https://machinelearningmastery.com/make-sample-forecasts-arima-python/
1.划分训练集测试集、这里讲最后7天的气温当做测试集
# split the dataset
from pandas import Series
series = Series.from_csv('daily-minimum-temperatures.csv', header=0)
split_point = len(series) - 7
dataset, validation = series[0:split_point], series[split_point:]
print('Dataset %d, Validation %d' % (len(dataset), len(validation)))
dataset.to_csv('dataset.csv')
validation.to_csv('validation.csv')2.1用forecat预测一步
The result of the forecast() function is an array containing the forecast value, the standard error of the forecast, and the confidence interval information. Now, we are only interested in the first element of this forecast, as follows.
from pandas import Series
from statsmodels.tsa.arima_model import ARIMA
import numpy
# create a differenced series
def difference(dataset, interval=1):
diff = list()
for i in range(interval, len(dataset)):
value = dataset[i] - dataset[i - interval]
diff.append(value)
return numpy.array(diff)
# invert differenced value减了之后要加回来再算mse衡量预测的好坏
# history[-interval]代表倒数第几个
def inverse_difference(history, yhat, interval=1):
return yhat + history[-interval]
# load dataset
series = Series.from_csv('dataset.csv', header=None)
# seasonal difference
X = series.values
days_in_year = 365
differenced = difference(X, days_in_year)
# fit model
model = ARIMA(differenced, order=(7,0,1))
model_fit = model.fit(disp=0)
# one-step out-of sample forecast一步预测
forecast = model_fit.forecast()[0]
# invert the differenced forecast to something usable
forecast = inverse_difference(X, forecast, days_in_year)
print('Forecast: %f' % forecast)结果：Forecast: 14.861669
之后拿这个结果去与测试集上进行对比即可
2.2用predict
The statsmodel ARIMAResults object also provides a predict() function for making forecasts.
The predict function can be used to predict arbitrary in-sample and out-of-sample time steps, including the next out-of-sample forecast time step.
The predict function requires a start and an end to be specified, these can be the indexes of the time steps relative to the beginning of the training data used to fit the model
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# one-step out of sample forecast start_index = len(differenced) end_index = len(differenced) forecast = model_fit.predict(start=start_index, end=end_index) |
The start and end can also be a datetime string or a “datetime” type; for example:
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start_index = '1990-12-25' end_index = '1990-12-25' forecast = model_fit.predict(start=start_index, end=end_index) |
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from pandas import datetime start_index = datetime(1990, 12, 25) end_index = datetime(1990, 12, 26) forecast = model_fit.predict(start=start_index, end=end_index) |
from pandas import Series
from statsmodels.tsa.arima_model import ARIMA
import numpy
from pandas import datetime
# create a differenced series
def difference(dataset, interval=1):
diff = list()
for i in range(interval, len(dataset)):
value = dataset[i] - dataset[i - interval]
diff.append(value)
return numpy.array(diff)
# invert differenced value
def inverse_difference(history, yhat, interval=1):
return yhat + history[-interval]
# load dataset
series = Series.from_csv('dataset.csv', header=None)
# seasonal difference
X = series.values
days_in_year = 365
differenced = difference(X, days_in_year)
# fit model
model = ARIMA(differenced, order=(7,0,1))
model_fit = model.fit(disp=0)
# one-step out of sample forecast
start_index = len(differenced)
end_index = len(differenced)
forecast = model_fit.predict(start=start_index, end=end_index)
# invert the differenced forecast to something usable
forecast = inverse_difference(X, forecast, days_in_year)
print('Forecast: %f' % forecast)Forecast: 14.861669
可以看出来predict更灵活，可以指定位置
3.1多步用forcast
这里要改变一下inverted
# multi-step out-of-sample forecast
forecast = model_fit.forecast(steps=7)[0]
# invert the differenced forecast to something usable
history = [x for x in X]
day = 1
for yhat in forecast:
inverted = inverse_difference(history, yhat, days_in_year)
print('Day %d: %f' % (day, inverted))
history.append(inverted)
day += 1解释一下：history[-interval]代表倒数第几个，本来预测最后一个，加上history[-interval]就可以，
可是这个是多步啊，所以倒数第二个要加上history[-（interval+1）]
但是 我每一步都history。append就不用该变原来代码啦
完整代码：
from pandas import Series
from statsmodels.tsa.arima_model import ARIMA
import numpy
# create a differenced series
def difference(dataset, interval=1):
diff = list()
for i in range(interval, len(dataset)):
value = dataset[i] - dataset[i - interval]
diff.append(value)
return numpy.array(diff)
# invert differenced value
def inverse_difference(history, yhat, interval=1):
return yhat + history[-interval]
# load dataset
series = Series.from_csv('dataset.csv', header=None)
# seasonal difference
X = series.values
days_in_year = 365
differenced = difference(X, days_in_year)
# fit model
model = ARIMA(differenced, order=(7,0,1))
model_fit = model.fit(disp=0)
# multi-step out-of-sample forecast
forecast = model_fit.forecast(steps=7)[0]
# invert the differenced forecast to something usable
history = [x for x in X]
day = 1
for yhat in forecast:
inverted = inverse_difference(history, yhat, days_in_year)
print('Day %d: %f' % (day, inverted))
history.append(inverted)
day += 1Day 1: 14.861669
Day 2: 15.628784
Day 3: 13.331349
Day 4: 11.722413
Day 5: 10.421523
Day 6: 14.415549
Day 7: 12.674711
3.2用predict
from pandas import Series
from statsmodels.tsa.arima_model import ARIMA
import numpy
# create a differenced series
def difference(dataset, interval=1):
diff = list()
for i in range(interval, len(dataset)):
value = dataset[i] - dataset[i - interval]
diff.append(value)
return numpy.array(diff)
# invert differenced value
def inverse_difference(history, yhat, interval=1):
return yhat + history[-interval]
# load dataset
series = Series.from_csv('dataset.csv', header=None)
# seasonal difference
X = series.values
days_in_year = 365
differenced = difference(X, days_in_year)
# fit model
model = ARIMA(differenced, order=(7,0,1))
model_fit = model.fit(disp=0)
# multi-step out-of-sample forecast
start_index = len(differenced)
end_index = start_index + 6
forecast = model_fit.predict(start=start_index, end=end_index)
# invert the differenced forecast to something usable
history = [x for x in X]
day = 1
for yhat in forecast:
inverted = inverse_difference(history, yhat, days_in_year)
print('Day %d: %f' % (day, inverted))
history.append(inverted)
day += 1Using time step indexes, we can specify the end index as 6 more time steps in the future; for example:
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# multi-step out-of-sample forecast start_index = len(differenced) end_index = start_index + 6 forecast = model_fit.predict(start=start_index, end=end_index) |
Day 1: 14.861669
Day 2: 15.628784
Day 3: 13.331349
Day 4: 11.722413
Day 5: 10.421523
Day 6: 14.415549
Day 7: 12.674711
注：我其实没有明白这个多步预测的原理是啥子，我猜测之前讲的模型2，
因为第2个样本的t-1时刻我们不知道啊，这个时候没法滚动了，可能只利用之前预测的当做输入