# 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：  ```py 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 ``` ```py 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 ```py from CAL.PyCAL import * # DataAPI.MktIdxdGet返回pandas.DataFrame格式 index = DataAPI.MktIdxdGet(indexID = "000001.ZICN", beginDate = "20140501", endDate = "20140901") ``` ```py 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 | ```py 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 ``` ```py 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