手工获取SARIMA模型参数的简介

背景：SARIMA，简单说就是AR+MA+差分+季节性因素+趋势。所以参数在statsmodels.tsa.statespace.sarimax.SARIMAX里边，用3个指标涵盖核心参数，order(p,d,q)、seasonal_order(P,D,Q,s)和trend.
Seasonal AutoRegessive Integrated Moving Average with eXogenous regressors model

一、步骤的文字描述：

"""准备阶段"""
# 第一、定义一个待传入参数的模型，及模型评分
# 第二、定义一组要测试的参数组合
"""开始"""
# 第三、定义一个函数，记录各个参数组合及传入模型后的评分
# 第四、选择评分最优的一组参数组合，组成模型
# 第五、使用模型

二、代码：(在原文基础上有调整)

from statsmodels.tsa.statespace.sarimax import SARIMAX
from sklearn.metrics import mean_squared_error
import pandas as pd
import warnings
import joblib
from multiprocessing import cpu_count

def walk_forward_validation(data, n_test, cfg):
	# 定义一个给一套参数cfg打分的函数
	predictions = []
	train, test = data[:-n_test], data[-n_test:]
	history = [i for i in train]
	for x in range(len(test)):
		order, sorder, trend = cfg
		model = SARIMAX(history,
						order=order, seasonal_order=sorder, trend=trend,
						enforce_stationarity=False,
						enforce_invertibility=False)
		model.fit(disp=False)
		yhat = model_fit.predict(len(history), len(history))
		predicions.append(yhat)
		history.append(test[x])
	error = mean_squared_error(test, predictions)
	return error


def score_model(data, n_test, cfg, debug=False):
	# 记录下一套参数，以及该参数下模型的得分
	key = str(cfg)
	if debug:
		error = walk_forward_validation(data, n_test, cfg)
	else:
		try:
			with warnings.catch_warnings():
				warnings.filterwarnings('ignore')
				error = warlk_forward_validation(data, n_test, cfg)
		except:
			error=None
	if error is not None:
		print(f'> Model{key} {error:.3f}')
	return key, error

def grid_search(data, cfg_list, n_test, parallel=True):
	# 把所有参数组合一一带入模型，并把所有参数组合及其对应模型得分记录下来，排序。
	if parallel:
		executor = joblib.Parallel(n_jobs=cpu_count(),
									backend='multiprocessing')
		tasks = (joblib.delayed(score_model)(data, n_test, cfg) for cfg in cfg_list)
		scores = executor(tasks)
	else:
		scores = [score_model(data, n_test, cfg) for cfg in cfg_list]
	scores = [r for r in scores if r[1] != None]
	scores.sort(key=lambda tup: tup[1)
	return scores

def sarima_config():
    # 造出自己预估的所有参数组合list
	cfg_list = []
	p_params = [0, 1, 2]
	d_params = [0, 1]
	q_params = [0, 1, 2]
	P_params = [0, 1, 2]
	D_params = [0, 1]
	Q_params = [0, 1, 2]
	s = [2, 4, 12]
	t = ['n', 'c', 't', 'ct']
	for p in p_params:
		for d in d_params:
			for q in q_params:
				for P in P_params:
					for D in D_params:
						for Q in Q_params:
							for s in s:
								for t in t:
									cfg = [(p,d,q), (P,D,Q,s),t]
									cfg_list.append(cfg)
	return cfg_list


if __name__ == '__main__':
	df = pd.read_csv('filepath+filename.csv')
	data = df.values
	n_test = number_of_test
	cfg_list = sarima_config()
	scores = grid_search(data, cfg_list, n_test)
	print('Done')
	for cfg, error in scores[:5]: # 取出前5个最优的参数组合及对应的模型得分
		print(cfg, error)

三、其他
pmdarima.arima.aotu_arima()可以自动使用训练数据集得到参数。但是很多人都不用它，应该是因为它找到的参数并不怎么好的缘故。
例如，如下的原始数据使用pmdarima.arima.auto_arima()，没有手工测试得到的好：
直接使用的话并不好

import numpy as np
import pmdarima as pm
import matplotlib.pyplot as plt
from pmdarima.model_selection import train_test_split
import pandas as pd
import warnings

warnings.filterwarnings('ignore')

df = pd.read_csv('path+filename')

y = df.values

train, test = train_test_split(y, train_size=0.7)

model = pm.arima.auto_arima(train, seasonal=True, m=10) 
# m等于(P,D,Q,s)的s。m=10是通过线图，肉眼观察得到的。（原始数据x是时间）
print(model.summary())


forecasets = model.predict(len(test))
x = np.arange(len(train))
plt.plot(x, y, c='black')
plt.plot(x[len(train):], forecasets, c='blue')
plt.show()

结果&图如下：


，作为对比使用最上边得到的参数貌似更好些，从AIC/BIC/HQIC看：
代码如下

from statsmodels.tsa.statespace.sarimax import SARIMAX
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from pmdarima.model_selection import train_test_split
import warnings

df = pd.read_csv('path+filename')
y = df.values
x = np.arange(len(y))

warnings.filterwarings('ignore')

train, test = trains_test_split(y, train_size=0.7)

model = SARIMAX(train,
				order = (0, 1, 0),
				seasonal_order=(2, 1, 0, 10),
				trend='n')  # 利用我们手动测试出来的最优参数组合
model_fit = model.fi(disp=False)
print(model_fit.summery())

f = model_fit.predict(1, end=len(y)+10)
plt.plot(x, y, c='black')
plt.plot(np.arange(len(y)+10), f, c='blue')
plt.show()