時間序列（或稱動態(tài)數(shù)列）是指將同一統(tǒng)計指標(biāo)的數(shù)值按其發(fā)生的時間先后順序排列而成的數(shù)列。時間序列分析的主要目的是根據(jù)已有的歷史數(shù)據(jù)對未來進行預(yù)測。
時間序列構(gòu)成要素：長期趨勢，季節(jié)變動，循環(huán)變動，不規(guī)則變動
- 長期趨勢（ T ）現(xiàn)象在較長時期內(nèi)受某種根本性因素作用而形成的總的變動趨勢
- 季節(jié)變動（ S ）現(xiàn)象在一年內(nèi)隨著季節(jié)的變化而發(fā)生的有規(guī)律的周期性變動
- 循環(huán)變動（ C ）現(xiàn)象以若干年為周期所呈現(xiàn)出的波浪起伏形態(tài)的有規(guī)律的變動
- 不規(guī)則變動（I ）是一種無規(guī)律可循的變動，包括嚴格的隨機變動和不規(guī)則的突發(fā)性影響很大的變動兩種類型
（1）原始時間序列數(shù)據(jù)（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(shù)據(jù)使之符合LSTM的要求
為了更加直觀的了解數(shù)據(jù)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(xué)習(xí)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(jié)構(gòu)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(xùn)練預(yù)測
1.直接預(yù)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(yù)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(yù)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(shù)據(jù)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(yù)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(yù)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'
)
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