時間序列流程

• 一、變平穩

1.1 去趨勢

     差分、取對數

1.2去週期性

     濾波、差分

1.3變平穩的原因除了1.1、1.2之外還有

    穩定方差、使數據呈現正態分佈、使週期效應累加

ARIMA模型的示例代碼

from pandas import read_csv
from pandas import datetime
from matplotlib import pyplot
from statsmodels.tsa.arima_model import ARIMA
from sklearn.metrics import mean_squared_error

def parser(p):
	return datetime.strptime('190'+p,'%Y-%m)

series = read_csv('input.csv',header = 0,parse_dates = [0],index_col = 0,squeeze = True,date_parser = parser)
P = series.values
size = int(len(P)*0.66)
train,test = P[0:size],P[size:len(P)]
history = [p for p in train]
predictions = list()
for t in range(len(test)):
	model = ARIMA(history,order=(5,1,0))
	model_fit = model.fit(disp=0)
	output = model_fit.forecast()
	yhat = output[0]
	predictions.append(yhat)
	obs = test[t]
	history.append(obs) # 滑動窗口
	print('predicted = %f,expected = %f' %(yhat,obs))
error = mean_squared_error(test,predictions)
print('Test MSE: %.3f' % error)
pyplot.plot(test)
pyplot.plot(predictions,color='red')
pyplot.show()

R代碼

auto.ARIMA模型的優點在於它自動查找數據的順序、趨勢和週期性

asm_weekwise <- read.csv('weekwise.csv',header = TRUE)
asm_weekwise$Week <- NULL

library(MASS)
library(tseries)
library(forecast)

asm_weekwise[is.na(asm_weekwise)] <- 0
asm_weekwise[asm_weekwise <= 0] <- mean(as.matrix(asm_weekwise))

weekjoyforecastvalues <- date.frame("asm"=interger(),"value" = integer(),stringsAaFactors=FALSE)

for (i in 2:ncol(asm_weekwise))
{
 asmname <- names(asm_weekwise)[i]
 temparimadata <- asm_weekwise[,i]
 m <- mean(as.matrix(temparimadata))
 s <- sd(temparimadata)
 temparimadata <- (temparimadata - m)
 temparimadata <- (temparimadata / s)
 temparima <- auto.arima(temparimadata,stationary = FALSE,seasonal = TRUE,allowdrift=TRUE,allowmean=FALSE,biasadj=FALSE)
 tempforecast <- forecast(temparima,h=12)
 temp_forecastes_data <- sum(data.frame(temp_forecastes$mean)*s + m)
 weekjoyforecastvalues[nrow(weekjoyforecastvalues) + 1, ] <- c(asmname,temp_forecasted_data)
 }
 
 weekjoyforecastvalues$value <- as.integer(weekjoyforecastvalues$value)