三次指數(shù)平滑在廣西生產(chǎn)總值指數(shù)預(yù)測(cè)分析中的應(yīng)用

1、三次指數(shù)平滑在廣西生產(chǎn)總值指數(shù)預(yù)測(cè)分析中的應(yīng)用摘 要：以廣西1978至2012年生產(chǎn)總值指數(shù)的統(tǒng)計(jì)數(shù)據(jù)為數(shù)據(jù)基礎(chǔ)，在簡(jiǎn)單分析指數(shù)平滑法的原理以及數(shù)學(xué)預(yù)測(cè)模型的基礎(chǔ)上，建立三次指數(shù)平滑預(yù)測(cè)模型，對(duì)未來(lái)幾年的廣西生產(chǎn)總值指數(shù)進(jìn)行了預(yù)測(cè)，結(jié)合預(yù)測(cè)結(jié)果廣西未來(lái)幾年總體經(jīng)濟(jì)運(yùn)行情況進(jìn)行了簡(jiǎn)單分析。 關(guān)鍵詞：三次指數(shù)平滑法；廣西生產(chǎn)總值指數(shù)；平滑指數(shù)；經(jīng)濟(jì)增長(zhǎng)率The Application of Cubic Exponential Smoothing in Guangxis GDP Index Forecast AnalysisAbstract:Bsed on the statistics data o

2、f Guangxi 1978-2012 GDP index, simply analyze the principles of Exponential Smoothing method and mathematical forecasting model, establish a cubic exponential smoothing predictive model, forecast Guangxi s GDP index for the coming years, and combine with predictions of Guangxi to analyze the overall

3、 economic performance in the coming years. Key words: Cubic exponential smoothing method; Guangxis GDP index; Smoothness index; Economic growth rate1 引言生產(chǎn)總值是一項(xiàng)非常重要的經(jīng)濟(jì)指標(biāo)，某地區(qū)的實(shí)際生產(chǎn)總值增長(zhǎng)率就是該地區(qū)的經(jīng)濟(jì)增長(zhǎng)率，生產(chǎn)總值指數(shù)是以統(tǒng)計(jì)基期的生產(chǎn)總值指數(shù)為100，再以可比價(jià)格計(jì)算出的各期的生產(chǎn)總值與基期的生產(chǎn)總值的比值乘以基礎(chǔ)指數(shù)100得到各期的生產(chǎn)總值指數(shù)，生產(chǎn)總值指數(shù)很清晰反應(yīng)了生產(chǎn)總值的真實(shí)的增減情況和幅度。以1978

4、年為100的廣西生產(chǎn)總值指數(shù)很清晰的反映了1978-2012以來(lái)的廣西生產(chǎn)總值的增長(zhǎng)率情況，通過(guò)任意兩年的生產(chǎn)總值指數(shù)相比較能得出一段時(shí)期內(nèi)廣西生產(chǎn)總值的增長(zhǎng)比例，即通過(guò)廣西生產(chǎn)總值指數(shù)能了解過(guò)去任意時(shí)間段內(nèi)的廣西經(jīng)濟(jì)增長(zhǎng)幅度以及以往每年的廣西經(jīng)濟(jì)增長(zhǎng)率，通過(guò)對(duì)廣西生產(chǎn)總值進(jìn)行預(yù)測(cè)，就能預(yù)測(cè)未來(lái)某年的廣西經(jīng)濟(jì)增長(zhǎng)率，當(dāng)前中央以“穩(wěn)中求進(jìn)”作為經(jīng)濟(jì)工作的基本思路，“穩(wěn)”體現(xiàn)在經(jīng)濟(jì)要穩(wěn)定的增長(zhǎng)，各省市都需對(duì)自身經(jīng)濟(jì)增長(zhǎng)情況作出一個(gè)預(yù)測(cè)作為制定經(jīng)濟(jì)政策的依據(jù)，通過(guò)對(duì)廣西未來(lái)幾年生產(chǎn)總值指數(shù)的預(yù)測(cè)就能對(duì)廣西未來(lái)幾年總體經(jīng)濟(jì)增長(zhǎng)情況作出預(yù)測(cè)，以往人們對(duì)生產(chǎn)總值指數(shù)的預(yù)測(cè)多采用灰色預(yù)測(cè)模型、回歸分析、AR

5、MA模型等方法的基礎(chǔ)上1-2，運(yùn)用三次指數(shù)平滑法進(jìn)行預(yù)測(cè)。指數(shù)平滑法作為一種很典型的趨勢(shì)外推法，其核心思想是對(duì)數(shù)據(jù)由近及遠(yuǎn)賦予逐級(jí)遞減的權(quán)重來(lái)預(yù)測(cè)數(shù)據(jù)未來(lái)的變動(dòng)趨勢(shì),其運(yùn)用非常廣泛，人們用其進(jìn)行各方面的預(yù)測(cè)分析3-9。它的優(yōu)點(diǎn)在于對(duì)數(shù)據(jù)的要求很簡(jiǎn)單，不需要對(duì)數(shù)據(jù)進(jìn)行復(fù)雜的處理，以及運(yùn)算比較簡(jiǎn)單，用Excel就能完成大部分的運(yùn)算，是很實(shí)用的一種短、中期預(yù)測(cè)方法。2指數(shù)平滑法2.1指數(shù)平滑預(yù)測(cè)模型 時(shí)間序列為，一次指數(shù)平滑公式為： （1）其中， 是第期的一次指數(shù)平滑值,是加權(quán)系數(shù)，01。一次指數(shù)平滑法以第t期的一次指數(shù)平滑值作為第t+1期的預(yù)測(cè)值，預(yù)測(cè)模型是： = （2）式（2）也可以改寫成：=

6、（I）這是一個(gè)非常關(guān)鍵的式子，本文把它記為式（I），這個(gè)式子說(shuō)明了指數(shù)平滑法只需要本期的實(shí)際值與上期的預(yù)測(cè)值就能對(duì)下一期進(jìn)行預(yù)測(cè)。表明了第t期的預(yù)誤差結(jié)合加權(quán)系數(shù)對(duì)t期的預(yù)測(cè)值的修正結(jié)果就是t+1期的預(yù)測(cè)值 。同時(shí)也表明了加權(quán)系數(shù)在指數(shù)平滑法中的重要性。說(shuō)明了的選取是指數(shù)平滑法進(jìn)行預(yù)測(cè)的最關(guān)鍵部分。將式（1）展開(kāi)，得到： = = = = （3） 結(jié)合式（2），有：= （4）從式（4）可以看出，第t+1期的預(yù)測(cè)值主要是由， ，的由近及遠(yuǎn)按幾何級(jí)數(shù)衰減的加權(quán)平均構(gòu)成。權(quán)數(shù)由近及遠(yuǎn)分別為：，所以指數(shù)平滑法運(yùn)用了所有的過(guò)去信息，而且指數(shù)平滑法是對(duì)近期的數(shù)據(jù)賦予較大的權(quán)數(shù)，對(duì)遠(yuǎn)期的數(shù)據(jù)賦予較小的權(quán)數(shù)，即

7、認(rèn)為事物或現(xiàn)象的最近影響因素對(duì)事物或現(xiàn)象的未來(lái)的影響力比過(guò)去的影響因素要大。符合事物或現(xiàn)象的一般發(fā)展規(guī)律，具有科學(xué)性。并且隨著加權(quán)系數(shù)取值的增大，近期數(shù)據(jù)對(duì)預(yù)測(cè)值的影響力進(jìn)一步加大。如果用代替式（1）中的，再一次進(jìn)行指數(shù)平滑，得到二次指數(shù)平滑公式： （5）二次指數(shù)平滑法的預(yù)測(cè)模型為： （6） （7） = （8）其中，為模型系數(shù)，t為當(dāng)前期數(shù)，h為預(yù)測(cè)的超前期數(shù)。用代替式（5）中的，進(jìn)行一次指數(shù)平滑，得到三次指數(shù)平滑公式： （9）三次指數(shù)平滑法的預(yù)測(cè)模型為： （11） = （12） = （13） = （14）其中，為模型系數(shù)。t為當(dāng)前期數(shù)。T為預(yù)測(cè)的超前期數(shù)。2.2指數(shù)平滑法運(yùn)用需要注意的一些問(wèn)

8、題2.2.1權(quán)系數(shù)的選取結(jié)合式（2），（I），（3），（4）可知加權(quán)系數(shù)的選取對(duì)預(yù)測(cè)結(jié)果影響很大，關(guān)于值的選取，一般采用經(jīng)驗(yàn)判斷法10,其主要內(nèi)容是：時(shí)間序列的變動(dòng)趨勢(shì)為水平趨勢(shì)時(shí)選用表叫小的值（0.05-0.20）；時(shí)間序列變動(dòng)趨勢(shì)較為平緩時(shí)選用較大一些的值（0.1-0.4）；當(dāng)時(shí)間序列的變動(dòng)趨勢(shì)很激烈且單調(diào)變動(dòng)時(shí)選用大的值（0.6-1.0）。2.2.2始平滑值的確定用指數(shù)平滑法進(jìn)行預(yù)測(cè)，需要先確定初始的平滑值，在進(jìn)行二次或者三次指數(shù)平滑預(yù)測(cè)時(shí)一般情況下是取=根據(jù)式（3）可知，伴隨t的增加。對(duì)預(yù)測(cè)值的影響越來(lái)越小。所以，當(dāng)樣本容量n較大的時(shí)候，可以用=。當(dāng)選用的樣本容量比較小的時(shí)候，則可以取

9、最初幾期樣本的均值。 3三次指數(shù)平滑法在廣西生產(chǎn)總值指數(shù)預(yù)測(cè)分析中的應(yīng)用以1978年到2012年的廣西生產(chǎn)總值指數(shù)統(tǒng)計(jì)資料（以可比價(jià)格計(jì)算，以1978年為100）為時(shí)間序列樣本。預(yù)測(cè)未來(lái)幾年廣西生產(chǎn)總值指數(shù)。3.1預(yù)測(cè)模型的確立3.1.1預(yù)測(cè)模型的選取 對(duì)現(xiàn)有的時(shí)間序列（1978-2012年，表1）進(jìn)行趨勢(shì)分析，本文采用的是做散點(diǎn)圖直接觀測(cè)其變動(dòng)趨勢(shì)，得到的的結(jié)果為圖1,由圖1可知廣西生產(chǎn)總值指數(shù)的時(shí)間序列變動(dòng)趨勢(shì)為明顯的二次曲線趨勢(shì)，所以本文用三次指數(shù)平滑法來(lái)預(yù)測(cè)是比較可行的9。表1 廣西1978-2012年生產(chǎn)總值指數(shù)統(tǒng)計(jì)表年份生產(chǎn)總值指數(shù)年份生產(chǎn)總值指數(shù)年份生產(chǎn)總值指數(shù)年份生產(chǎn)總值指數(shù)1

10、9781001987197.21996500.920051159.51979103.419882061997541.220061316.61980113.91989213.51998595.4200715151981123.11990228.41999643200817091982138.41991257.52000693.820091947.219831431992304.72001751.420102224.51984152.91993360.4200283120112498.11985169.71994415.22003915.820122779.51986180.61995462.42

11、0041023.8 注：資料來(lái)源于廣西統(tǒng)計(jì)年鑒。圖1 生產(chǎn)總值指數(shù)散點(diǎn)圖3.1.2初始平滑值的確定本文選取的時(shí)間序列樣本容量為35,屬于較大樣本容量，且基期值相對(duì)較小，對(duì)預(yù)測(cè)值的影響非常小幾乎可以忽略不計(jì)，于是本文選用基期值為初始平滑值，即=100。3.1.3加權(quán)系數(shù)的選取 由之前的分析可知，加權(quán)系數(shù)的選取是整個(gè)整個(gè)預(yù)測(cè)的最關(guān)鍵的一步，加權(quán)系數(shù)選取影響整個(gè)模型的預(yù)測(cè)精確度和科學(xué)性。必須慎重的選取加權(quán)系數(shù)。本文根據(jù)經(jīng)驗(yàn)判斷法結(jié)合圖1,先選取了可行的3個(gè)可行的加權(quán)系數(shù)值，分別為0.7,0.8，0.9。分別運(yùn)用這3數(shù)值個(gè)作為加權(quán)系數(shù)對(duì)原時(shí)間序列樣本進(jìn)行一次超前期數(shù)T=1的三次指數(shù)平滑預(yù)測(cè)。具體三次平

12、滑運(yùn)算情況見(jiàn)表2,表3，表4。再根據(jù)表2，表3，表4里預(yù)測(cè)值與相對(duì)誤差率這兩項(xiàng)數(shù)據(jù)制作表5。綜合分析不同取值下的預(yù)測(cè)平均絕對(duì)百分誤差以及最近6期的預(yù)測(cè)平均絕對(duì)百分誤差，來(lái)選取最合適的值進(jìn)行預(yù)測(cè)。相對(duì)誤差=平均絕對(duì)百分誤差=年份t相對(duì)誤差率197811001001001001000019792103.4102.38101.67101.17103.313.2491.17100-3.29%19803113.9110.44107.81105.82113.7210.873.48107.14-5.94%19814123.1119.3115.86112.84123.1911.272.38126.3342.6

13、3%19825138.4132.67127.63123.19138.3316.283.32135.644-1.99%19836143139.9136.22132.31143.366.925-1.2156.26399.28%19847152.9149145.17141.31152.818.784-0.1149.6689-2.11%19858169.7163.49157.99152.99169.4816.462.68161.5364-4.81%19869180.6175.47170.22165.05180.7812.760.39187.28333.70%198710197.2190.68184.5

14、4178.7197.1116.461.58193.7319-1.76%198811206201.4196.35191.05206.2310.05-1.3214.35384.06%198912213.5209.87205.81201.38213.566.725-2215.63521.00%199013228.4222.84217.73212.83228.1513.431.11219.2726-4.00%199114257.5247.1238.29230.65257.0929.226.38242.1343-5.97%199215304.7287.42272.68260.07304.2950.131

15、1.6289.493-4.99%199316360.4338.51318.76301.15360.461.911.7360.216-0.05%199417415.2392.19370.16349.46415.5561.217.23428.12543.11%199518462.4441.34419.98398.83462.8951.261.06480.3723.89%199619500.9483.03464.12444.53501.2739.16-3.7514.67992.75%199720541.2523.75505.86487.46541.1337.98-2.8538.5985-0.48%1

16、99821595.4573.9553.49533.68594.9252.13.29577.7233-2.97%199922643622.27601.64581.25643.1549.971.35648.66540.88%200023693.8672.34651.13630.17693.851.321.35693.80140.00%200124751.4727.68704.72682.35751.2558.023.27745.7943-0.75%200225831800771.42744.7830.4680.4910.2810.9075-2.42%200326915.8881.06848.178

17、17.13915.8190.4310.1916.03030.03%2004271023.8980.98941.14903.931023.5112.514.41011.281-1.22%2005281159.51105.91056.51010.71159.1142.5201143.128-1.41%2006291316.61253.41194.31139.31316.5167.321.71311.552-0.38%20073015151436.51363.91296.51514.5208.528.71494.639-1.34%20083117091627.31548.21472.71709.82

18、10.2191737.2961.66%2009321947.21851.21760.316741946.7246.125.11929.428-0.91%2010332224.52112.52006.919072224289.531.62205.415-0.86%2011342498.12382.42269.82160.92498.9291.320.92529.2861.25%2012352779.52660.42543.22428.52780.129213.72800.7410.76%表2 =0.7的3次指數(shù)平滑計(jì)算表表3 =0.8的3次指數(shù)平滑計(jì)算表年份t相對(duì)誤差率1978110010010

19、01001000019792103.4102.72102.18101.74103.373.9171.741100-3.29%19803113.9111.66109.77108.16113.8512.274.68108.16-5.04%19814123.1120.81118.6116.52123.1410.771.933128.4644.36%19825138.4134.88131.63128.6138.3716.763.736134.88-2.54%19836143141.38139.43137.26143.114.368-3.43156.99849.79%19847152.9150.6148

20、.36146.14152.849.1570.222145.7644-4.67%19858169.7165.88162.38159.13169.6418.124.108162.1106-4.47%19869180.6177.66174.6171.51180.6711.61-0.61189.81475.10%198710197.2193.29189.55185.94197.1617.012.061191.9824-2.65%198811206203.46200.68197.73206.078.473-2.65215.2034.47%198912213.5211.49209.33207.01213.

21、56.143-2.51213.2216-0.13%199013228.4225.02221.88218.91228.3215.172.618218.3869-4.38%199114257.5251245.18239.92257.432.429.121244.7992-4.93%199215304.7293.96284.2275.35304.6253.4314.41294.3788-3.39%199316360.4347.11334.53322.69360.4462.2511.92365.25131.35%199417415.2401.58388.17375.08415.3158.685.037

22、428.64773.24%199518462.4450.24437.82425.27462.5147.47-2.18476.50393.05%199619500.9490.77480.18469.2500.9636.08-6.27508.88741.59%199720541.2531.11520.93510.58541.1438.21-2.54533.9076-1.35%199821595.4582.54570.22558.29595.2655.626.328578.0789-2.91%199922643630.91618.77606.67643.0949.220.672654.04631.7

23、2%200023693.8681.22668.73656.32693.7951.221.262692.648-0.17%200124751.4737.36723.64710.17751.3559.124.209745.6447-0.77%200225831812.27794.55777.67830.8584.5513.64812.5734-2.22%200326915.8895.09874.98855.52915.8590.7910.35922.22550.70%2004271023.8998.06973.44949.861023.7114.916.491011.82-1.17%2005281

24、159.51127.21096.51067.11159.414622.941146.894-1.09%2006291316.61278.71242.31207.21316.6168.622.831316.8250.02%20073015151467.71422.61379.61514.9212.632.221496.652-1.21%20083117091660.71613.11566.41709.320514.521743.5632.02%2009321947.21889.91834.61780.91947249.127.661921.542-1.32%2010332224.52157.62

25、0932030.62224.4293.635.132209.911-0.66%2011342498.124302362.62296.22498.4285.615.982535.5021.50%2012352779.52709.62640.22571.42779.6287.29.5882791.9870.45%表4 =0.9的三次指數(shù)平滑計(jì)算表年份t相對(duì)誤差率197811001001001001000019792103.4103.06102.75102.48103.44.5442.48100-3.29%19803113.9112.82111.81110.88113.913.335.92109.1

26、8-4.14%19814123.1122.07121.05120.03123.119.780.75130.1865.76%19825138.4136.77135.19133.68138.3917.44.5133.264-3.71%19836143142.38141.66140.86143.021.793-6.5158.041910.52%19847152.9151.85150.83149.83152.8910.461.79141.5737-7.41%19858169.7167.91166.21164.57169.6919.545.77164.2457-3.21%19869180.6179.33

27、178.02176.67180.619.912-2.6192.11856.38%198710197.2195.41193.67191.97197.1917.963.19189.2079-4.05%198811206204.94203.81202.63206.016.787-4.6216.75135.22%198912213.5212.64211.76210.85213.56.185-2.4210.4767-1.42%199013228.4226.82225.32223.87228.3917.034.81218.4625-4.35%199114257.5254.43251.52248.76257

28、.4934.7711.9247.8202-3.76%199215304.7299.67294.86290.25304.6955.3316.6298.1912-2.14%199316360.4354.33348.38342.57360.4161.3410.8368.32782.20%199417415.2409.11403.04396.99415.2156.182.11427.16392.88%199518462.4457.07451.67446.2462.4144.86-5.2472.44482.17%199619500.9496.52492.03487.45500.934.62-8504.6

29、6250.75%199720541.2536.73532.26527.78541.1939.57-0.9531.5394-1.79%199821595.4589.53583.81578.2595.3858.8310.1580.299-2.54%199922643637.65632.27626.86643.0247.19-1.8659.26332.53%200023693.8688.19682.59677.02693.851.411.5689.3224-0.65%200124751.4745.08738.83732.65751.3960.195.47745.9537-0.72%200225831

30、822.41814.05805.91830.9887.9517.6814.3167-2.01%200326915.8906.46897.22888.09915.8189.618.92927.75391.31%2004271023.81012.11000.6989.331023.8117.119.11009.881-1.36%2005281159.51144.81130.31116.21159.5148.325.71150.449-0.78%2006291316.61299.41282.51265.91316.6168.622.71320.6140.30%20073015151493.41472

31、.31451.7151521636.21496.562-1.22%20083117091687.41665.91644.51709198.66.991749.0392.34%2009321947.21921.21895.71870.61947.2253.833.31911.169-1.85%2010332224.52194.22164.32134.92224.5296.338.32217.571-0.31%2011342498.12467.72437.42407.12498.1278.77.82539.9421.67%2012352779.52748.32717.22686.22779.528

32、4.86.912780.7250.04%表5 預(yù)測(cè)值與相對(duì)誤差率表年份t=0.7 =0.8=0.9相對(duì)誤差率相對(duì)誤差率相對(duì)誤差率1978119792100-3.29%100-3.29%100-3.29%19803107.14-5.94%108.16-5.04%109.18-4.14%19814126.3342.63%128.4644.36%130.1865.76%19825135.644-1.99%134.88-2.54%133.264-3.71%19836156.26399.28%156.99849.79%158.041910.52%19847149.6689-2.11%145.7644-4

33、.67%141.5737-7.41%19858161.5364-4.81%162.1106-4.47%164.2457-3.21%19869187.28333.70%189.81475.10%192.11856.38%198710193.7319-1.76%191.9824-2.65%189.2079-4.05%198811214.35384.06%215.2034.47%216.75135.22%198912215.63521.00%213.2216-0.13%210.4767-1.42%199013219.2726-4.00%218.3869-4.38%218.4625-4.35%1991

34、14242.1343-5.97%244.7992-4.93%247.8202-3.76%199215289.493-4.99%294.3788-3.39%298.1912-2.14%199316360.216-0.05%365.25131.35%368.32782.20%199417428.12543.11%428.64773.24%427.16392.88%199518480.3723.89%476.50393.05%472.44482.17%199619514.67992.75%508.88741.59%504.66250.75%199720538.5985-0.48%533.9076-1

35、.35%531.5394-1.79%199821577.7233-2.97%578.0789-2.91%580.299-2.54%199922648.66540.88%654.04631.72%659.26332.53%200023693.80140.00%692.648-0.17%689.3224-0.65%200124745.7943-0.75%745.6447-0.77%745.9537-0.72%200225810.9075-2.42%812.5734-2.22%814.3167-2.01%200326916.03030.03%922.22550.70%927.75391.31%200

36、4271011.281-1.22%1011.82-1.17%1009.881-1.36%2005281143.128-1.41%1146.894-1.09%1150.449-0.78%2006291311.552-0.38%1316.8250.02%1320.6140.30%2007301494.639-1.34%1496.652-1.21%1496.562-1.22%2008311737.2961.66%1743.5632.02%1749.0392.34%2009321929.428-0.91%1921.542-1.32%1911.169-1.85%2010332205.415-0.86%2

37、209.911-0.66%2217.571-0.31%2011342529.2861.25%2535.5021.50%2539.9421.67%2012352800.7410.76%2791.9870.45%2780.7250.04%平均絕對(duì)百分誤差2.43%2.58%2.79%最近六年平均絕對(duì)百分誤差1.13%1.19%1.24%通過(guò)觀察表5可以看出3個(gè)取值下的遠(yuǎn)期預(yù)測(cè)相對(duì)誤差明顯比近期預(yù)測(cè)相對(duì)誤差要大，于是在平均絕對(duì)百分誤差相差不多的情況下，需要對(duì)比最近幾年的平均絕對(duì)百分誤差來(lái)選出最優(yōu)的取值，表5比較分析可知取0.7時(shí) 預(yù)測(cè)的平均絕對(duì)百分誤差2.43%和最近六年平均百分誤差1.13%，均小

38、于取0.8和0.9時(shí)，所以取=0.7作為模型的加權(quán)系數(shù)。3.2運(yùn)用確立的三次指數(shù)模型對(duì)廣西未來(lái)幾年生產(chǎn)總值指數(shù)進(jìn)行預(yù)測(cè)3.2.1預(yù)測(cè)過(guò)程 由三次指數(shù)平滑預(yù)測(cè)模型： 可知理論上只要求得一組模型參數(shù)值就可對(duì)未來(lái)的數(shù)據(jù)進(jìn)行預(yù)測(cè)，但為了提高預(yù)測(cè)的精確度，一般采用離未來(lái)最近的一組模型參數(shù)值對(duì)未來(lái)進(jìn)行預(yù)測(cè)，本文為了更近一步的提高預(yù)測(cè)的精確度，本文采用離未來(lái)最近的3組模型參數(shù)分別對(duì)對(duì)未來(lái)3年廣西生產(chǎn)總值指數(shù)進(jìn)行預(yù)測(cè)，即用2010-2012年的幾組模型參數(shù)值分別預(yù)測(cè)2013-2015年的廣西生產(chǎn)總值指數(shù)，用其預(yù)測(cè)的平均值作為最后的預(yù)測(cè)結(jié)果。又因我們選取的是=0.7作為加權(quán)系數(shù)，所以表2就是我們實(shí)際用來(lái)計(jì)算模型

39、參數(shù)的三次指數(shù)平滑計(jì)算表，從表2中提取出模型參數(shù)數(shù)據(jù)建立一個(gè)新的表6。表6 三次指數(shù)平滑法的廣西生產(chǎn)總值指數(shù)模型參數(shù)值年份t197811000019792103.313.2491.1719803113.7210.873.4819814123.1911.272.3819825138.3316.283.3219836143.366.925-1.219847152.818.784-0.119858169.4816.462.6819869180.7812.760.39198710197.1116.461.58198811206.2310.05-1.3198912213.566.725-21990132

40、28.1513.431.11199114257.0929.226.38199215304.2950.1311.6199316360.461.911.7199417415.5561.217.23199518462.8951.261.06199619501.2739.16-3.7199720541.1337.98-2.8199821594.9252.13.29199922643.1549.971.35200023693.851.321.35200124751.2558.023.27200225830.4680.4910.2200326915.8190.4310.12004271023.5112.5

41、14.42005281159.1142.5202006291316.5167.321.72007301514.5208.528.72008311709.8210.2192009321946.7246.125.12010332224289.531.62011342498.9291.320.92012352780.129213.73.2.2預(yù)測(cè)結(jié)果利用表5里面第33-35期間的3組模型參數(shù)值分別對(duì)廣西2013-2017年的生產(chǎn)總值指數(shù)進(jìn)行預(yù)測(cè)，把2013-2015年每一年得到的3個(gè)預(yù)測(cè)值取平均值作為最后的預(yù)測(cè)值，并以預(yù)測(cè)的結(jié)果計(jì)算出預(yù)測(cè)的經(jīng)濟(jì)增長(zhǎng)率，以33期模型參數(shù)值對(duì)未來(lái)5年預(yù)測(cè)計(jì)算過(guò)程：=2224+3289.5+0.531.69=3234.7=2224+4289.5+0.531.616=