時(shí)間序列及其它預(yù)測(cè)案例

實(shí)用標(biāo)準(zhǔn)文案時(shí)間序列的分解方法時(shí)間序列的分解方法比較簡(jiǎn)單，下面用一個(gè)實(shí)例加以說明。表4-1是某商品銷售額的12年的季度數(shù)據(jù)。時(shí)間序列的分解一般是先計(jì)算季節(jié)指數(shù)，然后計(jì)算長(zhǎng)期趨勢(shì)和周期變動(dòng)。在本例介紹中，我們采用乘法模型，即Y=TxSxCxI,其中，Y代表表4-1中的實(shí)際銷售額，當(dāng)分解出T、S和C后，剩余部分即為I。某商品銷售額的12年數(shù)據(jù)季度(1)t(2)銷售額Y(3)四項(xiàng)平均(4)居中平均TC(5)Y/TC=SI(6)(%)長(zhǎng)期趨勢(shì)(7)周期變動(dòng)C(8)(%)199213017.612323043.542275.5132852.96497.214342741.333773.483372891.9180745094.3522820.699.6182930.87397.533199362805.6332522969.8278717809.842838.063115.3883008.78296.833283274.8835.568263047.736363932867.399110.3183086.6996.551410163.28840.558283125.6450319941122894.24900.82572.8863164.59996.411112114.312907.412513203.5539521332989.96984.685102.5733242.50896.750精彩文檔

實(shí)用標(biāo)準(zhǔn)文案314024.573353281.462024153071.365030.663109.7933320.41698.184199516327.483187.92383359.3718611733277.32129.643111.6253398.325100.127218493.4833232.6253437.27993192319.258375.47843476.234102.149420439.933298.289105.8363515.18841996213303.8833311.5743554.143102.957122490.7933111.2783593.09722233296.073299.97893632.051102.129324685.083337.213110.9473671.006942533316.64113709.96100.564199726661.23347.198371.712013748.914212723342.204103.5113787.86999.8863228378.43413.1853113.8873826.82399.48832933380.19193865.77798430459.55444.6783107.9393904.73299.46619983133428.93183943.68639132849.63501.935376.0763982.64199.75723333473.306794021.59513334701.18553.4053527.67101.6394060.54999.91543523394099.50478精彩文檔

實(shí)用標(biāo)準(zhǔn)文案199936642.38599.925576.665114.0354138.458100.35513733725.92334177.4121Z8585.523662.923106.6654216.367100.633394791.158314255.321740078.663758.53975.2544294.275101.9432000413851.5433821.35254333.233142907.063873.543107.0174372.184103.48224323862.54124411.1385344828.46872.3253112.3514450.093104.0954454089.53872.93324489.04752001464848.0283107.1174528.002104.112147339.613810.273860.17684566.95672484148.63801.4133829.1575.5524605.91103.308323789.313805.8432514916.453818.7883795.361106.672101.908200243909.5253804.049291084.643982.3183864.156111.4712100.060824242.424029.23945.921105.328198.449633997.584111.7384005.75975.7353697.19942881.014195.2254070.469104.45310320034036.234237.7684153.481110.502296.45914360.334326.2354216.496108.856522精彩文檔

實(shí)用標(biāo)準(zhǔn)文案24360.534394.984282.00177.9315797.02433172.184477.8734360.608101.6929844223.764509.824439.426111.241298.118324690.484496.8984493.846109.632898.650664694.484570.214503.35976.6487299.291753342.354611.0934533.554103.1828100.3634577.634642.7484590.651110.4947100.93564965.464481.6634626.92111.6067101.55675026.053470.144525.945258.715189.583596.763881.64562.20576.5434898.59037113.6547113.7516102.4742103.3102103.7066103.0002102.7751103.1586103.0713100.7554（一）季節(jié)指數(shù)5的計(jì)算季節(jié)指數(shù)的計(jì)算是先用移動(dòng)平均法剔除長(zhǎng)期趨勢(shì)和周期變動(dòng)，然后再用按月（季）平均精彩文檔實(shí)用標(biāo)準(zhǔn)文案法求出季節(jié)指數(shù)。由于一年有四個(gè)季度，因此，移動(dòng)平均項(xiàng)數(shù)要取4，需作兩次移動(dòng)，移動(dòng)平均結(jié)果見表4-1的第（5）欄，其中第（5）欄的第一個(gè)數(shù)據(jù)2773.483是經(jīng)過如下兩次移動(dòng)平均求得的：y+y+y+y3017.6+3043.54+2094.35+2809.84=2741.333y2+y3+y4+y5 3043.54+2094.35+2809.84+3274.8=2805.6332741.333+2805.633皿. =2773.483余下類推，即得到了不含季節(jié)因素和不規(guī)則變動(dòng)因素的序列TC（四項(xiàng)移動(dòng)平均也消除了不規(guī)則變動(dòng)I將Y除以TC，即得到了只含周期因素和不規(guī)則變動(dòng)因素的序列SI，見表4-1的第（6）欄。將序列SI重新排列得表4-2。該商品銷售額的季節(jié)指數(shù)如表4-2的最后一列所示。季節(jié)指數(shù)一般用百分?jǐn)?shù)表示，如在本例中，第一季度的季節(jié)指數(shù)為112.1397%。運(yùn)用按季平均法求季節(jié)指數(shù) 單位：%年份一季度二季度三季度四季度199275.5133799.61851993115.3886110.318872.8865121994109.7938111.625575.4784102.57351995111.2789110.947171.71201105.8364精彩文檔

實(shí)用標(biāo)準(zhǔn)文案1996113.8879107.939876.07679103.5111997114.0353106.665175.25425101.63991998112.3512107.117875.55225107.01721999111.4712105.328175.73536106.67222000110.5022108.856577.93157104.45312001111.2412109.632876.64872101.6922002110.4947111.606776.543481036547113.751698.59037同季合計(jì)1234.11203.79829.33271134.787同季平均季節(jié)指數(shù)112.1909109.435475.39388103.1625112.1397109.385575.35947103.1154同季平均和二400.18268%調(diào)整系數(shù)=400/400.18268=0.9995435季節(jié)指數(shù)=同季平均*調(diào)整系數(shù)=112.1909*0.9995435=112.1397%（二）長(zhǎng)期趨勢(shì)T的計(jì)算如作散點(diǎn)圖，可以看出，本例的銷售額Y具有較明顯的上升趨勢(shì)，且可以用直線趨勢(shì)擬合，以時(shí)間1作自變量，以銷售額Y作因變量，可求得如下回歸議程：T=2736.101+38.95436t根據(jù)長(zhǎng)期趨勢(shì)方程，即可求得各個(gè)季度的長(zhǎng)期趨勢(shì)值，如2003年第二季度仁46,其長(zhǎng)期趨勢(shì)為：T=2736.101+38.95436x46=4528.00156精彩文檔實(shí)用標(biāo)準(zhǔn)文案余下類推，即可求得長(zhǎng)期趨勢(shì)因素T序列，如表4-1中的第（7）欄所示。（三）周期變動(dòng)因素C的計(jì)算將序列TC除以T即可得到周期變動(dòng)因素C，如表4-1中的第（8）欄所示。（四）不規(guī)則變動(dòng)因素I的計(jì)算當(dāng)將時(shí)間序列的T、S、C分解出來后，剩余的即為不規(guī)則變動(dòng)，即：由于不規(guī)則變動(dòng)因素是不可預(yù)測(cè)的，因此，分解出不規(guī)則變動(dòng)因素對(duì)于時(shí)間序列的預(yù)測(cè)沒有多少價(jià)值。時(shí)間序列分解預(yù)測(cè)法的應(yīng)用在求出時(shí)間序列各因素之后，即可根據(jù)時(shí)間序列分解模型進(jìn)行預(yù)測(cè)。仍以上例為例，時(shí)間序列分解模型為：Yt=TtxStxCtxIt在作預(yù)測(cè)時(shí)，一般無法預(yù)測(cè)不規(guī)則變動(dòng)因素I,因此，時(shí)間序列分解法的預(yù)測(cè)模型可以表達(dá)為：精彩文檔實(shí)用標(biāo)準(zhǔn)文案Yt=TtxStxCt在上例中，如預(yù)測(cè)2004年第一季度的銷售額，則可按如下步驟進(jìn)行：首先求出2004年第一季度的長(zhǎng)期趨勢(shì)T,這可以根據(jù)長(zhǎng)期趨勢(shì)議程求得。由于2004年第一季度的t=49，因此，2004年第一季度的