机器学习多元时间序列（使用时间序列预测的Bitcoin）

机器学习多元时间序列（使用时间序列预测的Bitcoin）import refrom collections import Counterimport numpy as dragonimport pylab as pimport matplotlib.pyplot as plot

这篇文章是关于使用时间序列预测的Bitcoin Price预测。时间序列预测与其他机器学习模型有很大不同，因为 -

• 1.时间依赖性。因此，观测值是独立的线性回归模型的基本假设在这种情况下不成立。
• 2.随着增加或减少的趋势，大多数时间序列都有某种形式的季节性趋势，即特定时间范围内的变化。

因此，不能使用简单的机器学习模型，因此时间序列预测是一个不同的研究领域。在本文中，AR，MA和ARIMA等时间序列模型用于预测Bitcoin 的价格。

该数据集包含2013年4月至2017年8月Bitcoin的开盘价和收盘价

导入必要的库

import pandas as kunfu

import numpy as dragon

import pylab as p

import matplotlib.pyplot as plot

from collections import Counter

import re

#importing packages for the prediction of time-series data

import statsmodels.api as sm

import statsmodels.tsa.api as smt

import statsmodels.formula.api as smf

from sklearn.metrics import mean_squared_error

绘制时间序列

将数据加载到训练数据框中，然后使用日期作为索引，系列用x轴上的日期和y轴上的收盘价格绘制。

data = train['Close']

Date1 = train['Date']

train1 = train[['Date' 'Close']]

# Setting the Date as Index

train2 = train1.set_index('Date')

train2.sort_index(inplace=True)

print (type(train2))

print (train2.head())

plot.plot(train2)

plot.xlabel('Date' fontsize=12)

plot.ylabel('Price in USD' fontsize=12)

plot.title("Closing price distribution of bitcoin" fontsize=15)

plot.show()

测试平稳性

增强Dicky Fuller测试：

增强Dicky Fuller测试是一种称为单位根测试的统计测试。

单位根检验背后的直觉是它决定了时间序列由趋势定义的强度。

ADF单位根检验和是应用最广泛的一种

• 1. Null Hypothesis (H0):原假设(null hypothesis)亦称待验假设、虚无假设、解消假设，时间序列可以用非平稳的单位根表示。。
• 2. Alternative Hypothesis (H1): 备择假设（Alternative Hypothesis） 时间序列是固定的。

ADF值的解释：

• 1. p值 > 0.05：接原假设（H0），数据具有单位根并且是非平稳的。
• 2. p值 <= 0.05：拒绝原假设（H0），数据是固定的。

from statsmodels.tsa.stattools import adfuller

def test_stationarity(x):

#Determing rolling statistics

rolmean = x.rolling(window=22 center=False).mean()

rolstd = x.rolling(window=12 center=False).std()

#Plot rolling statistics:

orig = plot.plot(x color='blue' label='Original')

mean = plot.plot(rolmean color='red' label='Rolling Mean')

std = plot.plot(rolstd color='black' label = 'Rolling Std')

plot.legend(loc='best')

plot.title('Rolling Mean & Standard Deviation')

plot.show(block=False)

#Perform Dickey Fuller test

result=adfuller(x)

print('ADF Stastistic: %f'%result[0])

print('p-value: %f'%result[1])

pvalue=result[1]

for key value in result[4].items():

if result[0]>value:

print("The graph is non stationery")

break

else:

print("The graph is stationery")

break;

print('Critical values:')

for key value in result[4].items():

print('\t%s: %.3f ' % (key value))

ts = train2['Close']

test_stationarity(ts)

日志转换系列

日志转换用于纠正高度倾斜的数据。从而有助于预测过程。

ts_log = dragon.log（ts）

plot.plot（ts_log，color =“green”）

plot.show（）

test_stationarity（ts_log）

decomposition消除趋势和季节性

decomposition是一种技术，在该技术中，该序列的季节性、趋势成分被移除，然后将模型应用于残差序列。

# Naive decomposition of our Time Series as explained above

from statsmodels.tsa.seasonal import seasonal_decompose

decomposition = seasonal_decompose(ts_log model='multiplicative' freq = 7)

trend = decomposition.trend

seasonal = decomposition.seasonal

residual = decomposition.resid

plot.subplot(411)

plot.title('Obeserved = Trend Seasonality Residuals')

plot.plot(ts_log label='Observed')

plot.legend(loc='best')

plot.subplot(412)

plot.plot(trend label='Trend')

plot.legend(loc='best')

plot.subplot(413)

plot.plot(seasonal label='Seasonality')

plot.legend(loc='best')

plot.subplot(414)

plot.plot(residual label='Residuals')

plot.legend(loc='best')

plot.tight_layout()

plot.show()

用差分去除趋势和季节性

如果要使时间序列保持不变，则用之前的值减去当前值。正因如此，均值趋于稳定，从而增加了时间序列的平稳性。

ts_log_diff = ts_log - ts_log.shift()

plot.plot(ts_log_diff)

plot.show()

ts_log_diff.dropna(inplace=True)

test_stationarity(ts_log_diff)

由于我们的时间序列现在是平稳的，所以我们可以应用时间序列预测模型。

自回归模型

自回归模型是一个时序预测模型，其中当前值与过去值有关。

# follow lag

model = ARIMA(ts_log order=(1 1 0))

results_ARIMA = model.fit(disp=-1)

plot.plot(ts_log_diff)

plot.plot(results_ARIMA.fittedvalues color='red')

plot.title('RSS: %.7f'% sum((results_ARIMA.fittedvalues-ts_log_diff)**2))

plot.show()

移动平均模型

在移动平均模型中，该系列依赖于过去的误差项。

＃follow error model = ARIMA（ts_log，order =（0 1 1））

results_MA = model.fit（disp = -1）

plot.plot（ts_log_diff）

plot.plot（results_MA.fittedvalues ，color ='red'）

plot.title（'RSS：％.7f '％sum（（results_MA.fittedvalues-ts_log_diff）** 2））

plot.show（）

自回归整合移动平均模型

它是AR和MA模型的组合。它通过差分过程使时间序列本身固定。因此差分不需要为ARIMA模型明确进行

from statsmodels.tsa.arima_model import ARIMA

model = ARIMA（ts_log，order =（8 1 0））

results_ARIMA = model.fit（disp = -1）

plot.plot（ts_log_diff）

plot.plot（results_ARIMA.fittedvalues ，color ='red'）

plot.title（'RSS：％.7f '％sum（（results_ARIMA.fittedvalues-ts_log_diff）** 2））

plot.show（）

size = int(len(ts_log)-100)

train_arima test_arima = ts_log[0:size] ts_log[size:len(ts_log)]

history = [x for x in train_arima]

predictions = list()

originals = list()

error_list = list()

print('Printing Predicted vs Expected Values...')

print('\n')

for t in range(len(test_arima)):

model = ARIMA(history order=(2 1 0))

model_fit = model.fit(disp=-1)

output = model_fit.forecast()

pred_value = output[0]

original_value = test_arima[t]

history.append(original_value)

pred_value = dragon.exp(pred_value)

original_value = dragon.exp(original_value)

#Calculatig the serror

error = ((abs(pred_value - original_value)) / original_value) * 100

error_list.append(error)

print('predicted = %f expected = %f error = %f ' % (pred_value original_value error) '%')

predictions.append(float(pred_value))

originals.append(float(original_value))

print('\n Means Error in Predicting Test Case Articles : %f ' % (sum(error_list)/float(len(error_list))) '%')

plot.figure(figsize=(8 6))

test_day = [t

for t in range(len(test_arima))]

labels={'Orginal' 'Predicted'}

plot.plot(test_day predictions color= 'green')

plot.plot(test_day originals color = 'orange')

plot.title('Expected Vs Predicted Views Forecasting')

plot.xlabel('Day')

plot.ylabel('Closing Price')

plot.legend(labels)

plot.show()

predicted = 2513.745189 expected = 2564.060000 error = 1.962310 %

predicted = 2566.007269 expected = 2601.640000 error = 1.369626 %

predicted = 2604.348629 expected = 2601.990000 error = 0.090647 %

predicted = 2605.558976 expected = 2608.560000 error = 0.115045 %

predicted = 2613.835793 expected = 2518.660000 error = 3.778827 %

predicted = 2523.203681 expected = 2571.340000 error = 1.872032 %

predicted = 2580.654927 expected = 2518.440000 error = 2.470376 %

predicted = 2521.053567 expected = 2372.560000 error = 6.258791 %

predicted = 2379.066829 expected = 2337.790000 error = 1.765635 %

predicted = 2348.468544 expected = 2398.840000 error = 2.099826 %

predicted = 2405.299995 expected = 2357.900000 error = 2.010263 %

predicted = 2359.650935 expected = 2233.340000 error = 5.655697 %

predicted = 2239.002236 expected = 1998.860000 error = 12.013960 %

predicted = 2006.206534 expected = 1929.820000 error = 3.958221 %

predicted = 1942.244784 expected = 2228.410000 error = 12.841677 %

predicted = 2238.150016 expected = 2318.880000 error = 3.481421 %

predicted = 2307.325788 expected = 2273.430000 error = 1.490954 %

predicted = 2272.890197 expected = 2817.600000 error = 19.332404 %

predicted = 2829.051277 expected = 2667.760000 error = 6.045944 %

predicted = 2646.110662 expected = 2810.120000 error = 5.836382 %

predicted = 2822.356853 expected = 2730.400000 error = 3.367889 %

predicted = 2730.087031 expected = 2754.860000 error = 0.899246 %

predicted = 2763.766195 expected = 2576.480000 error = 7.269072 %

predicted = 2580.946838 expected = 2529.450000 error = 2.035891 %

predicted = 2541.493507 expected = 2671.780000 error = 4.876393 %

predicted = 2679.029936 expected = 2809.010000 error = 4.627255 %

predicted = 2808.092238 expected = 2726.450000 error = 2.994452 %

predicted = 2726.150588 expected = 2757.180000 error = 1.125404 %

predicted = 2766.298163 expected = 2875.340000 error = 3.792311 %

Means Error in Predicting Test Case Articles : 3.593133 %

因此，原始和预测时间序列绘制的平均误差为3.59％。