Time series (or dynamic series) is the number of columns the number of the same time their statistical indicators of the occurrence of arrayed order. The main purpose of time series analysis is to predict the future based on existing historical data. In this article we will share how to perform basic time-series analysis (hereinafter referred to as timing analysis) use historical stock data. First we will create a static prediction model, testing model validity, and then share some important tools for timing analysis.
Before you create the model, let's briefly outline some of the basic parameters of the time series, such as moving averages, trend, seasonal and so on.
retrieve data
In this paper we will use MRF past five years, "price adjustments", you can get the data from Yahoo Finance with pandas_datareader. We first need to import library:
import pandas as pd
import pandas_datareader as web
import matplotlib.pyplot as plt
import numpy as np
Now we get data datareader, mainly stock data from January 1, 2012 to December 21, 2017 of. Of course, you can also use only adjusted closing price, because it is the most relevant price, all applications in financial analysis.
stock = web.DataReader('MRF.BO','yahoo', start = "01-01-2012", end="31-12-2017")
stock = stock.dropna(how=’any’)
We can () function to check the data with the head.
stock.head()
We can use the imported matplotlib library to map out the price adjustment period again.
stock[‘Adj Close’].plot(grid = True)
Calculate and plot the daily earnings
Using time series, we can calculate the daily income changes with time, and draw the income chart. We will adjust the stock's closing price calculated daily earnings to the column name "ret" stored in the same data frame "stock" in.
stock['ret'] = stock['Adj Close'].pct_change()
stock['ret'].plot(grid=True)
Moving Average
And the same income, we can calculate and plot the closing price adjustment of moving average. Moving average line is widely used in a very important indicator of technical analysis. For the purpose of brief explanation, here we only 20 days moving average calculation as an example.
stock['20d'] = stock['Adj Close'].rolling(window=20, center=False).mean()
stock['20d'].plot(grid=True)
Before building the model prediction, we take a quick look at the time series and seasonal trends.
Trends and seasonality
In simple terms, the trend shows an overall development orientation time series over a period of time. Trends and trend analysis is also widely used in technical analysis. If some of the patterns appear regularly in the time series, we say the data is seasonal. Seasonal time series prediction model can affect the results, so it can not be taken lightly.
prediction
We'll discuss a simple linear model, assuming that the time series was static, and there is no seasonality. That is where we assume a linear trend in time series. Model can be expressed as:
Forecast (t) = a + b X t
这里的“a”为时间序列在Y轴上的截距，“b”为斜率。我们现在看看 a 和 b 的计算。我们考虑时间序列在时间段“t”内的值D（t）。
在这个方程式中，“n”是样本大小。我们可以通过用上面的模型计算 D（t）的预测值，并将值和实际观测值比较，进而验证我们的模型。我们可以计算出平均误差，即预测 D（t）值和实际 D（t）值之间的差距的平均值。
在我们的股票数据中，D（t）是 MRF 的调整收盘价。我们现在用 Python 计算 a,b,预测值和它们的误差值。
#Populates the time period number in stock under head t
stock['t'] = range (1,len(stock)+1)
#Computes t squared, tXD(t) and n
stock['sqr t']=stock['t']**2
stock['tXD']=stock['t']*stock['Adj Close']
n=len(stock)
#Computes slope and intercept
slope = (n*stock['tXD'].sum() - stock['t'].sum()*stock['Adj Close'].sum())/(n*stock['sqr t'].sum() - (stock['t'].sum())**2)
intercept = (stock['Adj Close'].sum()*stock['sqr t'].sum() - stock['t'].sum()*stock['tXD'].sum())/(n*stock['sqr t'].sum() - (stock['t'].sum())**2)
print ('The slope of the linear trend (b) is: ', slope)
print ('The intercept (a) is: ', intercept)
上面的代码会给出如下输出：
The slope of the linear trend (b) is: 41.2816591061
The intercept (a) is: 1272.6557803
我们现在可以通过计算预测值和平均误差来验证模型的效度。
#Computes the forecasted values
stock['forecast'] = intercept + slope*stock['t']
#Computes the error
stock['error'] = stock['Adj Close'] - stock['forecast']
mean_error=stock['error'].mean()
print ('The mean error is: ', mean_error)
输出的平均误差如下所示：
The mean error is: 1.0813935108094419e-10
从平均误差值可以看出，我们的模型给出的值非常接近实际值。因此数据没有受到任何季节性方面的影响。
下面我们讨论一些用于分析时序数据的很实用的工具，它们对于金融交易员在设计和预先测试交易策略时非常有帮助。
交易员们常常要处理大量的历史数据，并且根据这些时间序列进行数据分析。我们这里重点分享一下如何应对时间序列中的日期和频率，以及索引、切片等操作。主要会用到 datetime库。
我们首先将 datetime 库导入到程序中。
#Importing the required modules
from datetime import datetime
from datetime import timedelta
处理日期和时间的基本工具
先将当前日期和时间保存在变量“current_time”中，执行代码如下：
#Printing the current date and time
current_time = datetime.now()
current_time
Output: datetime.datetime(2018, 2, 14, 9, 52, 20, 625404)
我们可以用 datetime 计算两个日期的不同之处。
#Calculating the difference between two dates (14/02/2018 and 01/01/2018 09:15AM)
delta = datetime(2018,2,14)-datetime(2018,1,1,9,15)
delta
Output: datetime.timedelta(43, 53100)
使用如下代码将输出转换为用“天”或“秒”表达：
#Converting the output to days
delta.days
Output: 43
#Converting the output to seconds
delta.seconds
Output: 53100
如果我们想变换日期，可以用前面导入的 timedelta 模块。
#Shift a date using timedelta
my_date = datetime(2018,2,10)
#Shift the date by 10 days
my_date + timedelta(10)
Output: datetime.datetime(2018, 2, 20, 0, 0)
我们也可以用 timedelta 函数的乘法。
#Using multiples of timedelta function
my_date - 2*timedelta(10)
Output: datetime.datetime(2018, 1, 21, 0, 0)
我们前面看过了 datetime 模块的“datetime”和“timedelta”数据类型。我们简要说明一下在分析时间序列时用到的主要数据类型：
数据类型
描述
Date
用公历保存日历上的日期（年，月，日）
Time
将时间保存为小时、分钟、秒和微秒
Datetime
保存date和time两种数据类型
Timedelta
保存两个datetime值的不同之处
学习Python中的小伙伴，需要学习资料的话，可以到我们的python学习交流q–u–n【 784758214 】
这里有大牛整理了一套最新的python系统学习教程，包括从基础的python脚本到web开发、爬虫、数据分析、数据可视化、机器学习等。送给正在学习python的小伙伴！这里是python学习者聚集地，欢迎初学和进阶中的小伙伴！
*
字符串和 datetime 之间的转换*
我们可以将 datetime 格式转换为字符串，并以字符串变量进行保存。也可以反过来，将表示日期的字符串转换为 datetime 数据类型。
#Converting datetime to string
my_date1 = datetime(2018,2,14)
str(my_date1)
Output: '2018-02-14 00:00:00'
我们可以用 strptime 函数将字符串转换为 datetime。
#Converting a string to datetime
datestr = '2018-02-14'
datetime.strptime(datestr, '%Y-%m-%d')
Output: datetime.datetime(2018, 2, 14, 0, 0)
也可以用 Pandas 处理日期。我们先导入 Pandas。
#Importing pandas
import pandas as pd
在 Pandas 中用“to_datetime”将日期字符串转换为 date 数据类型。
#Using pandas to parse dates
datestrs = ['1/14/2018', '2/14/2018']
pd.to_datetime(datestrs)
Output: DatetimeIndex(['2018-01-14', '2018-02-14'], dtype='datetime64[ns]', freq=None)
在 Pandas 中，将缺失的时间或时间中的 NA 值表示为 NaT。
时间序列的索引和切片
为了更好的理解时间序列中的多种操作，我们用随机数字创建一个时间序列。
#Creating a time series with random numbers
import numpy as np
from random import random
dates = [datetime(2011, 1, 2), datetime(2011, 1, 5), datetime(2011, 1, 7), datetime(2011, 1, 8), datetime(2011, 1, 10), datetime(2011, 1, 12)]
ts = pd.Series(np.random.randn(6), index=dates)
ts
Output:
2011-01-02 0.888329
2011-01-05 -0.152267
2011-01-07 0.854689
2011-01-08 0.680432
2011-01-10 0.123229
2011-01-12 -1.503613
dtype: float64
用我们展示的索引，可以将该时间序列的元素调用为任何其它 Pandas 序列。
ts[’01/02/2011′] 或 ts[‘20110102’]会给出同样的输出0.888329
切片操作和我们对其它 Pandas 序列的切片操作相同。
时间序列中的重复索引
有时你的时间序列会包含重复索引。看一下如下时间序列：
#Slicing the time series
ts[datetime(2011,1,7):]
Output:
2011-01-07 0.854689
2011-01-08 0.680432
2011-01-10 0.123229
2011-01-12 -1.503613
dtype: float64
在上面的时间序列中，我们可以看到“2018-01-02”重复出现了 3 次。我们可以用 index 函数的“is_unique”属性检查这一点。
dup_ts.index.is_unique
Output: False
可以用 groupby 功能集合有相同索引的记录。
grouped=dup_ts.groupby(level=0)
我们现在可以根据自己的需求，使用这些记录的平均值、计数、总和等等。
grouped.mean()
Output:
2018-01-01 -0.471411
2018-01-02 -0.013973
2018-01-03 -0.611886
dtype: float64
grouped.count()
Output:
2018-01-01 1
2018-01-02 3
2018-01-03 1
dtype: int64
grouped.sum()
Output:
2018-01-01 -0.471411
2018-01-02 -0.041920
2018-01-03 -0.611886
dtype: float64
数据位移
我们可以用 shift 函数转移时间序列的索引。
#Shifting the time series
ts.shift(2)
Output:
2011-01-02 NaN
2011-01-05 NaN
2011-01-07 0.888329
2011-01-08 -0.152267
2011-01-10 0.854689
2011-01-12 0.680432
dtype: float64
总结
In this paper we briefly discuss some of the properties of time series, and how to calculate them with Python. Also with a simple linear model prediction time series. Finally, we share some basic functions used in the analysis of time series, such as the date of conversion from one format to another format.