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％。