時間序列（或稱動態數列）是指將同一統計指標的數值按其發生的時間先后順序排列而成的數列。時間序列分析的主要目的是根據已有的歷史數據對未來進行預測。
時間序列構成要素：長期趨勢，季節變動，循環變動，不規則變動
- 長期趨勢（ T ）現象在較長時期內受某種根本性因素作用而形成的總的變動趨勢
- 季節變動（ S ）現象在一年內隨著季節的變化而發生的有規律的周期性變動
- 循環變動（ C ）現象以若干年為周期所呈現出的波浪起伏形態的有規律的變動
- 不規則變動（I ）是一種無規律可循的變動，包括嚴格的隨機變動和不規則的突發性影響很大的變動兩種類型
（1）原始時間序列數據（只列出了18行）
1455.219971
1399.420044
1402.109985
1403.449951
1441.469971
1457.599976
1438.560059
1432.25
1449.680054
1465.150024
1455.140015
1455.900024
1445.569946
1441.359985
1401.530029
1410.030029
1404.089966
1398.560059
（ 2）處理數據使之符合LSTM的要求
為了更加直觀的了解數據格式，代碼中加入了一些打印（print），并且后面加了注釋，就是輸出值
def
load_data
(filename, seq_len)
:
f = open(filename,
'rb'
).read()
data = f.split(
'\n'
)
print(
'data len:'
,len(data))
#4172
print(
'sequence len:'
,seq_len)
#50
sequence_length = seq_len +
1
result = []
for
index
in
range(len(data) - sequence_length):
result.append(data[index: index + sequence_length])
#得到長度為seq_len+1的向量，最后一個作為label
print(
'result len:'
,len(result))
#4121
print(
'result shape:'
,np.array(result).shape)
#（4121,51）
result = np.array(result)
#劃分train、test
row = round(
0.9
* result.shape[
0
])
train = result[:row, :]
np.random.shuffle(train)
x_train = train[:, :-
1
]
y_train = train[:, -
1
]
x_test = result[row:, :-
1
]
y_test = result[row:, -
1
]
x_train = np.reshape(x_train, (x_train.shape[
0
], x_train.shape[
1
],
1
))
x_test = np.reshape(x_test, (x_test.shape[
0
], x_test.shape[
1
],
1
))
print(
'X_train shape:'
,X_train.shape)
#(3709L, 50L, 1L)
print(
'y_train shape:'
,y_train.shape)
#(3709L,)
print(
'X_test shape:'
,X_test.shape)
#(412L, 50L, 1L)
print(
'y_test shape:'
,y_test.shape)
#(412L,)
return
[x_train, y_train, x_test, y_test]
（3）LSTM模型
本文使用的是keras深度學習框架，讀者可能用的是其他的，諸如theano、tensorflow等，大同小異。
Keras LSTM官方文檔
LSTM的結構可以自己定制，Stack LSTM or Bidirectional LSTM
def
build_model
(layers)
:
#layers [1,50,100,1]
model = Sequential()
#Stack LSTM
model.add(LSTM(input_dim=layers[
0
],output_dim=layers[
1
],return_sequences=
True
))
model.add(Dropout(
0.2
))
model.add(LSTM(layers[
2
],return_sequences=
False
))
model.add(Dropout(
0.2
))
model.add(Dense(output_dim=layers[
3
]))
model.add(Activation(
"linear"
))
start = time.time()
model.compile(loss=
"mse"
, optimizer=
"rmsprop"
)
print(
"Compilation Time : "
, time.time() - start)
return
model
（4）LSTM訓練預測
1.直接預測
def
predict_point_by_point
(model, data)
:
predicted = model.predict(data)
print(
'predicted shape:'
,np.array(predicted).shape)
#(412L,1L)
predicted = np.reshape(predicted, (predicted.size,))
return
predicted
2.滾動預測
def predict_sequence_full(model, data, window_size): #data X_test
curr_frame = data[
0
] #(
50
L,
1
L)
predicted = []
for
i
in
xrange(len(data)):
#x = np.array(
[[[1],[2],[3]]
,
[[4],[5],[6]]
]) x.shape (
2
,
3
,
1
) x[
0
,
0
] = array([
1
]) x[:,np.newaxis,:,:].shape (
2
,
1
,
3
,
1
)
predicted.append(model.predict(curr_frame[newaxis,:,:])[
0
,
0
]) #np.array(curr_frame[newaxis,:,:]).shape (
1
L,
50
L,
1
L)
curr_frame = curr_frame[
1
:]
curr_frame = np.insert(curr_frame, [window_size-
1
], predicted[-
1
], axis=
0
) #numpy.insert(arr, obj, values, axis=None)
return
predicted
2.滑動窗口+滾動預測
def
predict_sequences_multiple
(model, data, window_size, prediction_len)
:
#window_size = seq_len
prediction_seqs = []
for
i
in
xrange(len(data)/prediction_len):
curr_frame = data[i*prediction_len]
predicted = []
for
j
in
xrange(prediction_len):
predicted.append(model.predict(curr_frame[newaxis,:,:])[
0
,
0
])
curr_frame = curr_frame[
1
:]
curr_frame = np.insert(curr_frame, [window_size-
1
], predicted[-
1
], axis=
0
)
prediction_seqs.append(predicted)
return
prediction_seqs
（5）完整代碼
示例數據集 sp500.csv
# -*- coding: utf-8 -*-
from
__future__
import
print_function
import
time
import
warnings
import
numpy
as
np
import
time
import
matplotlib.pyplot
as
plt
from
numpy
import
newaxis
from
keras.layers.core
import
Dense, Activation, Dropout
from
keras.layers.recurrent
import
LSTM
from
keras.models
import
Sequential
warnings.filterwarnings(
"ignore"
)
def
load_data
(filename, seq_len, normalise_window)
:
f = open(filename,
'rb'
).read()
data = f.split(
'\n'
)
print(
'data len:'
,len(data))
print(
'sequence len:'
,seq_len)
sequence_length = seq_len +
1
result = []
for
index
in
range(len(data) - sequence_length):
result.append(data[index: index + sequence_length])
#得到長度為seq_len+1的向量，最后一個作為label
print(
'result len:'
,len(result))
print(
'result shape:'
,np.array(result).shape)
print(result[:
1
])
if
normalise_window:
result = normalise_windows(result)
print(result[:
1
])
print(
'normalise_windows result shape:'
,np.array(result).shape)
result = np.array(result)
#劃分train、test
row = round(
0.9
* result.shape[
0
])
train = result[:row, :]
np.random.shuffle(train)
x_train = train[:, :-
1
]
y_train = train[:, -
1
]
x_test = result[row:, :-
1
]
y_test = result[row:, -
1
]
x_train = np.reshape(x_train, (x_train.shape[
0
], x_train.shape[
1
],
1
))
x_test = np.reshape(x_test, (x_test.shape[
0
], x_test.shape[
1
],
1
))
return
[x_train, y_train, x_test, y_test]
def
normalise_windows
(window_data)
:
normalised_data = []
for
window
in
window_data:
#window shape (sequence_length L ,) 即(51L,)
normalised_window = [((float(p) / float(window[
0
])) -
1
)
for
p
in
window]
normalised_data.append(normalised_window)
return
normalised_data
def
build_model
(layers)
:
#layers [1,50,100,1]
model = Sequential()
model.add(LSTM(input_dim=layers[
0
],output_dim=layers[
1
],return_sequences=
True
))
model.add(Dropout(
0.2
))
model.add(LSTM(layers[
2
],return_sequences=
False
))
model.add(Dropout(
0.2
))
model.add(Dense(output_dim=layers[
3
]))
model.add(Activation(
"linear"
))
start = time.time()
model.compile(loss=
"mse"
, optimizer=
"rmsprop"
)
print(
"Compilation Time : "
, time.time() - start)
return
model
#直接全部預測
def
predict_point_by_point
(model, data)
:
predicted = model.predict(data)
print(
'predicted shape:'
,np.array(predicted).shape)
#(412L,1L)
predicted = np.reshape(predicted, (predicted.size,))
return
predicted
#滾動預測
def
predict_sequence_full
(model, data, window_size)
:
#data X_test
curr_frame = data[
0
]
#(50L,1L)
predicted = []
for
i
in
xrange(len(data)):
#x = np.array([[[1],[2],[3]], [[4],[5],[6]]]) x.shape (2, 3, 1) x[0,0] = array([1]) x[:,np.newaxis,:,:].shape (2, 1, 3, 1)
predicted.append(model.predict(curr_frame[newaxis,:,:])[
0
,
0
])
#np.array(curr_frame[newaxis,:,:]).shape (1L,50L,1L)
curr_frame = curr_frame[
1
:]
curr_frame = np.insert(curr_frame, [window_size-
1
], predicted[-
1
], axis=
0
)
#numpy.insert(arr, obj, values, axis=None)
return
predicted
def
predict_sequences_multiple
(model, data, window_size, prediction_len)
:
#window_size = seq_len
prediction_seqs = []
for
i
in
xrange(len(data)/prediction_len):
curr_frame = data[i*prediction_len]
predicted = []
for
j
in
xrange(prediction_len):
predicted.append(model.predict(curr_frame[newaxis,:,:])[
0
,
0
])
curr_frame = curr_frame[
1
:]
curr_frame = np.insert(curr_frame, [window_size-
1
], predicted[-
1
], axis=
0
)
prediction_seqs.append(predicted)
return
prediction_seqs
def
plot_results
(predicted_data, true_data, filename)
:
fig = plt.figure(facecolor=
'white'
)
ax = fig.add_subplot(
111
)
ax.plot(true_data, label=
'True Data'
)
plt.plot(predicted_data, label=
'Prediction'
)
plt.legend()
plt.show()
plt.savefig(filename+
'.png'
)
def
plot_results_multiple
(predicted_data, true_data, prediction_len)
:
fig = plt.figure(facecolor=
'white'
)
ax = fig.add_subplot(
111
)
ax.plot(true_data, label=
'True Data'
)
#Pad the list of predictions to shift it in the graph to it's correct start
for
i, data
in
enumerate(predicted_data):
padding = [
None
for
p
in
xrange(i * prediction_len)]
plt.plot(padding + data, label=
'Prediction'
)
plt.legend()
plt.show()
plt.savefig(
'plot_results_multiple.png'
)
if
__name__==
'__main__'
:
global_start_time = time.time()
epochs =
1
seq_len =
50
print(
'> Loading data... '
)
X_train, y_train, X_test, y_test = lstm.load_data(
'sp500.csv'
, seq_len,
True
)
print(
'X_train shape:'
,X_train.shape)
#(3709L, 50L, 1L)
print(
'y_train shape:'
,y_train.shape)
#(3709L,)
print(
'X_test shape:'
,X_test.shape)
#(412L, 50L, 1L)
print(
'y_test shape:'
,y_test.shape)
#(412L,)
print(
'> Data Loaded. Compiling...'
)
model = lstm.build_model([
1
,
50
,
100
,
1
])
model.fit(X_train,y_train,batch_size=
512
,nb_epoch=epochs,validation_split=
0.05
)
multiple_predictions = lstm.predict_sequences_multiple(model, X_test, seq_len, prediction_len=
50
)
print(
'multiple_predictions shape:'
,np.array(multiple_predictions).shape)
#(8L,50L)
full_predictions = lstm.predict_sequence_full(model, X_test, seq_len)
print(
'full_predictions shape:'
,np.array(full_predictions).shape)
#(412L,)
point_by_point_predictions = lstm.predict_point_by_point(model, X_test)
print(
'point_by_point_predictions shape:'
,np.array(point_by_point_predictions).shape)
#(412L)
print(
'Training duration (s) : '
, time.time() - global_start_time)
plot_results_multiple(multiple_predictions, y_test,
50
)
plot_results(full_predictions,y_test,
'full_predictions'
)
plot_results(point_by_point_predictions,y_test,
'point_by_point_predictions'
)
更多文章、技術交流、商務合作、聯系博主
微信掃碼或搜索：z360901061
微信掃一掃加我為好友
QQ號聯系： 360901061
您的支持是博主寫作最大的動力，如果您喜歡我的文章，感覺我的文章對您有幫助，請用微信掃描下面二維碼支持博主2元、5元、10元、20元等您想捐的金額吧，狠狠點擊下面給點支持吧，站長非常感激您！手機微信長按不能支付解決辦法：請將微信支付二維碼保存到相冊，切換到微信，然后點擊微信右上角掃一掃功能，選擇支付二維碼完成支付。
【本文對您有幫助就好】元
