时间序列预测误差_时间序列-误差指标
时间序列预测误差
时间序列-误差指标 (Time Series - Error Metrics)
It is important for us to quantify the performance of a model to use it as a feedback and comparison. In this tutorial we have used one of the most popular error metric root mean squared error. There are various other error metrics available. This chapter discusses them in brief.
对我们来说，量化模型的性能以将其用作反馈和比较非常重要。 在本教程中，我们使用了最流行的误差度量均方根误差之一。 还有其他各种错误度量标准。 本章简要讨论它们。
均方误差 (Mean Square Error)
It is the average of square of difference between the predicted values and true values. Sklearn provides it as a function. It has the same units as the true and predicted values squared and is always positive.
它是预测值和真实值之间差异的平方的平均值。 Sklearn提供了它的功能。 它的单位与真实值和预测值的平方相同，并且始终为正。
$$MSE = \frac{1}{n} \displaystyle\sum\limits_{t=1}^n \lgroup y'_{t}\:-y_{t}\rgroup^{2}$$
$$ MSE = \ frac {1} {n} \ displaystyle \ sum \ limits_ {t = 1} ^ n \ lgroup y'_ {t} \：-y_ {t} \ rgroup ^ {2} $$
Where $y'_{t}$ is the predicted value,
其中$ y'_ {t} $是预测值，
$y_{t}$ is the actual value, and
$ y_ {t} $是实际值，并且
n is the total number of values in test set.
n是测试集中值的总数。
It is clear from the equation that MSE is more penalizing for larger errors, or the outliers.
从方程式中可以明显看出，MSE对于较大的错误或异常值的惩罚更大。
根均方误差 (Root Mean Square Error)
It is the square root of the mean square error. It is also always positive and is in the range of the data.
它是均方误差的平方根。 它也总是正的，并且在数据范围内。
$$RMSE = \sqrt{\frac{1}{n} \displaystyle\sum\limits_{t=1}^n \lgroup y'_{t}-y_{t}\rgroup ^2}$$
$$ RMSE = \ sqrt {\ frac {1} {n} \ displaystyle \ sum \ limits_ {t = 1} ^ n \ lgroup y'_ {t} -y_ {t} \ rgroup ^ 2} $$
Where, $y'_{t}$ is predicted value
其中， $ y'_ {t} $是预测值
$y_{t}$ is actual value, and
$ y_ {t} $是实际值，并且
n is total number of values in test set.
n是测试集中值的总数。
It is in the power of unity and hence is more interpretable as compared to MSE. RMSE is also more penalizing for larger errors. We have used RMSE metric in our tutorial.
它具有统一性，因此与MSE相比更具可解释性。 对于较大的错误，RMSE也会受到更大的惩罚。 我们在本教程中使用了RMSE指标。
平均绝对误差 (Mean Absolute Error)
It is the average of absolute difference between predicted values and true values. It has the same units as predicted and true value and is always positive.
它是预测值和真实值之间的绝对差的平均值。 它具有与预测值和真实值相同的单位，并且始终为正。
$$MAE = \frac{1}{n}\displaystyle\sum\limits_{t=1}^{t=n} | y'{t}-y_{t}\lvert$$
$$ MAE = \ frac {1} {n} \ displaystyle \ sum \ limits_ {t = 1} ^ {t = n} | y'{t} -y_ {t} \ lvert $$
Where, $y'_{t}$ is predicted value,
其中， $ y'_ {t} $是预测值，
$y_{t}$ is actual value, and
$ y_ {t} $是实际值，并且
n is total number of values in test set.
n是测试集中值的总数。
平均百分比误差 (Mean Percentage Error)
It is the percentage of average of absolute difference between predicted values and true values, divided by the true value.
它是预测值和真实值之间的绝对差平均值的平均值除以真实值的百分比。
$$MAPE = \frac{1}{n}\displaystyle\sum\limits_{t=1}^n\frac{y'_{t}-y_{t}}{y_{t}}*100\: \%$$
$$ MAPE = \ frac {1} {n} \ displaystyle \ sum \ limits_ {t = 1} ^ n \ frac {y'_ {t} -y_ {t}} {y_ {t}} * 100 \： \％$$
Where, $y'_{t}$ is predicted value,
其中， $ y'_ {t} $是预测值，
$y_{t}$ is actual value and n is total number of values in test set.
$ y_ {t} $是实际值，n是测试集中的值总数。
However, the disadvantage of using this error is that the positive error and negative errors can offset each other. Hence mean absolute percentage error is used.
但是，使用此误差的缺点是正误差和负误差会相互抵消。 因此，使用平均绝对百分比误差。
平均绝对百分比误差 (Mean Absolute Percentage Error)
It is the percentage of average of absolute difference between predicted values and true values, divided by the true value.
它是预测值和真实值之间的绝对差平均值的平均值除以真实值的百分比。
$$MAPE = \frac{1}{n}\displaystyle\sum\limits_{t=1}^n\frac{|y'_{t}-y_{t}\lvert}{y_{t}}*100\: \%$$
$$ MAPE = \ frac {1} {n} \ displaystyle \ sum \ limits_ {t = 1} ^ n \ frac {| y'_ {t} -y_ {t} \ lvert} {y_ {t}} * 100 \：\％$$
Where $y'_{t}$ is predicted value
其中$ y'_ {t} $是预测值
$y_{t}$ is actual value, and
$ y_ {t} $是实际值，并且
n is total number of values in test set.
n是测试集中值的总数。
翻译自: https://www.tutorialspoint.com/time_series/time_series_error_metrics.htm
时间序列预测误差