{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 时间序列分析\n",
"# 主要内容\n",
"- 1.平稳性检验\n",
"- 2.白噪声检验\n",
"- 3.建模\n",
" - 定阶\n",
" - ARIMA(0,1,1)建模\n",
"- 4.预测\n",
"\n",
"# 1.平稳性检验\n",
"- 1.时序图检验 \n",
"\n",
" 平稳序列的时序图应该在一个常数附近波动，并且波动的范围有界。如果有明显的趋势性或者周期性，则通常不是平稳序列。 \n",
" \n",
" \n",
"- 2.自相关图检验 \n",
"\n",
" 平稳序列具有短期相关性，这个性质表明对平稳序列而言通常只有近期的序列值对现时值的影响比较明显，间隔越远的过去值对现时值的影响越小。随着延迟期数k的增加，平稳序列的自相关系数$\\rho_k$(延迟k期)会比较快的衰减趋向于零，并在零附近随机波动，而非平稳序列的自相关系数衰减的速度比较慢，这就是利用自相关图进行平稳性检验的标准。 \n",
" \n",
" \n",
"- 2.单位根检验 \n",
" 单位根检验是指检验序列中是否存在单位根，如果存在单位根就是非平稳时间序列。"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import pandas as pd\n",
"data = pd.read_excel('data/arima_data.xls', index_col = u'日期')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" 销量 | \n",
"
\n",
" \n",
" | 日期 | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" | 2015-01-01 | \n",
" 3023 | \n",
"
\n",
" \n",
" | 2015-01-02 | \n",
" 3039 | \n",
"
\n",
" \n",
" | 2015-01-03 | \n",
" 3056 | \n",
"
\n",
" \n",
" | 2015-01-04 | \n",
" 3138 | \n",
"
\n",
" \n",
" | 2015-01-05 | \n",
" 3188 | \n",
"
\n",
" \n",
"
\n",
"
\n",
"\n",
" | Model: | ARIMA | Log-Likelihood: | -205.88 | \n",
"
\n",
"\n",
" | Dependent Variable: | D.y | Scale: | 1.0000 | \n",
"
\n",
"\n",
" | Date: | 2018-05-24 15:25 | Method: | css-mle | \n",
"
\n",
"\n",
" | No. Observations: | 36 | Sample: | 1 | \n",
"
\n",
"\n",
" | Df Model: | 2 | | 7 | \n",
"
\n",
"\n",
" | Df Residuals: | 34 | S.D. of innovations: | 73.086 | \n",
"
\n",
"\n",
" | AIC: | 417.7595 | HQIC: | 419.418 | \n",
"
\n",
"\n",
" | BIC: | 422.5101 | | | \n",
"
\n",
"
\n",
"\n",
"\n",
" | Coef. | Std.Err. | t | P>|t| | [0.025 | 0.975] | \n",
"
\n",
"\n",
" | const | 49.9557 | 20.1390 | 2.4805 | 0.0182 | 10.4840 | 89.4274 | \n",
"
\n",
"\n",
" | ma.L1.D.y | 0.6710 | 0.1648 | 4.0712 | 0.0003 | 0.3480 | 0.9941 | \n",
"
\n",
"
\n",
"\n",
"\n",
" | Real | Imaginary | Modulus | Frequency | \n",
"
\n",
"\n",
" | MA.1 | -1.4902 | 0.0000 | 1.4902 | 0.5000 | \n",
"
\n",
"
"
],
"text/plain": [
"\n",
"\"\"\"\n",
" Results: ARIMA\n",
"=================================================================\n",
"Model: ARIMA Log-Likelihood: -205.88\n",
"Dependent Variable: D.y Scale: 1.0000 \n",
"Date: 2018-05-24 15:25 Method: css-mle\n",
"No. Observations: 36 Sample: 1 \n",
"Df Model: 2 7 \n",
"Df Residuals: 34 S.D. of innovations: 73.086 \n",
"AIC: 417.7595 HQIC: 419.418\n",
"BIC: 422.5101 \n",
"------------------------------------------------------------------\n",
" Coef. Std.Err. t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------\n",
"const 49.9557 20.1390 2.4805 0.0182 10.4840 89.4274\n",
"ma.L1.D.y 0.6710 0.1648 4.0712 0.0003 0.3480 0.9941\n",
"-------------------------------------------------------------------------\n",
" Real Imaginary Modulus Frequency\n",
"-------------------------------------------------------------------------\n",
"MA.1 -1.4902 0.0000 1.4902 0.5000\n",
"=================================================================\n",
"\n",
"\"\"\""
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 建模\n",
"model = ARIMA(data, (p,1,q)).fit() #建立ARIMA(0, 1, 1)模型\n",
"model.summary2() #给出一份模型报告"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 4.预测"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 4873.96633816, 4923.9220861 , 4973.87783404, 5023.83358199,\n",
" 5073.78932993]),\n",
" array([ 73.08574304, 142.32679656, 187.54281698, 223.80281362,\n",
" 254.95703671]),\n",
" array([[ 4730.72091401, 5017.21176231],\n",
" [ 4644.96669081, 5202.87748139],\n",
" [ 4606.3006672 , 5341.45500089],\n",
" [ 4585.18812766, 5462.47903632],\n",
" [ 4574.08272038, 5573.49593948]]))"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.forecast(5) #作为期5天的预测，返回预测结果、标准误差、置信区间。"
]
}
],
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