時間序列論文

1、cam模型的股票價格分析和預(yù)測一、cam 模型的建立過程 ARCH模型是ARCH模型體系中理論較完善、應(yīng)用最廣泛的一種,即使某些時間序列更適合應(yīng)用其它模型擬合,但一般還是先建立ARCH模型,并通過其進(jìn)行深入地分析。本文將以ARCH類模型為例作基本分析。 時間序列模型的建立通常有四個步驟:第一步模型識別,第二步參數(shù)估計,第三步階數(shù)的確定,最后是模型檢驗。ARCH模型建模也要先依據(jù)常見的時間序列的建模過程,其詳細(xì)過程如下:(1)建立均值效應(yīng)模型并檢驗。對整理得到的序列建立一個時間序列的計量經(jīng)濟(jì)模型,判別出數(shù)據(jù)中相關(guān)性的先后,對大部分收益率時間序列數(shù)據(jù)來說,就是從時間序列數(shù)據(jù)中把樣本均值分離出來,接

2、著對殘差項,利用拉格朗日乘子法檢驗它是否存在ARCH效應(yīng)。(2)階的確定。如果檢驗統(tǒng)計量F,LM是顯著的,則認(rèn)為 存在條件異方差性,用的偏自相關(guān)函數(shù)來確定ARCH模型的階數(shù)。(3)參數(shù)估計。估計ARCH模型的參數(shù),通常使用極大似然估計法。(4)模型驗證。一般的ARCH模型,標(biāo)準(zhǔn)化抖動可以表示為,是一個獨立同分布的隨機(jī)變量且服從正態(tài)分布或標(biāo)準(zhǔn)化學(xué)生t分布。因而,可以通過驗證序列 來判定所擬合的ARCH模型是否合適。尤其是,可以用檢驗均值方程的方法來檢驗的Ljung-Box的統(tǒng)計量, 的Ljung-Box的統(tǒng)計量還可以對波動率方程有效性進(jìn)行檢驗。 的偏度、峰度圖能檢驗分布假設(shè)的有效性。二、ch 模

3、型在股票指數(shù)中的研究（一） 中小板指數(shù)的價格序列 ARCH 模型實證分析1、數(shù)據(jù)選取 為說明ARCH模型在股價序列中的應(yīng)用,本文選取中小板指數(shù)收盤價作比較詳細(xì)的研究。以下模型建立和選取采用的是2009年3月6日至2012年11月9日的中小板指數(shù)(399005.SZ)的收盤價,一共890個,本文用前885個數(shù)據(jù)來建立相應(yīng)的模型,然后通過建立的模型預(yù)測第886到890的值,并將預(yù)測值和實際值作對比分析。該數(shù)據(jù)來自于新浪財經(jīng)網(wǎng)。2、數(shù)據(jù)預(yù)處理 對于收集到的數(shù)據(jù),先作時間序列圖,并檢驗該組數(shù)據(jù)的自相關(guān)性。檢驗結(jié)果如下:圖1 中小板指數(shù)收盤價的時間序列圖 圖2 中小板指數(shù)收盤價的自相關(guān)和偏自相關(guān)圖 從上

4、面的時序圖和自相關(guān)圖可以看出中小板指數(shù)的收盤價序列是一個非平穩(wěn)的時間序列。 在實際的應(yīng)用中,一般采用對數(shù)收益率的數(shù)據(jù)來擬合模型,對數(shù)收益率的公式如下: 其中表示時刻 t 的資產(chǎn)價格,表示 t-1時刻的資產(chǎn)價格,表示相對收益。 對新建立的收益率序列作時間序列圖,結(jié)果如下:圖3 中小板指數(shù)收益率的時間序列圖 從對數(shù)收益率圖可以看出,收益率序列中出現(xiàn)了多個異常的峰值,可觀察到對數(shù)收益率波動的集群現(xiàn)象,波動在一些時間段內(nèi)較小,在有的時間段內(nèi)非常大,體現(xiàn)出序列波動的條件異方差現(xiàn)象,這說明這些序列大多不是隨機(jī)游動過程。3、數(shù)據(jù)分析 首先，進(jìn)行正態(tài)性檢驗，得到收益率序列的描述性統(tǒng)計量如下:圖3 中小板指數(shù)收

5、益率序列的描述性統(tǒng)計量 觀察上述檢驗結(jié)果發(fā)現(xiàn),樣本期內(nèi)的中小板指數(shù)收益率均值為0.000237,標(biāo)準(zhǔn)差為 0.016817。偏度為-0.542293,小于 0,說明此序列數(shù)據(jù)有較長的左拖尾的現(xiàn)象。左偏峰度為 4.109599,而正態(tài)分布的峰度值 3,中小板指數(shù)收益率的左偏峰度大于正態(tài)分布的峰度值,說明收益率具有尖峰和厚尾的特征。Jarque-Bera 統(tǒng)計量為 88.67755,P 值為 0.000000,說明該對數(shù)收益率序列拒絕正態(tài)分布的假設(shè)。 接著,利用單位根的方法檢驗序列的平穩(wěn)性。圖4 中小板指數(shù)收益率ADF檢驗結(jié)果 ADF 單位根檢驗的 t 統(tǒng)計量的值為-28.02253,小于在 1%

6、,5%,10%水平下的統(tǒng)計量值,且 P 值為 0,說明收益率的序列拒絕隨機(jī)游走的假設(shè),從而說明這個時間序列是平穩(wěn)的。 然后,檢驗收益率數(shù)據(jù)的自相關(guān)性中小板指數(shù)收益率序列的自相關(guān)和偏自相關(guān)圖 上圖左邊兩列是自相關(guān)和偏自相關(guān)的圖,本研究中使用的是Ljung-Box的Q統(tǒng)計量。觀察最后一列的P值,可以看到在置信水平5%下,序列存在5階、6階、10階等階數(shù)的自相關(guān)。4、模型建立 對收益率序列作過如上分析后,開始建立相應(yīng)的模型,序列存在自相關(guān),在多次的建模嘗試中,滯后5階的自回歸方程具有顯著性,故先建立AR(5)模型。圖5 中小板指數(shù)收益率序列的自回歸結(jié)果 用Ljung-Box Q 統(tǒng)計量對均值方程擬合

7、后的殘差及殘差平方做自相關(guān)檢驗,結(jié)果如下: 圖6 收益率殘差的自相關(guān)和偏自相關(guān)圖圖7 收益率殘差平方的自相關(guān)和偏自相關(guān)圖 分析比較上述結(jié)果得殘差在置信水平為5%時,不存在顯著自相關(guān),但是殘差平方有顯著的自相關(guān)性。對以上均值方程進(jìn)行ARCH效應(yīng)檢驗,采用ARCH LM檢驗礎(chǔ)上建立ARCH模型。圖8 AR(5)-ARCH(2)模型估計結(jié)果 以上顯示的計算結(jié)果,第一部分給出了均值方程的估計結(jié)果,第二部分是ARCH(2)方程的參數(shù)估計值,第三部分是均值方程的評價統(tǒng)計量,第四部分給出了均值方程對應(yīng)的特征根倒數(shù)值。均值方程的表達(dá)式為:ARCH(2)方程的表達(dá)式為:對以上建立的AR(5)-ARCH(2)模型

8、的殘差再進(jìn)行ARCH LM檢驗,結(jié)果如下2012-11-54202.1554236.0733.920.812012-11-64176.9044202.2226.3320.632012-11-74175.0324175.350.320.012012-11-84074.9964169.2494.242.312012-11-94054.2474075.8221.570.53 分析比較上表數(shù)據(jù),預(yù)測數(shù)據(jù)與實際數(shù)據(jù)的相對誤差都比較小,其中只有2012年11月8日的指數(shù)在作預(yù)測時的相對誤差值較大,這說明市場中存在一些其他因素的影響。通woyeshi jdejcdshusssikcmdssfiuerDvhj

9、dufdfggntriogEuetherewhrwuuergcsddc絕對誤差的時,誤差的值相對而言較大,這也恰好說明市場中各個因素的干擾使得中小板指數(shù)的波動不會特別遵循某一特定的規(guī)律或者模型,市場的投資者需要時刻關(guān)注股市動態(tài)和其他市場信息。總體而言,短期預(yù)測的效果還是比較令人滿意的,基于理想解法體系的模型評價和選擇有一定的科學(xué)合理性。2009/3/203588.3882010/2/125436.5172011/1/196314.322011/12/204479.5652009/3/233655.0862010/2/225412.9552011/1/206080.932011/12/21436

10、4.7892009/3/243681.4572010/2/235430.762011/1/216101.0942011/12/224331.1552009/3/253609.1822010/2/245554.2442011/1/245910.352011/12/234350.9442009/3/263681.9992010/2/255652.1712011/1/255845.7592011/12/264305.4862009/3/273712.6792010/2/265660.4892011/1/265967.192011/12/274201.8532009/3/303707.192010/3

11、/15723.482011/1/276076.0942011/12/284189.7232009/3/313747.4922010/3/25732.6832011/1/286121.612011/12/294209.2912009/4/13816.4362010/3/35792.342011/1/316180.6792011/12/304295.8622009/4/23882.3072010/3/45611.2212011/2/16196.8072012/1/44181.8142009/4/33868.7452010/3/55604.172011/2/96117.7072012/1/54034

12、.5292009/4/73890.1552010/3/85670.772011/2/106295.2042012/1/64042.3232009/4/83777.3482010/3/95669.5532011/2/116397.452012/1/94167.5042009/4/234024.7272010/3/245688.7062011/2/286732.9942012/1/314188.0372009/4/244039.2092010/3/255624.3952011/3/16758.6632012/2/14175.3012009/4/273889.4262010/3/265700.083

13、2011/3/26719.8642012/2/24252.1222009/4/283900.3812010/3/295750.7192011/3/36585.8562012/2/34330.3862009/4/293982.0512010/3/305806.9782011/3/46633.4252012/2/64369.1392009/4/304030.3962010/3/315829.4492011/3/76717.3992012/2/74292.9812009/5/44147.8932010/4/15922.5972011/3/86735.2132012/2/84416.6172009/5

14、/54175.7512010/4/25945.9022011/3/96760.1112012/2/94447.2192009/5/64274.5642010/4/65938.0252011/3/106734.3332012/2/104460.0542009/5/74253.0082010/4/75968.4422011/3/116712.6392012/2/134513.7182009/5/124135.0192010/4/126156.1372011/3/166812.782012/2/164539.9162009/5/134195.3492010/4/136057.482011/3/176

15、697.3962012/2/174517.5672009/5/144187.9252010/4/146108.8892011/3/186734.2572012/2/204528.2622009/5/154229.9192010/4/156033.5232011/3/216673.2412012/2/214583.172009/5/184243.3242010/4/166045.6752011/3/226631.2142012/2/224694.0092009/5/194266.1242010/4/195823.5012011/3/236714.9982012/2/234726.82009/5/

16、204270.2432010/4/205879.5632011/3/246707.2582012/2/244772.8952009/5/214192.1792010/4/216074.5052011/3/256743.7582012/2/274790.4652009/5/224175.6832010/4/226109.6172011/3/286653.0612012/2/284749.3992009/5/254200.4672010/4/236047.3232011/3/296499.9112012/2/294690.7892009/5/264211.7792010/4/266078.2452

17、011/3/306444.9122012/3/14709.1852009/5/274209.592010/4/275913.6572011/3/316397.6692012/3/24794.8962009/6/14269.2272010/4/285912.1792011/4/16456.6012012/3/54781.8162009/6/24279.9222010/4/295741.8332011/4/66405.6362012/3/64743.6862009/6/34290.5042010/4/305602.9742011/4/76442.4922012/3/74747.9552009/6/

18、44279.7112010/5/45590.5262011/4/86514.4632012/3/84806.2592009/6/54271.2722010/5/55752.0472011/4/116441.6472012/3/94902.8722009/6/84223.2232010/5/65582.4742011/4/126392.5412012/3/124924.4472009/6/94271.122010/5/75471.1242011/4/136483.6922012/3/134972.1552009/6/104321.7522010/5/105335.7712011/4/146465

19、.4542012/3/144783.7922009/6/114304.5452010/5/115211.7422011/4/156433.7992012/3/154766.252009/6/124215.7952010/5/125092.8352011/4/186428.1562012/3/164895.3752009/6/154298.5012010/5/135261.0222011/4/196372.7912012/3/194916.472009/6/164305.7522010/5/145296.0992011/4/206398.5532012/3/204786.9042009/6/17

20、4345.8932010/5/175027.912011/4/216428.6152012/3/214775.7582009/6/184385.0162010/5/185089.2222011/4/226371.2742012/3/224754.7032009/6/194347.7922010/5/195132.6072011/4/256262.982012/3/234688.3762009/6/224335.1442010/5/205083.0472011/4/266199.0732012/3/264707.5772009/6/234307.732010/5/215218.3642011/4

21、/276140.7032012/3/274680.3232009/6/244367.8752010/5/245419.2212011/4/285982.9072012/3/284494.032009/6/254370.5242010/5/255353.32011/4/296050.0542012/3/294426.892009/6/264367.5042010/5/265344.5412011/5/36120.372012/3/30 4413.172009/6/294370.5232010/5/275442.0572011/5/45980.8772012/4/54550.5482009/6/3

22、0 4363.7232010/5/285450.8382011/5/56006.9072012/4/64568.0012009/7/14398.1692010/5/315312.9242011/5/66054.7642012/4/94508.6422009/7/24450.1142010/6/15233.7222011/5/96090.2672012/4/104540.8082009/7/34446.8112010/6/25290.4912011/5/106102.7442012/4/114547.6182009/7/64441.0822010/6/35281.2482011/5/116087

23、.3112012/4/124641.3282009/7/74458.182010/6/45365.1592011/5/125993.0252012/4/134653.0772009/7/84492.0752010/6/75364.2182011/5/136016.4992012/4/164646.712009/7/94597.0032010/6/85415.2252011/5/166012.852012/4/174609.0312009/7/104596.2052010/6/95548.4422011/5/176012.2162012/4/184705.8162009/7/134630.116

24、2010/6/105566.1352011/5/186044.1192012/4/194692.8752009/7/144708.3342010/6/115514.7922011/5/196033.7392012/4/204718.9452009/7/154707.9152010/6/175409.8472011/5/206019.8492012/4/234637.0212009/7/164679.3082010/6/185198.0892011/5/235830.1352012/4/244615.8662009/7/174688.1212010/6/215313.172011/5/24580

25、3.4252012/4/254639.4842009/7/204793.6832010/6/225371.5792011/5/255707.3342012/4/264632.6612009/7/214649.7652010/6/235379.5642011/5/265645.0182012/4/274595.5662009/7/224710.9442010/6/245372.4542011/5/275532.4232012/5/24664.1832009/7/234729.1962010/6/255263.8782011/5/305488.3852012/5/34683.6182009/7/2

26、44678.2082010/6/285199.2642011/5/315580.7992012/5/44734.0712009/7/274765.5272010/6/294929.4592011/6/15638.122012/5/74797.5452009/7/284876.5622010/6/30 4880.6812011/6/25560.0292012/5/84793.7252009/7/294587.2022010/7/14786.9582011/6/35651.4492012/5/94715.2662009/7/304642.832010/7/24740.1612011/6/75711

27、.2652012/5/104729.1982009/7/314766.8992010/7/54726.572011/6/85716.1612012/5/114690.382009/8/34847.9312010/7/64863.2152011/6/95604.7762012/5/144661.6762009/8/44913.0732010/7/74927.8422011/6/105604.162012/5/154667.0022009/8/54956.8672010/7/84906.4552011/6/135588.0772012/5/164590.1162009/8/64929.881201

28、0/7/95043.1992011/6/145658.3832012/5/174644.1732009/8/74768.9512010/7/125074.2062011/6/155597.4672012/5/184578.2162009/8/104811.1072010/7/135026.4962011/6/165486.5542012/5/214599.0332009/8/114847.5832010/7/145028.8372011/6/175439.3772012/5/224659.6472009/8/124613.7352010/7/154922.8942011/6/205357.12

29、52012/5/234644.5412009/8/134610.5452010/7/164924.2942011/6/215423.3922012/5/244590.7362009/8/144433.9592010/7/195040.4392011/6/225431.7582012/5/254523.6272009/8/174125.0192010/7/205202.9432011/6/235544.8662012/5/284588.6322009/8/184196.6242010/7/215208.4242011/6/245678.8872012/5/294659.9412009/8/194

30、021.0712010/7/225271.3482011/6/275750.8582012/5/304671.3442009/8/204170.4532010/7/235287.1482011/6/285772.4622012/5/314704.3852009/8/214276.4522010/7/265365.1352011/6/295720.0752012/6/14685.3142009/8/244384.1522010/7/275372.0272011/6/30 5816.1182012/6/44572.3162009/8/254313.1612010/7/285505.1062011/

31、7/15838.9162012/6/54571.4362009/8/264442.2782010/7/295508.0572011/7/45967.8682012/6/64571.782009/8/274480.7692010/7/305495.7552011/7/55993.2812012/6/74535.862009/8/284361.2272010/8/25611.6442011/7/66032.5672012/6/84509.4922009/8/314076.5192010/8/35504.4492011/7/76056.5922012/6/114588.0992009/9/14063

32、.2532010/8/45540.3242011/7/86039.0992012/6/124585.5582009/9/24071.1752010/8/55588.1452011/7/116095.0272012/6/134667.6552009/9/34262.9672010/8/65703.7492011/7/126026.1862012/6/144637.4162009/9/44319.1792010/8/95777.6062011/7/136121.5012012/6/154634.7582009/9/74413.9372010/8/105576.9012011/7/146138.65

33、52012/6/184671.3382009/9/84505.1562010/8/115638.6792011/7/156177.9722012/6/194644.2742009/9/94544.3082010/8/125597.1662011/7/186197.92012/6/204633.9062009/9/104495.8562010/8/135717.6642011/7/196129.0762012/6/214559.5922009/9/114583.032010/8/165880.692011/7/206122.2682012/6/254472.3032009/9/144667.73

34、2010/8/175954.6862011/7/216055.6392012/6/264460.5212009/9/154727.3282010/8/185964.6632011/7/226082.8292012/6/274469.2772009/9/164726.992010/8/195965.5752011/7/255855.5472012/6/284423.0412009/9/174850.1462010/8/205809.4692011/7/265873.0552012/6/294477.7882009/9/184698.322010/8/235857.6052011/7/275965

35、.6232012/7/24550.0532009/9/214796.9852010/8/245939.6762011/7/285948.3112012/7/34571.7862009/9/224729.4582010/8/255830.5022011/7/295878.6792012/7/44537.2572009/9/234570.4362010/8/265871.9452011/8/15880.7332012/7/54463.6522009/9/244520.7992010/8/275950.3442011/8/25852.1192012/7/64568.3382009/9/254503.

36、6712010/8/306131.592011/8/35888.8412012/7/94506.7352009/9/284450.5722010/8/316182.4892011/8/45920.9442012/7/104470.7082009/9/294385.8292010/9/16124.5452011/8/55837.3732012/7/114501.312009/9/304436.6452010/9/26194.2482011/8/85628.9352012/7/124561.2682009/10/94663.3482010/9/36216.1632011/8/95634.21520

37、12/7/134541.2132009/10/124655.3792010/9/66196.0182011/8/105714.7662012/7/164374.692009/10/134703.4172010/9/76218.3462011/8/115810.7152012/7/174383.2242009/10/144692.3022010/9/86288.6912011/8/125858.9352012/7/184379.1492009/10/154679.7572010/9/96212.1522011/8/155920.4282012/7/194408.7682009/10/164685

38、.3532010/9/106307.3872011/8/165875.9852012/7/204355.222009/10/194784.2372010/9/136440.9892011/8/175838.8132012/7/234314.7832009/10/204850.9042010/9/146475.2092011/8/185720.1812012/7/244366.422009/10/214783.9272010/9/156365.4492011/8/195689.6862012/7/254350.352009/10/224778.7842010/9/166190.4992011/8

39、/225617.2242012/7/264318.0882009/10/234845.7532010/9/176209.2982011/8/235687.8582012/7/274289.3972009/10/264881.1492010/9/206162.1692011/8/245696.1922012/7/304223.5392009/10/274760.2562010/9/216169.1772011/8/255800.1222012/7/314178.3462009/10/284804.1372010/9/276337.5842011/8/265803.4962012/8/14235.

40、6272009/10/294745.3782010/9/286305.6682011/8/295759.7072012/8/24207.5432009/10/304792.9262010/9/296235.8392011/8/305710.7092012/8/34288.8532009/11/24958.5092010/9/306332.3612011/8/315675.072012/8/64389.9282009/11/35054.3342010/10/86492.4662011/9/15640.4652012/8/74436.8142009/11/45103.612010/10/11646

41、7.2632011/9/25585.1562012/8/84415.0572009/11/55121.9732010/10/126465.4642011/9/55477.7082012/8/94493.4612009/11/65131.4042010/10/136517.1592011/9/65405.0712012/8/104484.7962009/11/95154.3632010/10/146318.3682011/9/75514.4072012/8/134400.0362009/11/105157.6042010/10/156348.8352011/9/85489.8732012/8/1

42、44386.7732009/11/115169.7662010/10/186219.5332011/9/95441.7582012/8/154391.3072009/11/125226.8782010/10/196442.5352011/9/135352.6682012/8/164341.4162009/11/135322.962010/10/206500.9912011/9/145396.2282012/8/174313.2912009/11/165422.9922010/10/216577.4452011/9/155415.6212012/8/204323.2012009/11/17543

43、1.252010/10/226665.052011/9/165409.3682012/8/214379.2672009/11/185444.7932010/10/256859.0552011/9/195296.3382012/8/224339.8262009/11/195519.6652010/10/266895.4562011/9/205296.3562012/8/234346.2822009/11/205521.6012010/10/276829.0722011/9/215446.6822012/8/244278.3332009/11/235617.9742010/10/286826.24

44、22011/9/225298.7772012/8/274200.1522009/11/245342.9752010/10/296942.1562011/9/235254.5692012/8/284213.3172009/11/255512.4042010/11/17118.9622011/9/265159.552012/8/294205.2672009/11/265262.9912010/11/27028.8712011/9/275179.2942012/8/304123.262009/11/275174.4632010/11/36894.8662011/9/285109.4322012/8/

45、314137.8042009/11/305408.3122010/11/47046.1992011/9/294996.6462012/9/34231.872009/12/15537.3822010/11/57159.7642011/9/304990.4322012/9/44196.0812009/12/25589.2032010/11/87288.042011/10/104951.1932012/9/54222.1612009/12/35610.7942010/11/97329.4932011/10/114923.4792012/9/64271.5652009/12/45503.9732010

46、/11/107375.1212011/10/125094.1112012/9/74421.3682009/12/75595.6192010/11/117333.212011/10/135154.532012/9/104449.4582009/12/85570.4112010/11/126871.3852011/10/145125.4582012/9/114442.3812009/12/95485.8422010/11/157055.8762011/10/175158.3222012/9/124461.0182009/12/105533.4182010/11/166759.7492011/10/

47、185029.772012/9/134399.952009/12/115531.412010/11/176536.3922011/10/194986.512012/9/144401.4542009/12/145538.3482010/11/186673.4122011/10/204845.7552012/9/174296.9592009/12/155545.2442010/11/196898.2372011/10/214761.5632012/9/184271.3082009/12/165506.2942010/11/227007.1322011/10/244853.112012/9/1943

48、06.7422009/12/175364.2892010/11/236919.0952011/10/254991.3032012/9/204188.4822009/12/185207.2262010/11/247085.4512011/10/265030.4582012/9/214136.4852009/12/215238.2352010/11/257119.0462011/10/275034.1892012/9/244171.4662009/12/225142.3842010/11/267098.782011/10/285139.6852012/9/254150.4342009/12/235255.8772010/11/297104.4022011/10/315146.8012012/9/264057.7472009/12/245437.1552010/11/306936.9742011/11/15149.2052012/9/274163.0222009/12/255448.9732010/12/16914.8122011/11/25256.9642012/9/284264.8312009/12/2855