Trading softwares come with different types of moving averages already pre-installed and ready to charted. But it can be interesting to understand how to calculate these moving averages so as to be able to use them when you’re back-testing potential strategies.

交易软件带有不同类型的移动平均线，这些移动平均线已经预先安装并可以绘制图表。 但是，了解如何计算这些移动平均值，以便在对潜在策略进行回测时能够使用它们，可能会很有趣。

If you want a do-it-yourself method, then the below will surely interest you. All that is needed is a python interpreter such as SPYDER. The different “known” types of moving averages are:

如果您想自己动手做，那么下面的内容一定会让您感兴趣。 所需要的只是一个Python解释器，例如SPYDER。 移动平均的不同“已知”类型为：

• Simple moving average.

  简单的移动平均线。

• Exponential moving average.

  指数移动平均线。

• Smoothed moving average.

  平滑的移动平均线。

• Linear-weighted moving average.

  线性加权移动平均线。

We will go through each one, define it, code it, and chart it.

我们将仔细研究，定义，编码和绘制图表。

简单移动平均线 (Simple moving average)

As the name suggests, this is your plain simple average that is used everywhere in statistics and basically any other part in our lives. It is simply the total values of the observations divided by the number of observations.

顾名思义，这是您的简单平均数，可用于统计数据中以及我们生活中的其他任何部分。 它只是观测值的总值除以观测值的数量。

Mathematically speaking, it can be written down as:

从数学上讲，它可以记为：

In python, we can define a function that calculates moving averages as follows:

在python中，我们可以定义一个函数来计算移动平均值，如下所示：

def ma(Data, period, onwhat, where):

    for i in range(len(Data)):            try:                Data[i, where] = (Data[i - period:i + 1, onwhat].mean())

            except IndexError:                pass    return Data

The function takes your data structure represented by the Data variable, the moving average period (20, 60, 200, etc.) represented by the period variable, what do you want to apply it on (on OHLC data structures, choose 3 for close prices because python indexing starts at zero) represented by the onwhat variable, and the where variable is where do you want the moving average column to appear. Note that you must have an array of more than 4 columns for this to work, because it doesn’t automatically create a new column, but simply populate it.

该功能把你的数据结构表示由数据变量，移动平均周期(20，60，200，等) 期间变量表示，要应用它在做什么(上OHLC数据结构，选择3紧密价格(因为python索引从零开始)由onwhat变量表示，而where变量是您希望移动平均列显示的位置。 请注意，您必须具有超过4列的数组才能起作用，因为它不会自动创建新列，而只是填充它。

指数移动平均线 (Exponential moving average)

As opposed to the simple moving average that gives equal weights to all observations, the exponential moving average gives more weight to the more recent observations. It reacts more than the simple moving average with regards to recent movements.

与简单的移动平均线赋予所有观察值相同的权重相反，指数移动平均线赋予较新的观察值更多的权重。 对于最近的走势，它的React比简单的移动平均数还要多。

Mathematically speaking, it can be written down as:

从数学上讲，它可以记为：

The smoothing factor is often 2. Note, that if we increase the smoothing factor (also known as alpha) then, the more recent observations will have more weight.

平滑因子通常为2。请注意，如果我们增加平滑因子(也称为alpha)，则最近的观测值将具有更大的权重。

In python language, we can define a function that calculates the EMA as follows:

在python语言中，我们可以定义一个计算EMA的函数，如下所示：

def ema(Data, alpha, window, what, whereSMA, whereEMA):

    # alpha is the smoothing factor    # window is the lookback period    # what is the column that needs to have its average calculated    # where is where to put the exponential moving average

    alpha = alpha / (window + 1.0)    beta  = 1 - alpha

    # First value is a simple SMA    Data[window - 1, whereSMA] = np.mean(Data[:window - 1, what])

    # Calculating first EMA    Data[window, whereEMA] = (Data[window, what] * alpha) + (Data[window - 1, whereSMA] * beta)# Calculating the rest of EMA    for i in range(window + 1, len(Data)):            try:                Data[i, whereEMA] = (Data[i, what] * alpha) + (Data[i - 1, whereEMA] * beta)

            except IndexError:                pass    return Data

The function is self-explanatory as it merely reproduces the EMA function presented above.

该函数是不言自明的，因为它仅复制了上面介绍的EMA函数。

平滑的移动平均线 (Smoothed moving average)

This moving average takes into account the general picture and is less impacted by recent movements. It’s my favourite trend-following indicator. Mathematically speaking, it can be found by simply multiplying the Days variable in the EMA function by 2 and subtract 1. This means that to transform an exponential moving average into a smoothed one, we follow this equation in python language, that transforms the exponential moving average into a smoothed one:

该移动平均线考虑了总体情况，受近期走势的影响较小。 这是我最喜欢的趋势跟踪指标。 从数学上来说，可以通过将EMA函数中的Days变量乘以2并减去1来找到。这意味着要将指数移动平均值转换为平滑的均值，我们使用python语言遵循此方程式，从而转换了指数移动平均成一个平滑的：

smoothed = (exponential * 2) - 1 # From exponential to smoothed

线性加权移动平均 (Linear-weighted moving average)

It is a simple moving average that places more weight on recent data. The most recent observation has the biggest weight and each one prior to it has a progressively decreasing weight. Intuitively, it has less lag than the other moving averages but it’s also the least used, and hence, what it gains in lag reduction, it loses in popularity.

这是一个简单的移动平均线，对近期数据有更多的重视。 最近的观测值具有最大的权重，而在此之前的每个观测值的权重都逐渐减小。 从直觉上讲，它的滞后性比其他移动平均线要小，但使用最少，因此，减少滞后所获得的好处就不受欢迎了。

Mathematically speaking, it can be written down as:

从数学上讲，它可以记为：

In python language, we can define a function that calculates moving averages as follows:

在python语言中，我们可以定义一个函数来计算移动平均值，如下所示：

def lwma(Data, period):    weighted = []    for i in range(len(Data)):            try:                total = np.arange(1, period + 1, 1) # weight matrix

                matrix = Data[i - period + 1: i + 1, 3:4]                matrix = np.ndarray.flatten(matrix)                matrix = total * matrix # multiplication                wma = (matrix.sum()) / (total.sum()) # WMA                weighted = np.append(weighted, wma) # add to array            except ValueError:                pass    return weighted

Basically, if we have a dataset composed of two numbers [1, 2] and we want to calculate a linear weighted average, then we will do the following:

基本上，如果我们有一个由两个数字[1、2]组成的数据集，并且想要计算线性加权平均值，那么我们将执行以下操作：

• (2 x 2) + (1 x 1) = 5(2 x 2)+(1 x 1)= 5
• 5 / 3 = 1.665/3 = 1.66

This assumes a time series with the number 2 as being the most recent observation.

这假定数字为2的时间序列是最近的观测值。

结论 (Conclusion)

So, which one to choose? That question is left to the risk profile of the trader and her familiarity with the moving average. Some prefer plain simple moving averages while others try to dig deeper by using combinations of exponential and smoothed moving averages. It all depends on you to find your favourite one. My advice? Consider longer-term moving averages.

那么，选择哪一个呢？ 这个问题留给交易者的风险状况以及她对移动平均线的熟悉程度。 一些人更喜欢简单的简单移动平均线，而另一些人则试图通过使用指数移动平均线和平滑移动平均线的组合来更深入地研究。 这完全取决于您找到自己喜欢的一个。 我的建议？ 考虑长期移动平均线。