chuong3-day so thoi gian- group14
DESCRIPTION
Dãy số thời gianTRANSCRIPT
-
PHN TCH DY S THI GIANGROUP14- TF4-K34
-
THNH VIN NHM
H TNMSSVNHIM VGHI CH1. Hong Th Thm108209635Gii thiu v dy s thi gian v cu trc chui thi gian2. Nguyn Th Kim Uyn109208945Trung bnh trt n gin+ Trung bnh trt trung tm3. Nguyn Th Ba108209102Trung bnh trt kp+ Trung bnh trt c trng s4. Cao Xun Hi108209413Phn r v d bo m hnh cngV l do bnh phi nm vin nn khng tham gia thuyt trnh trn lp c5. Trn Th Thy Ngn108209125Phn r v d bo m hnh nhn
-
NI DUNG CHNH I. Dy s thi gian v cu trc chui thi gian II. Lm phng d liu III. M hnh nhn IV. M hnh cng
-
I.DY S THI GIAN V CU TRC CHUI THI GIAN.
Dy s thi gian l mt chui cc gi tr ca mt ch tiu nghin cu c sp xp theo th t thi gian.C 2 loi dy s thi gian 1.1 Dy s thi k 1.2 Dy s thi im
-
PHN TCH DY S THI GIAN L G? Phn tch dy s thi gian l nghin cu hnh vi khun mu trong qu kh ca mt bin s v s dng nhng thng tin ny d bo nhng thay i trong tng lai.
-
THNH PHN DY S THI GIAN 1.Thnh phn xu th 2.Thnh phn ma v 3.Thnh phn chu k 4.Thnh phn bt quy tc
-
THNH PHN XU TH( TREND COMPONENT) :
Thnh phn ny th hin chiu hng bin ng, tng hoc gim ca hin tng nghin cu trong mt thi gian di.Nguyn nhn ca s bin i c tnh xu hng c th do lm pht ,s tng dn s,tng thu nhp c nhn,thay i v cng ngh
-
THNH PHN MA V ( SEASONAL COMPONENT):Thnh phn ny th hin bin ng ca ch tiu nghin cu theo mt quy lut no gia cc thi im trong nm v lp li tng t nhng nm k tip.Bin ng thi v thng do cc nguyn nhn nh iu kin thi tit, kh hu ,tp qun x hi, tn ngng,
-
THNH PHN CHU K ( CYCLICAL COMPONENT)Thnh phn ny th hin bin ng ca chui thi gian theo mt quy lut no nu xt trong mt khong thi gian tng i di t 2 10 nm.Tnh chu k bt ngun t chu k kinh doanh.
-
THNH PHN KHNG THEO QUY LUT( ERROR COMPONENT)L nhng dao ng bt thng hay nhng sai bit khng d on c chiu hng trong dy s thi gian.Loi bin ng ny thng xy ra trong thi gian ngn v gn nh khng lp li, do nh hng ca thin tai, ng t, ni chin, chin tranh
-
Yt = f(St, Tt, Et) - Yt gi tr quan st ti t - St thnh phn ma v ti t - Tt thnh phn xu hng ti t - Et sai s ngu nhin ti t
-
M hnh cng Yt = St + Tt + EtM hnh nhn Yt = St * Tt * Et log Yt= log St +log Tt + log EtNgoi ra cn c m hnh cng-m cng Yt = Tt *(St + Et-1)
-
IU CHNH THNH PHN MA V
Tch yu t ma v ra khi dy s thi gianM hnh cng: Yt St = Tt + EtM hnh nhn: Yt / St = Tt * Et
-
II. LM PHNG D LIU
-
C nhiu chui thi gian, nh hng ca yu t ngu nhin c th rt ln, lm lu m cc yu t khc th khng th hin xu hng mt cch r rtGII THIU
-
Do , lm gim hay trit tiu nh hng ca yu t ngu nhin v vch r xu hng ca dy s thi gian ta s dng k thut lm phng d liuGROUP14 TF4
-
CC KHI NIMLm phng d liu l k thut c bn thng dng loi yu t ngu nhin khi chui thi gian, li cc thnh phn ma v, xu hng.Trong mt s trng hp, n cng c dng loi b c yu t ngu nhin ln ma v.
GROUP14 TF4
-
GROUP14 TF4
-
Trung bnh trt-Trung bnh trt l phng php th hin xu hng n gin ca dy s thi gian c xy dng trn c s cho rng nh hng ca yu t ngu nhin mt thi im no s b hn ch, loi tr nu gi tr thi im c tnh trung bnh vi cc quan st ln cny l mt trong nhng bc c bn trong phn tch dy s thi gianMc ch l lm phng d liu qu kh phc v cho cng tc d bo
-
CC CCH TNH TRUNG BNH TRT
GROUP14 TF4+Trung bnh trt n gin+ Trung bnh trt trung tm+ Trung bnh trt kp+ Trung bnh trt c trng s
-
Trung bnh trt n gin l trung bnh cng ca mt nhm k im trt (trung bnh trt trung tm gin n cp k hay k MA) -Khi tin hnh TB trt, m s quan st u v cui b mt i Dy s trung bnh cn bng v nm trung tm ca dy s ban u
TRUNG BNH TRT N GIN
Vi k = 2m+1, m N: l s im trt
-
3MA: k = 3:Yt = (Yt-1 + Yt + Yt+1)/3 m = 1
5MA: k = 5:Yt = (Yt-2 + Yt-1 + Yt + Yt+1 + Yt+2)/5 m = 2V D
-
thngY3MA11642148154.666731521484144150.33335155141.33336125144.33337153141.33338146145.6667913815810190173.333311192191.333312192
-
CHN K NH TH NO L PH HPNu bin ng ca dy s khng ln v tng s quan st ca dy l nh 3MANu bin ng ca dy s ln v tng s quan st ca dy ln 5MA, 7MATrong trng hp ta cn mt ng xu hng phng hn, t bng n nhng 3MA hay 5MA li th th ta cn thc hin trung bnh trt vi cp ln hn
-
GROUP14 TF4
-
Tuy nhin khi tnh bng trung bnh trt n gin s mt i m quan st u v cuiKhng tnh c mt s gi tr u v cui ca dy sCc gi tr cui thng quan trng cho d bo, v c th tnh nh sau:Tn+1 = (Tn-1+ Tn)/2IU CHNH CC QUAN ST CUIGROUP14 TF4
-
Thngy5MA116421483152152.64144144.85155145.86125144.67153143.48146150.49138163.810190171.611192167.7 = (163.8 +171,6)/212192169.65
-
TRUNG BNH TRT TRUNG TMMc ch c th tnh c trung bnh trt ca vi s im trt bt k nh 2,4,6.Khi nhm im trt l chn th sau khi tnh trung bnh trt, dy s thu c s khng nm trung tm ca dy s ban uGROUP14 TF4
-
Trung bnh trt trung tm k hiu l 2xk MA vi k chn Gm 2 bc:Tnh trung bnh trt ca mt s chn cc quan st.Tnh trung bnh trung tm bng cch ly trung bnh ca hai gi tr trung bnh trt va tnh.GROUP14 TF4
-
T2.5 = (Y1+Y2+Y3+Y4)/4T3.5 = (Y2+Y3+Y4+Y5)/4
T3 = (T2.5+T3.5)/2GROUP14 TF4
tYt4 MA2 x 4 MA12662145.9178.583183.1157.15167.864119.3162.80159.985180.3174.98168.896168.5201.28188.137231.8204.40202.848224.5193.00198.709192.8219.18206.0910122.9209.53214.3511336.5209.90209.7112185.9216.55213.2313194.314149.5
-
* La chn nhm k im trt bng bao nhiu?D liu chu k Vd: chu k 3 nm k=3, 6.. Nhng i hi d liu thi gian phi lni vi d liu qu k=4 hay bi s ca 4D liu thng k=12 hay bi s 12Trong trng hp ny c yu t ngu nhin v ma v s b loi b
-
GROUP14 TF4
-
TRUNG BNH TRT KPTrung bnh trt kp l p dng trung bnh trt trn mt trung bnh trt khc.Trung bnh trt trung tm l mt dng trung bnh kp.
-
3 x 3MA l trung bnh trt ca 3 quan st trn mt trung bnh trt ca 3 quan st
T2 = (Y1+Y2+Y3)/3T3 = (Y2+Y3+Y4)/3T4 = (Y3+Y4+Y5)/3
T3 = (T2+T3+T4)/3
Yt3 MA3 x 3 MA12662145.9198.33183.1149.4169.64119.3160.9155.55180.3156.0 170.136168.5193.5185.97231.8208.3206.78224.5216.4201.69192.8180.1204.610122.9217.4204.211336.5215.1223.812185.9238.9210.213194.3176.614149.5
-
SO SNH S BIN THIN GIA D LIU GC V S TRUNG BNH TRT GIN N V TRUNG BNH TRT KP.
Chart2
266198.3169.5333333333
145.9149.4155.4333333333
183.1160.9170.1333333333
119.3156185.9333333333
180.3193.5206.0666666667
168.5208.3201.6
231.8216.4204.6333333333
224.5180.1204.2
192.8217.4223.8
122.9215.1210.2
336.5238.9
185.9176.6
194.3
149.5
Sheet1
t4 MA2 x 4 MA
1266
2145.9178.58
3183.1157.15167.86
4119.3162.8159.98
5180.3174.98168.89
6168.5201.28188.13
7231.8204.4202.84
8224.5193198.7
9192.8219.18206.09
10122.9209.53214.35
11336.5209.9209.71
12185.9216.55213.23
13194.3
14149.5
198.3Yt3 MA3 x 3 MA
149.4169.53266
160.9155.43145.9198.3
156170.133183.1149.4169.53
193.5185.934119.3160.9155.43
208.3206.075180.3156170.13
216.4201.606168.5193.5185.93
180.1204.637231.8208.3206.07
217.4204.208224.5216.4201.60
215.1223.809192.8180.1204.63
238.9210.2010122.9217.4204.20
176.611336.5215.1223.80
12185.9238.9210.20
13194.3176.6
14149.5
Sheet1
266178.58167.86
145.9157.15159.98
183.1162.8168.89
119.3174.98188.13
180.3201.28202.84
168.5204.4198.7
231.8193206.09
224.5219.18214.35
192.8209.53209.71
122.9209.9213.23
336.5216.55
185.9
194.3
149.5
Sheet2
Sheet3
-
TRUNG BNH TRT C TRNG S
-
TRUNG BNH TRT C TRNG STrung bnh trt c trng s l mt dng khc ca trung bnh trt trong cc quan st c gn vi cc trng s.Trong trng s ln nht c gn trung tm, cc trng s khc gim dn tnh t quan st trung tm.
-
TRUNG BNH TRT C TRNG Sm = (k-1)/2 aj l cc trng s
-
YU CU TRN CC TRNG SCc trng s i xng v c tng bng 1
-
MT S NHM TRNG S C S DNG RNG RI.Spencer(1904): Dr. Charles A. Spencer was a professor at Geneva Medical College. 5x4x4MA gm 5 im trung bnh trt vi trng lng a0=1, a1=a-1=3/4, a2=a-2=-3/4.15 im trung bnh trt c trng lng: -0.009, -0.019, -0.016, 0.009, 0.006, 0.144, 0.209, 0.231,0.209, 0.144, 0.006, 0.009, -0.016,- 0.019, -0.009
-
MT S NHM TRNG S C S DNG RNG RI. Trung bnh trt 21 im ng vi cc trng s theo cch tnh ca Spencer cng c s dng rng ri. Henderson: Cc trung bnh trt 5,7,9,13,23 im trung bnh trt theo cch tnh ca Henderson trong Bng 3-4 tr_99 sch Forecasting.
-
MT S TRNG HP CA TRUNG BNH C TRNG SMi trung bnh trt u l dng c bit ca trung bnh c trng s Trung bnh n gin cp k l trung bnh c trng s 1/k.
-
Trung bnh trt kp cp 4:
-
MI QUAN H GIA CC PHNG PHP
Trung bnh trt n gin l TH c bit ca trung bnh trt c trng s vi cc trng s bng nhau.aj= 1/k. L d liu thc hin bc th 2 ca trung bnh trt trung tm v trung bnh trt kp.Trung bnh trt trung tm l mt trng hp ca TBT kp. Trng hp k chn v lun l 2xkMA.2xkMA tng ng vi 1MA c k+1 im trung bnh trt c trng s l 1/2k cho quan st u v cui v 1/k cho k-1 quan st cn li.
-
MI QUAN H GIA CC PHNG PHP:Trung bnh trt kp l 1 trng hp ca trung bnh trt c trng s.v d: 3x3MA tng ng vi TBT c 5 im vi trng s l: 0.1111, 0.2222, 0.3333, 0.2222, 0.1111.
-
Trung bnh trt trn s liu v house sales
Data
Spencer-0.750.7510.75-0.75
Trng s0.10.150.50.150.1
MonthHouseSales3MA4MA2x4MA3x3MATB trt c trng sTBT co trong so
155
26061.00
36863.6761.5063.3364.4570.25
46365.3364.0062.7564.0063.5572.00
56563.0064.2564.1362.7863.3066.50
66160.0060.7562.5059.5652.7559.8564.00
75455.6758.0059.3855.4451.2555.0555.50
85250.6753.2555.6351.0049.9251.3049.75
94646.6748.5050.8846.3348.8346.2048.25
104241.6744.2546.3841.5648.0041.6542.75
113736.3338.7541.5037.5647.4237.6028.75
123034.6736.5037.6336.0046.5034.7021.00
133737.0037.0036.7539.0046.0038.8023.50
144445.3341.5039.2544.3345.4244.1050.75
155550.6747.2544.3850.4445.0051.5556.50
165355.3352.5049.8853.2244.3352.8567.25
175853.6754.0053.2553.6743.7554.7558.00
185052.0052.2553.1351.1143.2550.7056.00
194847.6750.2551.2548.1142.5848.1545.00
204544.6746.0048.1344.1141.7544.2548.75
214140.0042.0044.0039.8940.8340.1541.75
223435.0037.5039.7534.7840.9234.5535.50
233029.3332.2534.8830.6740.8330.7021.00
242427.6729.2530.7528.6740.9227.6517.251D liu ban u v 3MA
252929.0029.2529.2530.7841.1730.6017.00
263435.6732.7531.0036.2241.8335.7530.25
274444.0040.2536.5043.7842.2543.8045.50
285451.6747.2543.7549.8943.2550.6566.00
295754.0051.5049.3852.8944.5853.7564.50
305153.0053.2552.3852.8945.8352.4051.75
315151.6753.0053.1351.5646.8351.4051.75
325350.0050.2551.6350.0048.4250.7553.00
334648.3349.0049.6348.1149.3347.5547.50
344646.0047.7548.3846.0050.0046.0046.00
354643.6744.2546.0043.8949.8344.4544.50
363942.0043.0043.6343.3350.2542.4530.00
374144.3344.7543.8845.3350.7544.4034.25
385349.6747.0045.8850.2251.2551.0049.25
395556.6752.7549.8854.5652.2554.3569.25
406257.3356.2554.5057.2253.0058.4062.75
415557.6757.0056.6357.0053.2556.4059.50
425656.0057.5057.2557.0053.9256.9049.25
435757.3356.7557.1357.1155.2557.0558.50
445958.0057.5057.1357.5656.5057.8562.00
455857.3357.2557.3856.4458.9256.7064.00
465554.0055.2556.2553.8960.5054.1555.75
474950.3352.2553.7551.7862.4251.3039.25D liu ban u v 4MA v 2x4MA
484751.0052.0052.1352.8963.9251.7034.25
495757.3355.2553.6359.3364.5059.0543.50
506869.6764.0059.6368.2265.7567.9577.75
518477.6772.5068.2576.1166.8377.8594.50
528181.0077.7575.1378.7867.5079.0096.00
537877.6779.2578.5076.8968.0077.0583.25
547472.0074.2576.7573.4468.3373.8064.25
556470.6772.5073.3870.7868.3369.1063.25
567469.6770.7571.6369.8967.9270.9572.50
577169.3368.0069.3867.3367.1767.9584.50
586363.0065.7566.8862.8967.5062.9063.75
595556.3360.0062.8857.8967.6757.4044.50
605154.3356.5058.2555.8967.9254.9040.50
615757.0056.5056.5058.7868.2558.6045.00
626365.0061.5059.0065.4468.0864.9060.00
637574.3370.0065.7573.1167.8373.4083.25
648580.0075.7572.8878.3368.4279.7596.25
658080.6779.2577.5078.5668.2578.6094.25
667775.0077.5078.3876.0068.1776.4070.25
676872.3374.2575.8872.2267.8371.1568.75
687269.3371.2572.7570.5667.4271.1063.75
696870.0069.5070.3867.6767.2567.4083.75D liu ban u v 12MA
707063.6765.7567.6363.7866.1765.3569.25
715357.6760.2563.0057.7865.1756.6052.25
725052.0056.5058.3854.4464.0053.7033.50
735353.6753.5055.0055.6763.6755.3039.50
745861.3358.5056.0060.8963.3360.1061.00
757367.6764.0061.2566.6762.6768.1079.75
767271.0067.7565.8868.7861.3369.2587.00
776867.6769.0068.3867.8960.3367.9566.50
786365.0066.7567.8865.8959.0865.3057.00
796465.0065.7566.2564.6758.2564.4566.25
806864.0063.7564.7563.2257.0864.3073.25
816060.6761.5062.6358.7854.6758.8072.75
825451.6755.7558.6351.8951.6752.4552.50
834143.3347.5051.6344.8949.6744.1530.50
843539.6743.2545.3841.2248.5839.9024.50
854340.6740.7542.0041.3347.8341.8538.50
864443.6741.5041.1341.8947.2542.1556.00
874441.3341.7541.6342.1146.4242.7038.75
883641.3342.0041.8842.0045.7540.6031.50
894443.3343.5042.7544.7845.5844.8034.25
905049.6746.2544.8849.4445.4249.5551.50
915555.3352.5049.3853.4444.9253.5567.75
926155.3354.0053.2554.3344.5855.8567.75D liu ban u v 3MA v 3x3MA
935052.3353.0053.5050.8945.0050.4559.75
944645.0049.0051.0045.5645.6745.7542.25
953939.3342.0045.5040.2245.7540.0533.00
963336.3338.7540.3837.4444.7536.5025.50
973736.6737.2538.0038.3343.1738.2525.75
984042.0039.7538.5041.0040.9240.6046.75
994944.3342.5041.1344.1139.0845.3050.50
1004446.0044.5043.5044.2237.6743.9056.00
1014542.3344.0044.2542.6736.6743.3042.75
1023839.6740.7542.3839.3336.3338.9540.25
1033636.0038.2539.5036.1135.5836.1035.25
1043432.6734.0036.1333.0034.6733.3031.75
1052830.3331.7532.8830.3333.5829.7528.00
1062928.0029.5030.6328.8932.5829.0523.00
1072728.3328.2528.8828.1131.8327.8028.50
1082928.0028.2528.2528.3331.5028.5526.75
1092828.6728.2528.2529.2231.0829.0024.25
1102931.0030.5029.3830.6731.2530.2031.25
1113632.3331.2530.8832.6732.1733.5533.75
1123234.6733.2532.2533.6733.0833.1038.75
1133634.0034.5033.8834.1134.0834.6035.25
1143433.6733.2533.8833.7834.4233.8533.25
1153133.6734.2533.7534.2235.7533.5027.25
1163635.3335.0034.6335.7837.1735.9033.00
1173938.3336.5035.7537.6738.9237.9043.50
1184039.3338.5037.5038.3341.1738.6046.75
1193937.3337.7538.1338.4443.5038.7531.50
1203338.6739.0038.3839.0045.5837.5530.75
1214441.0040.5039.7542.8947.2543.4531.25
1224649.0045.0042.7548.0048.4247.3552.75
1235754.0051.5048.2554.3349.1755.0554.75
1245960.0056.5054.0058.2250.0858.1571.00
1256460.6759.7558.1359.5650.5860.5071.50
1265958.0058.2559.0057.3351.8357.6563.50
1275153.3356.0057.1353.6752.5053.0548.75
1285049.6752.0054.0050.8953.5050.8541.75
1294849.6750.0051.0049.1154.0048.7551.75
1305148.0048.5049.2548.5654.1749.2547.25
1314548.0048.0048.2548.1153.7547.3544.25
1324848.3349.0048.5049.6753.6749.4539.00
1335252.6750.7549.8852.8953.7552.7050.50
1345857.6755.2553.0057.0053.5857.1562.50
1356360.6758.5056.8859.7854.0060.4569.00
1366161.0060.2559.3860.3354.3360.4065.50
1375959.3360.2560.2558.8954.0858.8562.00
1385856.3357.5058.8856.1153.2556.5559.50
1395252.6754.2555.8853.3352.9253.1047.50
1404851.0052.7553.5051.8952.6751.0542.00
1415352.0052.0052.3851.0053.0051.3559.75
1425550.0049.5050.7549.0052.9250.3561.75
1434245.0047.0048.2545.8953.4245.0536.00
1443842.6745.7546.3844.8954.0043.5023.00
1454847.0045.7545.7548.7854.9248.8536.00
1465556.6752.0048.8854.7856.0054.5567.75
1476760.6757.5054.7560.4456.0862.0568.50
1486064.0061.7559.6362.6755.8361.8069.00
1496563.3364.2563.0063.8956.5864.2561.25
1506564.3363.2563.7563.5657.3363.8070.25
1516363.0063.5063.3862.2257.9262.3068.25
1526159.3360.7562.1359.3358.2559.7561.00
1535455.6757.5059.1355.7860.0855.3553.25
1545252.3354.5056.0052.6762.0852.5549.75
1555150.0051.0052.7551.1162.9251.2543.50
1564751.0051.2551.1351.5663.0050.5043.25
1575553.6753.0052.1357.4462.5057.4029.50
1585967.6762.5057.7566.2261.7564.2068.75
1598977.3371.7567.1375.8962.2578.9598.75
1608482.6776.7574.2578.3362.4279.10113.25
1617575.0078.5077.6374.5662.1774.6078.00
1626666.0070.5074.5066.4462.3366.4063.00
1635758.3362.5066.5060.2262.1759.7044.25
1645256.3358.7560.6356.6762.1755.5549.75
1656055.3355.7557.2555.2260.8356.4060.75
1665454.0053.5054.6353.2259.8353.3059.25
1674850.3352.7553.1351.4458.7550.7540.50
1684950.0051.0051.8851.3358.0850.9540.00
1695353.6752.2551.6355.1157.9254.8043.25
1705961.6758.5055.3861.1158.2560.5062.75
1717368.0064.2561.3866.2257.5867.6585.00
1727269.0066.5065.3867.0057.4267.9585.50
1736264.0066.2566.3863.7857.0063.3063.50
1745858.3361.7564.0059.5656.0059.3549.75
1755556.3357.7559.7556.3355.1756.0055.00
1765654.3355.2556.5054.6754.8355.0553.75
1775253.3353.7554.5052.2254.4252.0059.50
1785249.0050.7552.2548.7854.0849.5553.50
1794344.0046.0048.3844.6754.2544.3538.50
1803741.0043.7544.8843.3354.8342.1021.25
1814345.0044.5044.1347.1155.0046.4028.75
1825555.3350.7547.6354.6755.2554.6559.50
1836863.6758.5054.6361.8955.4263.1580.00
1846866.6763.7561.1365.3355.8365.8077.00
1856465.6766.2565.0064.7855.8364.4570.00
1866562.0063.5064.8862.6756.2563.3560.50
1875760.3361.2562.3859.6757.0058.9061.50
1885956.6758.7560.0057.8956.6758.3550.75
1895456.6756.7557.7554.8955.8354.4066.00
1905751.3353.2555.0051.7855.1753.1554.00
1914347.3349.0051.1348.1154.9246.9537.75
1924245.6748.5048.7547.1154.3346.0532.25
1935248.3347.0047.7549.2254.7550.0546.00
1945153.6750.7548.8852.7854.9252.2057.00
1955856.3355.2553.0056.5654.5056.9556.50
1966059.6757.5056.3858.5654.0058.7567.50
1976159.6759.2558.3859.8954.3360.2059.50
1985860.3360.2559.7560.1154.1759.5559.50
1996260.3360.5060.3859.3353.5859.8568.75
2006157.3357.5059.0057.1153.5058.0562.50
2014953.6755.7556.6353.3353.5052.2051.25
2025149.0052.0053.8849.5652.8350.0047.25
2034746.0046.7549.3846.3351.9246.5544.75
2044044.0045.7546.2545.0051.2543.9033.25
2054545.0045.5045.6346.6749.9246.5033.75
2065051.0048.2546.8849.7848.6749.6558.25
2075853.3351.2549.7552.5647.7553.8063.25
2085253.3352.5051.8852.4446.5852.2058.00
2095050.6752.5052.5050.8945.5050.7048.50
2105048.6749.5051.0048.8944.5849.2048.50
2114647.3348.0048.7546.4443.3346.2052.00
2124643.3345.0046.5043.6742.5044.3043.75
2133840.3341.7543.3840.0041.5039.4540.25
2143736.3338.7540.2536.6741.0036.8034.75
2153433.3334.5036.6333.5640.7533.7032.50
2162931.0032.5033.5032.4440.5031.8019.25
2173033.0033.2532.8834.2240.2533.3521.75
2184038.6736.2534.7538.5640.2538.9040.75
2194644.0040.5038.3843.0040.1743.6052.75
2204646.3344.7542.6345.6740.5045.6550.50
2214746.6746.5045.6346.2240.9246.3550.00
2224745.6745.7546.1345.8941.5046.2045.50
2234345.3345.7545.7544.3343.0043.8549.75
2244642.0043.2544.5042.8944.2543.8040.00
2253741.3341.7542.5040.7845.0839.7540.75
2264139.0040.7541.2539.6745.6740.1036.50
2273938.6738.2539.5039.5646.0839.5533.00
2283641.0041.0039.6342.0046.5840.6529.25
2294846.3344.5042.7546.7847.3347.1545.00
2305553.0048.7546.6351.3348.1752.0066.25
2315654.6753.0050.8853.7849.3354.2062.00
2325353.6754.0053.5053.6749.9253.5053.00
2335252.6753.5053.7552.8950.1752.7050.50
2345352.3352.5053.0052.8950.6753.0049.25
2355253.6753.2552.8853.0050.3352.6556.50
2365653.0053.0053.1352.7849.9253.5557.50
2375151.6751.7552.3850.5650.2550.5058.50
2384847.0049.2550.5047.5651.3347.7544.25
2394244.0045.7547.5044.5651.8344.0038.25
2404242.6744.0044.8844.0052.3343.7033.00
2414445.3344.5044.2546.4452.5846.0036.50
2425051.3349.0046.7551.7852.6751.4047.00
2436058.6755.0052.0057.1153.1757.6070.50
2446661.3358.5056.7560.3353.8361.6072.75
2455861.0060.7559.6359.8954.7559.2565.50
2465957.3359.5060.1358.4455.5058.7551.50
2475557.0057.2558.3856.8955.5856.4055.75
2485756.3357.0057.1356.6756.2556.8054.75
2495756.6756.2556.6356.1157.4256.2560.75
2505655.3355.7556.0055.1157.3355.3057.50
2515353.3354.2555.0052.7857.9252.7556.75
2525149.6751.2552.7551.4457.5851.6039.00
2534551.3351.7551.5053.3357.3351.5531.50
2545859.0057.0054.3858.6757.5058.4560.25
2557465.6760.5058.7564.2257.2566.4583.75
2566568.0065.5063.0065.1157.3364.6584.50
2576561.6764.7565.1362.3356.6763.1060.50
2585557.3359.2562.0058.1155.7557.4549.75
2595255.3357.7558.5055.8955.9255.0048.25
2605955.0055.0056.3855.6755.0056.6054.50
2615456.6755.5055.2554.5653.8354.1068.25
2625752.0053.7554.6352.0053.2553.2557.00
2634547.3349.0051.3847.7853.0847.1542.00
2644044.0047.2548.1345.3353.8344.2031.00
2654744.6744.7546.0046.6754.8347.0533.50
2664751.3348.5046.6350.3355.1749.3553.75
2676055.0053.0050.7555.5655.2556.7556.25
2685860.3357.0055.0059.0055.0058.5567.00
2696361.6761.2559.1361.8954.9262.2061.50
2706463.6762.2561.7563.0051.5863.1568.50
2716463.6763.5062.8862.6762.8570.75
2726360.6761.5062.5060.5661.1563.75
2735557.3359.0060.2556.3355.8561.75
2745451.0054.0056.50
27544
Data
DataPlot
Solution
7MAPlot
TimePlots
WIN7:k=3, m=1 mt i 2m=2 d liu
WIN7:k=4, m=1.5, mt i 3 d liu.
WIN7:k=2, m=1 mt i 1 d liu => Khi ny chui d liu s tr thnh trung tm ca chui d liu ban u.
WIN7:Trung bnh trt kp
WIN7:k=12, aj= 1/12
TimePlots
63
65
61
54
52
46
42
37
30
37
44
55
53
58
50
48
45
41
34
30
24
29
34
44
54
57
51
51
53
46
46
46
39
41
53
55
62
55
56
57
59
58
55
49
47
57
68
84
81
78
74
64
74
71
63
55
51
57
63
75
85
80
77
68
72
68
70
53
50
53
58
73
72
68
63
64
68
60
54
41
35
43
44
44
36
44
50
55
61
50
46
39
33
37
40
49
44
45
38
36
34
28
29
27
29
28
29
36
32
36
34
31
36
39
40
39
33
44
46
57
59
64
59
51
50
48
51
45
48
52
58
63
61
59
58
52
48
53
55
42
38
48
55
67
60
65
65
63
61
54
52
51
47
55
59
89
84
75
66
57
52
60
54
48
49
53
59
73
72
62
58
55
56
52
52
43
37
43
55
68
68
64
65
57
59
54
57
43
42
52
51
58
60
61
58
62
61
49
51
47
40
45
50
58
52
50
50
46
46
38
37
34
29
30
40
46
46
47
47
43
46
37
41
39
36
48
55
56
53
52
53
52
56
51
48
42
42
44
50
60
66
58
59
55
57
57
56
53
51
45
58
74
65
65
55
52
59
54
57
45
40
47
47
60
58
63
64
64
63
55
54
44
Original
House Sales Data
SeasonalComponentPlot
12345678910111213
Wts for 7MA0.14285714290.14285714290.14285714290.14285714290.14285714290.14285714290.1428571429
Wts for 2x12MA0.04166666670.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0416666667
Orig. DataTrend-CycleDeTrended
Yt7MATt = 2x12MADt = Yt-TtMonthSj(t)Et = Yt-Tt-StNote Sj(t) values calculated in pivot table.
155-7.1058703939See below. (G282)
260-1.3274616364
3688.9982974848
46360.85714285718.003979803
56560.42857142867.1952700152
66158.42857142864.4049569365
75454.714285714351.99980733332.000192666771.21231460610.7878780606
8525150.58314833331.416851666782.7066306515-1.2897789848
9464649.374823-3.3748239-1.3899638333-1.9848591667
104242.571428571448.4164923333-6.416492333310-2.4562514697-3.9602408636
113741.142857142947.708163-10.70816311-8.8975391212-1.8106238788
123041.571428571446.958164-16.95816412-12.4448867121-4.5132772879
133742.571428571446.249832-9.2498321-7.1058703939-2.1439616061
144444.857142857145.7081666667-1.70816666672-1.3274616364-0.3807050303
155546.714285714345.2081679.79183338.99829748480.7935355152
165349.285714285744.66650066678.333499333348.0039798030.3295195303
175850.428571428644.041501666713.958498333357.19527001526.7632283182
18505043.4998356.50016564.40495693652.0952080635
19484742.9165065.08349471.21231460613.8711793939
204543.714285714342.1665112.83348982.70663065150.1268583485
214138.857142857141.291518-0.2915189-1.38996383331.0984458333
223435.857142857140.8748543333-6.874854333310-2.4562514697-4.4186028636
233033.857142857140.8748556667-10.874855666711-8.8975391212-1.9773165455
242433.714285714340.8748533333-16.874853333312-12.4448867121-4.4299666212
252935.571428571441.041519-12.0415191-7.1058703939-4.9356486061
263438.857142857141.4998503333-7.49985033332-1.3274616364-6.172388697
274441.857142857142.0415131.95848738.9982974848-7.0398104848
285445.714285714342.749842333311.250157666748.0039798033.2461778636
295749.142857142943.916503666713.083496333357.19527001525.8882263182
305150.857142857145.2081635.79183764.40495693651.3868800635
315151.142857142946.33315966674.666840333371.21231460613.4545257273
32535047.6248245.37517682.70663065152.6685453485
334647.428571428648.874821-2.8748219-1.3899638333-1.4848571667
34464649.6664873333-3.666487333310-2.4562514697-1.2102358636
354646.285714285749.9164856667-3.916485666711-8.89753912124.9810534545
363946.571428571450.0414843333-11.041484333312-12.44488671211.4034023788
374148.857142857150.499816-9.4998161-7.1058703939-2.3939456061
385350.142857142950.99981466672.00018533332-1.32746163643.3276469697
395551.571428571451.74981033333.250189666738.9982974848-5.7481078182
406254.142857142952.62480633339.375193666748.0039798031.3712138636
415556.714285714353.12480333331.875196666757.1952700152-5.3200733485
425657.428571428653.58313333332.416866666764.4049569365-1.9880902698
435757.428571428654.58313133332.416868666771.21231460611.2045540606
445955.571428571455.87479666673.125203333382.70663065150.4185726818
455854.428571428657.70812566670.29187433339-1.38996383331.6818381667
465554.571428571459.7081183333-4.708118333310-2.4562514697-2.2518668636
474956.142857142961.4581096667-12.458109666711-8.8975391212-3.5605705455
484759.714285714363.1664356667-16.166435666712-12.4448867121-3.7215489545
49576364.2080966667-7.20809666671-7.1058703939-0.1022262727
506866.285714285765.12476166672.87523833332-1.32746163644.2026999697
518469.857142857166.29142317.70857738.99829748488.7102795152
528172.285714285767.166417666713.833582333348.0039798035.8296025303
537874.714285714367.749746333310.250253666757.19527001523.0549836515
547475.142857142968.16641033335.833589666764.40495693651.4286327302
556472.142857142968.333079-4.33307971.2123146061-5.5453936061
567468.428571428668.12474933335.875250666782.70663065153.1686200152
577164.571428571467.5414233.4585779-1.38996383334.8485408333
586362.142857142967.3330916667-4.333091666710-2.4562514697-1.876840197
59556267.5830893333-12.583089333311-8.8975391212-3.6855502121
605162.142857142967.7914206667-16.791420666712-12.4448867121-4.3465339545
615764.142857142968.083083-11.0830831-7.1058703939-3.9772126061
626366.571428571468.1664183333-5.16641833332-1.3274616364-3.838956697
637569.714285714367.95808466677.041915333338.9982974848-1.9563821515
648572.142857142968.124749666716.875250333348.0039798038.8712705303
658074.285714285768.33307811.66692257.19527001524.4716519848
66777568.20807733338.791922666764.40495693654.3869657302
676874.285714285767.99974633330.000253666771.2123146061-1.2120609394
687269.714285714367.62474966674.375250333382.70663065151.6686196818
696865.428571428667.33308866670.66691133339-1.38996383332.0568751667
70706266.70809266673.291907333310-2.45625146975.748158803
715360.571428571465.6664286667-12.666428666711-8.8975391212-3.7688895455
725060.714285714364.5830983333-14.583098333312-12.4448867121-2.1382116212
735361.285714285763.8331-10.83311-7.1058703939-3.7272296061
74586163.4997693333-5.49976933332-1.3274616364-4.172307697
757362.428571428662.999769333310.000230666738.99829748481.0019331818
767264.428571428661.999772666710.000227333348.0039798031.9962475303
776866.571428571460.83310566677.166894333357.1952700152-0.0283756818
786366.857142857159.70810866673.291891333364.4049569365-1.1130656032
796464.142857142958.6664485.33355271.21231460614.1212373939
806859.714285714357.66645310.33354782.70663065157.6269163485
81605555.8747964.1252049-1.38996383335.5151678333
825452.142857142953.1664720.83352810-2.45625146973.2897794697
834149.285714285750.6664826667-9.666482666711-8.8975391212-0.7689435455
843545.857142857149.1248223333-14.124822333312-12.4448867121-1.6799356212
854342.428571428648.2081603333-5.20816033331-7.10587039391.8977100606
86444147.541498-3.5414982-1.3274616364-2.2140363636
874442.285714285746.8331643333-2.833164333338.9982974848-11.8314618182
883645.142857142946.0831656667-10.083165666748.003979803-18.0871454697
894447.714285714345.6664973333-1.666497333357.1952700152-8.8617673485
905048.571428571445.49982933334.500170666764.40495693650.0952137302
915548.857142857145.16649933339.833500666771.21231460618.6211860606
926149.285714285744.74983516.25016582.706630651513.5435343485
935047.714285714344.7915035.2084979-1.38996383336.5984608333
944645.857142857145.33316533330.666834666710-2.45625146973.1230861364
953943.714285714345.7081653333-6.708165333311-8.89753912122.1893737879
96334245.2498336667-12.249833666712-12.44488671210.1950530455
973741.142857142943.9581726667-6.95817266671-7.10587039390.1476977273
98404142.0415143333-2.04151433332-1.3274616364-0.714052697
994940.857142857139.9998539.00014738.99829748480.0018495152
1004441.285714285738.3748595.62514148.003979803-2.378838803
1014540.857142857137.1665297.83347157.19527001520.6382009848
1023839.142857142936.49986433331.500135666764.4049569365-2.9048212698
1033636.285714285735.95820033330.041799666771.2123146061-1.1705149394
1043433.857142857135.124871-1.12487182.7066306515-3.8315016515
1052831.571428571434.1248776667-6.12487766679-1.3899638333-4.7349138333
1062930.142857142933.0832136667-4.083213666710-2.4562514697-1.626962197
1072729.142857142932.208218-5.20821811-8.89753912123.6893211212
1082929.428571428631.666552-2.66655212-12.44488671219.7783347121
109283031.2915526667-3.29155266671-7.10587039393.8143177273
110293131.1665536667-2.16655366672-1.3274616364-0.8390920303
111363231.70821766674.291782333338.9982974848-4.7065151515
1123232.285714285732.624881-0.62488148.003979803-8.628860803
1133633.428571428633.583212.4167957.1952700152-4.7784800152
1143434.857142857134.2498733333-0.249873333364.4049569365-4.6548302698
1153135.428571428635.083205-4.08320571.2123146061-5.2955196061
1163636.428571428636.4582-0.458282.7066306515-3.1648306515
117393638.041530.958479-1.38996383332.3484338333
1184037.428571428640.0415216667-0.041521666710-2.45625146972.414729803
1193939.571428571442.3331806667-3.333180666711-8.89753912125.5643584545
1203342.571428571444.541504-11.54150412-12.44488671210.9033827121
1214445.428571428646.4164946667-2.41649466671-7.10587039394.6893757273
1224648.857142857147.8331563333-1.83315633332-1.3274616364-0.505694697
1235751.714285714348.7914868.20851438.9982974848-0.7897834848
1245954.285714285749.62481666679.375183333348.0039798031.3712035303
1256455.142857142950.33314613.66685457.19527001526.4715839848
1265955.428571428651.2081427.79185864.40495693653.3869010635
1275154.571428571452.166474-1.16647471.2123146061-2.3787886061
1285052.571428571452.9998053333-2.999805333382.7066306515-5.7064359848
1294850.285714285753.749805-5.7498059-1.3899638333-4.3598411667
1305149.285714285754.083137-3.08313710-2.4562514697-0.6268855303
1314550.285714285753.958138-8.95813811-8.8975391212-0.0605988788
1324852.142857142953.708138-5.70813812-12.44488671216.7367487121
133525453.7081356667-1.70813566671-7.10587039395.3977347273
1345855.142857142953.66646833334.33353166672-1.32746163645.660993303
135635753.79146833339.208531666738.99829748480.2102341818
1366157.571428571454.16646766676.833532333348.003979803-1.1704474697
137595754.2081314.79186957.1952700152-2.4034010152
1385856.285714285753.66646633334.333533666764.4049569365-0.0714232698
1395255.142857142953.0831376667-1.083137666771.2123146061-2.2954522727
1404852.428571428652.7914743333-4.791474333382.7066306515-7.4981049848
1415349.428571428652.83314366670.16685633339-1.38996383331.5568201667
142554852.95814166672.041858333310-2.45625146974.498109803
1434248.428571428653.1664746667-11.166474666711-8.8975391212-2.2689355455
1443851.142857142953.708139-15.70813912-12.4448867121-3.2632522879
1454852.142857142954.4581346667-6.45813466671-7.10587039390.6477357273
1465553.571428571455.4581296667-0.45812966672-1.32746163640.8693319697
1476756.857142857156.041460333310.958539666738.99829748481.9602421818
1486060.428571428655.95812733334.041872666748.003979803-3.9621071364
1496562.285714285756.2081248.79187657.19527001521.5966059848
1506562.142857142956.95811966678.041880333364.40495693653.6369233968
151636057.62478666675.375213333371.21231460614.1628987273
1526158.714285714358.083122.9168882.70663065150.2102493485
1535456.142857142959.166456-5.1664569-1.3899638333-3.7764921667
1545254.714285714361.083113-9.08311310-2.4562514697-6.6268615303
1555154.142857142962.4997733333-11.499773333311-8.8975391212-2.6022342121
1564758.142857142962.9581033333-15.958103333312-12.4448867121-3.5132166212
1575562.428571428662.749769-7.7497691-7.1058703939-0.6438986061
1585965.714285714362.1247703333-3.12477033332-1.3274616364-1.797308697
1598967.857142857161.99977127.00022938.998297484818.0019315152
1608469.285714285762.333101666721.666898333348.00397980313.6629185303
1617568.857142857162.29143412.70856657.19527001525.5132959848
162666962.2497673.75023364.4049569365-0.6547239365
163576462.249769-5.24976971.2123146061-6.4620836061
1645258.857142857162.1664376667-10.166437666782.7066306515-12.8730683182
1656055.142857142961.499781-1.4997819-1.3899638333-0.1098171667
1665453.285714285760.333118-6.33311810-2.4562514697-3.8768665303
1674853.571428571459.2914523333-11.291452333311-8.8975391212-2.3939132121
1684956.571428571458.4164536667-9.416453666712-12.44488671213.0284330455
1695358.285714285757.9997866667-4.99978666671-7.10587039392.1060837273
1705959.428571428658.0831190.9168812-1.32746163642.2443426364
1717360.857142857157.916453666715.083546333338.99829748486.0852488485
1727261.714285714357.499787666714.500212333348.0039798036.4962325303
1736262.142857142957.20811966674.791880333357.1952700152-2.4033896818
1745861.142857142956.49978833331.500211666764.4049569365-2.9047452698
1755558.142857142955.583127-0.58312771.2123146061-1.7954416061
176565454.9997991.00020182.7066306515-1.7064296515
1775250.428571428654.624805-2.6248059-1.3899638333-1.2348411667
1785248.285714285754.2498063333-2.249806333310-2.45625146970.2064451364
1794348.285714285754.166471-11.16647111-8.8975391212-2.2689318788
180375054.541469-17.54146912-12.4448867121-5.0965822879
1814352.285714285754.9164656667-11.91646566671-7.1058703939-4.8105952727
182555455.1247986667-0.12479866672-1.32746163641.2026629697
1836857.142857142955.333129666712.666870333338.99829748483.6685728485
184686055.624795666712.375204333348.0039798034.3712245303
1856462.285714285755.83312433338.166875666757.19527001520.9716056515
1866562.142857142956.04145566678.958544333364.40495693654.5535873968
1875760.571428571456.62478933330.375210666771.2123146061-0.8371039394
188595756.83312366672.166876333382.7066306515-0.5397543182
1895453.857142857156.249796-2.2497969-1.3899638333-0.8598321667
190575255.49979933331.500200666710-2.45625146973.9564521364
1914351.142857142955.0414673333-12.041467333311-8.8975391212-3.1439282121
192425154.624802-12.62480212-12.4448867121-0.1799152879
1935251.857142857154.5414683333-2.54146833331-7.10587039394.5644020606
1945152.428571428654.833134-3.8331342-1.3274616364-2.5056723636
1955854.571428571454.70813166673.291868333338.9982974848-5.7064291515
1966057.428571428654.2498015.75019948.003979803-2.253780803
1976158.714285714354.1664656.83353557.1952700152-0.3617350152
1985858.428571428654.24979666673.750203333364.4049569365-0.6547536032
1996257.428571428653.87480066678.125199333371.21231460616.9128847273
2006155.571428571453.54146933337.458530666782.70663065154.7519000152
2014952.571428571453.4998053333-4.49980533339-1.3899638333-3.1098415
2025150.714285714353.1664726667-2.166472666710-2.45625146970.289778803
203474952.374809-5.37480911-8.89753912123.5227301212
2044048.571428571451.583145-11.58314512-12.44488671210.8617417121
205454950.583149-5.5831491-7.10587039391.5227213939
2065048.857142857149.29148733330.70851266672-1.32746163642.035974303
2075849.285714285748.2081559.79184538.99829748480.7935475152
2085250.142857142947.16649266674.833507333348.003979803-3.1704724697
2095050.285714285746.0414963.95850457.1952700152-3.2367660152
2105048.571428571445.0414984.95850264.40495693650.5535450635
2114645.571428571443.958172.0418371.21231460610.8295153939
212464342.916513.0834982.70663065150.3768593485
213384041.9998493333-3.99984933339-1.3899638333-2.6098855
2143737.142857142941.2498513333-4.249851333310-2.4562514697-1.7935998636
2153436.285714285740.8748526667-6.874852666711-8.89753912122.0226864545
2162936.285714285740.6248536667-11.624853666712-12.44488671210.8200330455
2173037.428571428640.3748533333-10.37485333331-7.1058703939-3.2689829394
2184038.857142857140.2498543333-0.24985433332-1.32746163641.077607303
2194640.714285714340.2081855.79181538.9982974848-3.2064824848
2204642.714285714340.3331855.66681548.003979803-2.337164803
221474540.70818266676.291817333357.1952700152-0.9034526818
2224744.571428571441.20817933335.791820666764.40495693651.3868637302
2234343.857142857142.2498440.75015671.2123146061-0.4621586061
2244642.857142857143.62484133332.375158666782.7066306515-0.3314719848
2253741.285714285744.666505-7.6665059-1.3899638333-6.2765411667
2264141.428571428645.374835-4.37483510-2.4562514697-1.9185835303
2273943.142857142945.874833-6.87483311-8.89753912122.0227061212
2283644.571428571446.3331646667-10.333164666712-12.44488671212.1117220455
2294846.857142857146.95816133331.04183866671-7.10587039398.1477090606
2305548.428571428647.7498267.2501742-1.32746163648.5776356364
2315650.428571428648.74981966677.250180333338.9982974848-1.7481171515
2325352.714285714349.62481633333.375183666748.003979803-4.6287961364
2335253.857142857150.041481.9585257.1952700152-5.2367500152
2345353.285714285750.4164782.58352264.4049569365-1.8214349365
2355252.142857142950.49981333331.500186666771.21231460610.2878720606
2365650.571428571450.1248175.87518382.70663065153.1685523485
2375149.142857142950.08315233330.91684766679-1.38996383332.3068115
2384847.857142857150.7914833333-2.791483333310-2.4562514697-0.3352318636
2394247.571428571451.5831453333-9.583145333311-8.8975391212-0.6856062121
2404248.142857142952.0831436667-10.083143666712-12.44488671212.3617430455
2414450.285714285752.4581413333-8.45814133331-7.1058703939-1.3522709394
2425051.714285714352.6248083333-2.62480833332-1.3274616364-1.297346697
2436054.142857142952.9164737.08352738.9982974848-1.9147704848
244665653.499803333312.500196666748.0039798034.4962168636
2455857.857142857154.29146533333.708534666757.1952700152-3.4867353485
2465958.857142857155.1247953.87520564.4049569365-0.5297519365
2475558.285714285755.5414593333-0.541459333371.2123146061-1.7537739394
2485756.428571428655.9164611.08353982.7066306515-1.6230916515
2495755.428571428656.83312833330.16687166679-1.38996383331.5568355
2505653.428571428657.3747923333-1.374792333310-2.45625146971.0814591364
2515353.857142857157.62479-4.6247911-8.89753912124.2727491212
2525156.285714285757.749788-6.74978812-12.44488671215.6950987121
2534557.428571428657.4581213333-12.45812133331-7.1058703939-5.3522509394
2545858.714285714357.41645633330.58354366672-1.32746163641.911005303
255745957.37478916.62521138.99829748487.6269135152
2566559.142857142957.29145633337.708543666748.003979803-0.2954361364
2576561.142857142956.99978833338.000211666757.19527001520.8049416515
2585560.571428571456.2081236667-1.208123666764.4049569365-5.6130806032
2595258.142857142955.8331253333-3.833125333371.2123146061-5.0454399394
2605955.285714285755.4581293.54187182.70663065150.8352403485
2615451.714285714354.4164713333-0.41647133339-1.38996383330.9734925
2625750.571428571453.5414733.45852710-2.45625146975.9147784697
2634549.857142857153.1664753333-8.166475333311-8.89753912120.7310637879
264405053.4581393333-13.458139333312-12.4448867121-1.0132526212
2654750.571428571454.3331353333-7.33313533331-7.1058703939-0.2272649394
2664751.428571428654.9998003333-7.99980033332-1.3274616364-6.672338697
2676054.142857142955.20813066674.791869333338.9982974848-4.2064281515
2685857.571428571455.1247982.87520248.003979803-5.128777803
2696359.857142857154.95812833338.041871666757.19527001520.8466016515
2706461
2716460.1428571429
2726358.1428571429
27355
27454
27544
To calculate the Sj(t) values using a Pivot Table:
ValueMonth1. Copy the Yt-Tt and Month columns into a clear area (D284:E546).
2.000192666772. Add the Headings (Value & Month) to identify the columns
1.416851666783. Select Data/PivotTable
-3.37482394. At step 3 select Existing worksheet.
-6.4164923333105. Enter the position of the top left cell for the pivot table (G295)
-10.708163116. Click Finish; the Pivot Table is then created
-16.958164127. The pivot table form is displayed
-9.24983218. Drag The Month button onto the Row Fields position
-1.708166666729. Drag the Value button into the main Data Fields Position
9.791833310. Click the little "i" menu button in the Pivot Table form and select Average
8.3334993333411. The Total column gives the Sj values.
13.9584983333512 Copy these into the Sj(t) (blue) column, starting at G12..
6.5001656Average of Value
5.0834947MonthTotal
2.83348981-7.1058703939
-0.29151892-1.3274616364
-6.87485433331038.9982974848
-10.87485566671148.003979803
-16.87485333331257.1952700152
-12.041519164.4049569365
-7.4998503333271.2123146061
1.958487382.7066306515
11.250157666749-1.3899638333
13.0834963333510-2.4562514697
5.791837611-8.8975391212
4.6668403333712-12.4448867121
5.3751768Grand Total-0.1088078999
-2.8748219
-3.666487333310
-3.916485666711
-11.041484333312
-9.4998161
2.00018533332
3.25018966673
9.37519366674
1.87519666675
2.41686666676
2.41686866677
3.12520333338
0.29187433339
-4.708118333310
-12.458109666711
-16.166435666712
-7.20809666671
2.87523833332
17.7085773
13.83358233334
10.25025366675
5.83358966676
-4.3330797
5.87525066678
3.4585779
-4.333091666710
-12.583089333311
-16.791420666712
-11.0830831
-5.16641833332
7.04191533333
16.87525033334
11.6669225
8.79192266676
0.00025366677
4.37525033338
0.66691133339
3.291907333310
-12.666428666711
-14.583098333312
-10.83311
-5.49976933332
10.00023066673
10.00022733334
7.16689433335
3.29189133336
5.3335527
10.3335478
4.1252049
0.83352810
-9.666482666711
-14.124822333312
-5.20816033331
-3.5414982
-2.83316433333
-10.08316566674
-1.66649733335
4.50017066676
9.83350066677
16.2501658
5.2084979
0.666834666710
-6.708165333311
-12.249833666712
-6.95817266671
-2.04151433332
9.0001473
5.6251414
7.8334715
1.50013566676
0.04179966677
-1.1248718
-6.12487766679
-4.083213666710
-5.20821811
-2.66655212
-3.29155266671
-2.16655366672
4.29178233333
-0.6248814
2.416795
-0.24987333336
-4.0832057
-0.45828
0.958479
-0.041521666710
-3.333180666711
-11.54150412
-2.41649466671
-1.83315633332
8.2085143
9.37518333334
13.6668545
7.7918586
-1.1664747
-2.99980533338
-5.7498059
-3.08313710
-8.95813811
-5.70813812
-1.70813566671
4.33353166672
9.20853166673
6.83353233334
4.7918695
4.33353366676
-1.08313766677
-4.79147433338
0.16685633339
2.041858333310
-11.166474666711
-15.70813912
-6.45813466671
-0.45812966672
10.95853966673
4.04187266674
8.7918765
8.04188033336
5.37521333337
2.916888
-5.1664569
-9.08311310
-11.499773333311
-15.958103333312
-7.7497691
-3.12477033332
27.0002293
21.66689833334
12.7085665
3.7502336
-5.2497697
-10.16643766678
-1.4997819
-6.33311810
-11.291452333311
-9.416453666712
-4.99978666671
0.9168812
15.08354633333
14.50021233334
4.79188033335
1.50021166676
-0.5831277
1.0002018
-2.6248059
-2.249806333310
-11.16647111
-17.54146912
-11.91646566671
-0.12479866672
12.66687033333
12.37520433334
8.16687566675
8.95854433336
0.37521066677
2.16687633338
-2.2497969
1.500200666710
-12.041467333311
-12.62480212
-2.54146833331
-3.8331342
3.29186833333
5.7501994
6.8335355
3.75020333336
8.12519933337
7.45853066678
-4.49980533339
-2.166472666710
-5.37480911
-11.58314512
-5.5831491
0.70851266672
9.7918453
4.83350733334
3.9585045
4.9585026
2.041837
3.083498
-3.99984933339
-4.249851333310
-6.874852666711
-11.624853666712
-10.37485333331
-0.24985433332
5.7918153
5.6668154
6.29181733335
5.79182066676
0.7501567
2.37515866678
-7.6665059
-4.37483510
-6.87483311
-10.333164666712
1.04183866671
7.2501742
7.25018033333
3.37518366674
1.958525
2.5835226
1.50018666677
5.8751838
0.91684766679
-2.791483333310
-9.583145333311
-10.083143666712
-8.45814133331
-2.62480833332
7.0835273
12.50019666674
3.70853466675
3.8752056
-0.54145933337
1.0835398
0.16687166679
-1.374792333310
-4.6247911
-6.74978812
-12.45812133331
0.58354366672
16.6252113
7.70854366674
8.00021166675
-1.20812366676
-3.83312533337
3.5418718
-0.41647133339
3.45852710
-8.166475333311
-13.458139333312
-7.33313533331
-7.99980033332
4.79186933333
2.8752024
8.04187166675
ResidualPlot
ResidualPlot
6360.8571428571
6560.4285714286
6158.4285714286
5454.7142857143
5251
4646
4242.5714285714
3741.1428571429
3041.5714285714
3742.5714285714
4444.8571428571
5546.7142857143
5349.2857142857
5850.4285714286
5050
4847
4543.7142857143
4138.8571428571
3435.8571428571
3033.8571428571
2433.7142857143
2935.5714285714
3438.8571428571
4441.8571428571
5445.7142857143
5749.1428571429
5150.8571428571
5151.1428571429
5350
4647.4285714286
4646
4646.2857142857
3946.5714285714
4148.8571428571
5350.1428571429
5551.5714285714
6254.1428571429
5556.7142857143
5657.4285714286
5757.4285714286
5955.5714285714
5854.4285714286
5554.5714285714
4956.1428571429
4759.7142857143
5763
6866.2857142857
8469.8571428571
8172.2857142857
7874.7142857143
7475.1428571429
6472.1428571429
7468.4285714286
7164.5714285714
6362.1428571429
5562
5162.1428571429
5764.1428571429
6366.5714285714
7569.7142857143
8572.1428571429
8074.2857142857
7775
6874.2857142857
7269.7142857143
6865.4285714286
7062
5360.5714285714
5060.7142857143
5361.2857142857
5861
7362.4285714286
7264.4285714286
6866.5714285714
6366.8571428571
6464.1428571429
6859.7142857143
6055
5452.1428571429
4149.2857142857
3545.8571428571
4342.4285714286
4441
4442.2857142857
3645.1428571429
4447.7142857143
5048.5714285714
5548.8571428571
6149.2857142857
5047.7142857143
4645.8571428571
3943.7142857143
3342
3741.1428571429
4041
4940.8571428571
4441.2857142857
4540.8571428571
3839.1428571429
3636.2857142857
3433.8571428571
2831.5714285714
2930.1428571429
2729.1428571429
2929.4285714286
2830
2931
3632
3232.2857142857
3633.4285714286
3434.8571428571
3135.4285714286
3636.4285714286
3936
4037.4285714286
3939.5714285714
3342.5714285714
4445.4285714286
4648.8571428571
5751.7142857143
5954.2857142857
6455.1428571429
5955.4285714286
5154.5714285714
5052.5714285714
4850.2857142857
5149.2857142857
4550.2857142857
4852.1428571429
5254
5855.1428571429
6357
6157.5714285714
5957
5856.2857142857
5255.1428571429
4852.4285714286
5349.4285714286
5548
4248.4285714286
3851.1428571429
4852.1428571429
5553.5714285714
6756.8571428571
6060.4285714286
6562.2857142857
6562.1428571429
6360
6158.7142857143
5456.1428571429
5254.7142857143
5154.1428571429
4758.1428571429
5562.4285714286
5965.7142857143
8967.8571428571
8469.2857142857
7568.8571428571
6669
5764
5258.8571428571
6055.1428571429
5453.2857142857
4853.5714285714
4956.5714285714
5358.2857142857
5959.4285714286
7360.8571428571
7261.7142857143
6262.1428571429
5861.1428571429
5558.1428571429
5654
5250.4285714286
5248.2857142857
4348.2857142857
3750
4352.2857142857
5554
6857.1428571429
6860
6462.2857142857
6562.1428571429
5760.5714285714
5957
5453.8571428571
5752
4351.1428571429
4251
5251.8571428571
5152.4285714286
5854.5714285714
6057.4285714286
6158.7142857143
5858.4285714286
6257.4285714286
6155.5714285714
4952.5714285714
5150.7142857143
4749
4048.5714285714
4549
5048.8571428571
5849.2857142857
5250.1428571429
5050.2857142857
5048.5714285714
4645.5714285714
4643
3840
3737.1428571429
3436.2857142857
2936.2857142857
3037.4285714286
4038.8571428571
4640.7142857143
4642.7142857143
4745
4744.5714285714
4343.8571428571
4642.8571428571
3741.2857142857
4141.4285714286
3943.1428571429
3644.5714285714
4846.8571428571
5548.4285714286
5650.4285714286
5352.7142857143
5253.8571428571
5353.2857142857
5252.1428571429
5650.5714285714
5149.1428571429
4847.8571428571
4247.5714285714
4248.1428571429
4450.2857142857
5051.7142857143
6054.1428571429
6656
5857.8571428571
5958.8571428571
5558.2857142857
5756.4285714286
5755.4285714286
5653.4285714286
5353.8571428571
5156.2857142857
4557.4285714286
5858.7142857143
7459
6559.1428571429
6561.1428571429
5560.5714285714
5258.1428571429
5955.2857142857
5451.7142857143
5750.5714285714
4549.8571428571
4050
4750.5714285714
4751.4285714286
6054.1428571429
5857.5714285714
6359.8571428571
6461
6460.1428571429
6358.1428571429
55
54
44
Original
7MA
House Sales Data
6360.8571428571
6560.4285714286
6158.4285714286
5454.714285714351.9998073333
525150.5831483333
464649.374823
4242.571428571448.4164923333
3741.142857142947.708163
3041.571428571446.958164
3742.571428571446.249832
4444.857142857145.7081666667
5546.714285714345.208167
5349.285714285744.6665006667
5850.428571428644.0415016667
505043.499835
484742.916506
4543.714285714342.166511
4138.857142857141.291518
3435.857142857140.8748543333
3033.857142857140.8748556667
2433.714285714340.8748533333
2935.571428571441.041519
3438.857142857141.4998503333
4441.857142857142.041513
5445.714285714342.7498423333
5749.142857142943.9165036667
5150.857142857145.208163
5151.142857142946.3331596667
535047.624824
4647.428571428648.874821
464649.6664873333
4646.285714285749.9164856667
3946.571428571450.0414843333
4148.857142857150.499816
5350.142857142950.9998146667
5551.571428571451.7498103333
6254.142857142952.6248063333
5556.714285714353.1248033333
5657.428571428653.5831333333
5757.428571428654.5831313333
5955.571428571455.8747966667
5854.428571428657.7081256667
5554.571428571459.7081183333
4956.142857142961.4581096667
4759.714285714363.1664356667
576364.2080966667
6866.285714285765.1247616667
8469.857142857166.291423
8172.285714285767.1664176667
7874.714285714367.7497463333
7475.142857142968.1664103333
6472.142857142968.333079
7468.428571428668.1247493333
7164.571428571467.541423
6362.142857142967.3330916667
556267.5830893333
5162.142857142967.7914206667
5764.142857142968.083083
6366.571428571468.1664183333
7569.714285714367.9580846667
8572.142857142968.1247496667
8074.285714285768.333078
777568.2080773333
6874.285714285767.9997463333
7269.714285714367.6247496667
6865.428571428667.3330886667
706266.7080926667
5360.571428571465.6664286667
5060.714285714364.5830983333
5361.285714285763.8331
586163.4997693333
7362.428571428662.9997693333
7264.428571428661.9997726667
6866.571428571460.8331056667
6366.857142857159.7081086667
6464.142857142958.666448
6859.714285714357.666453
605555.874796
5452.142857142953.166472
4149.285714285750.6664826667
3545.857142857149.1248223333
4342.428571428648.2081603333
444147.541498
4442.285714285746.8331643333
3645.142857142946.0831656667
4447.714285714345.6664973333
5048.571428571445.4998293333
5548.857142857145.1664993333
6149.285714285744.749835
5047.714285714344.791503
4645.857142857145.3331653333
3943.714285714345.7081653333
334245.2498336667
3741.142857142943.9581726667
404142.0415143333
4940.857142857139.999853
4441.285714285738.374859
4540.857142857137.166529
3839.142857142936.4998643333
3636.285714285735.9582003333
3433.857142857135.124871
2831.571428571434.1248776667
2930.142857142933.0832136667
2729.142857142932.208218
2929.428571428631.666552
283031.2915526667
293131.1665536667
363231.7082176667
3232.285714285732.624881
3633.428571428633.58321
3434.857142857134.2498733333
3135.428571428635.083205
3636.428571428636.4582
393638.04153
4037.428571428640.0415216667
3939.571428571442.3331806667
3342.571428571444.541504
4445.428571428646.4164946667
4648.857142857147.8331563333
5751.714285714348.791486
5954.285714285749.6248166667
6455.142857142950.333146
5955.428571428651.208142
5154.571428571452.166474
5052.571428571452.9998053333
4850.285714285753.749805
5149.285714285754.083137
4550.285714285753.958138
4852.142857142953.708138
525453.7081356667
5855.142857142953.6664683333
635753.7914683333
6157.571428571454.1664676667
595754.208131
5856.285714285753.6664663333
5255.142857142953.0831376667
4852.428571428652.7914743333
5349.428571428652.8331436667
554852.9581416667
4248.428571428653.1664746667
3851.142857142953.708139
4852.142857142954.4581346667
5553.571428571455.4581296667
6756.857142857156.0414603333
6060.428571428655.9581273333
6562.285714285756.208124
6562.142857142956.9581196667
636057.6247866667
6158.714285714358.08312
5456.142857142959.166456
5254.714285714361.083113
5154.142857142962.4997733333
4758.142857142962.9581033333
5562.428571428662.749769
5965.714285714362.1247703333
8967.857142857161.999771
8469.285714285762.3331016667
7568.857142857162.291434
666962.249767
576462.249769
5258.857142857162.1664376667
6055.142857142961.499781
5453.285714285760.333118
4853.571428571459.2914523333
4956.571428571458.4164536667
5358.285714285757.9997866667
5959.428571428658.083119
7360.857142857157.9164536667
7261.714285714357.4997876667
6262.142857142957.2081196667
5861.142857142956.4997883333
5558.142857142955.583127
565454.999799
5250.428571428654.624805
5248.285714285754.2498063333
4348.285714285754.166471
375054.541469
4352.285714285754.9164656667
555455.1247986667
6857.142857142955.3331296667
686055.6247956667
6462.285714285755.8331243333
6562.142857142956.0414556667
5760.571428571456.6247893333
595756.8331236667
5453.857142857156.249796
575255.4997993333
4351.142857142955.0414673333
425154.624802
5251.857142857154.5414683333
5152.428571428654.833134
5854.571428571454.7081316667
6057.428571428654.249801
6158.714285714354.166465
5858.428571428654.2497966667
6257.428571428653.8748006667
6155.571428571453.5414693333
4952.571428571453.4998053333
5150.714285714353.1664726667
474952.374809
4048.571428571451.583145
454950.583149
5048.857142857149.2914873333
5849.285714285748.208155
5250.142857142947.1664926667
5050.285714285746.041496
5048.571428571445.041498
4645.571428571443.95817
464342.91651
384041.9998493333
3737.142857142941.2498513333
3436.285714285740.8748526667
2936.285714285740.6248536667
3037.428571428640.3748533333
4038.857142857140.2498543333
4640.714285714340.208185
4642.714285714340.333185
474540.7081826667
4744.571428571441.2081793333
4343.857142857142.249844
4642.857142857143.6248413333
3741.285714285744.666505
4141.428571428645.374835
3943.142857142945.874833
3644.571428571446.3331646667
4846.857142857146.9581613333
5548.428571428647.749826
5650.428571428648.7498196667
5352.714285714349.6248163333
5253.857142857150.04148
5353.285714285750.416478
5252.142857142950.4998133333
5650.571428571450.124817
5149.142857142950.0831523333
4847.857142857150.7914833333
4247.571428571451.5831453333
4248.142857142952.0831436667
4450.285714285752.4581413333
5051.714285714352.6248083333
6054.142857142952.916473
665653.4998033333
5857.857142857154.2914653333
5958.857142857155.124795
5558.285714285755.5414593333
5756.428571428655.916461
5755.428571428656.8331283333
5653.428571428657.3747923333
5353.857142857157.62479
5156.285714285757.749788
4557.428571428657.4581213333
5858.714285714357.4164563333
745957.374789
6559.142857142957.2914563333
6561.142857142956.9997883333
5560.571428571456.2081236667
5258.142857142955.8331253333
5955.285714285755.458129
5451.714285714354.4164713333
5750.571428571453.541473
4549.857142857153.1664753333
405053.4581393333
4750.571428571454.3331353333
4751.428571428654.9998003333
6054.142857142955.2081306667
5857.571428571455.124798
6359.857142857154.9581283333
6461
6460.1428571429
6358.1428571429
55
54
44
Original
7MA
2X12MA
House Sales Data
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
4.4049569365
1.2123146061
2.7066306515
-1.3899638333
-2.4562514697
-8.8975391212
-12.4448867121
-7.1058703939
-1.3274616364
8.9982974848
8.003979803
7.1952700152
Seasonal
0.7878780606
-1.2897789848
-1.9848591667
-3.9602408636
-1.8106238788
-4.5132772879
-2.1439616061
-0.3807050303
0.7935355152
0.3295195303
6.7632283182
2.0952080635
3.8711793939
0.1268583485
1.0984458333
-4.4186028636
-1.9773165455
-4.4299666212
-4.9356486061
-6.172388697
-7.0398104848
3.2461778636
5.8882263182
1.3868800635
3.4545257273
2.6685453485
-1.4848571667
-1.2102358636
4.9810534545
1.4034023788
-2.3939456061
3.3276469697
-5.7481078182
1.3712138636
-5.3200733485
-1.9880902698
1.2045540606
0.4185726818
1.6818381667
-2.2518668636
-3.5605705455
-3.7215489545
-0.1022262727
4.2026999697
8.7102795152
5.8296025303
3.0549836515
1.4286327302
-5.5453936061
3.1686200152
4.8485408333
-1.876840197
-3.6855502121
-4.3465339545
-3.9772126061
-3.838956697
-1.9563821515
8.8712705303
4.4716519848
4.3869657302
-1.2120609394
1.6686196818
2.0568751667
5.748158803
-3.7688895455
-2.1382116212
-3.7272296061
-4.172307697
1.0019331818
1.9962475303
-0.0283756818
-1.1130656032
4.1212373939
7.6269163485
5.5151678333
3.2897794697
-0.7689435455
-1.6799356212
1.8977100606
-2.2140363636
-11.8314618182
-18.0871454697
-8.8617673485
0.0952137302
8.6211860606
13.5435343485
6.5984608333
3.1230861364
2.1893737879
0.1950530455
0.1476977273
-0.714052697
0.0018495152
-2.378838803
0.6382009848
-2.9048212698
-1.1705149394
-3.8315016515
-4.7349138333
-1.626962197
3.6893211212
9.7783347121
3.8143177273
-0.8390920303
-4.7065151515
-8.628860803
-4.7784800152
-4.6548302698
-5.2955196061
-3.1648306515
2.3484338333
2.414729803
5.5643584545
0.9033827121
4.6893757273
-0.505694697
-0.7897834848
1.3712035303
6.4715839848
3.3869010635
-2.3787886061
-5.7064359848
-4.3598411667
-0.6268855303
-0.0605988788
6.7367487121
5.3977347273
5.660993303
0.2102341818
-1.1704474697
-2.4034010152
-0.0714232698
-2.2954522727
-7.4981049848
1.5568201667
4.498109803
-2.2689355455
-3.2632522879
0.6477357273
0.8693319697
1.9602421818
-3.9621071364
1.5966059848
3.6369233968
4.1628987273
0.2102493485
-3.7764921667
-6.6268615303
-2.6022342121
-3.5132166212
-0.6438986061
-1.797308697
18.0019315152
13.6629185303
5.5132959848
-0.6547239365
-6.4620836061
-12.8730683182
-0.1098171667
-3.8768665303
-2.3939132121
3.0284330455
2.1060837273
2.2443426364
6.0852488485
6.4962325303
-2.4033896818
-2.9047452698
-1.7954416061
-1.7064296515
-1.2348411667
0.2064451364
-2.2689318788
-5.0965822879
-4.8105952727
1.2026629697
3.6685728485
4.3712245303
0.9716056515
4.5535873968
-0.8371039394
-0.5397543182
-0.8598321667
3.9564521364
-3.1439282121
-0.1799152879
4.5644020606
-2.5056723636
-5.7064291515
-2.253780803
-0.3617350152
-0.6547536032
6.9128847273
4.7519000152
-3.1098415
0.289778803
3.5227301212
0.8617417121
1.5227213939
2.035974303
0.7935475152
-3.1704724697
-3.2367660152
0.5535450635
0.8295153939
0.3768593485
-2.6098855
-1.7935998636
2.0226864545
0.8200330455
-3.2689829394
1.077607303
-3.2064824848
-2.337164803
-0.9034526818
1.3868637302
-0.4621586061
-0.3314719848
-6.2765411667
-1.9185835303
2.0227061212
2.1117220455
8.1477090606
8.5776356364
-1.7481171515
-4.6287961364
-5.2367500152
-1.8214349365
0.2878720606
3.1685523485
2.3068115
-0.3352318636
-0.6856062121
2.3617430455
-1.3522709394
-1.297346697
-1.9147704848
4.4962168636
-3.4867353485
-0.5297519365
-1.7537739394
-1.6230916515
1.5568355
1.0814591364
4.2727491212
5.6950987121
-5.3522509394
1.911005303
7.6269135152
-0.2954361364
0.8049416515
-5.6130806032
-5.0454399394
0.8352403485
0.9734925
5.9147784697
0.7310637879
-1.0132526212
-0.2272649394
-6.672338697
-4.2064281515
-5.128777803
0.8466016515
Residuals
-
K= ? Th ttPhng php no th tt?
-
PHN R CHUI THI GIAN
-
Xt m hnh cng Y = T+S+E. Phn r theo m hnh cng bao gm 4 bcBc 1: Tnh trung bnh trt trung tm cp 12 (i vi d liu qu tnh trung bnh trt trung tm cp 4)K hiu chui ny l Tt, cha yu t xu hng Bc 2: Loi b yu t xu hng:NSt = Yt Tt = St +EtIII. PHN R THEO M HNH CNG
-
Bc 3: Tnh ch s ma v cho mi thng bng cch ly gi tr trung bnh ca tt c cc thng:Gi s c nj gi tr cho thng th j
-
Bc 4: c lng sai s ngn nhin bng cch loi yu t ma v l ch s ma v ca thng j tng ng vi quan st Yt
-
Trung bnh ca Dt ca thng 7 cc nm
Orig. DataTrend-CycleDeTrendedYtTt = 2x12MADt = Yt-TtMonthSj(t)Et = Yt-Tt-St15526036846356566175451.99982.000271.21230.787985250.58311.416982.7066-1.289894649.3748-3.37489-1.3900-1.9849104248.4165-6.416510-2.4563-3.9602113747.7082-10.708211-8.8975-1.8106123046.9582-16.958212-12.4449-4.5133133746.2498-9.249813-7.1059-2.1440144445.7082-1.708214-1.3275-0.3807155545.20829.7918158.99830.7935165344.66658.3335168.00400.3295175844.041513.9585177.19536.7632185043.49986.5002184.40502.0952194842.91655.0835191.21233.8712
-
*Xy dng hm hi quy ca Tt theo thi gian:D bo theo m hnh cngThay t =0,1,2, c T mi kThm yu t ma v:
-
Phn tch s liu house sales da trn m hnh cng
Data
MonthHouseSalesMonthHouseSales
155
260
368
463
565
661
754
852
946
1042
1137
1230
1337
1444
1555
1653
1758
1850
1948
2045
2141
2234
2330
2424
2529
2634
2744
2854
2957
3051
3151
3253
3346
3446
3546
3639
3741
3853
3955
4062
4155
4256
4357
4459
4558
4655
4749
4847
4957
5068
5184
5281
5378
5474
5564
5674
5771
5863
5955
6051
6157
6263
6375
6485
6580
6677
6768
6872
6968
7070
7153
7250
7353
7458
7573
7672
7768
7863
7964
8068
8160
8254
8341
8435
8543
8644
8744
8836
8944
9050
9155
9261
9350
9446
9539
9633
9737
9840
9949
10044
10145
10238
10336
10434
10528
10629
10727
10829
10928
11029
11136
11232
11336
11434
11531
11636
11739
11840
11939
12033
12144
12246
12357
12459
12564
12659
12751
12850
12948
13051
13145
13248
13352
13458
13563
13661
13759
13858
13952
14048
14153
14255
14342
14438
14548
14655
14767
14860
14965
15065
15163
15261
15354
15452
15551
15647
15755
15859
15989
16084
16175
16266
16357
16452
16560
16654
16748
16849
16953
17059
17173
17272
17362
17458
17555
17656
17752
17852
17943
18037
18143
18255
18368
18468
18564
18665
18757
18859
18954
19057
19143
19242
19352
19451
19558
19660
19761
19858
19962
20061
20149
20251
20347
20440
20545
20650
20758
20852
20950
21050
21146
21246
21338
21437
21534
21629
21730
21840
21946
22046
22147
22247
22343
22446
22537
22641
22739
22836
22948
23055
23156
23253
23352
23453
23552
23656
23751
23848
23942
24042
24144
24250
24360
24466
24558
24659
24755
24857
24957
25056
25153
25251
25345
25458
25574
25665
25765
25855
25952
26059
26154
26257
26345
26440
26547
26647
26760
26858
26963
27064
27164
27263
27355
27454
27544
DataPlot
DataPlot
63
65
61
54
52
46
42
37
30
37
44
55
53
58
50
48
45
41
34
30
24
29
34
44
54
57
51
51
53
46
46
46
39
41
53
55
62
55
56
57
59
58
55
49
47
57
68
84
81
78
74
64
74
71
63
55
51
57
63
75
85
80
77
68
72
68
70
53
50
53
58
73
72
68
63
64
68
60
54
41
35
43
44
44
36
44
50
55
61
50
46
39
33
37
40
49
44
45
38
36
34
28
29
27
29
28
29
36
32
36
34
31
36
39
40
39
33
44
46
57
59
64
59
51
50
48
51
45
48
52
58
63
61
59
58
52
48
53
55
42
38
48
55
67
60
65
65
63
61
54
52
51
47
55
59
89
84
75
66
57
52
60
54
48
49
53
59
73
72
62
58
55
56
52
52
43
37
43
55
68
68
64
65
57
59
54
57
43
42
52
51
58
60
61
58
62
61
49
51
47
40
45
50
58
52
50
50
46
46
38
37
34
29
30
40
46
46
47
47
43
46
37
41
39
36
48
55
56
53
52
53
52
56
51
48
42
42
44
50
60
66
58
59
55
57
57
56
53
51
45
58
74
65
65
55
52
59
54
57
45
40
47
47
60
58
63
64
64
63
55
54
44
Original
House Sales Data
Solution
12345678910111213
Wts for 7MA0.14285714290.14285714290.14285714290.14285714290.14285714290.14285714290.1428571429
Wts for 2x12MA0.04166666670.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0833330.0416666667
Orig. DataTrend-CycleDeTrended
Yt7MATt = 2x12MADt = Yt-TtMonthSj(t)Et = Yt-Tt-StNote Sj(t) values calculated in pivot table.
155-7.1058703939See below. (G282)
260-1.3274616364
3688.9982974848
46360.85714285718.003979803
56560.42857142867.1952700152
66158.42857142864.4049569365
75454.714285714351.99980733332.000192666771.21231460610.7878780606
8525150.58314833331.416851666782.7066306515-1.2897789848
9464649.374823-3.3748239-1.3899638333-1.9848591667
104242.571428571448.4164923333-6.416492333310-2.4562514697-3.9602408636
113741.142857142947.708163-10.70816311-8.8975391212-1.8106238788
123041.571428571446.958164-16.95816412-12.4448867121-4.5132772879
133742.571428571446.249832-9.2498321-7.1058703939-2.1439616061
144444.857142857145.7081666667-1.70816666672-1.3274616364-0.3807050303
155546.714285714345.2081679.79183338.99829748480.7935355152
165349.285714285744.66650066678.333499333348.0039798030.3295195303
175850.428571428644.041501666713.958498333357.19527001526.7632283182
18505043.4998356.50016564.40495693652.0952080635
19484742.9165065.08349471.21231460613.8711793939
204543.714285714342.1665112.83348982.70663065150.1268583485
214138.857142857141.291518-0.2915189-1.38996383331.0984458333
223435.857142857140.8748543333-6.874854333310-2.4562514697-4.4186028636
233033.857142857140.8748556667-10.874855666711-8.8975391212-1.9773165455
242433.714285714340.8748533333-16.874853333312-12.4448867121-4.4299666212
252935.571428571441.041519-12.0415191-7.1058703939-4.9356486061
263438.857142857141.4998503333-7.49985033332-1.3274616364-6.172388697
274441.857142857142.0415131.95848738.9982974848-7.0398104848
285445.714285714342.749842333311.250157666748.0039798033.2461778636
295749.142857142943.916503666713.083496333357.19527001525.8882263182
305150.857142857145.2081635.79183764.40495693651.3868800635
315151.142857142946.33315966674.666840333371.21231460613.4545257273
32535047.6248245.37517682.70663065152.6685453485
334647.428571428648.874821-2.8748219-1.3899638333-1.4848571667
34464649.6664873333-3.666487333310-2.4562514697-1.2102358636
354646.285714285749.9164856667-3.916485666711-8.89753912124.9810534545
363946.571428571450.0414843333-11.041484333312-12.44488671211.4034023788
374148.857142857150.499816-9.4998161-7.1058703939-2.3939456061
385350.142857142950.99981466672.00018533332-1.32746163643.3276469697
395551.571428571451.74981033333.250189666738.9982974848-5.7481078182
406254.142857142952.62480633339.375193666748.0039798031.3712138636
415556.714285714353.12480333331.875196666757.1952700152-5.3200733485
425657.428571428653.58313333332.416866666764.4049569365-1.9880902698
435757.428571428654.58313133332.416868666771.21231460611.2045540606
445955.571428571455.87479666673.125203333382.70663065150.4185726818
455854.428571428657.70812566670.29187433339-1.38996383331.6818381667
465554.571428571459.7081183333-4.708118333310-2.4562514697-2.2518668636
474956.142857142961.4581096667-12.458109666711-8.8975391212-3.5605705455
484759.714285714363.1664356667-16.166435666712-12.4448867121-3.7215489545
49576364.2080966667-7.20809666671-7.1058703939-0.1022262727
506866.285714285765.12476166672.87523833332-1.32746163644.2026999697
518469.857142857166.29142317.70857738.99829748488.7102795152
528172.285714285767.166417666713.833582333348.0039798035.8296025303
537874.714285714367.749746333310.250253666757.19527001523.0549836515
547475.142857142968.16641033335.833589666764.40495693651.4286327302
556472.142857142968.333079-4.33307971.2123146061-5.5453936061
567468.428571428668.12474933335.875250666782.70663065153.1686200152
577164.571428571467.5414233.4585779-1.38996383334.8485408333
586362.142857142967.3330916667-4.333091666710-2.4562514697-1.876840197
59556267.5830893333-12.583089333311-8.8975391212-3.6855502121
605162.142857142967.7914206667-16.791420666712-12.4448867121-4.3465339545
615764.142857142968.083083-11.0830831-7.1058703939-3.9772126061
626366.571428571468.1664183333-5.16641833332-1.3274616364-3.838956697
637569.714285714367.95808466677.041915333338.9982974848-1.9563821515
648572.142857142968.124749666716.875250333348.0039798038.8712705303
658074.285714285768.33307811.66692257.19527001524.4716519848
66777568.20807733338.791922666764.40495693654.3869657302
676874.285714285767.99974633330.000253666771.2123146061-1.2120609394
687269.714285714367.62474966674.375250333382.70663065151.6686196818
696865.428571428667.33308866670.66691133339-1.38996383332.0568751667
70706266.70809266673.291907333310-2.45625146975.748158803
715360.571428571465.6664286667-12.666428666711-8.8975391212-3.7688895455
725060.714285714364.5830983333-14.583098333312-12.4448867121-2.1382116212
735361.285714285763.8331-10.83311-7.1058703939-3.7272296061
74586163.4997693333-5.49976933332-1.3274616364-4.172307697
757362.428571428662.999769333310.000230666738.99829748481.0019331818
767264.428571428661.999772666710.000227333348.0039798031.9962475303
776866.571428571460.83310566677.166894333357.1952700152-0.0283756818
786366.857142857159.70810866673.291891333364.4049569365-1.1130656032
796464.142857142958.6664485.33355271.21231460614.1212373939
806859.714285714357.66645310.33354782.70663065157.6269163485
81605555.8747964.1252049-1.38996383335.5151678333
825452.142857142953.1664720.83352810-2.45625146973.2897794697
834149.285714285750.6664826667-9.666482666711-8.8975391212-0.7689435455
843545.857142857149.1248223333-14.124822333312-12.4448867121-1.6799356212
854342.428571428648.2081603333-5.20816033331-7.10587039391.8977100606
86444147.541498-3.5414982-1.3274616364-2.2140363636
874442.285714285746.8331643333-2.833164333338.9982974848-11.8314618182
883645.142857142946.0831656667-10.083165666748.003979803-18.0871454697
894447.714285714345.6664973333-1.666497333357.1952700152-8.8617673485
905048.571428571445.49982933334.500170666764.40495693650.0952137302
915548.857142857145.16649933339.833500666771.21231460618.6211860606
926149.285714285744.74983516.25016582.706630651513.5435343485
935047.714285714344.7915035.2084979-1.38996383336.5984608333
944645.857142857145.33316533330.666834666710-2.45625146973.1230861364
953943.714285714345.7081653333-6.708165333311-8.89753912122.1893737879
96334245.2498336667-12.249833666712-12.44488671210.1950530455
973741.142857142943.9581726667-6.95817266671-7.10587039390.1476977273
98404142.0415143333-2.04151433332-1.3274616364-0.714052697
994940.857142857139.9998539.00014738.99829748480.0018495152
1004441.285714285738.3748595.62514148.003979803-2.378838803
1014540.857142857137.1665297.83347157.19527001520.6382009848
1023839.142857142936.49986433331.500135666764.4049569365-2.9048212698
1033636.285714285735.95820033330.041799666771.2123146061-1.1705149394
1043433.857142857135.124871-1.12487182.7066306515-3.8315016515
10