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ARMA時(shí)序分析

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Time Series Analysis

AR

自回歸模型，過去的觀察值和現(xiàn)在的干擾值的聯(lián)系組合預(yù)測(cè) Xt=c ∑i=1pφiXt?i εt? $$X_t=c \sum\limits_{i=1}^p\varphi_iX_{t-i} \varepsilon_{t\cdot} </p> <h1 id="ma"> MA </h1> <p> 滑動(dòng)平均模型， 過去的感染治和現(xiàn)在的干擾值的線性組合預(yù)測(cè) </p> <p> <nobr>Xt=μ εt ∑t=1qθiεt?i</nobr> <script type="math/tex; mode=display" id="MathJax-Element-2"> X_t=\mu \varepsilon_t \sum\limits_{t=1}^q\theta_i\varepsilon_{t-i} </p> <h1 id="arma"> ARMA </h1> <p> ARMA(Autoregressive–moving-average model) </p> <p> Wiki <nobr>Xt=c εt ∑i=1pφiXt?i ∑t=1qθiεt?i?</nobr> <script type="math/tex; mode=display" id="MathJax-Element-3"> X_t=c \varepsilon_{t} \sum\limits_{i=1}^p\varphi_iX_{t-i} \sum\limits_{t=1}^q\theta_i\varepsilon_{t-i\cdot} </p> <p> <nobr>c</nobr> <script type="math/tex" id="MathJax-Element-4">c is a constant </p> <p> <nobr>ε</nobr> <script type="math/tex" id="MathJax-Element-5">\varepsilon is white noise </p> <p> <nobr>μ</nobr> <script type="math/tex" id="MathJax-Element-6">\mu is the expectation of <nobr>Xt</nobr> <script type="math/tex" id="MathJax-Element-7">X_t </p> <p> <nobr>φ</nobr> <script type="math/tex" id="MathJax-Element-8">\varphi and <nobr>θ</nobr> <script type="math/tex" id="MathJax-Element-9">\theta are the parameters </p> <h1 id="arima分析步驟"> ARIMA分析步驟 </h1> <p> ARIMA(p,d,q) ，非平穩(wěn)序列經(jīng)過k階差分后變成平穩(wěn)序列運(yùn)用ARMA模型 </p> <p> 繪制時(shí)序圖看看數(shù)據(jù)長(zhǎng)什么樣，猜測(cè)是平穩(wěn)還是非平穩(wěn) </p> <p> ADF(Augmented Dickey-Fuller unit root test)單位根平穩(wěn)檢驗(yàn) </p> <nobr>p&lt;a</nobr> <script type="math/tex" id="MathJax-Element-10">p : 平穩(wěn)序列，進(jìn)入下一步 <nobr>p&gt;a</nobr> <script type="math/tex" id="MathJax-Element-11">p>a : 非平穩(wěn)序列，嘗試進(jìn)行K步差分回到步驟2繼續(xù)進(jìn)行平穩(wěn)檢驗(yàn) <p> 隨機(jī)序列(白噪聲)檢驗(yàn) </p> <p> <strong>方法</strong>：Q統(tǒng)計(jì)量、LB統(tǒng)計(jì)量 </p> <nobr>p&lt;a</nobr> <script type="math/tex" id="MathJax-Element-12">p : 平穩(wěn)非白噪聲序列，進(jìn)入下一步 <nobr>p&gt;a</nobr> <script type="math/tex" id="MathJax-Element-13">p>a : 白噪聲序列，停止分析 <p> 繪制ACF(Autocorrelation)自相關(guān)圖，自相關(guān)系數(shù)<nobr>ρk</nobr> <script type="math/tex" id="MathJax-Element-14">\rho_k具有k階截尾性則是平穩(wěn)序列 </p> <p> <nobr>AR(p)</nobr> <script type="math/tex" id="MathJax-Element-15">AR(p)模型具有拖尾性，<nobr>MA(q)</nobr> <script type="math/tex" id="MathJax-Element-16">MA(q)具有q階截尾性 </p> <p> PACF(Partial Autocorrelation)偏自相關(guān)圖， </p> <p> <nobr>AR(p)</nobr> <script type="math/tex" id="MathJax-Element-17">AR(p)模型具有p階截尾性，<nobr>MA(q)</nobr> <script type="math/tex" id="MathJax-Element-18">MA(q)有拖尾性 </p> <p> BIC信息量**小選擇p,q </p> <p> p, q 階數(shù)一般不超過length/10 </p> <p> 模型檢驗(yàn)和參數(shù)估計(jì) </p> <p> ARIMA模型預(yù)測(cè) </p> <p> <strong>拖尾</strong>：始終有非零取值，不會(huì)在k大于某個(gè)常數(shù)后就恒等于零(或在0附近隨機(jī)波動(dòng)) </p> <p> <strong>截尾</strong>：在大于某個(gè)常數(shù)k后快速趨于0為k階截尾 </p> <h1 id="python"> Python </h1> <p> statsmodels </p> <p> Time Series analysis </p> <p> ARIMA </p> import statsmodels.api as sm import pandas as pd df = pd.DataFrame(data) #dataframe x = #LOAD YOUR DATA index = pd.Index(sm.tsa.datetools.dates_from_range( 1959Q1 , 2009Q3 )) #or dates = sm.tsa.datetools.dates_from_range( 1980m1 , length=nobs) df = pd.DataFrame(X,colomns=[ x ],index=index) #plot df.plot(df) #ACF sm.tsa.acf(df) sm.graphics.tsa.plot_acf(df) #PACF sm.tsa.pacf(df) sm.graphics.tsa.plot_pacf(df) #ADF sm.tsa.adfuller(df.x) #df.loc[:, x ] | df.iloc[:,0] #diff差分 pd.diff() #diagnostic白噪聲檢驗(yàn), 返回stats和p sm.stats.diagnostic.acorr_ljungbox(df, lags=1) #model #from statsmodels.tsa.arima_model import ARIMA #ARMA model = sm.tsa.ARIMA(df, order=(p,d,q)) model = sm.tsa.ARMA() arma_res = model.fit(trend= nc , disp=-1) #BIC model.bic #模型報(bào)告 model.summary2() model.summary() model.tail() #擬合結(jié)果 model.PR</a>edict() #預(yù)測(cè)圖 fig, ax = plt.subplots(figsize=(10,8)) fig = arma_res.plot_predict(start= 1999m6 , end= 2001m5 , ax=ax) legend = ax.legend(loc= upper left ) #預(yù)測(cè)接下來5個(gè)數(shù) model.forecast(5) </p> <p> <b>相關(guān)推薦：</b> </p> <hr /> <p> <a href="http://m.k67r.cn/px189_jssz/" target="_blank">蘇州JAVA培訓(xùn)</a>&nbsp; &nbsp;<a href="http://m.k67r.cn/px189_jssz/" target="_blank">蘇州JAVA培訓(xùn)班</a>&nbsp; &nbsp;<a href="http://m.k67r.cn/px189_jssz/" target="_blank">蘇州JAVA培訓(xùn)機(jī)構(gòu)</a> </p>$$