# 5.11 Fisher Transform · Using Fisher Transform Indicator

## 策略思路：

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；

## 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

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