這篇文章是關於使用時間序列預測的Bitcoin Price預測。時間序列預測與其他機器學習模型有很大不同，因為 -
- 1.時間依賴性。因此，觀測值是獨立的線性迴歸模型的基本假設在這種情況下不成立。
- 2.隨著增加或減少的趨勢，大多數時間序列都有某種形式的季節性趨勢，即特定時間範圍內的變化。
因此，不能使用簡單的機器學習模型，因此時間序列預測是一個不同的研究領域。在本文中，AR，MA和ARIMA等時間序列模型用於預測Bitcoin 的價格。
該數據集包含2013年4月至2017年8月Bitcoin的開盤價和收盤價
導入必要的庫
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
繪製時間序列
將數據加載到訓練數據框中，然後使用日期作為索引，系列用x軸上的日期和y軸上的收盤價格繪製。
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()
測試平穩性
增強Dicky Fuller測試：
增強Dicky Fuller測試是一種稱為單位根測試的統計測試。
單位根檢驗背後的直覺是它決定了時間序列由趨勢定義的強度。
ADF單位根檢驗和是應用最廣泛的一種
- 1. Null Hypothesis (H0):原假設(null hypothesis)亦稱待驗假設、虛無假設、解消假設，時間序列可以用非平穩的單位根表示。。
- 2. Alternative Hypothesis (H1): 備擇假設（Alternative Hypothesis）,時間序列是固定的。
ADF值的解釋：
- 1. p值 > 0.05：接原假設（H0），數據具有單位根並且是非平穩的。
- 2. p值 <= 0.05：拒絕原假設（H0），數據是固定的。
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)
日誌轉換系列
日誌轉換用於糾正高度傾斜的數據。從而有助於預測過程。
ts_log = dragon.log（ts）
plot.plot（ts_log，color =“green”）
plot.show（）
test_stationarity（ts_log）
decomposition消除趨勢和季節性
decomposition是一種技術，在該技術中，該序列的季節性、趨勢成分被移除，然後將模型應用於殘差序列。
# 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()
用差分去除趨勢和季節性
如果要使時間序列保持不變，則用之前的值減去當前值。正因如此，均值趨於穩定，從而增加了時間序列的平穩性。
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)
由於我們的時間序列現在是平穩的，所以我們可以應用時間序列預測模型。
自迴歸模型
自迴歸模型是一個時序預測模型，其中當前值與過去值有關。
# 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()
移動平均模型
在移動平均模型中，該系列依賴於過去的誤差項。
＃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（）
自迴歸整合移動平均模型
它是AR和MA模型的組合。它通過差分過程使時間序列本身固定。因此差分不需要為ARIMA模型明確進行
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，原始和預測時間序列繪製的平均誤差為3.59％。
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