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ARIMA model
Full ARIMA model is autoregressive moving average model, a commonly used statistical models to predict time series, generally referred to as ARIMA (p, d, q).
Adaptation of ARIMA
ARIMA model is relatively simple to use. In applying the ARIMA model, to ensure the following:
Time series data is relatively stable, substantially constant overall rise absent or decreased, it may be unstable if a differential manner by stabilized.
Non-linear processing not only linear processing
determines the timing data is stable
The basic determination method: stability data, there is no generally rising and falling trend, there is no periodicity, variance tends to a stable value.
ARIMA mathematical expression
ARIMA (p, d, q), where p is the number of lags the data itself, i.e. is autoregressive model AR model parameters. d is the difference a few time-series data required to get stable data. q is the number of lags prediction error, i.e., the model MA is slidably average model parameters.
a) p AR model parameters
AR model describes the relationship between the current value and the historical value, AR model of order p hysteresis can be expressed as: 
where u is a constant, et represents the error.
b) q model parameters MA
MA model describes the relationship between the current value from the cumulative error of the regression portion, MA lag model of order q may be expressed as: 
where u is a constant, et represents the error.
c) d and the differential parameter
First difference: 
second order difference: 
D) the ARIMA the AR + MA = 
the ARIMA model using procedure
Acquiring time series data
observed whether the data is smooth, or differential, into a stationary timing data to determine D
PACF p and q is determined by observing the autocorrelation coefficients of the autocorrelation coefficients ACF and Partial 
obtained after p, D, q using ARIMA ( p, d, q) is trained to predict
Python calls ARIMA
#差分处理
diff_series = diff_series.diff(1)#一阶
diff_series2 = diff_series.diff(1)#二阶
#ACF与PACF
#从scipy导入包
from scipy import stats
import statsmodels.api as sm
#画出acf和pacf
sm.graphics.tsa.plot_acf(diff_series)
sm.graphics.tsa.plot_pacf(diff_series)
#arima模型
from statsmodels.tsa.arima_model import ARIMA
model = ARIMA(train_data,order=(p,d,q),freq='')#freq是频率,根据数据填写
arima = model.fit()#训练
print(arima)
pred = arima.predict(start='',end='')#预测
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