = market_data['Close'].ewm(200).mean()
market_data['diff_pc'] = (market_data['Close'] / market_data['ema']) - 1

#Defining bull/bear signal
TH = 0
market_data['Signal'] = np.where(market_data['diff_pc'] > TH, 1, 0)
market_data['Signal'] = np.where(market_data['diff_pc'] < -TH, -1, market_data['Signal'])


# Plot data and fits

import seaborn as sns  # This is just to get nicer plots

signal = market_data['Signal']

# How many consecutive signals are needed to change trend
min_signal = 2

# Find segments bounds
bounds = (np.diff(signal) != 0) & (signal[1:] != 0)
bounds = np.concatenate(([signal[0] != 0], bounds))
bounds_idx = np.where(bounds)[0]
# Keep only significant bounds
relevant_bounds_idx = np.array([idx for idx in bounds_idx if np.all(signal[idx] == signal[idx:idx + min_signal])])
# Make sure start and end are included
if relevant_bounds_idx[0] != 0:
    relevant_bounds_idx = np.concatenate(([0], relevant_bounds_idx))
if relevant_bounds_idx[-1] != len(signal) - 1:
    relevant_bounds_idx = np.concatenate((relevant_bounds_idx, [len(signal) - 1]))

# Iterate segments
for start_idx, end_idx in zip(relevant_bounds_idx[:-1], relevant_bounds_idx[1:]):
    # Slice segment
    segment = market_data.iloc[start_idx:end_idx + 1, :]
    x = np.array(mdates.date2num(segment.index.to_pydatetime()))
    # Plot data
    data_color = 'green' if signal[start_idx] > 0 else 'red'
    plt.plot(segment.index, segment['Close'], color=data_color)
    # Plot fit
    coef, intercept = np.polyfit(x, segment['Close'], 1)
    fit_val = coef * x + intercept
    fit_color = 'yellow' if coef > 0 else 'blue'
    plt.plot(segment.index, fit_val, color=fit_color)

结果如下：