时间序列–残差分析

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残差=y-yhat

一般我们就停止在这里了

但是如果残差表现的有某种形式,代表我们的模型需要进一步改进,如果残差表现的杂乱无章,代表确实没什么别的信息好提取了

现在用最naive的model–上一个时间的值=yhat看看残差表现吧

关于残差,可以看我的另一篇文章

https://mp.csdn.net/postedit/82989567

from pandas import Series
from pandas import DataFrame
from pandas import concat
series = Series.from_csv('daily-total-female-births.csv', header=0)
# create lagged dataset
values = DataFrame(series.values)
dataframe = concat([values.shift(1), values], axis=1)
dataframe.columns = ['t-1', 't+1']
# split into train and test sets
X = dataframe.values
train_size = int(len(X) * 0.66)
train, test = X[1:train_size], X[train_size:]
train_X, train_y = train[:,0], train[:,1]
test_X, test_y = test[:,0], test[:,1]
# persistence model
predictions = [x for x in test_X]
# calculate residuals
residuals = [test_y[i]-predictions[i] for i in range(len(predictions))]
residuals = DataFrame(residuals)
print(residuals.head())
residuals.plot()
pyplot.show()

残差表现如下:

Line Plot of Residual Errors for the Daily Female Births Dataset

现在看看基本信息

1.均值–越接近0越好

A value close to zero suggests no bias in the forecasts, whereas positive and negative values suggest a positive or negative bias in the forecasts made.

print(residuals.describe())

结果如下

count  125.000000

mean     0.064000

std      9.187776

min    -28.000000

25%     -6.000000

50%     -1.000000

75%      5.000000

max     30.000000

mean和0还是有点差距

2.直方图密度图about残差

我们希望残差分布越接近正太越好

If the plot showed a distribution that was distinctly non-Gaussian, it would suggest that assumptions made by the modeling process were perhaps incorrect and that a different modeling method may be required.

A large skew may suggest the opportunity for performing a transform to the data prior to modeling, such as taking the log or square root.

# histogram plot

residuals.hist()

pyplot.show()

# density plot

residuals.plot(kind=’kde’)

pyplot.show()

Histogram Plot of Residual Errors for the Daily Female Births Dataset

Density Plot of Residual Errors for the Daily Female Births Dataset

3.QQ图检验正太更快速的方式

from pandas import Series
from pandas import DataFrame
from pandas import concat
from matplotlib import pyplot
import numpy
from statsmodels.graphics.gofplots import qqplot
series = Series.from_csv('daily-total-female-births.csv', header=0)
# create lagged dataset
values = DataFrame(series.values)
dataframe = concat([values.shift(1), values], axis=1)
dataframe.columns = ['t-1', 't+1']
# split into train and test sets
X = dataframe.values
train_size = int(len(X) * 0.66)
train, test = X[1:train_size], X[train_size:]
train_X, train_y = train[:,0], train[:,1]
test_X, test_y = test[:,0], test[:,1]
# persistence model
predictions = [(x-0.064000) for x in test_X]
# calculate residuals
residuals = [test_y[i]-predictions[i] for i in range(len(predictions))]
residuals = numpy.array(residuals)
qqplot(residuals)
pyplot.show()

Q-Q Plot of Residual Errors for the Daily Female Births Dataset
越接近对角线越好

4.自回归图

残差的自回归越小越好!

Autocorrelation Plot of Residual Errors for the Daily Female Births Dataset

We do not see an obvious autocorrelation trend across the plot. There may be some positive autocorrelation worthy of further investigation at lag 7 that seems significant.


https://machinelearningmastery.com/visualize-time-series-residual-forecast-errors-with-python/