Question

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