5.11 Fisher Transform · Using Fisher Transform Indicator

来源:https://uqer.io/community/share/54b5c288f9f06c276f651a16

策略思路:

在技术分析中,很多时候,人们都把股价数据当作正态分布的数据来分析。但是,其实股价数据分布并不符合正态分布。Fisher Transformation是一个可以把股价数据变为类似于正态分布的方法。

Fisher Transformation将市场数据的走势平滑化,去掉了一些尖锐的短期振荡;利用今日和前一日该指标的交错可以给出交易信号;

例如,对于沪深300指数使用Fisher变换的结果见本文后面的具体讨论。

Fisher Transformation

  • 定义今日中间价:

    mid=(low+high)/2
    
  • 确定计算周期,例如可使用10日为周期。计算周期内最高价和最低价:

    lowestLow=周期内最低价,    highestHigh=周期内最高价
    
  • 定义价变参数(其中的ratio为0-1之间常数,例如可取0.5或0.33):

  • 对价变参数x使用Fisher变换,得到Fisher指标:

import quartz
import quartz.backtest    as qb
import quartz.performance as qp
from   quartz.api         import *

import pandas as pd
import numpy  as np
from datetime   import datetime
from matplotlib import pylab
start = datetime(2014, 1, 1)                # 回测起始时间
end   = datetime(2014, 12, 10)                # 回测结束时间
benchmark = 'HS300'                            # 使用沪深 300 作为参考标准
universe = set_universe('SH50')    # 股票池
capital_base = 100000                       # 起始资金


refresh_rate = 1
window = 10

# 本策略对于window非常非常敏感!!!

histFish = pd.DataFrame(0.0, index = universe, columns = ['preDiff', 'preFish', 'preState'])

def initialize(account):                    # 初始化虚拟账户状态
    account.amount = 10000
    account.universe = universe
    add_history('hist', window)


def handle_data(account):                # 每个交易日的买入卖出指令

    for stk in account.universe:
        prices = account.hist[stk]
        if prices is None:
            return

        preDiff = histFish.at[stk, 'preDiff']
        preFish = histFish.at[stk, 'preFish']
        preState = histFish.at[stk, 'preState']

        diff, fish = FisherTransIndicator(prices, preDiff, preFish)
        if fish > preFish:
            state = 1
        elif fish < preFish:
            state = -1
        else:
            state = 0

        if state == 1 and preState == -1:
            #stkAmount = int(account.amount / prices.iloc[-1]['openPrice'])
            order(stk, account.amount)
        elif state == -1 and preState == 1:
            order_to(stk, 0)

        histFish.at[stk, 'preDiff'] = diff
        histFish.at[stk, 'preFish'] = fish
        histFish.at[stk, 'preState'] = state


def FisherTransIndicator(windowData, preDiff, preFish):
    # This function calculate the Fisher Transform indicator based on the data
    # in the windowData. 
    minLowPrice = min(windowData['lowPrice'])
    maxHghPrice = max(windowData['highPrice'])
    tdyMidPrice = (windowData.iloc[-1]['lowPrice'] + windowData.iloc[-1]['highPrice'])/2.0

    diffRatio = 0.33
    # 本策略对于diffRatio同样非常敏感!!!

    diff = (tdyMidPrice - minLowPrice)/(maxHghPrice - minLowPrice) - 0.5
    diff = 2 * diff
    diff = diffRatio * diff + (1.0 - diffRatio) * preDiff

    if diff > 0.99:
        diff = 0.999
    elif diff < -0.99:
        diff = -0.999

    fish = np.log((1.0 + diff)/(1.0 - diff))
    fish = 0.5 * fish + 0.5 * fish

    return diff, fish

沪深300指数上使用Fisher Transformation

  • 对最近半年的沪深300进行Fisher变换,得到的指标能够比较温和准确反映出指数的变化
from CAL.PyCAL import *

# DataAPI.MktIdxdGet返回pandas.DataFrame格式
index =  DataAPI.MktIdxdGet(indexID = "000001.ZICN", beginDate = "20140501", endDate = "20140901")
index.head()
indexID tradeDate ticker secShortName exchangeCD preCloseIndex openIndex lowestIndex highestIndex closeIndex turnoverVol turnoverValue CHG CHGPct
0 000001.ZICN 2014-05-05 1 上证综指 XSHG 2026.358 2022.178 2007.351 2028.957 2027.353 7993339500 60093487736 0.995 0.00049
1 000001.ZICN 2014-05-06 1 上证综指 XSHG 2027.353 2024.256 2021.485 2038.705 2028.038 7460941100 57548110850 0.685 0.00034
2 000001.ZICN 2014-05-07 1 上证综指 XSHG 2028.038 2023.152 2008.451 2024.631 2010.083 7436019200 57558051925 -17.955 -0.00885
3 000001.ZICN 2014-05-08 1 上证综指 XSHG 2010.083 2006.853 2005.685 2036.941 2015.274 7786539300 59529365546 5.191 0.00258
4 000001.ZICN 2014-05-09 1 上证综指 XSHG 2015.274 2016.501 2001.300 2020.454 2011.135 7622424400 57505383717 -4.139 -0.00205
def FisherTransIndicator(windowData, preDiff, preFish, state):
    # This function calculate the Fisher Transform indicator based on the data
    # in the windowData. 
    minLowPrice = min(windowData['lowestIndex'])
    maxHghPrice = max(windowData['highestIndex'])
    tdyMidPrice = (windowData.iloc[-1]['lowestIndex'] + windowData.iloc[-1]['highestIndex'])/2.0

    diffRatio = 0.5

    diff = (tdyMidPrice - minLowPrice)/(maxHghPrice - minLowPrice) - 0.5
    diff = 2 * diff

    if state == 1:
        diff = diffRatio * diff + (1 - diffRatio) * preDiff

    if diff > 0.995:
        diff = 0.999
    elif diff < -0.995:
        diff = -0.999

    fish = np.log((1 + diff)/(1 - diff))
    if state == 1:
        fish = 0.5 * fish + 0.5 * fish

    return diff, fish
window = 10

index['diff'] = 0.0
index['fish'] = 0.0
index['preFish'] = 0.0

for i in range(window, index.shape[0]):
    windowData = index.iloc[i-window : i]
    if i == window:
        diff, fish = FisherTransIndicator(windowData, 0, 0, 1)
        index.at[i,'preFish'] = 0
        index.at[i,'diff'] = diff
        index.at[i,'fish'] = fish
    else:
        preDiff = index.iloc[i-1]['diff']
        preFish = index.iloc[i-1]['fish']
        diff, fish = FisherTransIndicator(windowData, preDiff, preFish, 1)
        index.at[i,'preFish'] = preFish
        index.at[i,'diff'] = diff
        index.at[i,'fish'] = fish


Plot(index, settings = {'x':'tradeDate','y':'closeIndex', 'title':u'沪深300指数历史收盘价'})
Plot(index, settings = {'x':'tradeDate','y':['fish', 'preFish'], 'title':u'沪深300指数Fisher Transform Indicator'})

  • 上图中的蓝色曲线表示Fisher指标,绿色曲线表示前一日的Fisher指标,两个指标的交错可以给出沪深300指数涨跌情况的信号

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