如何计算和绘制时间序列的多个线性趋势? [英] How to calculate and plot multiple linear trends for a time series?

问题描述

将线性趋势拟合到一组数据很简单.但是，如何将多个趋势线拟合到一个时间序列中?我将上下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，我需要拟合一个正趋势，而当趋势变为负时，则需要一个新的负趋势线，依此类推.在我的熊猫数据框中market_data['Signal']下面的代码中，告诉我趋势是向上+1还是向下-1.

Fitting a linear trend to a set of data is straight forward. But how can I fit multiple trend lines to one time series? I define up and down trends as prices above or below a exponential moving average. When the price is above the EMA I need to fit a positive trend and when the trend turns negative a new negative trend line and so forth. In my code below the market_data['Signal'] in my pandas dataframe tells me if the trend is up +1 or down -1.

我猜我需要某种循环，但是我无法弄清楚逻辑……

I'm guessing I need some kind of a loop, but I cannot work out the logic...

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'])

为适应趋势线，我希望使用numpy polyfit

To fit the trend lines I wan to use 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超过n个周期的趋势.

Ideally I would like to only plot the trends where the signal last more than n periods.

结果应如下所示:

推荐答案

这是一个解决方案. min_signal是一行中更改趋势所需的连续信号数.我导入了 Seaborn 以获得更好看的情节，但如果没有这一行，它的效果就一样:

Here is a solution. min_signal is the number of consecutive signals in a row that are needed to change trend. I imported Seaborn to get a better-looking plot, but it works all the same without that line:

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)

这是结果:

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