小一笔记（8）：物流需求预测的误差分析

摘要：由于物流系统的复杂性与不确定性，要准确预测未来的物流需求是一件困难的事情。因为需求含有系统需求部分与随机需求部分，随机需求部分就会以预测误差的形式表现出来。预测误差是指某一时间间隔内预测需求与实际需求的差异，公式如下：

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“小一笔记（8）：物流需求预测的误差分析”

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"Xiaoyi Notes (6):Error analysis of logistics demand forecasting"

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（四）物流需求预测误差分析Logistics demand forecast error analysis

由于物流系统的复杂性与不确定性，要准确预测未来的物流需求是一件困难的事情。因为需求含有系统需求部分与随机需求部分，随机需求部分就会以预测误差的形式表现出来。预测误差是指某一时间间隔内预测需求与实际需求的差异，公式如下：

Due to the complexity and uncertainty of logistics systems, it is difficult to accurately predict future logistics demand. Because the demand contains a systematic demand component and a random demand component, the random demand component will be expressed in the form of forecast error. Forecast error is the difference between the forecast demand and the actual demand in a certain time interval, the formula is as follows:

式中，e（t）表示第t期的预测误差； S（t）表示第t期的预测值； A（t）第t期的实际需求量。

where e(t) denotes the forecast error in period t; S(t) denotes the forecast value in period t; A(t) the actual demand in period t.

预测误差包含了重要的信息，做需求预测时要认真进行分析，这是因为：

Forecast errors contain important information that should be carefully analyzed when doing demand forecasts, this is because:

①通过误差分析，可以帮助预测者判断目前的预测是否准确地预测了系统需求部分。如果预测误差持续出现正值，说明预测方法过高地预测了系统需求，应采取适当的修正方法加以修正。

The error analysis can help the forecaster determine whether the current forecast accurately predicts the system demand component. If the forecasting error is consistently positive, the forecasting method is over-predicting the system demand and should be corrected by adopting an appropriate correction method.

②误差放映了意外事件与需求的不确定性，通过估计误差，有助于物流系统的柔性设计。

Error reflects the uncertainty of unexpected events and demand, and by estimating the error, it contributes to the flexible design of the logistics system.

③由于物流系统的复杂性，应给予预测误差一个可以接受的偏差范围。如果误差超过这一偏差范围，就需要采取措施加以纠正。如果预测误差大大超过这个范围，则可能是另外一个信号，说明目前的预测方法不太适用，需要改变预测方法了。

Because of the complexity of logistics systems, forecast errors should be given an acceptable margin of error. If the error exceeds this range, measures need to be taken to correct it. If the prediction error greatly exceeds this range, it may be another signal that the current prediction method is not very suitable and that a change in the prediction method is needed.

衡量预测误差的方法除了以上式子外，还有如下几种。

In addition to the above formula, there are several methods for measuring prediction error.

1.平均方差（meansquarederror,MSE）

平均方差是前t期预测误差平方和的平均值,其计算公式如下：

The mean variance is the average of the sum of squares of the prediction errors in the previous t periods, which is calculated as follows:

式中,MSE（t）预测误差的离散程度。

Where, the degree of dispersion of the MSE(t) prediction error.

2.平均绝对偏差（meanabsolutedeviation，MAD）

平均绝对偏差定义为前期预测误差绝对值的平均值，其计算公式如下：

The mean absolute deviation is defined as the average of the absolute value of the prediction error in the previous period, which is calculated as follows:

3.平均绝对百分比误差（meanabsolutepercentageerror,MAPE）

平均绝对百分比误差是前t期预测误差与实际需求量比值的绝对值的平均值，其计算公式如下：

The average absolute percentage error is the average of the absolute values of the ratio of the forecast error to the actual demand for the previous t periods, which is calculated by the following formula:

式中，e（i）是第i期的预测误差； A（i）是第i期的实际需求量。

where e(i) is the forecast error in period i; A(i) is the actual demand in period i.

4.路径信号（trackingsignal,TS)

路径信号是前t期预测误差之和与MAD的比值，其公式如下：

The path signal is the ratio of the sum of the prediction errors of the previous t periods to the MAD, which is given by the following equation:

TS可以判断所用的预测方法是否持续低估或高估了需求。通常，如果某个时期的TS在+6或-6的范围之外，这就说明预测出现了偏差，高估（TS>+6）或低估（TS

TS can determine whether the forecasting methodology used consistently underestimates or overestimates demand. Typically, if the TS for a given period is outside the range of +6 or -6, this is an indication that the forecast has been biased, either by overestimating (TS > +6) or underestimating (TS

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