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### Á¿»¯½»ÒײßÂÔ£º½áºÏ²¼ÁÖ´ø£¨BB£©ÓëBearsÖ¸±êµÄºÕ×ÈÁ¿»¯·ÖÎö3 v0 S) o* p" U$ `
²¼ÁÖ´ø£¨Bollinger Bands, BB£©ºÍBearsÖ¸±êÊǽðÈÚÊг¡Öг£Óõļ¼Êõ·ÖÎö¹¤¾ß£¬ÓÃÓÚÅжÏÊг¡µÄ²¨¶¯ÐÔºÍDZÔڵļ۸ñ·´×ªµã¡£±¾ÎĽ«Õ¹Ê¾ÈçºÎ½«ÕâÁ½¸öÖ¸±êÓëºÕ×ÈÁ¿»¯·ÖÎöÏà½áºÏ£¬ÒÔÉè¼ÆÒ»¸öÁ¿»¯½»ÒײßÂÔ£¬²¢ÌṩÏà¹ØPython´úÂëʵÏÖ¡£/ f3 p8 q- g; x( J$ ?) M
#### 1. ²¼ÁÖ´ø£¨BB£©¸ÅÊö
0 K/ d2 x+ N) A. T+ A1 ]% e3 z2 i²¼ÁÖ´øÓÉÖмäµÄ¼òµ¥Òƶ¯Æ½¾ùÏߣ¨SMA£©ºÍÎ§ÈÆÆäÉÏϵÄÁ½Ìõ±ê×¼²îÏß×é³É¡£ÕâЩ´ø×´Ïß¿ÉÒÔ°ïÖú·ÖÎö¹É¼ÛµÄ²¨¶¯·¶Î§ºÍÊг¡µÄ²¨¶¯ÐÔ£¬Í¨³£¹É¼Û´¥¼°ÉÏ´ø»òÏ´ø¿ÉÄܱíʾDZÔڵĻص÷»ò·´×ª¡£
- y/ O; ?, K6 L, m/ Y#### 2. BearsÖ¸±ê¸ÅÊö) A8 V9 y- P1 V& y% Y6 T1 M
BearsÖ¸±êͨ³£ÓÃÓÚÏÔʾÊг¡Âô·½Ñ¹Á¦£¬¼ÆË㷽ʽÊÇÈ¡ÌØ¶¨ÖÜÆÚÄÚµÄ×îµÍ¼ÛºÍÊÕÅ̼ÛÖ®¼äµÄ²îÖµ¡£ÔöÇ¿µÄBearsÖµ¿ÉÄܰµÊ¾ÏµøÇ÷ÊÆµÄ¼ÓÇ¿¡£7 g# S, {+ N2 C% U6 p* e
#### 3. ºÕ×ÈÁ¿»¯·ÖÎö) U5 A3 h9 H5 B4 X* g; X' j
ºÕ×ÈÁ¿»¯·ÖÎöÔÚ±¾²ßÂÔÖÐÓÃÓÚʶ±ð²¼ÁÖ´øºÍBearsÖ¸±êµÄƵÂÊÏìÓ¦£¬Í¨¹ý¿ìËÙ¸µÀïÒ¶±ä»»£¨FFT£©·ÖÎöÊý¾ÝµÄÖÜÆÚÐÔºÍÕñ·ù£¬´Ó¶ø¸¨ÖúÈ·¶¨×î¼Ñ½»Ò×ʱ»ú¡£! F* z6 S& Q" Y5 `
#### 4. ½»ÒײßÂÔÉè¼ÆÓëPython´úÂëʵÏÖ
4 u( Y) w+ r: m$ A& YÒÔÏÂÊÇʵÏÖÕâÒ»²ßÂԵļò»¯²½Öè¼°ÆäPython´úÂ룺
  U0 P* O- P. {* B##### ²½Öè1: Êý¾Ý×¼±¸
' o" ~. n/ N- i6 B& }Ê×ÏÈ£¬µ¼Èë±ØÒªµÄPython¿â£¬²¢¼ÓÔØ¹ÉƱÊý¾Ý£º5 V+ i: W' r# N' b- U# y
```python
3 X0 w6 I  e" q: N& c3 }( o) \import numpy as np% `+ [" W7 T/ Y1 [7 X. |- F
import pandas as pd) s& G; v7 d. e( w- @$ M9 I
import matplotlib.pyplot as plt
. Y9 P3 Y6 u# t) B2 Xfrom scipy.fft import fft2 D3 u5 U4 E+ H# Z8 Z0 T
# ¼ÓÔØÊý¾Ý£¬ÕâÀïÒÔ'DATA.csv'ΪÀý£¬°üº¬Open, High, Low, CloseÁÐ
8 K2 k; ]% J. y  T: Rdata = pd.read_csv('DATA.csv', parse_dates=True, index_col='Date')
, c1 a; _5 R. {- s1 c```" g. N# w, y* K, R& n; a
##### ²½Öè2: ¼ÆËã²¼ÁÖ´øÓëBearsÖ¸±ê5 A- T5 Z' a( c! Z' |, e$ r) q
```python
6 ?- ^6 z0 _! q( }# ¼ÆËã¼òµ¥Òƶ¯Æ½¾ùÏߺͱê×¼²î
) k  u9 @; J0 G9 U1 ywindow = 20  # ²¼ÁÖ´øµÄÖÜÆÚ
- u2 s1 b3 K) _9 `$ U/ Hdata['SMA'] = data['Close'].rolling(window=window).mean()
4 S7 t" O# F" {7 @data['STD'] = data['Close'].rolling(window=window).std()" N7 Y- b5 W8 }' J( E
# ¼ÆËã²¼ÁÖ´ø4 M7 P! i# e( p: i1 ~
data['Upper'] = data['SMA'] + (data['STD'] * 2)/ o1 \) L4 ]6 f% n
data['Lower'] = data['SMA'] - (data['STD'] * 2)$ {) A6 y( _8 v6 s7 b2 k- W2 p& Z
# ¼ÆËãBearsÖ¸±ê
4 a  z  l- j' T" \& }. b) pdata['Bears'] = data['Low'] - data['Close'], l% S$ a1 I& G5 p% X: o+ l
```
: ^1 @' S/ s. M0 @9 x2 i6 V##### ²½Öè3: ºÕ×ÈÁ¿»¯·ÖÎö1 }4 ~& r: E& H
```python
7 b; s& x( d5 Z/ D+ l8 r1 _& ?# FFT񄯯* H! P$ t7 t! Q( r8 ~4 N' g
fft_values = fft(data['Bears'].dropna())5 L3 }9 q4 z0 f
frequencies = np.fft.fftfreq(len(fft_values))
1 d3 L2 i) X6 |! k; K9 m  ?+ k# ÕÒµ½Ö÷ҪƵÂÊ
  Y/ y7 w! ^, Kmain_freq = frequencies[np.argmax(np.abs(fft_values))]
+ C( X, ^) g3 u% M, i: l9 C```3 T5 E, O7 w. f- ^/ R: ^; t* R
##### ²½Öè4: ²ßÂÔʵʩ
4 U' f' F% b5 w# M; c/ i: t2 I```python
8 I: O7 F  ?3 H' w# O* f# É趨ÂòÈëÂô³öÌõ¼þ  `  Y: n3 b' W4 I
data['Buy'] = (data['Close'] < data['Lower']) & (data['Bears'] > 0)
* e5 X  ^# h. H$ W) w  g& Fdata['Sell'] = (data['Close'] > data['Upper']) & (data['Bears'] < 0)
+ C3 r3 M; w( q$ I9 L# »æÖÆÂòÈëÂô³öµã
) q3 D4 C9 k1 h' G; Dplt.figure(figsize=(14, 7))
3 |! V8 s. Z7 y8 q) Bplt.plot(data['Close'], label='Close')9 \, T7 G* k8 o3 E1 ?; k  F
plt.plot(data['Upper'], label='Upper Band')
1 m9 o, p5 Q0 Cplt.plot(data['Lower'], label='Lower Band')
. r& T4 e; h6 i9 a) y; Aplt.plot(data.index, data['Buy'] * data['Close'], '^', markersize=10, color='g', lw=0, label='Buy Signal')
" o# H" N% e* s# e; y) p2 X, @* d3 L. Fplt.plot(data.index, data['Sell'] * data['Close'], 'v', markersize=10, color='r', lw=0, label='Sell Signal')) P/ G2 d) b- k% y2 g4 ^! m
plt
0 u7 D2 z( y7 ~0 V) u8 U) a.title('Bollinger Bands with Buy and Sell Signals')
3 c: J8 Z5 Q* a0 hplt.legend()
0 L. q- s4 t9 l. D0 \plt.show()9 F5 I4 A& I2 b) G' I( X, W
```. _. {' t; `( `( }4 w, h. x
#### 5.
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