MovingAverage-滑动平均

MovingAverage可翻译为滑动平均或移动平均，是做时间序列预测时用到的简单方法。

计算方法：对于一个给定的数列，首先设定一个固定的值k，然后分别计算第1项到第k项，第2项到第k+1项，第3项到第k+2项的平均值，依次类推。

下面代码取自TensorFlow源代码：

class MovingAverage {
 public:
  explicit MovingAverage(int window);
  ~MovingAverage();

  void Clear();

  double GetAverage() const;
  void AddValue(double v);

 private:
  const int window_;  // Max size of interval
  double sum_;        // Sum over interval
  double* data_;      // Actual data values
  int head_;          // Offset of the newest statistic in data_
  int count_;         // # of valid data elements in window
};

// 构造函数
MovingAverage::MovingAverage(int window)
    : window_(window),
      sum_(0.0),
      data_(new double[window_]),
      head_(0),
      count_(0) {
  CHECK_GE(window, 1);
}
// 析构函数
MovingAverage::~MovingAverage() { delete[] data_; }

void MovingAverage::Clear() {
  count_ = 0;
  head_ = 0;
  sum_ = 0;
}
double MovingAverage::GetAverage() const {
  if (count_ == 0) {
    return 0;
  } else {
    return static_cast<double>(sum_) / count_;
  }
}
void MovingAverage::AddValue(double v) {
  if (count_ < window_) {
    // This is the warmup phase. We don't have a full window's worth of data.
    head_ = count_;
    data_[count_++] = v;
  } else {
    if (window_ == ++head_) {
      head_ = 0;
    }
    // Toss the oldest element
    sum_ -= data_[head_];
    // Add the newest element
    data_[head_] = v;
  }
  sum_ += v;
}

以1、2、3、4、5共5个数为例，window为3，计算过程为：（1+2+3）/3=2，（2+3+4）/3=3，（3+4+5）/3=4。

...
    MovingAverage ma(3);

    ma.AddValue(1);
    ma.AddValue(2);
    ma.AddValue(3);
    printf("%lf\n", ma.GetAverage()); // 2.0
    ma.AddValue(4);
    printf("%lf\n", ma.GetAverage()); // 3.0
    ma.AddValue(5);
    printf("%lf\n", ma.GetAverage()); // 4.0
...

一图胜千言

数据取自：<TensorFlow练习19: 预测天朝铁路客运量>

import matplotlib.pyplot as plt
import pandas as pd
import requests
import io
import numpy as np

def moving_average(l, N):
    sum = 0
    result = list( 0 for x in l)

    for i in range( 0, N ):
        sum = sum + l[i]
        result[i] = sum / (i+1)

    for i in range( N, len(l) ):
        sum = sum - l[i-N] + l[i]
        result[i] = sum / N

    return result

# 使用效率更高的numpy
# http://stackoverflow.com/questions/13728392/moving-average-or-running-mean
def fast_moving_average(x, N):
    return np.convolve(x, np.ones((N,))/N)[(N-1):]

url = 'http://blog.topspeedsnail.com/wp-content/uploads/2016/12/铁路客运量.csv'
ass_data = requests.get(url).content

df = pd.read_csv(io.StringIO(ass_data.decode('utf-8')))  # python2使用StringIO.StringIO

data = np.array(df['铁路客运量_当期值(万人)'])

ma_data = moving_average(data.to_list(), 3)

plt.figure()
plt.plot(data, color='g')
plt.plot(ma_data, color='r')
plt.show()

当window/N=3：

红线是MovingAverage，注意看，它慢了一拍

当window/N=10：

可以用来中和掉一些异常值

还有一个类似的东西，叫Moving Median，Median是中位数。

中位数定义：把数列按顺利排好，中间的那个数就是中位数，如果数列个数是偶数，那么取中间两个数的平均值。

---

正在看马哥的告别演说，转眼8年过去了，真TM快，这货头发全白了。

马哥的演技还是这么牛，期待大嘴巴川普的就职演说。

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