Reference¶

technical_indicators¶

This module provides some technical indicators for analysing stocks.

When I can I will add more. If anyone wishes to contribute with new code or corrections/suggestions, feel free.

Features:

Relative Strength Index (RSI), ROC, MA envelopes Simple Moving Average (SMA), Weighted Moving Average (WMA), Exponential Moving Average (EMA) Bollinger Bands (BB), Bollinger Bandwidth, %B

Dependencies:

It requires numpy. This module was tested under Windows with Python 2.7.3 and numpy 1.6.1.

technical_indicators.technical_indicators.bb(prices, period, num_std_dev=2.0)[source]¶

Bollinger bands (BB) are volatility bands placed above and below a moving average. Volatility is based on the standard deviation, which changes as volatility increases and decreases. The bands automatically widen when volatility increases and narrow when volatility decreases. This dynamic nature of Bollinger Bands also means they can be used on different securities with the standard settings. For signals, Bollinger Bands can be used to identify M-Tops and W-Bottoms or to determine the strength of the trend. Signals derived from narrowing BandWidth are also important.

Bollinger BandWidth is an indicator that derives from Bollinger Bands, and measures the percentage difference between the upper band and the lower band. BandWidth decreases as Bollinger Bands narrow and increases as Bollinger Bands widen. Because Bollinger Bands are based on the standard deviation, falling BandWidth reflects decreasing volatility and rising BandWidth reflects increasing volatility.

%B quantifies a security’s price relative to the upper and lower Bollinger Band. There are six basic relationship levels: %B equals 1 when price is at the upper band %B equals 0 when price is at the lower band %B is above 1 when price is above the upper band %B is below 0 when price is below the lower band %B is above .50 when price is above the middle band (20-day SMA) %B is below .50 when price is below the middle band (20-day SMA)

They were developed by John Bollinger. Bollinger suggests increasing the standard deviation multiplier to 2.1 for a 50-period SMA and decreasing the standard deviation multiplier to 1.9 for a 10-period SMA.

http://www.csidata.com/?page_id=797 http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:bollinger_bands http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:bollinger_band_width http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:bollinger_band_perce

Input:: prices ndarray period int > 1 and < len(prices) num_std_dev float > 0.0 (optional and defaults to 2.0)
Output:: bbs ndarray with upper, middle, lower bands, bandwidth, range and %B

Test:

>>> import numpy as np
>>> import technical_indicators as tai
>>> prices = np.array([86.16, 89.09, 88.78, 90.32, 89.07, 91.15, 89.44,
... 89.18, 86.93, 87.68, 86.96, 89.43, 89.32, 88.72, 87.45, 87.26, 89.50,
... 87.90, 89.13, 90.70, 92.90, 92.98, 91.80, 92.66, 92.68, 92.30, 92.77,
... 92.54, 92.95, 93.20, 91.07, 89.83, 89.74, 90.40, 90.74, 88.02, 88.09,
... 88.84, 90.78, 90.54, 91.39, 90.65])
>>> period = 20
>>> print(tai.bb(prices, period))
[[  9.12919107e+01   8.87085000e+01   8.61250893e+01   5.82449423e-02
    5.16682146e+00   6.75671306e-03]
 [  9.19497209e+01   8.90455000e+01   8.61412791e+01   6.52300429e-02
    5.80844179e+00   5.07661263e-01]
 [  9.26132536e+01   8.92400000e+01   8.58667464e+01   7.55995881e-02
    6.74650724e+00   4.31816571e-01]
 [  9.29344497e+01   8.93910000e+01   8.58475503e+01   7.92797873e-02
    7.08689946e+00   6.31086945e-01]
 [  9.33114122e+01   8.95080000e+01   8.57045878e+01   8.49848539e-02
    7.60682430e+00   4.42420124e-01]
 [  9.37270110e+01   8.96885000e+01   8.56499890e+01   9.00563838e-02
    8.07702198e+00   6.80945403e-01]
 [  9.38972812e+01   8.97460000e+01   8.55947188e+01   9.25117832e-02
    8.30256250e+00   4.63143909e-01]
 [  9.42636418e+01   8.99125000e+01   8.55613582e+01   9.67861377e-02
    8.70228361e+00   4.15826692e-01]
 [  9.45630193e+01   9.00805000e+01   8.55979807e+01   9.95225220e-02
    8.96503854e+00   1.48579313e-01]
 [  9.47851634e+01   9.03815000e+01   8.59778366e+01   9.74461225e-02
    8.80732672e+00   1.93266744e-01]
 [  9.50411874e+01   9.06575000e+01   8.62738126e+01   9.67087637e-02
    8.76737475e+00   7.82660026e-02]
 [  9.49062071e+01   9.08630000e+01   8.68197929e+01   8.89956780e-02
    8.08641429e+00   3.22789193e-01]
 [  9.49015375e+01   9.08830000e+01   8.68644625e+01   8.84332063e-02
    8.03707509e+00   3.05526266e-01]
 [  9.48939343e+01   9.09040000e+01   8.69140657e+01   8.77834713e-02
    7.97986867e+00   2.26311285e-01]
 [  9.48594576e+01   9.09880000e+01   8.71165424e+01   8.50982021e-02
    7.74291521e+00   4.30661576e-02]
 [  9.46722663e+01   9.11525000e+01   8.76327337e+01   7.72280810e-02
    7.03953265e+00  -5.29486389e-02]
 [  9.45543042e+01   9.11905000e+01   8.78266958e+01   7.37753219e-02
    6.72760849e+00   2.48722001e-01]
 [  9.46761721e+01   9.11200000e+01   8.75638279e+01   7.80546993e-02
    7.11234420e+00   4.72660054e-02]
 [  9.45733946e+01   9.11670000e+01   8.77606054e+01   7.47286754e-02
    6.81278915e+00   2.01003516e-01]
 [  9.45322396e+01   9.12495000e+01   8.79667604e+01   7.19508503e-02
    6.56547911e+00   4.16304661e-01]
 [  9.45303313e+01   9.12415000e+01   8.79526687e+01   7.20906879e-02
    6.57766250e+00   7.52141243e-01]
 [  9.43672335e+01   9.11660000e+01   8.79647665e+01   7.02286710e-02
    6.40246702e+00   7.83328285e-01]
 [  9.41460689e+01   9.10495000e+01   8.79529311e+01   6.80194599e-02
    6.19313782e+00   6.21182512e-01]]

technical_indicators.technical_indicators.ema(prices, period, ema_type=0)[source]¶

Exponencial Moving Average (EMA) are used to smooth the data in an array to help eliminate noise and identify trends. Exponential moving averages reduce the lag by applying more weight to recent prices. The weighting applied to the most recent price depends on the number of periods in the moving average.

They do not predict price direction, but can be used to identify the direction of the trend or define potential support and resistance levels.

EMA type 0 EMAn = w.Pn + (1 - w).EMAn-1 EMAn = EMAn-1 + w.(Pn - EMAn-1) EMAn = w.Pn + w.(1 - w).Pn-1 + w.(1 - w)^2.Pn-2 + ... + w.(1 - w)^(n-1).P1 + w.(1 - w)^n.EMA0 where w = 2 / (n + 1) and EMA0 = mean(oldest period) or EMAn = w.EMAn-1 + (1 - w).Pn where w = 1 - 2 / (n + 1) and Pn is the most recent price and EMA0 = mean(oldest period)

EMA type 1 The above formulas with EMA0 = P1 (oldest price)

EMA type 2 EMA = (Pn + w.Pn-1 + w^2.Pn-2 + w^3.Pn-3 + ... ) / K where K = 1 + w + w^2 + ... = 1 / (1 - w) and Pn is the most recent price and w = 2 / (N + 1)

http://www.financialwebring.org/gummy-stuff/MA-stuff.htm

http://www.csidata.com/?page_id=797 http://stockcharts.com/school/doku.php?st=moving+average&id=chart_school:technical_indicators:moving_averages

Input:: prices ndarray period int > 1 and < len(prices) ema_type can be 0, 1 or 2
Output:: emas ndarray

Tests:

>>> import numpy as np
>>> import technical_indicators as tai
>>> prices = np.array([22.27, 22.19, 22.08, 22.17, 22.18, 22.13, 22.23,
... 22.43, 22.24, 22.29, 22.15, 22.39, 22.38, 22.61, 23.36, 24.05, 23.75,
... 23.83, 23.95, 23.63, 23.82, 23.87, 23.65, 23.19, 23.10, 23.33, 22.68,
... 23.10, 22.40, 22.17])
>>> period = 10
>>> print(tai.ema(prices, period))
[ 22.221       22.20809091  22.24116529  22.26640796  22.32887924
  22.51635574  22.79520015  22.96880013  23.12538192  23.27531248
  23.33980112  23.42711001  23.50763546  23.53351992  23.47106176
  23.40359598  23.39021489  23.26108491  23.23179675  23.08056097
  22.91500443]
>>> print(tai.ema(prices, period, 1))
[ 22.27        22.25545455  22.22355372  22.21381668  22.20766819
  22.1935467   22.20017457  22.24196102  22.24160447  22.25040366
  22.23214845  22.26084873  22.2825126   22.34205576  22.52713653
  22.8040208   22.97601702  23.13128665  23.28014362  23.34375387
  23.43034408  23.51028152  23.53568488  23.47283308  23.40504525
  23.39140066  23.26205508  23.23259052  23.08121043  22.9155358 ]
>>> print(tai.ema(prices, period, 2))
[ 22.28588695  22.174706    22.35085492  22.37470018  22.5672175
  23.21585701  23.89833692  23.77696963  23.82035739  23.9264279
  23.68389526  23.79525297  23.85640891  23.68752817  23.28045894
  23.13280996  23.29414649  22.79166223  23.04393782  22.51707883
  22.23310448]

technical_indicators.technical_indicators.ma_env(prices, period, percent, ma_type=0)[source]¶

Moving Average Envelopes are percentage-based envelopes set above and below a moving average. They can be used as a trend following indicator. The envelopes can also be used to identify overbought and oversold levels when the trend is relatively flat.

Upper Envelope: MA + (MA x percent) Lower Envelope: MA - (MA x percent)

http://www.csidata.com/?page_id=797

http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_average_envel

http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:bollinger_band_perce

Input:: prices ndarray period int > 1 and < len(prices) percent float > 0.00 and < 1.00 ma_type 0=EMA type 0, 1=EMA type 1, 2=EMA type 2, 3=WMA, 4=SMA
Output:: ma_envs ndarray with upper, middle, lower bands, range and %B

Test:

>>> import numpy as np
>>> import technical_indicators as tai
>>> prices = np.array([86.16, 89.09, 88.78, 90.32, 89.07, 91.15, 89.44,
... 89.18, 86.93, 87.68, 86.96, 89.43, 89.32, 88.72, 87.45, 87.26, 89.50,
... 87.90, 89.13, 90.70, 92.90, 92.98, 91.80, 92.66, 92.68, 92.30, 92.77,
... 92.54, 92.95, 93.20, 91.07, 89.83, 89.74, 90.40, 90.74, 88.02, 88.09,
... 88.84, 90.78, 90.54, 91.39, 90.65])
>>> period = 20
>>> print(tai.ma_env(prices, period, 0.1, 4))
[[  97.57935      88.7085       79.83765      17.7417        0.35635537]
 [  97.95005      89.0455       80.14095      17.8091        0.50249872]
 [  98.164        89.24         80.316        17.848         0.4742268 ]
 [  98.3301       89.391        80.4519       17.8782        0.55196273]
 [  98.4588       89.508        80.5572       17.9016        0.47553291]
 [  98.65735      89.6885       80.71965      17.9377        0.58147644]
 [  98.7206       89.746        80.7714       17.9492        0.48295189]
 [  98.90375      89.9125       80.92125      17.9825        0.45926595]
 [  99.08855      90.0805       81.07245      18.0161        0.32512863]
 [  99.41965      90.3815       81.34335      18.0763        0.35055017]
 [  99.72325      90.6575       81.59175      18.1315        0.29607313]
 [  99.9493       90.863        81.7767       18.1726        0.42114502]
 [  99.9713       90.883        81.7947       18.1766        0.41401032]
 [  99.9944       90.904        81.8136       18.1808        0.37987327]
 [ 100.0868       90.988        81.8892       18.1976        0.30557876]
 [ 100.26775      91.1525       82.03725      18.2305        0.28648419]
 [ 100.30955      91.1905       82.07145      18.2381        0.40730942]
 [ 100.232        91.12         82.008        18.224         0.32330992]
 [ 100.2837       91.167        82.0503       18.2334        0.38828194]
 [ 100.37445      91.2495       82.12455      18.2499        0.46989025]
 [ 100.36565      91.2415       82.11735      18.2483        0.59088518]
 [ 100.2826       91.166        82.0494       18.2332        0.59948884]
 [ 100.15445      91.0495       81.94455      18.2099        0.54121385]]

technical_indicators.technical_indicators.roc(prices, period=21)[source]¶

The Rate-of-Change (ROC) indicator, a.k.a. Momentum, is a pure momentum oscillator that measures the percent change in price from one period to the next. The plot forms an oscillator that fluctuates above and below the zero line as the Rate-of-Change moves from positive to negative. ROC signals include centerline crossovers, divergences and overbought-oversold readings. Identifying overbought or oversold extremes comes natural to the Rate-of-Change oscillator. It can be used to measure the ROC of any data series, such as price or another indicator. Also known as PROC when used with price.

ROC = [(Close - Close n periods ago) / (Close n periods ago)] * 100

http://www.csidata.com/?page_id=797 http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:rate_of_change_roc_a

Input:: prices ndarray period int > 1 and < len(prices) (optional and defaults to 21)
Output:: rocs ndarray

Test:

>>> import numpy as np
>>> import technical_indicators as tai
>>> prices = np.array([11045.27, 11167.32, 11008.61, 11151.83, 10926.77,
... 10868.12, 10520.32, 10380.43, 10785.14, 10748.26, 10896.91, 10782.95,
... 10620.16, 10625.83, 10510.95, 10444.37, 10068.01, 10193.39, 10066.57,
... 10043.75])
>>> print(tai.roc(prices, period=12))
[-3.84879682 -4.84888048 -4.52064339 -6.34389154 -7.85923013 -6.20834146
 -4.31308173 -3.24341092]

technical_indicators.technical_indicators.rsi(prices, period=14)[source]¶

The Relative Strength Index (RSI) is a momentum oscillator. It oscillates between 0 and 100. It is considered overbought/oversold when it’s over 70/below 30. Some traders use 80/20 to be on the safe side. RSI becomes more accurate as the calculation period (min_periods) increases. This can be lowered to increase sensitivity or raised to decrease sensitivity. 10-day RSI is more likely to reach overbought or oversold levels than 20-day RSI. The look-back parameters also depend on a security’s volatility.

Like many momentum oscillators, overbought and oversold readings for RSI work best when prices move sideways within a range.

You can also look for divergence with price. If the price has new highs/lows, and the RSI hasn’t, expect a reversal. Signals can also be generated by looking for failure swings and centerline crossovers.

RSI can also be used to identify the general trend.

The RSI was developed by J. Welles Wilder and was first introduced in his article in the June, 1978 issue of Commodities magazine, now known as Futures magazine. It is detailed in his book New Concepts In Technical Trading Systems.

http://www.csidata.com/?page_id=797 http://stockcharts.com/help/doku.php?id=chart_school:technical_indicators:relative_strength_in

Input:: prices ndarray period int > 1 and < len(prices) (optional and defaults to 14)
Output:: rsis ndarray

Test:

>>> import numpy as np
>>> import technical_indicators as tai
>>> prices = np.array([44.55, 44.3, 44.36, 43.82, 44.46, 44.96, 45.23,
... 45.56, 45.98, 46.22, 46.03, 46.17, 45.75, 46.42, 46.42, 46.14, 46.17,
... 46.55, 46.36, 45.78, 46.35, 46.39, 45.85, 46.59, 45.92, 45.49, 44.16,
... 44.31, 44.35, 44.7, 43.55, 42.79, 43.26])
>>> print(tai.rsi(prices))
[ 70.02141328  65.77440817  66.01226849  68.95536568  65.88342192
  57.46707948  62.532685    62.86690858  55.64975092  62.07502976
  54.39159393  50.10513101  39.68712141  41.17273382  41.5859395
  45.21224077  37.06939108  32.85768734  37.58081218]

technical_indicators.technical_indicators.sma(prices, period)[source]¶

Simple Moving Average (SMA) are used to smooth the data in an array to help eliminate noise and identify trends. In SMA, each value in the time period carries equal weight.

They do not predict price direction, but can be used to identify the direction of the trend or define potential support and resistance levels.

SMA = (P1 + P2 + ... + Pn) / K where K = n and Pn is the most recent price

http://www.financialwebring.org/gummy-stuff/MA-stuff.htm

http://www.csidata.com/?page_id=797 http://stockcharts.com/school/doku.php?st=moving+average&id=chart_school:technical_indicators:moving_averages

Input:: prices ndarray period int > 1 and < len(prices)
Output:: smas ndarray

Test:

>>> import numpy as np
>>> import technical_indicators as tai
>>> prices = np.array([22.27, 22.19, 22.08, 22.17, 22.18, 22.13, 22.23,
... 22.43, 22.24, 22.29, 22.15, 22.39, 22.38, 22.61, 23.36, 24.05, 23.75,
... 23.83, 23.95, 23.63, 23.82, 23.87, 23.65, 23.19, 23.10, 23.33, 22.68,
... 23.10, 22.40, 22.17])
>>> period = 10
>>> print(tai.sma(prices, period))
[ 22.221  22.209  22.229  22.259  22.303  22.421  22.613  22.765  22.905
  23.076  23.21   23.377  23.525  23.652  23.71   23.684  23.612  23.505
  23.432  23.277  23.131]

technical_indicators.technical_indicators.wma(prices, period)[source]¶

Weighted Moving Average (WMA) is a type of moving average that assigns a higher weighting to recent price data.

WMA = (P1 + 2 P2 + 3 P3 + ... + n Pn) / K where K = (1+2+...+n) = n(n+1)/2 and Pn is the most recent price after the 1st WMA we can use another formula WMAn = WMAn-1 + w.(Pn - SMA(prices, n-1)) where w = 2 / (n + 1)

http://www.csidata.com/?page_id=797

http://www.financialwebring.org/gummy-stuff/MA-stuff.htm

http://www.investopedia.com/terms/l/linearlyweightedmovingaverage.asp

http://fxtrade.oanda.com/learn/forex-indicators/weighted-moving-average

Input:: prices ndarray period int > 1 and < len(prices)
Output:: wmas ndarray

Test:

>>> import numpy as np
>>> import technical_indicators as tai
>>> prices = np.array([77, 79, 79, 81, 83, 49, 55])
>>> period = 5
>>> print(tai.wma(prices, period))
[ 80.73333333  70.46666667  64.06666667]