【连载】CB Predictor操作手册(Crystal Ball Predictor 水晶球预测)

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Seasonal smoothing methods季节性平滑方法

Seasonal exponential smoothing methods extend the simple exponential smoothing methods by adding an additional component to capture the seasonal behavior of the data. There are four seasonal exponential smoothing methods used in CB Predictor.
季节性指数平滑方法是一个增加了额外的特点周期性行为的数据的单边指数平滑方法。在CB Predictor中一共有四种季节性指数平滑的方法。

Seasonal Additive Smoothing季节跌加平滑

Calculates a seasonal index for historical data that don’t have a trend. The method produces exponentially smoothed values for the level of the forecast and the seasonal adjustment to the forecast. The seasonal adjustment is added to the forecasted level, producing the Seasonal Additive forecast.
对没有趋势性的季节性特征的历史数据进行计算。这种方法得到的预测水平和季节性调整的预测值的指数平滑值。这种季节性调整是对预测水平的增强，得到季节跌加预测。

This method is best for data without trend but with seasonality that doesn’t increase over time. It results in a curved forecast that reproduces the seasonal changes in the data.
这种方法最适合用于没有趋势性但是季节性不顺着时间增加而增加的历史数据。它的结果是在数据复制季节性变化的弯曲预测。


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Seasonal Multiplicative Smoothing季节乘积平滑

Calculates a seasonal index for historical data that don’t have a trend. The method produces exponentially smoothed values for the level of the forecast and the seasonal adjustment to the forecast. The seasonal adjustment is multiplied by the forecasted level, producing the Seasonal Multiplicative forecast.
对没有趋势性的季节性特征的历史数据进行计算。这种方法得到的预测水平和季节性调整的预测值的指数平滑值。种季节性调整是对预测水平的增强，得到季节乘积预测

This method is best for data without trend but with seasonality that increases or decreases over time. It results in a curved forecast that reproduces the seasonal changes in the data.
这种方法最适合用于没有趋势性但是季节性不顺着时间增加而增加的历史数据。它的结果是在数据复制季节性变化的弯曲预测。


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Holt-Winters’ Additive Seasonal Smoothing霍尔特季节迭加平滑

Is an extension of Holt's exponential smoothing that captures seasonality. This method is based upon three equations that can be found in Appendix B. The method produces exponentially smoothed values for the level of the forecast, the trend of the forecast, and the seasonal adjustment to the forecast. This seasonal additive method adds the seasonality factor to the trended forecast, producing the Holt-Winters’ Additive forecast.
它是对有季节特征的霍尔特指数平滑的扩展。这种方法是在三个方程式基础上建立的，这三种方程式可以在附录B中查看。这种方法得到预测水平、预测趋势和季节性调整预测的指数平滑值。这种季节跌加方法增加了趋势预测季节性因素，得到霍尔特跌加预测。

This method is best for data with trend and seasonality that doesn’t increase over time. It results in a curved forecast that shows the seasonal changes in the data.
这种方法最适合用于有趋势性并且季节性不会随着时间增加而增加的数据。它的结果是弯曲预测，表示的是数据的季节性变化。

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Holt-Winters’ Multiplicative Seasonal Smoothing霍尔特季节乘积平滑

Is similar to the Holt-Winters’ Additive method. This method also calculates exponentially smoothed values for level, trend, and seasonal adjustment to the forecast. This method's equations can also be found in Appendix B. This seasonal multiplicative method multiplies the trended forecast by the seasonality, producing the Holt-Winters’ Multiplicative forecast.
这种方法与霍尔特季节跌加方法很相似。它会对预测水平、趋势和季节性调整计算出指数平滑值。这种方法的公式可以在附录B中找到。这种季节乘积方法对预测季节性因素进行乘积，得到霍尔特季节乘积平滑。

This method is best for data with trend and with seasonality that increases over time. It results in a curved forecast that reproduces the seasonal changes in the data
这种方法最适合用于有趋势性并且季节性会随着时间增加而增加的数据。它的结果是在数据复制季节性变化的弯曲预测。

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Seasonal smoothing parameters季节平滑参数

There are three smoothing parameters used by the seasonal methods: alpha, beta, and gamma.
有三个季节平滑参数：α，β，和γ。

alpha (α) Smoothing parameter for the level component of the forecast. The value of alpha can be any number between 0 and 1, not inclusive.
(α) 预测水平组成的平滑参数。这个值可以是0到1之间除了0和1的的任何值。

beta (β)  Smoothing parameter for the trend component of the forecast. The value of beta can be any number between 0 and 1, not inclusive.
beta (β)  预测水平趋势的平滑参数。这个值可以是0到1之间除了0和1的的任何值。

gamma (γ) Smoothing parameter for the seasonality component of the forecast. The value of gamma can be any number between 0 and 1, not inclusive.
gamma (γ) 预测季节性的平滑参数。这个值可以是0到1之间除了0和1的的任何值。

Each seasonal method uses some or all of these parameters, depending on the forecasting method. For example, the seasonal additive smoothing method doesn’t account for trend, so it doesn’t use the beta parameter.
每种季节性方法根据预测方法的不通都有许多的参数。例如，季节跌加平滑方法不能计算趋势，所以它没有beta (β)参数。

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Time-series forecasting error measures时间序列预测误差度量

One component of every time-series forecast is the data’s random error that is not explained by the forecast formula or by the trend and seasonal patterns. The error is measured by fitting points for the time periods with historical data, and then comparing the fitted points to the historical data.
每个时间序列预测的一个组成部分是数据的随机偏差，这个偏差是无法通过预测公式和季节性结构趋势来解释的。偏差是对同一时间的历史数据和拟合点的度量的差异，并对它们进行比较。

All the examples are based on the set of data illustrated in the chart below. Most of the formulas refer to the actual points (Y) and the fitted points (^Y). In the chart below, the horizontal axis illustrates the time periods (t) and the vertical axis illustrates the data point values.
在下面的图中有案例说明，大多数的公式指的实际点是（Y），拟合点是（^Y），在下面的图表中横轴表示时间周期（t），纵轴表示数据点值。

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CB Predictor measures the error using one of the following methods:
CB Predictor对误差度量使用下列方法之一：

•RMSE, below
•MAD, page 43
•MAPE, page 43
•均方根RMSE，如下
•平均绝对偏差MAD
•平均绝对百分比误差MAPE

RMSE
RMSE (root mean squared error) is an absolute error measure that squares the deviations to keep the positive and negative deviations from cancelling out each other. This measure also tends to exaggerate large errors, which can help eliminate methods with large errors.
RMSE（误差的平方根）是对绝对误差的度量，它是将误差进行平方对正负相互抵消。
这种方法也会对误差进行扩大，可以帮助我们通过扩大的误差进行消除。

MAD
MAD (mean absolute deviation) is an absolute error measure that originally became very popular (in the days before hand-held calculators) because it didn’t require the calculation of squares or square roots. While it is still fairly reliable and widely used, it is most accurate for normally distributed data.
MAD（平均绝对偏差）是对绝对误差的度量，在之前用手提电脑计算时非常受欢迎。因为它不需要计算平方或者平方根。现在它也十分可靠并被普通的使用，它能对正态分布数据计算的更精确。

MAPE
MAPE (mean absolute percentage error) is a relative error measure that uses absolute values. There are two advantages of this measure. First, the absolute values keep the positive and negative errors from cancelling out each other. Second, because relative errors don’t depend on the scale of the dependent variable, this measure lets you compare forecast accuracy between differently scaled time-series data.
MAPE（平均觉得百分比误差）是使用绝对值的相关误差的度量。这种度量有两个好处：第一是绝对值可以是的正负的误差相互抵消，第二由于相对误差不依赖于自变量的规模，这一措施可以对不同规模的时间序列数据之间更准确的预测。

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Time-series forecasting techniques时间序列预测技术

CB Predictor uses one of four forecasting techniques to perform time-series forecasting: standard, simple lead, weighted lead, and holdout.
CB Predictor使用时间序列预测四种预测技术中的一种：标准预测、简单领先预测、加权领先预测、抵抗预测。

Standard forecasting 标准预测

Standard forecasting optimizes the forecasting parameters to minimize the error measure between the fit values and the historical data for the same period. For example, if your historical data were:
通过减少同一周期的历史数据和拟合点之前的度量误差来优化标准预测的预测参数。

Period   1   2    3    4     5    6    7
Value    472 599  714  892   874  896  890
And your fit data were: 拟合值为：
Period   1   2    3    4     5    6    7
Value   488  609  702  888   890  909  870

CB Predictor calculates the RMSE using the differences between the historical data and the fit data from the same periods. For example:
CB Predictor对同一周期的历史数据和拟合点之间的差异用RMSE的方法进行计算。
(472-488)2 + (599-609)2 + (714-702)2 + (892-888)2 + ...

For standard forecasting, CB Predictor optimizes the forecasting parameters so that the RMSE calculated in this way is minimized.
对于标准预测，CB Predictor优化预测参数，使RMSE的计算方法最小化。

Simple lead forecasting简单领先预测

Simple lead forecasting optimizes the forecasting parameters to minimize the error measure between the historical data and the fit values, offset by a specified number of periods (lead). Use this forecasting technique when a forecast for some future time period has the greatest importance, more so than the forecasts for the previous or later periods.
通过减少同一周期的历史数据和拟合点之前的度量误差来优化简单领先预测的预测参数，从而抵消一定数量周期的情况。当对未来周期的预测远远比对近期或稍早时间的预测更为重要的时候使用这种预测技术。

For example, your company must order extremely expensive manufacturing components two months in advance, making any forecast for two months out the most important. For the same historical and fit example data described above in Standard Forecasting, CB Predictor calculates the RMSE using the difference between the historical data and the fit data from an offset number of periods (lead). With a lead of 2, the differences used in the RMSE calculation are:
例如，你的公司必须将花费极其巨大的制造部分提前2个月完成，对这两个月的预测是比其他更为重要的。同样是标准预测中案例的历史数据和拟合数据，CB Predictor使用RMSE的方法计算一段时期历史数据和拟合点之间的差异，如果要提前2个月，使用RMSE的方法就会不同：
(472-702)2 + (599-888)2 + (714-890)2 + (892-909)2 + ...

For simple lead forecasting, CB Predictor optimizes the forecasting parameters so that the RMSE calculated in this way is minimized.
对于简单领先预测，CB Predictor优化预测参数，使RMSE的计算方法最小化。

Weighted lead forecasting加权领先预测
Weighted lead forecasting optimizes the forecasting parameters to minimize the average error measure between the historical data and the fit values, offset by 0, 1, 2, etc., up to the specified number of periods (weighted lead). It uses the simple lead technique for several lead periods and then averages the forecast over the periods, optimizing this average value. Use this technique when the future forecast for several periods is most important.
加权导致预测预报优化参数，以尽量减少历史数据和拟合点之间的平均误差，从而抵消了0，1，2等，到指定的周期。，对前面的周期使用简单的领先技术，然后平均预测的周期，优化这一平均值。当预测未来几期是最重要的时候使用这种技术。

For example, your company must order extremely expensive manufacturing components zero, one, and two months in advance, making any forecast for all the time periods up to two months out the most important. For the same historical and fit example data described above in Standard Forecasting, CB Predictor calculates the RMSE for each lead up to the weighted lead using the difference between the historical data and the fit data from a set of offset periods (individual leads). With a weighted lead of 2, the differences used in the RMSE calculations are:
例如，您的公司必须事先以非常昂贵价格在开始的第1.2个月进行生产，对于两个月以内的任何时间段的预测是最重要的。对于相同的历史和上述标准预测中案例的数据，CB Predictor对一段时间内历史数据和适合数据之间的误差用加权的方法计算每个数值的RMSE。对领先2个周期的加权，在均方根误差计算中使用的区别是：
(472-488)2 + (599-609)2 + (714-702)2 + ... (lead of 0)
(472-609)2 + (599-702)2 + (714-888)2 + ... (lead of 1)
(472-702)2 + (599-888)2 + (714-890)2 + ... (lead of

Then CB Predictor averages the RMSE for the lead of 0, the lead of 1, and the lead of 2. For weighted lead forecasting, CB Predictor optimizes the forecasting parameters to minimize the average of the RMSE calculations.
CB Predictor会计算领先0个周期，领先1个周期，领先2个周期的RMSE平均值。CB Predictor预测的参数优化，以尽量减少对均方根误差计算的平均水平。

Holdout霍特尔预测
Holdout forecasting:

1.Removes the last few data points of your historical data.
1、去除过去一些数据点的历史数据

2.Calculates the fit and forecast points using the remaining historical data.
2、使用遗留下的历史数据计算拟合点和预测点

3.Compares the error between the forecasted points and their corresponding, excluded, historical data points.
3、对比预测数据和相对应已去除的数历史数据之间的误差。

4.Changes the parameters to minimize the error between the forecasted points and the excluded points.
4、改变参数，以减小预测点和已去除的点之间的误差。

CB Predictor determines the optimal forecast parameters using only the non-holdout set of data.
CB Predictor决定只使用没有去除的一系列数据来优化预测参数。

CB Predictor Note: If you have a small amount of data and want to use seasonal forecasting methods, using the holdout technique might restrict you to nonseasonal methods.
注意：如果你只有少部分的数据想用季节性预测方法，使用抵抗技术方法可以对非季节性方法进行控制。


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Time-series forecasting statistics时间序列预测统计

Theil’s U泰尔U预测

Theil’s U statistic is a relative error measure that compares the forecasted results with a naive forecast. It also squares the deviations to give more weight to large errors and to exaggerate errors, which can help eliminate methods with large errors. For the formula, see page 137.
泰尔U统计是相对误差的度量，它对预测结果和简单的预测进行比较。通常对误差进行平方，以便对最大和最小的误差进行加权，这样可以找到消除最大误差的方法。公式在137页。

Table 2.1 Interpreting Theil’s U

Theil’s U statistic泰尔U统计	Means:含义
Less than 1小于1	The forecasting technique is better than guessing.预测技术比预计的更好
1等于1	The forecasting technique is about as good as guessing.预测技术和预计的一样好
More than 1大于1	The forecasting technique is worse than guessing. 预测技术比预计的更差

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lanj

明天说回归统计{:8_306:}

漂在生活

我一直在等你更新。。。(weixiao:

xinxijie531

感谢分享！继续努力哈！

米老鼠

非常有帮助的文章,顶一个!

lqbz

好好学习，天天向上。

lanj

Multiple linear regression多元线性回归

Multiple linear regression is used for data where one data series (the dependent variable) is a function of, or depends on, other data series (the independent variables). For example, the yield of a lettuce crop depends on the amount of water provided, the hours of sunlight each day, and the amount of fertilizer used.
多元线性回归方法一般是用在一系列数据（因变量）是有影响的，或浇水的数量，每天日照的小时和每天的化肥使用数量。

The goal of multiple linear regression is to find an equation that most closely matches the historical data. The word “multiple” indicates that you can use more than one independent variable to define your dependent variable in the regression equation. The word “linear” indicates that the regression equation is a linear equation.
多元线性回归的目的是找到最适合历史数据的方程式。“多元”是指在回归方程有一个以上的自变量会对因变量有影响。“线性”是指回归方程是一个线性方程。

The linear equation describes how the independent variables (x1, x2, x3,...) combine to define the single dependent variable (y). Multiple linear regression finds the coefficients for the equation:
线性方程是指有多个自变量（x1、x2、x3…）如何对单独的一个因变量（y）的关系。
y = b0 + b1x1 + b2x2 + b3x3 + ... + e

where b1, b2, and b3, are the coefficients of the independent variables, b0 is the y-intercept, and e is the error.
b1、b2和b3是自变量的系数，b0是y的截距，e是误差。

If there is only one independent variable, the equation defines a straight line. This uses a special case of multiple linear regression called simple linear regression, with the equation:
如果只有一个自变量，方程得到的是一条直线。这种情况的多元线性回归成为一元线性回归，方程是：
y = b0 + b1x + e

where b0 is where on the graph the line crosses the y axis, x is the independent variable, and e is the error. When the regression equation has only two independent variables, it defines a plane. When the regression equation has more than two independent variables, it defines a hyperplane.
b0是图表中图线与y轴相交的值，x是自变量，e是误差。当回归方程只有两个自变量时，形成的是一个平面。当回归方程有2个以上的自变量时，形成的是一个超平面。

To find the coefficients of these equations, CB Predictor uses singular value decomposition. For more information on this technique, see “Singular value decomposition” on page 143.
为了找到这些方程的系数，CB Predictor会使用奇异值分解的方法。


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