Tugas MPDW praktikum Pertemuan 4
Muthi’ah Iffa Karimah
2025-09-20
1. MA(2)
A. Menggunakan Teknik Manual
Bangkitkan data dari set.seed
Bangkitkan data MA(2) dengan \(\theta_1 = 0.4\) dan \(\phi_2 = 0.6\) sebanyak 300 data menggunakan fungsi arima.sim
# Set seed agar hasil replikasi sama
set.seed(123)White Noise
# Menentukan parameter dan panjang data
n = 300 # Banyak data yang dibangkitkan
theta1 = 0.4 # theta_1 untuk MA(2)
theta2 = 0.6 # theta_2 untuk MA(2)wn = rnorm(300)
ts.plot(wn)
par(mfrow = c(1, 2))
acf(wn)
acf(wn, xlim = c(1, 20))
# Asumsi umum
ma2_man = numeric(n)
ma2_man[1] = wn[1] # Y1 = e1
# Untuk t = 2, Y_2 = e2 + theta_1*e1 + theta_2*e0 (denagn e0 = 0)
ma2_man[2] = wn[2] + theta1 * wn[1] # Y2 = e2 + theta1*e1# Pembangkitan model MA (2) manual melalui iterasi
for (t in 3:n) {
ma2_man[t] <- wn[t] + theta1 * wn[t - 1] + theta2 * wn[t - 2]
}
ma2_man## [1] -0.560475647 -0.454367748 1.130351930 0.555885223 1.092716080
## [6] 1.809085116 1.224514842 -0.051655760 -0.916327622 -1.479439852
## [11] 0.633705298 0.582049364 1.279146060 0.486879592 -0.271105178
## [16] 1.630986312 0.879111052 -0.695329083 0.213419326 -1.372219341
## [21] -0.836126728 -0.928779242 -1.753888638 -1.270077957 -1.532198429
## [26] -2.374043755 -0.211913841 -0.523528051 -0.574115463 0.890584017
## [31] 0.245108028 0.627803158 1.032975601 1.059140862 1.709909873
## [36] 1.544152779 1.322322404 0.572839503 0.001623244 -0.540003093
## [41] -1.030472978 -0.714082670 -1.765387450 1.538047058 1.316306573
## [46] 0.661449795 -0.127351070 -1.301674438 0.351572076 -0.051376231
## [51] 0.687949958 0.022759210 0.097701949 1.334326048 0.295947654
## [56] 2.247323581 -1.077627154 0.874994991 -0.571551939 0.616251516
## [61] 0.540328657 -0.220902719 -0.306353075 -1.453252408 -1.679145810
## [66] -0.736333079 -0.073453501 0.414405323 1.212395026 2.450794209
## [71] 0.882363189 -1.275530531 -0.212547725 -1.692406678 -0.368245807
## [76] 0.324847466 -0.287349629 -0.719284093 -0.477847409 -0.798800598
## [81] 0.058989729 0.304251258 -0.213089360 0.727280776 -0.185131961
## [86] 0.630213268 1.097259862 1.072986274 0.506244419 1.279543879
## [91] 1.257467952 1.635083073 1.054192832 -0.203375206 1.252729059
## [96] -0.432742253 2.763620627 2.047388071 1.689743687 -0.201134668
## [101] -1.262395139 -0.643131457 -0.570182333 -0.292089125 -1.238650734
## [106] -0.634200711 -1.373886700 -2.008920359 -1.518345977 -0.233859161
## [111] -0.435884231 0.929223503 -1.719905157 -0.337936456 -0.473547207
## [116] 0.475579064 0.537781861 -0.417743513 -1.042581033 -1.748434134
## [121] -0.801827527 -1.514893250 -0.798959331 -1.020799938 1.447090662
## [126] -0.068060415 1.080923815 -0.219054463 -0.789440351 -0.409274230
## [131] 0.838913643 0.986539545 1.088565058 -0.135101232 -2.197506201
## [136] 0.056540225 -2.240053518 0.834493811 1.328698531 -0.236283227
## [141] 1.269689213 -0.847819652 -1.255952554 -2.300843811 -3.150689731
## [146] -2.080321584 -2.635039898 -0.215329374 1.498222299 -0.034236836
## [151] 1.532992021 0.311919494 1.112462784 -0.414070232 -0.323481703
## [156] -0.933202343 0.379159835 -0.315480144 1.165791604 -0.207254757
## [161] 1.489063154 -0.852840935 -1.048199168 2.107471633 0.123465239
## [166] 2.076108517 0.505746158 -0.050216201 0.705291598 0.285440970
## [171] 0.242322530 0.200519547 -0.137178345 2.154000818 0.089604311
## [176] -0.115459566 -0.845411765 -0.332001651 0.583388818 -0.097467491
## [181] -0.984758180 0.562835523 -0.482371998 -0.247461912 -0.792274947
## [186] -0.810995440 0.889282191 0.410399871 1.453900876 -0.146828128
## [191] 0.467160774 -0.538482998 0.093376349 -1.052341494 -1.612196760
## [196] 0.935674757 0.613113258 0.187340199 -0.751249167 -2.180709268
## [201] 1.357918765 1.480649065 1.579106343 1.224583822 -0.356149358
## [206] -0.316066438 -1.227705564 -1.195806539 0.939898858 0.249564501
## [211] 1.088178467 0.258968649 1.401497992 0.123138978 -0.459447156
## [216] 0.969055774 -0.366388734 0.105886903 -1.790197437 -2.213064552
## [221] -1.829623640 -0.382433008 1.012658378 1.522319100 0.585286928
## [226] 0.338840031 -0.898890867 -0.963206785 0.175005356 -1.092063276
## [231] 2.079847233 0.082442445 1.351587368 -0.706903930 -0.741076476
## [236] -1.989888231 -1.054365055 -0.444397430 0.382142073 -0.400425306
## [241] -0.906653959 -1.286569399 0.822008000 -0.840198584 0.263663359
## [246] 1.148359012 0.552538887 -0.258813565 -1.269290648 -0.596352217
## [251] -0.580280541 -0.420841525 -0.794029503 -0.384196065 1.428357090
## [256] 0.605136385 2.004478714 1.009934847 0.787141448 -1.199905492
## [261] -1.202462056 -1.618058582 -0.461464139 1.025138179 2.841451105
## [266] 3.244931855 1.861728844 -0.881239146 -1.171281401 -1.120221160
## [271] 0.647427975 1.354057504 1.576328419 -0.544033797 0.702118963
## [276] -0.943864608 0.505965641 -0.123462073 0.562868856 0.240672395
## [281] -1.400705045 0.084310915 -0.319860104 0.330656581 0.243499802
## [286] 0.021905475 0.345521633 1.809677141 0.569899769 1.064952932
## [291] 1.104179799 1.622373803 2.267965844 0.513145857 2.458653396
## [296] 0.521213162 3.095021831 -0.564141426 0.600733619 0.447766394B. Menggunakan arima.sim
# Membuat data time series dari model MA(2) dengan parameter theta_1 = 0.4 dan theta_2 = 0.6 sebanyak n = 300 observasi
ma2_data <- arima.sim(list(order = c(0,0,2), ma = c(0.4, 0.6)), n = 300)
ma2_data## Time Series:
## Start = 1
## End = 300
## Frequency = 1
## [1] -1.668759603 -1.879542142 -1.421288067 -0.475192608 -2.144034549
## [6] -0.394996262 0.112940921 2.659432297 2.858210627 2.499789572
## [11] -0.643314898 -0.838134009 -1.628687379 0.201801295 -0.035489647
## [16] -0.878802820 1.117573456 0.829976398 1.612648214 1.859915494
## [21] -0.709072680 0.856175749 -1.061848830 0.871072750 -0.101071172
## [26] 1.018879244 1.552208727 0.921273564 1.821785242 -0.777036526
## [31] -0.586442872 0.517515514 0.552112393 -0.989737004 -1.958493796
## [36] -1.977729689 -0.032955473 0.123959897 1.102901812 1.147550413
## [41] 2.429169463 1.299841891 0.973057684 -1.740420082 -0.633156493
## [46] -1.584061436 -1.143153050 -0.912620099 0.358574931 -1.694714958
## [51] -0.615412779 -1.249923525 -1.102920229 0.046602285 0.009066556
## [56] 0.331877574 -2.232254705 1.565277173 -0.656254915 2.111948466
## [61] 0.411064249 1.524895800 1.391788635 0.732074548 0.784846172
## [66] -0.920017625 0.705660142 -0.685514433 2.746511825 -0.960962558
## [71] 0.325657211 -0.350844372 0.561892146 0.109799898 -0.926493629
## [76] -0.607925215 -0.554585577 -1.709318780 -0.690145876 -0.870118000
## [81] 0.271549164 -0.870988294 0.158962299 0.936013223 1.293344425
## [86] -0.125951827 -0.616139016 -0.509507651 -0.769991465 -2.208802416
## [91] -0.367035093 -1.770365085 -0.374800823 0.776789934 -0.516720848
## [96] 1.438413934 -1.386877221 -0.351376630 -0.971782708 -1.410799274
## [101] -1.146342446 -0.983931714 0.278310389 -1.399573088 -0.607555275
## [106] -0.373823183 -0.446099128 0.465612121 0.259859843 0.601101596
## [111] 1.055728828 0.299295420 -0.070805370 -2.882244754 -1.398406507
## [116] -1.192781082 0.651748108 -0.082947997 1.878630874 0.665058573
## [121] 1.308587372 1.494647775 -0.133769994 0.025634955 1.786237298
## [126] 0.699907005 3.076491584 -0.778401764 0.214221593 -0.560886804
## [131] 0.337098025 -0.658566499 -0.202972102 -1.673098699 0.293290629
## [136] 0.723404028 -1.363455665 0.996563438 -2.081759730 0.699767548
## [141] 0.097183648 0.336932789 -0.329128305 -0.212658458 0.117878735
## [146] 1.158022913 -1.435724635 -1.927332370 -0.455551556 0.636962223
## [151] 1.712181892 1.517271295 1.464419650 -1.864945787 0.596212928
## [156] -1.637430437 0.702788050 -0.493903627 0.892271932 -0.176781148
## [161] 0.902293759 -0.392366942 -0.937958941 0.538484640 0.569231890
## [166] 2.746628550 1.199398835 2.185621662 2.464512512 1.183687154
## [171] -0.250292526 -0.937421281 -1.103552534 -0.077546932 1.644552435
## [176] 0.449786401 1.269930085 -0.274168538 0.153179876 0.185627508
## [181] 1.466108187 0.841038854 1.558298489 1.136787984 1.654022675
## [186] 0.258830774 1.945987356 -0.074840985 0.717961865 1.133162557
## [191] 1.792233513 0.270071851 -0.532617406 -2.361302583 -0.885227031
## [196] -0.577267691 0.539159350 0.796708110 -0.162560948 -0.903161101
## [201] 0.268169912 0.565556170 -0.592670983 -0.248177284 -1.839506725
## [206] -2.486218670 -1.215748991 -1.261614299 -0.038981873 0.129677809
## [211] 0.910504621 0.688275095 -0.004717742 -0.858015086 -0.795584000
## [216] -0.183583682 -0.994755234 -0.414170818 0.269735501 0.168041492
## [221] -0.161372348 -0.620281490 0.585218077 0.830336278 2.125482512
## [226] 0.963794554 1.207919719 -0.310888159 0.628152962 -0.599259422
## [231] -1.259876520 -0.744033362 1.144709101 1.656050606 2.653129856
## [236] 1.305505683 0.234137145 -0.230350293 -0.719278756 -0.699343536
## [241] 0.352738508 -1.196916457 0.809921102 0.492280838 -0.333141685
## [246] 0.678534546 1.966850036 0.798570378 2.080154040 -0.778569438
## [251] 1.304773225 0.224788180 2.418272131 -0.648309740 0.356263057
## [256] -1.422826768 -0.438813671 -1.024639796 -1.204033999 -0.132562303
## [261] -1.356397913 1.396232071 -1.245142641 0.517015076 -0.138303004
## [266] 0.860578545 0.252741044 0.310844533 0.812016952 -1.024259059
## [271] -0.787567587 -0.866173121 -0.785664880 1.384332591 0.954386274
## [276] 1.163470694 -1.074938299 -0.533702650 -1.210630169 -0.213252726
## [281] -1.412347353 -0.035373555 -1.548428759 -0.342609731 -0.332436827
## [286] -0.766678646 0.498440588 -1.553423313 -2.986583996 -1.448848122
## [291] -0.659337784 0.329351302 0.894111981 -1.125773277 -0.287039464
## [296] -2.685927734 0.328284377 1.167472192 2.526685140 1.518204455Plot Time Series
Melihat pola data
# Membuat time series plot
ts.plot(ma2_data, main = "Plot Time Series MA(2)", ylab = "Yt")
Fluktuasi acak, cenderung tidak terlihat adanya tren sesuai dengan karakter MA
Plot ACF (Autocorrelation Function)
Mengidentifikasi keteganntungan antarlag
# Membuat plot fungsi ACF
acf(ma2_data, main = "Autocorrelation Function (ACF)")
Ada lag yang cut off di lag ke-2
Plot PACF (Partial Autocorrelation Function)
Menentukan orde AR
# Membuat plot fungsi PACF
pacf(ma2_data, main = "Partial Autocorrelation Function (PACF)")
Plot PACF untuk model MA(2) ini menunjukkan adanya tails off
Plot EACF (Extended Autocorrelation Function)
Mengidentifikasi model MA(q) vs AR(p)
# Mengitung EACF
library(TSA)##
## Attaching package: 'TSA'## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tareacf(ma2_data)## AR/MA
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13
## 0 x x o o o o o o o o o o o o
## 1 x x x o o o o o o o o o o o
## 2 x x x x o o o o o o o o o o
## 3 x x x o o o o o o o o o o o
## 4 x x x o o x o o o o o o o o
## 5 x x o o o x x o o o o o o o
## 6 x x o o x x x x o o o o o o
## 7 x x o x x x x x x o o o o oBerdasarkan pola segitiga nol pada plot EACF, terlihat bahwa segitiga nol berada pada ordo AR(0) dan ordo MA(2)
Scatter Plot
# Yt
yt_ma2 = ma2_data[-c(1:3)] # Buang 3 data awal agar sejajar dengan Yt-1, Yt-2, Yt-3
# Yt-1
yt_1_ma2 = ma2_data[-c(300, 1:2)] # buang 2 data awal + 1 data akhir
# Yt-2
yt_2_ma2 = ma2_data[-c((199):300, 1)] # buang 1 data awal + 2 data akhir
# Yt-3
yt_3_ma2 = ma2_data[-c((298):300)] # buang 3 data akhir# Perbandingan Yt dengan Yt-1
yt_ma2## [1] -0.475192608 -2.144034549 -0.394996262 0.112940921 2.659432297
## [6] 2.858210627 2.499789572 -0.643314898 -0.838134009 -1.628687379
## [11] 0.201801295 -0.035489647 -0.878802820 1.117573456 0.829976398
## [16] 1.612648214 1.859915494 -0.709072680 0.856175749 -1.061848830
## [21] 0.871072750 -0.101071172 1.018879244 1.552208727 0.921273564
## [26] 1.821785242 -0.777036526 -0.586442872 0.517515514 0.552112393
## [31] -0.989737004 -1.958493796 -1.977729689 -0.032955473 0.123959897
## [36] 1.102901812 1.147550413 2.429169463 1.299841891 0.973057684
## [41] -1.740420082 -0.633156493 -1.584061436 -1.143153050 -0.912620099
## [46] 0.358574931 -1.694714958 -0.615412779 -1.249923525 -1.102920229
## [51] 0.046602285 0.009066556 0.331877574 -2.232254705 1.565277173
## [56] -0.656254915 2.111948466 0.411064249 1.524895800 1.391788635
## [61] 0.732074548 0.784846172 -0.920017625 0.705660142 -0.685514433
## [66] 2.746511825 -0.960962558 0.325657211 -0.350844372 0.561892146
## [71] 0.109799898 -0.926493629 -0.607925215 -0.554585577 -1.709318780
## [76] -0.690145876 -0.870118000 0.271549164 -0.870988294 0.158962299
## [81] 0.936013223 1.293344425 -0.125951827 -0.616139016 -0.509507651
## [86] -0.769991465 -2.208802416 -0.367035093 -1.770365085 -0.374800823
## [91] 0.776789934 -0.516720848 1.438413934 -1.386877221 -0.351376630
## [96] -0.971782708 -1.410799274 -1.146342446 -0.983931714 0.278310389
## [101] -1.399573088 -0.607555275 -0.373823183 -0.446099128 0.465612121
## [106] 0.259859843 0.601101596 1.055728828 0.299295420 -0.070805370
## [111] -2.882244754 -1.398406507 -1.192781082 0.651748108 -0.082947997
## [116] 1.878630874 0.665058573 1.308587372 1.494647775 -0.133769994
## [121] 0.025634955 1.786237298 0.699907005 3.076491584 -0.778401764
## [126] 0.214221593 -0.560886804 0.337098025 -0.658566499 -0.202972102
## [131] -1.673098699 0.293290629 0.723404028 -1.363455665 0.996563438
## [136] -2.081759730 0.699767548 0.097183648 0.336932789 -0.329128305
## [141] -0.212658458 0.117878735 1.158022913 -1.435724635 -1.927332370
## [146] -0.455551556 0.636962223 1.712181892 1.517271295 1.464419650
## [151] -1.864945787 0.596212928 -1.637430437 0.702788050 -0.493903627
## [156] 0.892271932 -0.176781148 0.902293759 -0.392366942 -0.937958941
## [161] 0.538484640 0.569231890 2.746628550 1.199398835 2.185621662
## [166] 2.464512512 1.183687154 -0.250292526 -0.937421281 -1.103552534
## [171] -0.077546932 1.644552435 0.449786401 1.269930085 -0.274168538
## [176] 0.153179876 0.185627508 1.466108187 0.841038854 1.558298489
## [181] 1.136787984 1.654022675 0.258830774 1.945987356 -0.074840985
## [186] 0.717961865 1.133162557 1.792233513 0.270071851 -0.532617406
## [191] -2.361302583 -0.885227031 -0.577267691 0.539159350 0.796708110
## [196] -0.162560948 -0.903161101 0.268169912 0.565556170 -0.592670983
## [201] -0.248177284 -1.839506725 -2.486218670 -1.215748991 -1.261614299
## [206] -0.038981873 0.129677809 0.910504621 0.688275095 -0.004717742
## [211] -0.858015086 -0.795584000 -0.183583682 -0.994755234 -0.414170818
## [216] 0.269735501 0.168041492 -0.161372348 -0.620281490 0.585218077
## [221] 0.830336278 2.125482512 0.963794554 1.207919719 -0.310888159
## [226] 0.628152962 -0.599259422 -1.259876520 -0.744033362 1.144709101
## [231] 1.656050606 2.653129856 1.305505683 0.234137145 -0.230350293
## [236] -0.719278756 -0.699343536 0.352738508 -1.196916457 0.809921102
## [241] 0.492280838 -0.333141685 0.678534546 1.966850036 0.798570378
## [246] 2.080154040 -0.778569438 1.304773225 0.224788180 2.418272131
## [251] -0.648309740 0.356263057 -1.422826768 -0.438813671 -1.024639796
## [256] -1.204033999 -0.132562303 -1.356397913 1.396232071 -1.245142641
## [261] 0.517015076 -0.138303004 0.860578545 0.252741044 0.310844533
## [266] 0.812016952 -1.024259059 -0.787567587 -0.866173121 -0.785664880
## [271] 1.384332591 0.954386274 1.163470694 -1.074938299 -0.533702650
## [276] -1.210630169 -0.213252726 -1.412347353 -0.035373555 -1.548428759
## [281] -0.342609731 -0.332436827 -0.766678646 0.498440588 -1.553423313
## [286] -2.986583996 -1.448848122 -0.659337784 0.329351302 0.894111981
## [291] -1.125773277 -0.287039464 -2.685927734 0.328284377 1.167472192
## [296] 2.526685140 1.518204455yt_1_ma2## [1] -1.421288067 -0.475192608 -2.144034549 -0.394996262 0.112940921
## [6] 2.659432297 2.858210627 2.499789572 -0.643314898 -0.838134009
## [11] -1.628687379 0.201801295 -0.035489647 -0.878802820 1.117573456
## [16] 0.829976398 1.612648214 1.859915494 -0.709072680 0.856175749
## [21] -1.061848830 0.871072750 -0.101071172 1.018879244 1.552208727
## [26] 0.921273564 1.821785242 -0.777036526 -0.586442872 0.517515514
## [31] 0.552112393 -0.989737004 -1.958493796 -1.977729689 -0.032955473
## [36] 0.123959897 1.102901812 1.147550413 2.429169463 1.299841891
## [41] 0.973057684 -1.740420082 -0.633156493 -1.584061436 -1.143153050
## [46] -0.912620099 0.358574931 -1.694714958 -0.615412779 -1.249923525
## [51] -1.102920229 0.046602285 0.009066556 0.331877574 -2.232254705
## [56] 1.565277173 -0.656254915 2.111948466 0.411064249 1.524895800
## [61] 1.391788635 0.732074548 0.784846172 -0.920017625 0.705660142
## [66] -0.685514433 2.746511825 -0.960962558 0.325657211 -0.350844372
## [71] 0.561892146 0.109799898 -0.926493629 -0.607925215 -0.554585577
## [76] -1.709318780 -0.690145876 -0.870118000 0.271549164 -0.870988294
## [81] 0.158962299 0.936013223 1.293344425 -0.125951827 -0.616139016
## [86] -0.509507651 -0.769991465 -2.208802416 -0.367035093 -1.770365085
## [91] -0.374800823 0.776789934 -0.516720848 1.438413934 -1.386877221
## [96] -0.351376630 -0.971782708 -1.410799274 -1.146342446 -0.983931714
## [101] 0.278310389 -1.399573088 -0.607555275 -0.373823183 -0.446099128
## [106] 0.465612121 0.259859843 0.601101596 1.055728828 0.299295420
## [111] -0.070805370 -2.882244754 -1.398406507 -1.192781082 0.651748108
## [116] -0.082947997 1.878630874 0.665058573 1.308587372 1.494647775
## [121] -0.133769994 0.025634955 1.786237298 0.699907005 3.076491584
## [126] -0.778401764 0.214221593 -0.560886804 0.337098025 -0.658566499
## [131] -0.202972102 -1.673098699 0.293290629 0.723404028 -1.363455665
## [136] 0.996563438 -2.081759730 0.699767548 0.097183648 0.336932789
## [141] -0.329128305 -0.212658458 0.117878735 1.158022913 -1.435724635
## [146] -1.927332370 -0.455551556 0.636962223 1.712181892 1.517271295
## [151] 1.464419650 -1.864945787 0.596212928 -1.637430437 0.702788050
## [156] -0.493903627 0.892271932 -0.176781148 0.902293759 -0.392366942
## [161] -0.937958941 0.538484640 0.569231890 2.746628550 1.199398835
## [166] 2.185621662 2.464512512 1.183687154 -0.250292526 -0.937421281
## [171] -1.103552534 -0.077546932 1.644552435 0.449786401 1.269930085
## [176] -0.274168538 0.153179876 0.185627508 1.466108187 0.841038854
## [181] 1.558298489 1.136787984 1.654022675 0.258830774 1.945987356
## [186] -0.074840985 0.717961865 1.133162557 1.792233513 0.270071851
## [191] -0.532617406 -2.361302583 -0.885227031 -0.577267691 0.539159350
## [196] 0.796708110 -0.162560948 -0.903161101 0.268169912 0.565556170
## [201] -0.592670983 -0.248177284 -1.839506725 -2.486218670 -1.215748991
## [206] -1.261614299 -0.038981873 0.129677809 0.910504621 0.688275095
## [211] -0.004717742 -0.858015086 -0.795584000 -0.183583682 -0.994755234
## [216] -0.414170818 0.269735501 0.168041492 -0.161372348 -0.620281490
## [221] 0.585218077 0.830336278 2.125482512 0.963794554 1.207919719
## [226] -0.310888159 0.628152962 -0.599259422 -1.259876520 -0.744033362
## [231] 1.144709101 1.656050606 2.653129856 1.305505683 0.234137145
## [236] -0.230350293 -0.719278756 -0.699343536 0.352738508 -1.196916457
## [241] 0.809921102 0.492280838 -0.333141685 0.678534546 1.966850036
## [246] 0.798570378 2.080154040 -0.778569438 1.304773225 0.224788180
## [251] 2.418272131 -0.648309740 0.356263057 -1.422826768 -0.438813671
## [256] -1.024639796 -1.204033999 -0.132562303 -1.356397913 1.396232071
## [261] -1.245142641 0.517015076 -0.138303004 0.860578545 0.252741044
## [266] 0.310844533 0.812016952 -1.024259059 -0.787567587 -0.866173121
## [271] -0.785664880 1.384332591 0.954386274 1.163470694 -1.074938299
## [276] -0.533702650 -1.210630169 -0.213252726 -1.412347353 -0.035373555
## [281] -1.548428759 -0.342609731 -0.332436827 -0.766678646 0.498440588
## [286] -1.553423313 -2.986583996 -1.448848122 -0.659337784 0.329351302
## [291] 0.894111981 -1.125773277 -0.287039464 -2.685927734 0.328284377
## [296] 1.167472192 2.526685140# Perbandingan Yt dengan Yt-2
yt_ma2## [1] -0.475192608 -2.144034549 -0.394996262 0.112940921 2.659432297
## [6] 2.858210627 2.499789572 -0.643314898 -0.838134009 -1.628687379
## [11] 0.201801295 -0.035489647 -0.878802820 1.117573456 0.829976398
## [16] 1.612648214 1.859915494 -0.709072680 0.856175749 -1.061848830
## [21] 0.871072750 -0.101071172 1.018879244 1.552208727 0.921273564
## [26] 1.821785242 -0.777036526 -0.586442872 0.517515514 0.552112393
## [31] -0.989737004 -1.958493796 -1.977729689 -0.032955473 0.123959897
## [36] 1.102901812 1.147550413 2.429169463 1.299841891 0.973057684
## [41] -1.740420082 -0.633156493 -1.584061436 -1.143153050 -0.912620099
## [46] 0.358574931 -1.694714958 -0.615412779 -1.249923525 -1.102920229
## [51] 0.046602285 0.009066556 0.331877574 -2.232254705 1.565277173
## [56] -0.656254915 2.111948466 0.411064249 1.524895800 1.391788635
## [61] 0.732074548 0.784846172 -0.920017625 0.705660142 -0.685514433
## [66] 2.746511825 -0.960962558 0.325657211 -0.350844372 0.561892146
## [71] 0.109799898 -0.926493629 -0.607925215 -0.554585577 -1.709318780
## [76] -0.690145876 -0.870118000 0.271549164 -0.870988294 0.158962299
## [81] 0.936013223 1.293344425 -0.125951827 -0.616139016 -0.509507651
## [86] -0.769991465 -2.208802416 -0.367035093 -1.770365085 -0.374800823
## [91] 0.776789934 -0.516720848 1.438413934 -1.386877221 -0.351376630
## [96] -0.971782708 -1.410799274 -1.146342446 -0.983931714 0.278310389
## [101] -1.399573088 -0.607555275 -0.373823183 -0.446099128 0.465612121
## [106] 0.259859843 0.601101596 1.055728828 0.299295420 -0.070805370
## [111] -2.882244754 -1.398406507 -1.192781082 0.651748108 -0.082947997
## [116] 1.878630874 0.665058573 1.308587372 1.494647775 -0.133769994
## [121] 0.025634955 1.786237298 0.699907005 3.076491584 -0.778401764
## [126] 0.214221593 -0.560886804 0.337098025 -0.658566499 -0.202972102
## [131] -1.673098699 0.293290629 0.723404028 -1.363455665 0.996563438
## [136] -2.081759730 0.699767548 0.097183648 0.336932789 -0.329128305
## [141] -0.212658458 0.117878735 1.158022913 -1.435724635 -1.927332370
## [146] -0.455551556 0.636962223 1.712181892 1.517271295 1.464419650
## [151] -1.864945787 0.596212928 -1.637430437 0.702788050 -0.493903627
## [156] 0.892271932 -0.176781148 0.902293759 -0.392366942 -0.937958941
## [161] 0.538484640 0.569231890 2.746628550 1.199398835 2.185621662
## [166] 2.464512512 1.183687154 -0.250292526 -0.937421281 -1.103552534
## [171] -0.077546932 1.644552435 0.449786401 1.269930085 -0.274168538
## [176] 0.153179876 0.185627508 1.466108187 0.841038854 1.558298489
## [181] 1.136787984 1.654022675 0.258830774 1.945987356 -0.074840985
## [186] 0.717961865 1.133162557 1.792233513 0.270071851 -0.532617406
## [191] -2.361302583 -0.885227031 -0.577267691 0.539159350 0.796708110
## [196] -0.162560948 -0.903161101 0.268169912 0.565556170 -0.592670983
## [201] -0.248177284 -1.839506725 -2.486218670 -1.215748991 -1.261614299
## [206] -0.038981873 0.129677809 0.910504621 0.688275095 -0.004717742
## [211] -0.858015086 -0.795584000 -0.183583682 -0.994755234 -0.414170818
## [216] 0.269735501 0.168041492 -0.161372348 -0.620281490 0.585218077
## [221] 0.830336278 2.125482512 0.963794554 1.207919719 -0.310888159
## [226] 0.628152962 -0.599259422 -1.259876520 -0.744033362 1.144709101
## [231] 1.656050606 2.653129856 1.305505683 0.234137145 -0.230350293
## [236] -0.719278756 -0.699343536 0.352738508 -1.196916457 0.809921102
## [241] 0.492280838 -0.333141685 0.678534546 1.966850036 0.798570378
## [246] 2.080154040 -0.778569438 1.304773225 0.224788180 2.418272131
## [251] -0.648309740 0.356263057 -1.422826768 -0.438813671 -1.024639796
## [256] -1.204033999 -0.132562303 -1.356397913 1.396232071 -1.245142641
## [261] 0.517015076 -0.138303004 0.860578545 0.252741044 0.310844533
## [266] 0.812016952 -1.024259059 -0.787567587 -0.866173121 -0.785664880
## [271] 1.384332591 0.954386274 1.163470694 -1.074938299 -0.533702650
## [276] -1.210630169 -0.213252726 -1.412347353 -0.035373555 -1.548428759
## [281] -0.342609731 -0.332436827 -0.766678646 0.498440588 -1.553423313
## [286] -2.986583996 -1.448848122 -0.659337784 0.329351302 0.894111981
## [291] -1.125773277 -0.287039464 -2.685927734 0.328284377 1.167472192
## [296] 2.526685140 1.518204455yt_2_ma2## [1] -1.879542142 -1.421288067 -0.475192608 -2.144034549 -0.394996262
## [6] 0.112940921 2.659432297 2.858210627 2.499789572 -0.643314898
## [11] -0.838134009 -1.628687379 0.201801295 -0.035489647 -0.878802820
## [16] 1.117573456 0.829976398 1.612648214 1.859915494 -0.709072680
## [21] 0.856175749 -1.061848830 0.871072750 -0.101071172 1.018879244
## [26] 1.552208727 0.921273564 1.821785242 -0.777036526 -0.586442872
## [31] 0.517515514 0.552112393 -0.989737004 -1.958493796 -1.977729689
## [36] -0.032955473 0.123959897 1.102901812 1.147550413 2.429169463
## [41] 1.299841891 0.973057684 -1.740420082 -0.633156493 -1.584061436
## [46] -1.143153050 -0.912620099 0.358574931 -1.694714958 -0.615412779
## [51] -1.249923525 -1.102920229 0.046602285 0.009066556 0.331877574
## [56] -2.232254705 1.565277173 -0.656254915 2.111948466 0.411064249
## [61] 1.524895800 1.391788635 0.732074548 0.784846172 -0.920017625
## [66] 0.705660142 -0.685514433 2.746511825 -0.960962558 0.325657211
## [71] -0.350844372 0.561892146 0.109799898 -0.926493629 -0.607925215
## [76] -0.554585577 -1.709318780 -0.690145876 -0.870118000 0.271549164
## [81] -0.870988294 0.158962299 0.936013223 1.293344425 -0.125951827
## [86] -0.616139016 -0.509507651 -0.769991465 -2.208802416 -0.367035093
## [91] -1.770365085 -0.374800823 0.776789934 -0.516720848 1.438413934
## [96] -1.386877221 -0.351376630 -0.971782708 -1.410799274 -1.146342446
## [101] -0.983931714 0.278310389 -1.399573088 -0.607555275 -0.373823183
## [106] -0.446099128 0.465612121 0.259859843 0.601101596 1.055728828
## [111] 0.299295420 -0.070805370 -2.882244754 -1.398406507 -1.192781082
## [116] 0.651748108 -0.082947997 1.878630874 0.665058573 1.308587372
## [121] 1.494647775 -0.133769994 0.025634955 1.786237298 0.699907005
## [126] 3.076491584 -0.778401764 0.214221593 -0.560886804 0.337098025
## [131] -0.658566499 -0.202972102 -1.673098699 0.293290629 0.723404028
## [136] -1.363455665 0.996563438 -2.081759730 0.699767548 0.097183648
## [141] 0.336932789 -0.329128305 -0.212658458 0.117878735 1.158022913
## [146] -1.435724635 -1.927332370 -0.455551556 0.636962223 1.712181892
## [151] 1.517271295 1.464419650 -1.864945787 0.596212928 -1.637430437
## [156] 0.702788050 -0.493903627 0.892271932 -0.176781148 0.902293759
## [161] -0.392366942 -0.937958941 0.538484640 0.569231890 2.746628550
## [166] 1.199398835 2.185621662 2.464512512 1.183687154 -0.250292526
## [171] -0.937421281 -1.103552534 -0.077546932 1.644552435 0.449786401
## [176] 1.269930085 -0.274168538 0.153179876 0.185627508 1.466108187
## [181] 0.841038854 1.558298489 1.136787984 1.654022675 0.258830774
## [186] 1.945987356 -0.074840985 0.717961865 1.133162557 1.792233513
## [191] 0.270071851 -0.532617406 -2.361302583 -0.885227031 -0.577267691
## [196] 0.539159350 0.796708110# Perbandingan Yt dengan Yt-3
yt_ma2## [1] -0.475192608 -2.144034549 -0.394996262 0.112940921 2.659432297
## [6] 2.858210627 2.499789572 -0.643314898 -0.838134009 -1.628687379
## [11] 0.201801295 -0.035489647 -0.878802820 1.117573456 0.829976398
## [16] 1.612648214 1.859915494 -0.709072680 0.856175749 -1.061848830
## [21] 0.871072750 -0.101071172 1.018879244 1.552208727 0.921273564
## [26] 1.821785242 -0.777036526 -0.586442872 0.517515514 0.552112393
## [31] -0.989737004 -1.958493796 -1.977729689 -0.032955473 0.123959897
## [36] 1.102901812 1.147550413 2.429169463 1.299841891 0.973057684
## [41] -1.740420082 -0.633156493 -1.584061436 -1.143153050 -0.912620099
## [46] 0.358574931 -1.694714958 -0.615412779 -1.249923525 -1.102920229
## [51] 0.046602285 0.009066556 0.331877574 -2.232254705 1.565277173
## [56] -0.656254915 2.111948466 0.411064249 1.524895800 1.391788635
## [61] 0.732074548 0.784846172 -0.920017625 0.705660142 -0.685514433
## [66] 2.746511825 -0.960962558 0.325657211 -0.350844372 0.561892146
## [71] 0.109799898 -0.926493629 -0.607925215 -0.554585577 -1.709318780
## [76] -0.690145876 -0.870118000 0.271549164 -0.870988294 0.158962299
## [81] 0.936013223 1.293344425 -0.125951827 -0.616139016 -0.509507651
## [86] -0.769991465 -2.208802416 -0.367035093 -1.770365085 -0.374800823
## [91] 0.776789934 -0.516720848 1.438413934 -1.386877221 -0.351376630
## [96] -0.971782708 -1.410799274 -1.146342446 -0.983931714 0.278310389
## [101] -1.399573088 -0.607555275 -0.373823183 -0.446099128 0.465612121
## [106] 0.259859843 0.601101596 1.055728828 0.299295420 -0.070805370
## [111] -2.882244754 -1.398406507 -1.192781082 0.651748108 -0.082947997
## [116] 1.878630874 0.665058573 1.308587372 1.494647775 -0.133769994
## [121] 0.025634955 1.786237298 0.699907005 3.076491584 -0.778401764
## [126] 0.214221593 -0.560886804 0.337098025 -0.658566499 -0.202972102
## [131] -1.673098699 0.293290629 0.723404028 -1.363455665 0.996563438
## [136] -2.081759730 0.699767548 0.097183648 0.336932789 -0.329128305
## [141] -0.212658458 0.117878735 1.158022913 -1.435724635 -1.927332370
## [146] -0.455551556 0.636962223 1.712181892 1.517271295 1.464419650
## [151] -1.864945787 0.596212928 -1.637430437 0.702788050 -0.493903627
## [156] 0.892271932 -0.176781148 0.902293759 -0.392366942 -0.937958941
## [161] 0.538484640 0.569231890 2.746628550 1.199398835 2.185621662
## [166] 2.464512512 1.183687154 -0.250292526 -0.937421281 -1.103552534
## [171] -0.077546932 1.644552435 0.449786401 1.269930085 -0.274168538
## [176] 0.153179876 0.185627508 1.466108187 0.841038854 1.558298489
## [181] 1.136787984 1.654022675 0.258830774 1.945987356 -0.074840985
## [186] 0.717961865 1.133162557 1.792233513 0.270071851 -0.532617406
## [191] -2.361302583 -0.885227031 -0.577267691 0.539159350 0.796708110
## [196] -0.162560948 -0.903161101 0.268169912 0.565556170 -0.592670983
## [201] -0.248177284 -1.839506725 -2.486218670 -1.215748991 -1.261614299
## [206] -0.038981873 0.129677809 0.910504621 0.688275095 -0.004717742
## [211] -0.858015086 -0.795584000 -0.183583682 -0.994755234 -0.414170818
## [216] 0.269735501 0.168041492 -0.161372348 -0.620281490 0.585218077
## [221] 0.830336278 2.125482512 0.963794554 1.207919719 -0.310888159
## [226] 0.628152962 -0.599259422 -1.259876520 -0.744033362 1.144709101
## [231] 1.656050606 2.653129856 1.305505683 0.234137145 -0.230350293
## [236] -0.719278756 -0.699343536 0.352738508 -1.196916457 0.809921102
## [241] 0.492280838 -0.333141685 0.678534546 1.966850036 0.798570378
## [246] 2.080154040 -0.778569438 1.304773225 0.224788180 2.418272131
## [251] -0.648309740 0.356263057 -1.422826768 -0.438813671 -1.024639796
## [256] -1.204033999 -0.132562303 -1.356397913 1.396232071 -1.245142641
## [261] 0.517015076 -0.138303004 0.860578545 0.252741044 0.310844533
## [266] 0.812016952 -1.024259059 -0.787567587 -0.866173121 -0.785664880
## [271] 1.384332591 0.954386274 1.163470694 -1.074938299 -0.533702650
## [276] -1.210630169 -0.213252726 -1.412347353 -0.035373555 -1.548428759
## [281] -0.342609731 -0.332436827 -0.766678646 0.498440588 -1.553423313
## [286] -2.986583996 -1.448848122 -0.659337784 0.329351302 0.894111981
## [291] -1.125773277 -0.287039464 -2.685927734 0.328284377 1.167472192
## [296] 2.526685140 1.518204455yt_3_ma2## [1] -1.668759603 -1.879542142 -1.421288067 -0.475192608 -2.144034549
## [6] -0.394996262 0.112940921 2.659432297 2.858210627 2.499789572
## [11] -0.643314898 -0.838134009 -1.628687379 0.201801295 -0.035489647
## [16] -0.878802820 1.117573456 0.829976398 1.612648214 1.859915494
## [21] -0.709072680 0.856175749 -1.061848830 0.871072750 -0.101071172
## [26] 1.018879244 1.552208727 0.921273564 1.821785242 -0.777036526
## [31] -0.586442872 0.517515514 0.552112393 -0.989737004 -1.958493796
## [36] -1.977729689 -0.032955473 0.123959897 1.102901812 1.147550413
## [41] 2.429169463 1.299841891 0.973057684 -1.740420082 -0.633156493
## [46] -1.584061436 -1.143153050 -0.912620099 0.358574931 -1.694714958
## [51] -0.615412779 -1.249923525 -1.102920229 0.046602285 0.009066556
## [56] 0.331877574 -2.232254705 1.565277173 -0.656254915 2.111948466
## [61] 0.411064249 1.524895800 1.391788635 0.732074548 0.784846172
## [66] -0.920017625 0.705660142 -0.685514433 2.746511825 -0.960962558
## [71] 0.325657211 -0.350844372 0.561892146 0.109799898 -0.926493629
## [76] -0.607925215 -0.554585577 -1.709318780 -0.690145876 -0.870118000
## [81] 0.271549164 -0.870988294 0.158962299 0.936013223 1.293344425
## [86] -0.125951827 -0.616139016 -0.509507651 -0.769991465 -2.208802416
## [91] -0.367035093 -1.770365085 -0.374800823 0.776789934 -0.516720848
## [96] 1.438413934 -1.386877221 -0.351376630 -0.971782708 -1.410799274
## [101] -1.146342446 -0.983931714 0.278310389 -1.399573088 -0.607555275
## [106] -0.373823183 -0.446099128 0.465612121 0.259859843 0.601101596
## [111] 1.055728828 0.299295420 -0.070805370 -2.882244754 -1.398406507
## [116] -1.192781082 0.651748108 -0.082947997 1.878630874 0.665058573
## [121] 1.308587372 1.494647775 -0.133769994 0.025634955 1.786237298
## [126] 0.699907005 3.076491584 -0.778401764 0.214221593 -0.560886804
## [131] 0.337098025 -0.658566499 -0.202972102 -1.673098699 0.293290629
## [136] 0.723404028 -1.363455665 0.996563438 -2.081759730 0.699767548
## [141] 0.097183648 0.336932789 -0.329128305 -0.212658458 0.117878735
## [146] 1.158022913 -1.435724635 -1.927332370 -0.455551556 0.636962223
## [151] 1.712181892 1.517271295 1.464419650 -1.864945787 0.596212928
## [156] -1.637430437 0.702788050 -0.493903627 0.892271932 -0.176781148
## [161] 0.902293759 -0.392366942 -0.937958941 0.538484640 0.569231890
## [166] 2.746628550 1.199398835 2.185621662 2.464512512 1.183687154
## [171] -0.250292526 -0.937421281 -1.103552534 -0.077546932 1.644552435
## [176] 0.449786401 1.269930085 -0.274168538 0.153179876 0.185627508
## [181] 1.466108187 0.841038854 1.558298489 1.136787984 1.654022675
## [186] 0.258830774 1.945987356 -0.074840985 0.717961865 1.133162557
## [191] 1.792233513 0.270071851 -0.532617406 -2.361302583 -0.885227031
## [196] -0.577267691 0.539159350 0.796708110 -0.162560948 -0.903161101
## [201] 0.268169912 0.565556170 -0.592670983 -0.248177284 -1.839506725
## [206] -2.486218670 -1.215748991 -1.261614299 -0.038981873 0.129677809
## [211] 0.910504621 0.688275095 -0.004717742 -0.858015086 -0.795584000
## [216] -0.183583682 -0.994755234 -0.414170818 0.269735501 0.168041492
## [221] -0.161372348 -0.620281490 0.585218077 0.830336278 2.125482512
## [226] 0.963794554 1.207919719 -0.310888159 0.628152962 -0.599259422
## [231] -1.259876520 -0.744033362 1.144709101 1.656050606 2.653129856
## [236] 1.305505683 0.234137145 -0.230350293 -0.719278756 -0.699343536
## [241] 0.352738508 -1.196916457 0.809921102 0.492280838 -0.333141685
## [246] 0.678534546 1.966850036 0.798570378 2.080154040 -0.778569438
## [251] 1.304773225 0.224788180 2.418272131 -0.648309740 0.356263057
## [256] -1.422826768 -0.438813671 -1.024639796 -1.204033999 -0.132562303
## [261] -1.356397913 1.396232071 -1.245142641 0.517015076 -0.138303004
## [266] 0.860578545 0.252741044 0.310844533 0.812016952 -1.024259059
## [271] -0.787567587 -0.866173121 -0.785664880 1.384332591 0.954386274
## [276] 1.163470694 -1.074938299 -0.533702650 -1.210630169 -0.213252726
## [281] -1.412347353 -0.035373555 -1.548428759 -0.342609731 -0.332436827
## [286] -0.766678646 0.498440588 -1.553423313 -2.986583996 -1.448848122
## [291] -0.659337784 0.329351302 0.894111981 -1.125773277 -0.287039464
## [296] -2.685927734 0.328284377# Scatterplot Yt vs Yt-1
plot(ma2_data[-300], ma2_data[-1], main = "Scatterplot Yt vs Yt-1", xlab = "Yt-1", ylab = "Yt")
# Scatterplot Yt vs Yt-2
plot(ma2_data[-c(299:300)], ma2_data[-c(1:2)], main = "Scatterplot Yt vs Yt-2", xlab = "Yt-2", ylab = "Yt")
# Scatterplot Yt vs Yt-3
plot(ma2_data[-c(298:300)], ma2_data[-c(1:3)], main = "Scatterplot Yt vs Yt-3", xlab = "Yt-3", ylab = "Yt")
Hitung Autokorelasi dari hasil simulasi
acf_values <- acf(ma2_data, plot = FALSE)
acf_values$acf[1:5] # Menampilkan dari lag 1 sampai lag 5 ## [1] 0.31992344 0.34346072 -0.11124814 -0.05630001 -0.08545317Hitung Autokorelasi teoritis untuk MA(2)
Rumus: \(\rho_k\) = \(\gamma_k\) / \(\gamma_0\), dengan
\(\gamma_0\) = (1 + \(\theta_1^2\)+ \(\theta_2^2\)) * \(\sigma^2\)
\(\gamma_1\) = ( \(\theta_1\) + \(\theta_1\theta_2\)) \(\sigma^2\)
\(\gamma_2\) = \(\theta_{2}\) * \(\sigma^2\)
\(\gamma_k\) = 0 untuk k > 2
# Hitung theta
theta1 = 0.4
theta2 = 0.6
sigma2 = 1# Hitung gamma
gamma0 = (1 + theta1^2 + theta2^2) * sigma2 # Varians dari proses
gamma1 = (theta1 + theta1*theta2) * sigma2 # Kovarians lag 1
gamma2 = theta2 * sigma2 # Kovarians lag 2# Hitung rho
rho1 = gamma1 / gamma0
rho2 = gamma2 / gamma0
rho3 = 0# Tampilkan hasil autokorelasi teoritis untuk MA(2)
c(rho1, rho2, rho3)## [1] 0.4210526 0.3947368 0.0000000Hasil ACF, PACF, dan EACF menunnjukkan bahwa hasil simulai model MA(2) itu stationer karena
ACF cut off setelah lag 2
PACF tails off
EACF menunjukkan pola sesuai dengan MA(2) yaitu segitiga nol berada pada ordo AR(0)
2. AR(2)
A. Menggunakan Teknik Manual
\[ Y_t = e_t+0.5Y_{t-1}+0.2Y_{t-2} \]
Bangkitkan data dari set.seed
Bangkitkan data AR(2) dengan \(\phi_1 = 0.4\) dan \(\phi_2 = 0.6\) sebanyak 300 data menggunakan fungsi arima.sim
set.seed(1234)White Noise
set.seed(1234)
n = 300
wn = rnorm(n) # white noise
y_ar2 = numeric(n) # kosongkan vektor
# Bangkitkan AR(2): Yt = 0.5*Yt-1 + 0.2*Yt-2 + wn[t]
y_ar2 [1:2] = wn[1:2] # nilai awal
for (t in 3:n) {
y_ar2[t] <- 0.5*y_ar2[t-1] + 0.2*y_ar2[t-2] + wn[t]
}
y_ar2## [1] -1.207065749 0.277429242 0.981742648 -1.799340530 -0.274197047
## [6] 0.009089263 -0.625034738 -0.857331372 -1.118124633 -1.620566420
## [11] -1.511100836 -2.078050147 -2.117499135 -1.409900780 -0.168956158
## [16] -0.476743729 -0.783172602 -1.398130464 -1.692871432 1.289773370
## [21] 0.440400618 -0.012530914 -0.358733205 0.277716656 -0.626608560
## [26] -1.705965859 -0.403548921 -1.566623355 -0.879159762 -1.688853153
## [31] 0.082039017 -0.772344201 -1.079204335 -1.195329068 -2.442598870
## [36] -2.627984511 -3.982551678 -3.857865933 -3.019737161 -2.747339308
## [41] -0.528120821 -1.882170996 -1.902074296 -1.608094349 -2.178802110
## [46] -2.379534243 -2.732845736 -3.094315602 -2.617555067 -2.424490611
## [51] -3.541787576 -2.837867835 -3.236181057 -3.200626105 -2.409858787
## [56] -1.281998796 0.524846317 -0.767330024 1.327213880 -0.647667612
## [61] 0.598197434 2.718556265 1.444157230 0.596156288 0.579304834
## [66] 2.185968123 0.070237292 1.840139450 2.263681974 1.836341674
## [71] 1.377800070 0.600699632 0.209385897 0.873119442 2.548707762
## [76] 1.295579357 -0.233169716 -0.581050764 -0.078897563 -0.472718049
## [81] -0.429928495 -0.479501934 -1.698038552 -1.118706833 -0.048728870
## [86] 0.449502910 0.765003032 0.069670123 -0.003758103 -1.182472906
## [91] -0.645146892 -0.303872027 1.424998615 1.653238155 0.616035357
## [96] 0.994215607 -0.514293169 0.819900164 1.280008202 2.925101239
## [101] 2.133075794 1.176839671 1.081028488 0.273404396 -0.473090691
## [106] -0.014875187 -0.998320358 -0.333949829 -0.011670725 -0.124730445
## [111] -0.260633986 -0.804332834 -1.564060446 -0.093622587 -0.337260856
## [116] 0.643785672 -0.989847187 -0.197140045 0.376626847 0.122609038
## [121] -0.054762280 -0.784765979 1.654826542 1.420961528 2.865654375
## [126] 1.797079134 0.840261143 -0.733741722 -0.834918463 -0.337906043
## [131] 0.677753633 0.524045743 -0.774374715 0.386336120 -1.611807818
## [136] -1.094488933 -1.185724359 -2.760006013 -0.697090356 -1.523417976
## [141] -1.235163709 0.472882443 0.626082891 0.299186237 0.788572475
## [146] 0.853395292 2.247268589 1.570206756 1.740829719 1.532008186
## [151] 0.736932389 0.772487295 2.172374770 0.365092370 0.738781138
## [156] 1.804539704 0.815404992 -0.284772371 -0.849088793 -0.871625900
## [161] -1.452980782 -1.161454963 -1.285743344 -1.058213462 -0.379199302
## [166] 0.223390785 1.714061276 0.833015141 0.438479913 1.856848702
## [171] 2.720449731 1.774838644 1.098851949 -0.917841714 1.172111931
## [176] -0.435094811 -1.106887814 2.403303017 1.215295254 1.055049620
## [181] -1.961635662 -0.869598495 0.148905355 0.314401894 1.099304179
## [186] 2.596264669 2.687101684 1.354066761 1.918633896 1.031714026
## [191] 0.361513003 -2.468659348 -1.951673926 -0.981754197 1.286820656
## [196] 0.947754103 1.351451386 -0.100626697 0.382631637 -1.907047063
## [201] -0.391770383 0.119474174 0.166896926 0.808076813 0.749098821
## [206] 1.296627135 2.640596958 2.691986747 1.906776723 0.377336746
## [211] 0.988081540 0.169272882 1.775745851 -0.685353438 -0.403279337
## [216] 0.083298017 -0.190743395 -0.684863209 -0.685301353 0.149912782
## [221] 0.833068101 1.106729238 2.993461760 2.891574300 2.332189230
## [226] 1.084639381 3.927897667 2.858292210 1.530405295 1.523353172
## [231] 0.743364345 0.401648589 -0.584006177 -0.094828026 0.154944990
## [236] -1.019035233 -3.711680751 -2.314522075 -1.870079357 -0.803670320
## [241] -0.716715863 -0.105693101 -1.293961898 0.043055688 0.481624195
## [246] 0.501074304 1.704136427 1.356751546 1.283567328 1.181177877
## [251] 1.284232981 1.938475972 1.678274979 1.890031299 0.144297091
## [256] 0.079657288 1.545657652 -0.435143467 0.349628185 0.492788204
## [261] 1.292123061 0.395742435 0.614921269 -1.376645945 -0.226742672
## [266] -1.055265554 -0.811627936 -1.804632361 -0.679706446 -0.034200180
## [271] -0.457655268 1.589343394 1.373700014 1.953351259 3.300818634
## [276] 1.389965960 2.163765979 2.346456796 1.599810798 1.588249116
## [281] 0.102264815 0.838949778 -0.261042480 0.850951578 -0.438163491
## [286] 0.270506057 -0.798902323 -0.591113129 -2.008196040 -0.993886613
## [291] 0.086860875 0.027900638 -1.734906719 -1.482406929 0.567858229
## [296] 1.797253114 -0.162838565 -0.088671919 0.276721777 0.439782725B. Menggunakan arima.sim
ar2 = arima.sim(list(order = c(2,0,0), ar = c(0.5, 0.2)), n = 300)
ar2## Time Series:
## Start = 1
## End = 300
## Frequency = 1
## [1] -1.51198789 0.14622636 -1.18196985 0.56474307 -0.60306545 0.10388597
## [7] 0.83003262 -0.08294885 0.67897065 0.23492188 -0.88195786 -0.66407416
## [13] 1.11136122 0.20873461 -0.49114292 -0.25784746 0.10298930 0.95524977
## [19] 1.64218262 1.11266366 2.04934360 0.48294459 -1.69317239 -1.22168070
## [25] -1.46533032 -3.29303745 -1.37711303 -2.13093915 -1.56694617 -2.79676390
## [31] -1.16424698 0.74975075 -0.73605113 -0.33063433 1.63618567 1.68578230
## [37] 3.08318771 1.87351626 1.40113562 0.56563940 1.99762053 -0.17390039
## [43] 0.61988813 0.22884545 2.49024215 0.68285644 -0.66981152 0.03429730
## [49] -0.15646235 -0.91049678 -0.35424977 -0.63474899 -1.06698309 -0.15960541
## [55] -0.62486164 -2.17933215 -3.86637965 -2.94963843 -0.79390827 -0.14875244
## [61] 0.98189570 1.44370281 1.23399457 -0.60132478 0.15170631 1.55281629
## [67] -2.58931413 -1.76544609 -0.29812123 0.02659519 0.74306775 0.83395242
## [73] 1.10442287 0.73364504 -0.32878204 -1.24447710 -0.65184209 -0.99620958
## [79] -1.52783762 -0.54571941 -0.42498249 1.14164792 -0.63567504 -0.60729602
## [85] -0.50573010 -1.78211434 -1.27690906 -1.70304857 -3.25454510 -2.25171943
## [91] -2.31084090 -0.47275414 -1.30261417 -0.18834632 -0.21206670 -1.38056283
## [97] -0.35855078 -0.56147408 -0.18638521 0.45254743 0.30295959 1.82714845
## [103] 1.08971958 -0.34370956 0.78795392 -0.89766657 -2.21013663 -2.09453802
## [109] -2.23397357 -2.14340031 0.08826470 1.25105173 1.36926990 -0.33898963
## [115] 0.12750572 0.48307617 0.13001173 0.33336658 -0.75210828 -1.59700113
## [121] 0.45884352 0.17739422 -0.22793183 0.24678415 2.14028668 1.48216713
## [127] 2.58054554 2.95425051 1.58605822 2.14642094 0.73922129 -0.67476095
## [133] -1.39120201 -0.97927367 1.02918519 0.42354658 -0.38522765 0.12247046
## [139] 0.68216489 -0.92962519 -1.38305984 -2.81906245 -2.95570378 -2.92910319
## [145] -2.34760812 -0.34953064 0.24435449 0.32524543 -0.35514785 -0.15273178
## [151] 0.40021679 -0.33447128 0.97187785 1.51649823 -0.21387994 -0.55055164
## [157] 0.88868693 -1.35298674 -0.07904609 -0.07662163 3.14178116 -1.17411409
## [163] -0.79949661 0.03945755 1.53415596 1.61465657 -0.31420896 2.40521501
## [169] -0.61750051 -0.94072334 -0.63700216 1.71894116 1.23838673 1.69337765
## [175] 2.82244377 2.73467738 0.70708957 1.61020648 0.83730116 2.52329977
## [181] 1.18566544 -0.42961435 0.51416028 0.52566093 0.34803618 -0.77740005
## [187] -1.15800745 -0.74710945 0.43295393 -0.29740264 -0.93356001 -3.23046356
## [193] -1.30769394 -0.87259936 0.61135239 1.59787897 0.77815390 2.00716647
## [199] 1.16052756 0.30528700 -0.46344759 -0.51760749 -0.12401382 -0.19292981
## [205] 0.07961012 0.20016177 0.83060226 0.18215171 1.89254377 1.42039611
## [211] -0.10482904 -0.04498510 0.47242469 -0.18384001 0.34755998 0.57140785
## [217] 1.65869361 0.29193246 0.46082409 -0.27889392 -1.17441501 -2.49195660
## [223] -1.28533225 -0.53949222 0.11234560 -1.44171846 -1.82806796 -2.34353187
## [229] -2.22605103 -1.41153407 -0.55649381 -1.37558637 -3.66343878 -1.15301318
## [235] -0.69390958 -1.27842813 -1.85165732 -1.48150548 -1.00297764 -0.07458915
## [241] 1.15220499 -0.28769873 0.37731448 1.46529352 -0.09323250 0.02367904
## [247] -1.77827501 -0.59697944 -1.29533649 -1.69200177 -1.88504565 -0.83641981
## [253] -2.95768804 -2.07163888 -2.64107471 -2.69698416 -1.40207239 -0.88867876
## [259] -0.83177421 -0.05610560 -0.79651254 -2.43277504 -0.22126875 -0.82788238
## [265] -0.82328371 -0.41970040 0.39142528 0.53785953 1.27448022 0.79094661
## [271] 0.14608371 -0.06921823 0.81752360 -0.45435064 -1.01728070 -0.28603176
## [277] 0.26600129 -1.61528894 0.03025442 -0.29600544 -0.32320713 0.88614975
## [283] 1.85782832 -0.04125533 1.36259238 0.04097593 0.42536776 0.70180513
## [289] 0.56915374 -1.03792656 -0.91153431 0.87631077 0.42864214 -0.44624070
## [295] -0.79332063 0.57165763 0.47324818 -0.54623092 -0.17220061 0.40132402Plot Simulasi AR(2)
# Plot Simulasi AR(2)
ts.plot(ar2, main = "Simulasi AR(2)", ylab = "Yt")
Plot ACF (Autocorrelation Function)
# Plot ACF
acf(ar2, main = "ACF AR(2)")
Plot ACF untuk model AR(2) menunjukkan bahwa adanya tails off
Plot PACF (Partial Autocorrelation Function)
# Plot PACF
pacf(ar2, main = "PACF AR(2)")
Plot PACF untuk model AR(2) menunjukkan adanya cut off pada lag 1
Plot EACF (Extended Autocorrelation Function)
# Menghitung EACF
library(TSA)
eacf(ar2)## AR/MA
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13
## 0 x x x x o o o o o o o o o o
## 1 x o o x o o o o o o o o o o
## 2 x o o x o o o o o o o o o o
## 3 x x o o o o o o o o o o o o
## 4 x x x x o o o o o o o o o o
## 5 o x o x o o o o o o o o o o
## 6 o x x o x o o o o o o o o o
## 7 x o o o x x o o o o o o o oBerdasarkan pola segitiga nol pada plot EACF, terlihat bahwa segitiga nol berada pada ordo AR(2) dan ordo MA(0).
Scatterplot
# Buat lag
yt_ar2 = ar2[4:n] # Yt
yt_1_ar2 = ar2[3:(n-1)] # Yt-1
yt_2_ar2 = ar2[2:(n-2)] # Yt-2
yt_3_ar2 = ar2[1:(n-3)] # Yt-3# Perbandingan Yt dengan Yt-1
yt_ar2## [1] 0.56474307 -0.60306545 0.10388597 0.83003262 -0.08294885 0.67897065
## [7] 0.23492188 -0.88195786 -0.66407416 1.11136122 0.20873461 -0.49114292
## [13] -0.25784746 0.10298930 0.95524977 1.64218262 1.11266366 2.04934360
## [19] 0.48294459 -1.69317239 -1.22168070 -1.46533032 -3.29303745 -1.37711303
## [25] -2.13093915 -1.56694617 -2.79676390 -1.16424698 0.74975075 -0.73605113
## [31] -0.33063433 1.63618567 1.68578230 3.08318771 1.87351626 1.40113562
## [37] 0.56563940 1.99762053 -0.17390039 0.61988813 0.22884545 2.49024215
## [43] 0.68285644 -0.66981152 0.03429730 -0.15646235 -0.91049678 -0.35424977
## [49] -0.63474899 -1.06698309 -0.15960541 -0.62486164 -2.17933215 -3.86637965
## [55] -2.94963843 -0.79390827 -0.14875244 0.98189570 1.44370281 1.23399457
## [61] -0.60132478 0.15170631 1.55281629 -2.58931413 -1.76544609 -0.29812123
## [67] 0.02659519 0.74306775 0.83395242 1.10442287 0.73364504 -0.32878204
## [73] -1.24447710 -0.65184209 -0.99620958 -1.52783762 -0.54571941 -0.42498249
## [79] 1.14164792 -0.63567504 -0.60729602 -0.50573010 -1.78211434 -1.27690906
## [85] -1.70304857 -3.25454510 -2.25171943 -2.31084090 -0.47275414 -1.30261417
## [91] -0.18834632 -0.21206670 -1.38056283 -0.35855078 -0.56147408 -0.18638521
## [97] 0.45254743 0.30295959 1.82714845 1.08971958 -0.34370956 0.78795392
## [103] -0.89766657 -2.21013663 -2.09453802 -2.23397357 -2.14340031 0.08826470
## [109] 1.25105173 1.36926990 -0.33898963 0.12750572 0.48307617 0.13001173
## [115] 0.33336658 -0.75210828 -1.59700113 0.45884352 0.17739422 -0.22793183
## [121] 0.24678415 2.14028668 1.48216713 2.58054554 2.95425051 1.58605822
## [127] 2.14642094 0.73922129 -0.67476095 -1.39120201 -0.97927367 1.02918519
## [133] 0.42354658 -0.38522765 0.12247046 0.68216489 -0.92962519 -1.38305984
## [139] -2.81906245 -2.95570378 -2.92910319 -2.34760812 -0.34953064 0.24435449
## [145] 0.32524543 -0.35514785 -0.15273178 0.40021679 -0.33447128 0.97187785
## [151] 1.51649823 -0.21387994 -0.55055164 0.88868693 -1.35298674 -0.07904609
## [157] -0.07662163 3.14178116 -1.17411409 -0.79949661 0.03945755 1.53415596
## [163] 1.61465657 -0.31420896 2.40521501 -0.61750051 -0.94072334 -0.63700216
## [169] 1.71894116 1.23838673 1.69337765 2.82244377 2.73467738 0.70708957
## [175] 1.61020648 0.83730116 2.52329977 1.18566544 -0.42961435 0.51416028
## [181] 0.52566093 0.34803618 -0.77740005 -1.15800745 -0.74710945 0.43295393
## [187] -0.29740264 -0.93356001 -3.23046356 -1.30769394 -0.87259936 0.61135239
## [193] 1.59787897 0.77815390 2.00716647 1.16052756 0.30528700 -0.46344759
## [199] -0.51760749 -0.12401382 -0.19292981 0.07961012 0.20016177 0.83060226
## [205] 0.18215171 1.89254377 1.42039611 -0.10482904 -0.04498510 0.47242469
## [211] -0.18384001 0.34755998 0.57140785 1.65869361 0.29193246 0.46082409
## [217] -0.27889392 -1.17441501 -2.49195660 -1.28533225 -0.53949222 0.11234560
## [223] -1.44171846 -1.82806796 -2.34353187 -2.22605103 -1.41153407 -0.55649381
## [229] -1.37558637 -3.66343878 -1.15301318 -0.69390958 -1.27842813 -1.85165732
## [235] -1.48150548 -1.00297764 -0.07458915 1.15220499 -0.28769873 0.37731448
## [241] 1.46529352 -0.09323250 0.02367904 -1.77827501 -0.59697944 -1.29533649
## [247] -1.69200177 -1.88504565 -0.83641981 -2.95768804 -2.07163888 -2.64107471
## [253] -2.69698416 -1.40207239 -0.88867876 -0.83177421 -0.05610560 -0.79651254
## [259] -2.43277504 -0.22126875 -0.82788238 -0.82328371 -0.41970040 0.39142528
## [265] 0.53785953 1.27448022 0.79094661 0.14608371 -0.06921823 0.81752360
## [271] -0.45435064 -1.01728070 -0.28603176 0.26600129 -1.61528894 0.03025442
## [277] -0.29600544 -0.32320713 0.88614975 1.85782832 -0.04125533 1.36259238
## [283] 0.04097593 0.42536776 0.70180513 0.56915374 -1.03792656 -0.91153431
## [289] 0.87631077 0.42864214 -0.44624070 -0.79332063 0.57165763 0.47324818
## [295] -0.54623092 -0.17220061 0.40132402yt_1_ar2## [1] -1.18196985 0.56474307 -0.60306545 0.10388597 0.83003262 -0.08294885
## [7] 0.67897065 0.23492188 -0.88195786 -0.66407416 1.11136122 0.20873461
## [13] -0.49114292 -0.25784746 0.10298930 0.95524977 1.64218262 1.11266366
## [19] 2.04934360 0.48294459 -1.69317239 -1.22168070 -1.46533032 -3.29303745
## [25] -1.37711303 -2.13093915 -1.56694617 -2.79676390 -1.16424698 0.74975075
## [31] -0.73605113 -0.33063433 1.63618567 1.68578230 3.08318771 1.87351626
## [37] 1.40113562 0.56563940 1.99762053 -0.17390039 0.61988813 0.22884545
## [43] 2.49024215 0.68285644 -0.66981152 0.03429730 -0.15646235 -0.91049678
## [49] -0.35424977 -0.63474899 -1.06698309 -0.15960541 -0.62486164 -2.17933215
## [55] -3.86637965 -2.94963843 -0.79390827 -0.14875244 0.98189570 1.44370281
## [61] 1.23399457 -0.60132478 0.15170631 1.55281629 -2.58931413 -1.76544609
## [67] -0.29812123 0.02659519 0.74306775 0.83395242 1.10442287 0.73364504
## [73] -0.32878204 -1.24447710 -0.65184209 -0.99620958 -1.52783762 -0.54571941
## [79] -0.42498249 1.14164792 -0.63567504 -0.60729602 -0.50573010 -1.78211434
## [85] -1.27690906 -1.70304857 -3.25454510 -2.25171943 -2.31084090 -0.47275414
## [91] -1.30261417 -0.18834632 -0.21206670 -1.38056283 -0.35855078 -0.56147408
## [97] -0.18638521 0.45254743 0.30295959 1.82714845 1.08971958 -0.34370956
## [103] 0.78795392 -0.89766657 -2.21013663 -2.09453802 -2.23397357 -2.14340031
## [109] 0.08826470 1.25105173 1.36926990 -0.33898963 0.12750572 0.48307617
## [115] 0.13001173 0.33336658 -0.75210828 -1.59700113 0.45884352 0.17739422
## [121] -0.22793183 0.24678415 2.14028668 1.48216713 2.58054554 2.95425051
## [127] 1.58605822 2.14642094 0.73922129 -0.67476095 -1.39120201 -0.97927367
## [133] 1.02918519 0.42354658 -0.38522765 0.12247046 0.68216489 -0.92962519
## [139] -1.38305984 -2.81906245 -2.95570378 -2.92910319 -2.34760812 -0.34953064
## [145] 0.24435449 0.32524543 -0.35514785 -0.15273178 0.40021679 -0.33447128
## [151] 0.97187785 1.51649823 -0.21387994 -0.55055164 0.88868693 -1.35298674
## [157] -0.07904609 -0.07662163 3.14178116 -1.17411409 -0.79949661 0.03945755
## [163] 1.53415596 1.61465657 -0.31420896 2.40521501 -0.61750051 -0.94072334
## [169] -0.63700216 1.71894116 1.23838673 1.69337765 2.82244377 2.73467738
## [175] 0.70708957 1.61020648 0.83730116 2.52329977 1.18566544 -0.42961435
## [181] 0.51416028 0.52566093 0.34803618 -0.77740005 -1.15800745 -0.74710945
## [187] 0.43295393 -0.29740264 -0.93356001 -3.23046356 -1.30769394 -0.87259936
## [193] 0.61135239 1.59787897 0.77815390 2.00716647 1.16052756 0.30528700
## [199] -0.46344759 -0.51760749 -0.12401382 -0.19292981 0.07961012 0.20016177
## [205] 0.83060226 0.18215171 1.89254377 1.42039611 -0.10482904 -0.04498510
## [211] 0.47242469 -0.18384001 0.34755998 0.57140785 1.65869361 0.29193246
## [217] 0.46082409 -0.27889392 -1.17441501 -2.49195660 -1.28533225 -0.53949222
## [223] 0.11234560 -1.44171846 -1.82806796 -2.34353187 -2.22605103 -1.41153407
## [229] -0.55649381 -1.37558637 -3.66343878 -1.15301318 -0.69390958 -1.27842813
## [235] -1.85165732 -1.48150548 -1.00297764 -0.07458915 1.15220499 -0.28769873
## [241] 0.37731448 1.46529352 -0.09323250 0.02367904 -1.77827501 -0.59697944
## [247] -1.29533649 -1.69200177 -1.88504565 -0.83641981 -2.95768804 -2.07163888
## [253] -2.64107471 -2.69698416 -1.40207239 -0.88867876 -0.83177421 -0.05610560
## [259] -0.79651254 -2.43277504 -0.22126875 -0.82788238 -0.82328371 -0.41970040
## [265] 0.39142528 0.53785953 1.27448022 0.79094661 0.14608371 -0.06921823
## [271] 0.81752360 -0.45435064 -1.01728070 -0.28603176 0.26600129 -1.61528894
## [277] 0.03025442 -0.29600544 -0.32320713 0.88614975 1.85782832 -0.04125533
## [283] 1.36259238 0.04097593 0.42536776 0.70180513 0.56915374 -1.03792656
## [289] -0.91153431 0.87631077 0.42864214 -0.44624070 -0.79332063 0.57165763
## [295] 0.47324818 -0.54623092 -0.17220061# Perbandingan Yt dengan Yt-2
yt_ar2## [1] 0.56474307 -0.60306545 0.10388597 0.83003262 -0.08294885 0.67897065
## [7] 0.23492188 -0.88195786 -0.66407416 1.11136122 0.20873461 -0.49114292
## [13] -0.25784746 0.10298930 0.95524977 1.64218262 1.11266366 2.04934360
## [19] 0.48294459 -1.69317239 -1.22168070 -1.46533032 -3.29303745 -1.37711303
## [25] -2.13093915 -1.56694617 -2.79676390 -1.16424698 0.74975075 -0.73605113
## [31] -0.33063433 1.63618567 1.68578230 3.08318771 1.87351626 1.40113562
## [37] 0.56563940 1.99762053 -0.17390039 0.61988813 0.22884545 2.49024215
## [43] 0.68285644 -0.66981152 0.03429730 -0.15646235 -0.91049678 -0.35424977
## [49] -0.63474899 -1.06698309 -0.15960541 -0.62486164 -2.17933215 -3.86637965
## [55] -2.94963843 -0.79390827 -0.14875244 0.98189570 1.44370281 1.23399457
## [61] -0.60132478 0.15170631 1.55281629 -2.58931413 -1.76544609 -0.29812123
## [67] 0.02659519 0.74306775 0.83395242 1.10442287 0.73364504 -0.32878204
## [73] -1.24447710 -0.65184209 -0.99620958 -1.52783762 -0.54571941 -0.42498249
## [79] 1.14164792 -0.63567504 -0.60729602 -0.50573010 -1.78211434 -1.27690906
## [85] -1.70304857 -3.25454510 -2.25171943 -2.31084090 -0.47275414 -1.30261417
## [91] -0.18834632 -0.21206670 -1.38056283 -0.35855078 -0.56147408 -0.18638521
## [97] 0.45254743 0.30295959 1.82714845 1.08971958 -0.34370956 0.78795392
## [103] -0.89766657 -2.21013663 -2.09453802 -2.23397357 -2.14340031 0.08826470
## [109] 1.25105173 1.36926990 -0.33898963 0.12750572 0.48307617 0.13001173
## [115] 0.33336658 -0.75210828 -1.59700113 0.45884352 0.17739422 -0.22793183
## [121] 0.24678415 2.14028668 1.48216713 2.58054554 2.95425051 1.58605822
## [127] 2.14642094 0.73922129 -0.67476095 -1.39120201 -0.97927367 1.02918519
## [133] 0.42354658 -0.38522765 0.12247046 0.68216489 -0.92962519 -1.38305984
## [139] -2.81906245 -2.95570378 -2.92910319 -2.34760812 -0.34953064 0.24435449
## [145] 0.32524543 -0.35514785 -0.15273178 0.40021679 -0.33447128 0.97187785
## [151] 1.51649823 -0.21387994 -0.55055164 0.88868693 -1.35298674 -0.07904609
## [157] -0.07662163 3.14178116 -1.17411409 -0.79949661 0.03945755 1.53415596
## [163] 1.61465657 -0.31420896 2.40521501 -0.61750051 -0.94072334 -0.63700216
## [169] 1.71894116 1.23838673 1.69337765 2.82244377 2.73467738 0.70708957
## [175] 1.61020648 0.83730116 2.52329977 1.18566544 -0.42961435 0.51416028
## [181] 0.52566093 0.34803618 -0.77740005 -1.15800745 -0.74710945 0.43295393
## [187] -0.29740264 -0.93356001 -3.23046356 -1.30769394 -0.87259936 0.61135239
## [193] 1.59787897 0.77815390 2.00716647 1.16052756 0.30528700 -0.46344759
## [199] -0.51760749 -0.12401382 -0.19292981 0.07961012 0.20016177 0.83060226
## [205] 0.18215171 1.89254377 1.42039611 -0.10482904 -0.04498510 0.47242469
## [211] -0.18384001 0.34755998 0.57140785 1.65869361 0.29193246 0.46082409
## [217] -0.27889392 -1.17441501 -2.49195660 -1.28533225 -0.53949222 0.11234560
## [223] -1.44171846 -1.82806796 -2.34353187 -2.22605103 -1.41153407 -0.55649381
## [229] -1.37558637 -3.66343878 -1.15301318 -0.69390958 -1.27842813 -1.85165732
## [235] -1.48150548 -1.00297764 -0.07458915 1.15220499 -0.28769873 0.37731448
## [241] 1.46529352 -0.09323250 0.02367904 -1.77827501 -0.59697944 -1.29533649
## [247] -1.69200177 -1.88504565 -0.83641981 -2.95768804 -2.07163888 -2.64107471
## [253] -2.69698416 -1.40207239 -0.88867876 -0.83177421 -0.05610560 -0.79651254
## [259] -2.43277504 -0.22126875 -0.82788238 -0.82328371 -0.41970040 0.39142528
## [265] 0.53785953 1.27448022 0.79094661 0.14608371 -0.06921823 0.81752360
## [271] -0.45435064 -1.01728070 -0.28603176 0.26600129 -1.61528894 0.03025442
## [277] -0.29600544 -0.32320713 0.88614975 1.85782832 -0.04125533 1.36259238
## [283] 0.04097593 0.42536776 0.70180513 0.56915374 -1.03792656 -0.91153431
## [289] 0.87631077 0.42864214 -0.44624070 -0.79332063 0.57165763 0.47324818
## [295] -0.54623092 -0.17220061 0.40132402yt_2_ar2## [1] 0.14622636 -1.18196985 0.56474307 -0.60306545 0.10388597 0.83003262
## [7] -0.08294885 0.67897065 0.23492188 -0.88195786 -0.66407416 1.11136122
## [13] 0.20873461 -0.49114292 -0.25784746 0.10298930 0.95524977 1.64218262
## [19] 1.11266366 2.04934360 0.48294459 -1.69317239 -1.22168070 -1.46533032
## [25] -3.29303745 -1.37711303 -2.13093915 -1.56694617 -2.79676390 -1.16424698
## [31] 0.74975075 -0.73605113 -0.33063433 1.63618567 1.68578230 3.08318771
## [37] 1.87351626 1.40113562 0.56563940 1.99762053 -0.17390039 0.61988813
## [43] 0.22884545 2.49024215 0.68285644 -0.66981152 0.03429730 -0.15646235
## [49] -0.91049678 -0.35424977 -0.63474899 -1.06698309 -0.15960541 -0.62486164
## [55] -2.17933215 -3.86637965 -2.94963843 -0.79390827 -0.14875244 0.98189570
## [61] 1.44370281 1.23399457 -0.60132478 0.15170631 1.55281629 -2.58931413
## [67] -1.76544609 -0.29812123 0.02659519 0.74306775 0.83395242 1.10442287
## [73] 0.73364504 -0.32878204 -1.24447710 -0.65184209 -0.99620958 -1.52783762
## [79] -0.54571941 -0.42498249 1.14164792 -0.63567504 -0.60729602 -0.50573010
## [85] -1.78211434 -1.27690906 -1.70304857 -3.25454510 -2.25171943 -2.31084090
## [91] -0.47275414 -1.30261417 -0.18834632 -0.21206670 -1.38056283 -0.35855078
## [97] -0.56147408 -0.18638521 0.45254743 0.30295959 1.82714845 1.08971958
## [103] -0.34370956 0.78795392 -0.89766657 -2.21013663 -2.09453802 -2.23397357
## [109] -2.14340031 0.08826470 1.25105173 1.36926990 -0.33898963 0.12750572
## [115] 0.48307617 0.13001173 0.33336658 -0.75210828 -1.59700113 0.45884352
## [121] 0.17739422 -0.22793183 0.24678415 2.14028668 1.48216713 2.58054554
## [127] 2.95425051 1.58605822 2.14642094 0.73922129 -0.67476095 -1.39120201
## [133] -0.97927367 1.02918519 0.42354658 -0.38522765 0.12247046 0.68216489
## [139] -0.92962519 -1.38305984 -2.81906245 -2.95570378 -2.92910319 -2.34760812
## [145] -0.34953064 0.24435449 0.32524543 -0.35514785 -0.15273178 0.40021679
## [151] -0.33447128 0.97187785 1.51649823 -0.21387994 -0.55055164 0.88868693
## [157] -1.35298674 -0.07904609 -0.07662163 3.14178116 -1.17411409 -0.79949661
## [163] 0.03945755 1.53415596 1.61465657 -0.31420896 2.40521501 -0.61750051
## [169] -0.94072334 -0.63700216 1.71894116 1.23838673 1.69337765 2.82244377
## [175] 2.73467738 0.70708957 1.61020648 0.83730116 2.52329977 1.18566544
## [181] -0.42961435 0.51416028 0.52566093 0.34803618 -0.77740005 -1.15800745
## [187] -0.74710945 0.43295393 -0.29740264 -0.93356001 -3.23046356 -1.30769394
## [193] -0.87259936 0.61135239 1.59787897 0.77815390 2.00716647 1.16052756
## [199] 0.30528700 -0.46344759 -0.51760749 -0.12401382 -0.19292981 0.07961012
## [205] 0.20016177 0.83060226 0.18215171 1.89254377 1.42039611 -0.10482904
## [211] -0.04498510 0.47242469 -0.18384001 0.34755998 0.57140785 1.65869361
## [217] 0.29193246 0.46082409 -0.27889392 -1.17441501 -2.49195660 -1.28533225
## [223] -0.53949222 0.11234560 -1.44171846 -1.82806796 -2.34353187 -2.22605103
## [229] -1.41153407 -0.55649381 -1.37558637 -3.66343878 -1.15301318 -0.69390958
## [235] -1.27842813 -1.85165732 -1.48150548 -1.00297764 -0.07458915 1.15220499
## [241] -0.28769873 0.37731448 1.46529352 -0.09323250 0.02367904 -1.77827501
## [247] -0.59697944 -1.29533649 -1.69200177 -1.88504565 -0.83641981 -2.95768804
## [253] -2.07163888 -2.64107471 -2.69698416 -1.40207239 -0.88867876 -0.83177421
## [259] -0.05610560 -0.79651254 -2.43277504 -0.22126875 -0.82788238 -0.82328371
## [265] -0.41970040 0.39142528 0.53785953 1.27448022 0.79094661 0.14608371
## [271] -0.06921823 0.81752360 -0.45435064 -1.01728070 -0.28603176 0.26600129
## [277] -1.61528894 0.03025442 -0.29600544 -0.32320713 0.88614975 1.85782832
## [283] -0.04125533 1.36259238 0.04097593 0.42536776 0.70180513 0.56915374
## [289] -1.03792656 -0.91153431 0.87631077 0.42864214 -0.44624070 -0.79332063
## [295] 0.57165763 0.47324818 -0.54623092# Perbandingan Yt dengan Yt-3
yt_ar2## [1] 0.56474307 -0.60306545 0.10388597 0.83003262 -0.08294885 0.67897065
## [7] 0.23492188 -0.88195786 -0.66407416 1.11136122 0.20873461 -0.49114292
## [13] -0.25784746 0.10298930 0.95524977 1.64218262 1.11266366 2.04934360
## [19] 0.48294459 -1.69317239 -1.22168070 -1.46533032 -3.29303745 -1.37711303
## [25] -2.13093915 -1.56694617 -2.79676390 -1.16424698 0.74975075 -0.73605113
## [31] -0.33063433 1.63618567 1.68578230 3.08318771 1.87351626 1.40113562
## [37] 0.56563940 1.99762053 -0.17390039 0.61988813 0.22884545 2.49024215
## [43] 0.68285644 -0.66981152 0.03429730 -0.15646235 -0.91049678 -0.35424977
## [49] -0.63474899 -1.06698309 -0.15960541 -0.62486164 -2.17933215 -3.86637965
## [55] -2.94963843 -0.79390827 -0.14875244 0.98189570 1.44370281 1.23399457
## [61] -0.60132478 0.15170631 1.55281629 -2.58931413 -1.76544609 -0.29812123
## [67] 0.02659519 0.74306775 0.83395242 1.10442287 0.73364504 -0.32878204
## [73] -1.24447710 -0.65184209 -0.99620958 -1.52783762 -0.54571941 -0.42498249
## [79] 1.14164792 -0.63567504 -0.60729602 -0.50573010 -1.78211434 -1.27690906
## [85] -1.70304857 -3.25454510 -2.25171943 -2.31084090 -0.47275414 -1.30261417
## [91] -0.18834632 -0.21206670 -1.38056283 -0.35855078 -0.56147408 -0.18638521
## [97] 0.45254743 0.30295959 1.82714845 1.08971958 -0.34370956 0.78795392
## [103] -0.89766657 -2.21013663 -2.09453802 -2.23397357 -2.14340031 0.08826470
## [109] 1.25105173 1.36926990 -0.33898963 0.12750572 0.48307617 0.13001173
## [115] 0.33336658 -0.75210828 -1.59700113 0.45884352 0.17739422 -0.22793183
## [121] 0.24678415 2.14028668 1.48216713 2.58054554 2.95425051 1.58605822
## [127] 2.14642094 0.73922129 -0.67476095 -1.39120201 -0.97927367 1.02918519
## [133] 0.42354658 -0.38522765 0.12247046 0.68216489 -0.92962519 -1.38305984
## [139] -2.81906245 -2.95570378 -2.92910319 -2.34760812 -0.34953064 0.24435449
## [145] 0.32524543 -0.35514785 -0.15273178 0.40021679 -0.33447128 0.97187785
## [151] 1.51649823 -0.21387994 -0.55055164 0.88868693 -1.35298674 -0.07904609
## [157] -0.07662163 3.14178116 -1.17411409 -0.79949661 0.03945755 1.53415596
## [163] 1.61465657 -0.31420896 2.40521501 -0.61750051 -0.94072334 -0.63700216
## [169] 1.71894116 1.23838673 1.69337765 2.82244377 2.73467738 0.70708957
## [175] 1.61020648 0.83730116 2.52329977 1.18566544 -0.42961435 0.51416028
## [181] 0.52566093 0.34803618 -0.77740005 -1.15800745 -0.74710945 0.43295393
## [187] -0.29740264 -0.93356001 -3.23046356 -1.30769394 -0.87259936 0.61135239
## [193] 1.59787897 0.77815390 2.00716647 1.16052756 0.30528700 -0.46344759
## [199] -0.51760749 -0.12401382 -0.19292981 0.07961012 0.20016177 0.83060226
## [205] 0.18215171 1.89254377 1.42039611 -0.10482904 -0.04498510 0.47242469
## [211] -0.18384001 0.34755998 0.57140785 1.65869361 0.29193246 0.46082409
## [217] -0.27889392 -1.17441501 -2.49195660 -1.28533225 -0.53949222 0.11234560
## [223] -1.44171846 -1.82806796 -2.34353187 -2.22605103 -1.41153407 -0.55649381
## [229] -1.37558637 -3.66343878 -1.15301318 -0.69390958 -1.27842813 -1.85165732
## [235] -1.48150548 -1.00297764 -0.07458915 1.15220499 -0.28769873 0.37731448
## [241] 1.46529352 -0.09323250 0.02367904 -1.77827501 -0.59697944 -1.29533649
## [247] -1.69200177 -1.88504565 -0.83641981 -2.95768804 -2.07163888 -2.64107471
## [253] -2.69698416 -1.40207239 -0.88867876 -0.83177421 -0.05610560 -0.79651254
## [259] -2.43277504 -0.22126875 -0.82788238 -0.82328371 -0.41970040 0.39142528
## [265] 0.53785953 1.27448022 0.79094661 0.14608371 -0.06921823 0.81752360
## [271] -0.45435064 -1.01728070 -0.28603176 0.26600129 -1.61528894 0.03025442
## [277] -0.29600544 -0.32320713 0.88614975 1.85782832 -0.04125533 1.36259238
## [283] 0.04097593 0.42536776 0.70180513 0.56915374 -1.03792656 -0.91153431
## [289] 0.87631077 0.42864214 -0.44624070 -0.79332063 0.57165763 0.47324818
## [295] -0.54623092 -0.17220061 0.40132402yt_3_ar2## [1] -1.51198789 0.14622636 -1.18196985 0.56474307 -0.60306545 0.10388597
## [7] 0.83003262 -0.08294885 0.67897065 0.23492188 -0.88195786 -0.66407416
## [13] 1.11136122 0.20873461 -0.49114292 -0.25784746 0.10298930 0.95524977
## [19] 1.64218262 1.11266366 2.04934360 0.48294459 -1.69317239 -1.22168070
## [25] -1.46533032 -3.29303745 -1.37711303 -2.13093915 -1.56694617 -2.79676390
## [31] -1.16424698 0.74975075 -0.73605113 -0.33063433 1.63618567 1.68578230
## [37] 3.08318771 1.87351626 1.40113562 0.56563940 1.99762053 -0.17390039
## [43] 0.61988813 0.22884545 2.49024215 0.68285644 -0.66981152 0.03429730
## [49] -0.15646235 -0.91049678 -0.35424977 -0.63474899 -1.06698309 -0.15960541
## [55] -0.62486164 -2.17933215 -3.86637965 -2.94963843 -0.79390827 -0.14875244
## [61] 0.98189570 1.44370281 1.23399457 -0.60132478 0.15170631 1.55281629
## [67] -2.58931413 -1.76544609 -0.29812123 0.02659519 0.74306775 0.83395242
## [73] 1.10442287 0.73364504 -0.32878204 -1.24447710 -0.65184209 -0.99620958
## [79] -1.52783762 -0.54571941 -0.42498249 1.14164792 -0.63567504 -0.60729602
## [85] -0.50573010 -1.78211434 -1.27690906 -1.70304857 -3.25454510 -2.25171943
## [91] -2.31084090 -0.47275414 -1.30261417 -0.18834632 -0.21206670 -1.38056283
## [97] -0.35855078 -0.56147408 -0.18638521 0.45254743 0.30295959 1.82714845
## [103] 1.08971958 -0.34370956 0.78795392 -0.89766657 -2.21013663 -2.09453802
## [109] -2.23397357 -2.14340031 0.08826470 1.25105173 1.36926990 -0.33898963
## [115] 0.12750572 0.48307617 0.13001173 0.33336658 -0.75210828 -1.59700113
## [121] 0.45884352 0.17739422 -0.22793183 0.24678415 2.14028668 1.48216713
## [127] 2.58054554 2.95425051 1.58605822 2.14642094 0.73922129 -0.67476095
## [133] -1.39120201 -0.97927367 1.02918519 0.42354658 -0.38522765 0.12247046
## [139] 0.68216489 -0.92962519 -1.38305984 -2.81906245 -2.95570378 -2.92910319
## [145] -2.34760812 -0.34953064 0.24435449 0.32524543 -0.35514785 -0.15273178
## [151] 0.40021679 -0.33447128 0.97187785 1.51649823 -0.21387994 -0.55055164
## [157] 0.88868693 -1.35298674 -0.07904609 -0.07662163 3.14178116 -1.17411409
## [163] -0.79949661 0.03945755 1.53415596 1.61465657 -0.31420896 2.40521501
## [169] -0.61750051 -0.94072334 -0.63700216 1.71894116 1.23838673 1.69337765
## [175] 2.82244377 2.73467738 0.70708957 1.61020648 0.83730116 2.52329977
## [181] 1.18566544 -0.42961435 0.51416028 0.52566093 0.34803618 -0.77740005
## [187] -1.15800745 -0.74710945 0.43295393 -0.29740264 -0.93356001 -3.23046356
## [193] -1.30769394 -0.87259936 0.61135239 1.59787897 0.77815390 2.00716647
## [199] 1.16052756 0.30528700 -0.46344759 -0.51760749 -0.12401382 -0.19292981
## [205] 0.07961012 0.20016177 0.83060226 0.18215171 1.89254377 1.42039611
## [211] -0.10482904 -0.04498510 0.47242469 -0.18384001 0.34755998 0.57140785
## [217] 1.65869361 0.29193246 0.46082409 -0.27889392 -1.17441501 -2.49195660
## [223] -1.28533225 -0.53949222 0.11234560 -1.44171846 -1.82806796 -2.34353187
## [229] -2.22605103 -1.41153407 -0.55649381 -1.37558637 -3.66343878 -1.15301318
## [235] -0.69390958 -1.27842813 -1.85165732 -1.48150548 -1.00297764 -0.07458915
## [241] 1.15220499 -0.28769873 0.37731448 1.46529352 -0.09323250 0.02367904
## [247] -1.77827501 -0.59697944 -1.29533649 -1.69200177 -1.88504565 -0.83641981
## [253] -2.95768804 -2.07163888 -2.64107471 -2.69698416 -1.40207239 -0.88867876
## [259] -0.83177421 -0.05610560 -0.79651254 -2.43277504 -0.22126875 -0.82788238
## [265] -0.82328371 -0.41970040 0.39142528 0.53785953 1.27448022 0.79094661
## [271] 0.14608371 -0.06921823 0.81752360 -0.45435064 -1.01728070 -0.28603176
## [277] 0.26600129 -1.61528894 0.03025442 -0.29600544 -0.32320713 0.88614975
## [283] 1.85782832 -0.04125533 1.36259238 0.04097593 0.42536776 0.70180513
## [289] 0.56915374 -1.03792656 -0.91153431 0.87631077 0.42864214 -0.44624070
## [295] -0.79332063 0.57165763 0.47324818par(mfrow=c(1,3))# Scatterplot Yt vs Yt-1
plot(yt_ar2, yt_1_ar2, main="Scatterplot Yt vs Yt-1", xlab="Yt", ylab="Yt-1")
# Scatterplot Yt vs Yt-2
plot(yt_ar2, yt_2_ar2, main="Scatterplot Yt vs Yt-2", xlab="Yt", ylab="Yt-2")
# Scatterplot Yt vs Yt-3
plot(yt_ar2, yt_3_ar2, main="Scatterplot Yt vs Yt-3", xlab="Yt", ylab="Yt-3")
Autokorelasi dari data bangkitan
\(\rho_k\) = \(\phi_1\)\(\rho_{k-1}\)+\(\phi_2\)\(\rho_{k-2}\)
\(\rho_1\) = \(\phi_1\)/1 - \(\phi_2\) ; \(\rho_2\) = \(\phi1\)\(\rho_2\)+\(\rho_2\)
phi1 = 0.5
phi2 = 0.2
rho_theo = numeric(20) # simpan beberapa lag
# rho0
rho_theo[1] = 1
# rho1
rho_theo[2] = phi1 / (1 - phi2)
# rho2
rho_theo[3] = phi1 * rho_theo[2] + phi2
# rekursi untuk rho_k (k>=3)
for (k in 4:20) {
rho_theo[k] <- phi1 * rho_theo[k-1] + phi2 * rho_theo[k-2]
}
# tampilkan rho1..rho6
rho_theo[2:7]## [1] 0.6250000 0.5125000 0.3812500 0.2931250 0.2228125 0.1700312Autokorelasi dari data empiris
acf_emp = acf(ar2, plot = FALSE)$acf[1:6] # Menampilkan data dari lag 1 sampai lag 5
acf_emp## [1] 0.60100713 0.41537866 0.29859908 0.19740462 0.05960827 0.01234154Hasil ACF, PACF, dan EACF menunnjukkan bahwa hasil simulai model AR(2) itu stationer karena
ACF tails off
PACF cut off di lag 2
EACF menunjukkan pola sesuai dengan MA(2) yaitu segitiga nol berada pada ordo MA(0)
3. ARMA(2,2)
Bentuk umum data berpola ARMA:
\[Yt = 0.5 Y_{t-1} + 0.2Y_{t-1} + e_t +0.4e_{t-1} + 0.6*e_{t-2}\]
- \(0.5 Y_{t-1} + 0.2Y_{t-1}\) adalah bagian dari AR
- \(e_t +0.4e_{t-1} + 0.6*e_{t-2}\) adalah bagian dari MA
Di sini akan dibangkitkan data dengan model ARMA(2,2) dengan \(\phi_1 = 0.5\) dan \(\phi_2 = 0.2\) kemudian dengan \(\theta_1 = 0.4\) dan \(\theta_2 = 0.6\) .
A. Menggunakan Teknik Manual
Bangkitkan data dari set.seed
Bangkitkan data AR(2) dengan \(\phi_1 = 0.5\) dan \(\phi_2 = 0.2\) dan \(\theta_1 = 0.4\) dan \(\theta_2 = 0.6\) sebanyak 300 data menggunakan fungsi arima.sim.
set.seed(1234) # Mengatur random seed generator
n = 300 # Banyak data yang akan dibangkitkan
# Koefisien AR dan MA
phi1 = 0.5 # koefisien AR lag 1
phi2 = 0.2 # koefisien AR lag 2
theta1 = 0.4 # koefisien MA lag 1
theta2 = 0.6 # koefisien MA lag 2# White noise
wn = rnorm(n)
# Vektor kosong berisi n angka nol
y.arma = numeric(n) # Akan diisi dengan data deret waktu Yt # Iterasi dari t = 3 sampai t = 300
# Mulai dari t = 3 karena model AR(2) dan MA(2) butuh lag hingga 2
for (i in 3:n) {
y.arma[i] <- phi1 * y.arma[i-1] +
phi2 * y.arma[i-2] +
wn[i] +
theta1 * wn[i-1] +
theta2 * wn[i-2]
}
y.arma## [1] 0.00000000 0.00000000 0.47117342 -1.50987697 -0.51919349 -1.29128499
## [7] -0.86432398 -1.16331330 -1.88247016 -2.61769548 -2.85722080 -3.67543572
## [13] -3.87108611 -3.51570481 -2.01254438 -1.39722573 -1.08054901 -2.00149017
## [19] -2.72511044 -0.22860399 -0.06120480 0.93612730 -0.10054661 0.12591091
## [25] -0.73136706 -1.79044069 -1.46225215 -2.75189059 -1.74814288 -2.98064692
## [31] -1.12111691 -1.75293106 -1.33898765 -2.09046996 -3.56829323 -4.32225209
## [37] -6.49932813 -7.02769509 -6.95242810 -6.26996407 -3.43890672 -3.74182891
## [43] -2.97181976 -3.49823015 -3.96328709 -4.21591372 -4.99194225 -5.61517562
## [49] -5.49498965 -5.32810268 -6.08211738 -5.70927763 -6.49640104 -6.19781946
## [55] -5.63181804 -4.16631811 -1.43386858 -1.32659085 1.33518960 -0.57718012
## [61] 1.13545868 2.56923465 2.89049818 2.80495292 1.68426168 2.77538382
## [67] 1.29220743 3.17981524 3.04188012 3.84589813 3.47054592 2.25362466
## [73] 1.27634579 1.31729358 3.02358708 2.83893413 1.81428668 0.10302896
## [79] -0.45121970 -0.85290753 -0.66635425 -0.93510416 -2.14779642 -2.08562341
## [85] -1.51503473 -0.24121274 0.91556687 0.64537308 0.48311177 -1.14217407
## [91] -1.12039092 -1.27141453 0.91636167 2.04091439 2.13232979 2.23257264
## [97] 0.25301429 1.21071226 1.29939237 3.92904462 4.07112121 3.78513073
## [103] 2.83160983 1.41191959 0.28488816 -0.04006883 -1.28812485 -0.74220308
## [109] -0.74424287 -0.32976863 -0.31752860 -0.98342470 -2.04217397 -1.20184647
## [115] -1.31314616 0.45270778 -0.93468943 -0.20680752 -0.29613748 0.15497575
## [121] 0.22025744 -0.73310547 1.30806278 1.61203256 4.42693491 3.79591780
## [127] 3.27848542 0.68061022 -0.62425847 -1.11211846 0.04164014 0.59240357
## [133] -0.15810424 0.39101368 -1.92189820 -1.50741039 -2.59060462 -3.89098912
## [139] -2.51252738 -3.45825773 -2.26278511 -0.93523383 0.07413764 0.83334886
## [145] 1.28389670 1.34833602 3.06177019 2.98115137 3.71727357 3.17046413
## [151] 2.39423349 1.98646516 2.92352912 1.69753466 2.18824295 2.31910758
## [157] 1.98048956 1.12411345 -0.47375475 -1.38212484 -2.31108442 -2.26562282
## [163] -2.62211380 -2.26938378 -1.57393069 -0.56321701 1.57589801 1.65267412
## [169] 1.80012273 2.53204975 3.72627716 3.97712776 3.44105725 0.58660225
## [175] 1.46428641 -0.51695507 -0.57765858 1.69949100 1.51248377 2.98314953
## [181] -0.81043866 -1.02122299 -1.37591544 -0.14779506 1.31440815 3.22462748
## [187] 4.38519006 3.98666624 4.07252161 2.61160764 1.92537895 -1.70502573
## [193] -2.72222986 -3.24361938 -0.27688538 0.87342985 2.50264542 1.00860632
## [199] 1.15325179 -1.81437043 -0.92501023 -1.18146222 -0.02037563 0.94652009
## [205] 1.17246770 2.08111275 3.60870710 4.52620181 4.56792960 2.75523948
## [211] 2.28308227 0.79090755 2.43630393 0.12650863 0.38802680 -0.48922578
## [217] -0.39939179 -0.71118176 -1.07369267 -0.53512569 0.48185240 1.52990415
## [223] 3.93599432 4.75299655 5.28489601 3.75245965 5.76106696 5.08023491
## [229] 5.03046078 3.85049062 2.27094879 1.61300623 0.02267186 -0.08744134
## [235] -0.23338993 -1.01395405 -4.02632785 -4.41061552 -5.02289664 -2.94041531
## [241] -2.16023161 -0.87458164 -1.76626866 -0.53794493 -0.27753067 0.71955739
## [247] 2.19354067 2.33905070 2.84874980 2.50865574 2.52684453 3.16087589
## [253] 3.22420516 3.72442687 1.90727460 1.27139490 1.66409882 0.23091397
## [259] 1.10296539 0.37155340 1.69901525 1.20826458 1.54849208 -0.89323198
## [265] -0.40844829 -1.97195019 -1.36977976 -2.76244287 -1.88853615 -1.38886217
## [271] -0.87915921 1.38576118 1.73484421 3.45643730 4.90637915 3.88230417
## [277] 4.70024354 4.04594276 3.83665310 3.63604751 1.69745094 1.83280517
## [283] 0.13589632 1.24990445 -0.25440835 0.60581161 -0.95359799 -0.74837042
## [289] -2.72398269 -2.15183291 -1.51561139 -0.53368698 -1.67162994 -2.15962923
## [295] -1.06604857 1.13495225 0.89677762 0.92454452 0.14354987 0.49726828B. Menggunakan arma.sim
# Kak ini aku ga bisa pake fungsi arma.sim soalnya error terus, udah dicari caranya tapi ttp gabisa :(
arma22 = arima.sim(model = list(ar = c(0.5, 0.2), ma = c(0.4, 0.6)), n = 300)
arma22## Time Series:
## Start = 1
## End = 300
## Frequency = 1
## [1] -2.0296272586 0.1804874357 -1.0857429326 0.2019685297 0.5101006237
## [6] 0.3116647978 1.1440157679 0.4568971792 -0.3804875233 -0.8758133113
## [11] 0.3166261152 0.2548874061 0.2592079202 -0.3290331722 -0.2948120396
## [16] 0.8417548499 2.0860897066 2.3426969416 3.4797265438 1.9702862497
## [21] -0.2703838028 -1.6091794075 -2.9699033669 -4.6121759676 -3.5735246545
## [26] -4.6576056483 -3.2455887429 -4.7021051669 -3.2231197169 -1.3940059863
## [31] -1.1346987187 -0.1752041013 1.0623014400 2.1418761113 4.7392121372
## [36] 4.1182608009 4.0004548088 2.2502034531 3.0645576995 0.9645314951
## [41] 1.7489003118 0.3724604884 2.9537132225 1.8162605804 1.0974763535
## [46] 0.1760865572 -0.5446303408 -0.9525033432 -0.8123258962 -1.3227469686
## [51] -1.5334325506 -0.9672480418 -1.3288936550 -2.5250400524 -5.1130294931
## [56] -5.8037895789 -4.2935914351 -2.2360988083 0.4460497638 1.7472096231
## [61] 2.4006131137 0.7584947290 0.6515731377 1.2527039433 -1.8771638270
## [66] -1.8694819688 -2.5578881435 -1.1519209603 0.5748330869 1.1471366303
## [71] 1.8838444926 1.6757856446 0.6273297035 -0.9358028910 -1.3469021544
## [76] -2.0036326762 -2.3174267020 -1.7545802003 -1.5599728217 0.6442232795
## [81] -0.4340053617 -0.1765772798 -1.1300535322 -2.3487839887 -2.2931928545
## [86] -3.2830807993 -4.7019099638 -4.5753666098 -5.1642557266 -2.7481221530
## [91] -2.8782203654 -0.9930444704 -1.0689737305 -1.5783972995 -1.0380159333
## [96] -1.5332320899 -0.6261053110 0.0411088954 0.3721474367 2.2198607384
## [101] 2.0023547146 1.1884673403 1.3043018409 -0.7887107383 -2.0964309112
## [106] -3.5171926149 -4.3978707535 -4.2937125479 -2.1094795649 0.0003174271
## [111] 1.9226494154 0.9593493745 0.8134718138 0.3306846828 0.3997456277
## [116] 0.6752169718 -0.5407546124 -1.6978244943 -0.6312219023 -0.5972690490
## [121] 0.1183319718 0.2620479526 2.1022412464 2.4863522906 4.4575844054
## [126] 4.8757690067 4.3160857500 4.5533945371 2.5494245996 0.9087801371
## [131] -1.2175736136 -1.9406110437 -0.1972454851 0.2476564511 0.4017020994
## [136] 0.2225073455 0.5000164875 -0.5832769633 -1.3456109790 -3.9300614982
## [141] -4.9131646646 -5.8028221737 -5.2926716626 -3.0460358047 -1.3040226410
## [146] 0.2132688421 -0.0784369871 -0.0996436572 0.1260353647 -0.2660236350
## [151] 1.0782194035 1.7045666001 0.9758460554 0.2737953256 0.5401383054
## [156] -1.3278429554 -0.0870286339 -0.9200321168 3.0637048543 0.0366253987
## [161] 0.6159264510 -0.9848095514 1.0702410108 2.2519934840 1.2521472479
## [166] 3.2483253660 0.1560601148 0.2554054546 -1.3837918100 0.8997062858
## [171] 1.5437618975 3.2200970376 4.2428268660 4.8796814776 3.4944267802
## [176] 3.5338487343 1.9056374923 3.8243441222 2.6973660425 1.5586316888
## [181] 1.0537138077 0.4735564378 0.8667967201 -0.3227890170 -1.2601457680
## [186] -1.6767524636 -0.5606943256 -0.5724867409 -0.7927487057 -3.7823291437
## [191] -3.1600153700 -3.3339550694 -0.5223037166 1.3188603092 1.7841169179
## [196] 3.2771554059 2.4302864848 1.9737979026 0.3549837497 -0.5198143292
## [201] -0.6091253699 -0.5530998375 -0.0719700978 0.1162479295 0.9584330444
## [206] 0.6344896787 2.4637658099 2.2867046454 1.5988556633 0.7653209481
## [211] 0.3915332251 -0.0218611922 0.5574787959 0.6001278409 2.0957927366
## [216] 1.2982546155 1.5728132382 0.0805951955 -1.0094781239 -3.1290589551
## [221] -2.9867638935 -2.5487990772 -0.8746506343 -1.7204755510 -2.3373479869
## [226] -3.9397901303 -4.2603045521 -3.7080736007 -2.4567380560 -2.4451043371
## [231] -4.5475696207 -3.4437405213 -3.3531781238 -2.2477998694 -2.7793743188
## [236] -2.9892252870 -2.7065742281 -1.3646835008 0.5205827432 0.1284297696
## [241] 0.9535579764 1.4436000747 0.7192735976 0.8655621589 -1.8247428875
## [246] -1.2940820209 -2.6010932672 -2.5683240349 -3.3390482543 -2.6056391336
## [251] -4.4232833523 -3.7565659797 -5.2443430811 -4.9963973684 -4.0655108800
## [256] -3.0676982101 -2.0284891531 -0.9220225427 -1.3180193115 -2.7850434151
## [261] -1.6722862864 -2.3760548989 -1.2871979057 -1.2457433091 -0.2704251019
## [266] 0.4426094002 1.7244792000 1.6234544126 1.2271504803 0.4637832128
## [271] 0.8774865319 -0.1688721412 -0.7085067912 -0.9655544239 -0.4587798338
## [276] -1.6805074767 -0.4562603842 -1.2530770377 -0.4234566530 0.5792636344
## [281] 2.0183639459 1.2335658487 2.4607872362 0.5612596789 1.2593135541
## [286] 0.8965377884 1.1050964502 -0.3891819897 -0.9852126937 -0.1110588970
## [291] 0.2322458578 0.2510026152 -0.7146316233 -0.0134150381 0.2259188584
## [296] -0.0139370725 -0.1067440762 0.0047052158 1.9459829310 1.1392060539Plot simulasi ARMA(2,2)
# Plot simulasi
ts.plot(arma22,
main="Simulasi ARMA(2,2)",
ylab="Yt")
Plot ACF (Autocorrelation Function)
# Plot ACF
acf(arma22, main="ACF ARMA(2,2)") 
Plot ACF dari ARMA(2,2) yang sudah dibangkitkan menunjukkan adanya tails off.
Hal ini menandakan adanya ciri khas dari komponen AR
Plot PACF (Partial Autocorrelation Function)
# Plot PACF
pacf(arma22, main="PACF ARMA(2,2)")
Plot PACF dari ARMA(2,2) yang sudah dibangkitkan menunjukkan adanya cut off di lag 2.
Hal ini menandakan adanya ciri khas dari komponen MA
Plot EACF (Extended Autocorrelation Function)
# Plot EACF
library(TSA)
eacf(arma22)## AR/MA
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13
## 0 x x x x x o o o o o o o o x
## 1 x x o o o o o o o o o o o o
## 2 x x x x o o o o o o o o o o
## 3 x x o x o o o o o o o o o o
## 4 x x o x x o o o o o o o o o
## 5 x x x x o o o o o o o o o o
## 6 x x x x o x o o o o o o o o
## 7 x x o x x x x o o o o o o oBerdasarkan pola segitiga nol pada plot EACF, terlihat bahwa segitiga nol berada pada ordo AR(2) dan ordo MA(2).
Scatterplot
# Yt
yt_arma22 = arma22[-c(1:3)]
# Yt-1
yt_1_arma22 = arma22[-c((n-2):n)]
# Yt-2
yt_2_arma22 = arma22[-c((n-1):n)]
yt_2_arma22 = yt_2_arma22[-1]
# Yt-3
yt_3_arma22 = arma22[-n]
yt_3_arma22 = yt_3_arma22[-c(1:2)] # Perbandingan Yt dengan Yt-1
yt_arma22## [1] 0.2019685297 0.5101006237 0.3116647978 1.1440157679 0.4568971792
## [6] -0.3804875233 -0.8758133113 0.3166261152 0.2548874061 0.2592079202
## [11] -0.3290331722 -0.2948120396 0.8417548499 2.0860897066 2.3426969416
## [16] 3.4797265438 1.9702862497 -0.2703838028 -1.6091794075 -2.9699033669
## [21] -4.6121759676 -3.5735246545 -4.6576056483 -3.2455887429 -4.7021051669
## [26] -3.2231197169 -1.3940059863 -1.1346987187 -0.1752041013 1.0623014400
## [31] 2.1418761113 4.7392121372 4.1182608009 4.0004548088 2.2502034531
## [36] 3.0645576995 0.9645314951 1.7489003118 0.3724604884 2.9537132225
## [41] 1.8162605804 1.0974763535 0.1760865572 -0.5446303408 -0.9525033432
## [46] -0.8123258962 -1.3227469686 -1.5334325506 -0.9672480418 -1.3288936550
## [51] -2.5250400524 -5.1130294931 -5.8037895789 -4.2935914351 -2.2360988083
## [56] 0.4460497638 1.7472096231 2.4006131137 0.7584947290 0.6515731377
## [61] 1.2527039433 -1.8771638270 -1.8694819688 -2.5578881435 -1.1519209603
## [66] 0.5748330869 1.1471366303 1.8838444926 1.6757856446 0.6273297035
## [71] -0.9358028910 -1.3469021544 -2.0036326762 -2.3174267020 -1.7545802003
## [76] -1.5599728217 0.6442232795 -0.4340053617 -0.1765772798 -1.1300535322
## [81] -2.3487839887 -2.2931928545 -3.2830807993 -4.7019099638 -4.5753666098
## [86] -5.1642557266 -2.7481221530 -2.8782203654 -0.9930444704 -1.0689737305
## [91] -1.5783972995 -1.0380159333 -1.5332320899 -0.6261053110 0.0411088954
## [96] 0.3721474367 2.2198607384 2.0023547146 1.1884673403 1.3043018409
## [101] -0.7887107383 -2.0964309112 -3.5171926149 -4.3978707535 -4.2937125479
## [106] -2.1094795649 0.0003174271 1.9226494154 0.9593493745 0.8134718138
## [111] 0.3306846828 0.3997456277 0.6752169718 -0.5407546124 -1.6978244943
## [116] -0.6312219023 -0.5972690490 0.1183319718 0.2620479526 2.1022412464
## [121] 2.4863522906 4.4575844054 4.8757690067 4.3160857500 4.5533945371
## [126] 2.5494245996 0.9087801371 -1.2175736136 -1.9406110437 -0.1972454851
## [131] 0.2476564511 0.4017020994 0.2225073455 0.5000164875 -0.5832769633
## [136] -1.3456109790 -3.9300614982 -4.9131646646 -5.8028221737 -5.2926716626
## [141] -3.0460358047 -1.3040226410 0.2132688421 -0.0784369871 -0.0996436572
## [146] 0.1260353647 -0.2660236350 1.0782194035 1.7045666001 0.9758460554
## [151] 0.2737953256 0.5401383054 -1.3278429554 -0.0870286339 -0.9200321168
## [156] 3.0637048543 0.0366253987 0.6159264510 -0.9848095514 1.0702410108
## [161] 2.2519934840 1.2521472479 3.2483253660 0.1560601148 0.2554054546
## [166] -1.3837918100 0.8997062858 1.5437618975 3.2200970376 4.2428268660
## [171] 4.8796814776 3.4944267802 3.5338487343 1.9056374923 3.8243441222
## [176] 2.6973660425 1.5586316888 1.0537138077 0.4735564378 0.8667967201
## [181] -0.3227890170 -1.2601457680 -1.6767524636 -0.5606943256 -0.5724867409
## [186] -0.7927487057 -3.7823291437 -3.1600153700 -3.3339550694 -0.5223037166
## [191] 1.3188603092 1.7841169179 3.2771554059 2.4302864848 1.9737979026
## [196] 0.3549837497 -0.5198143292 -0.6091253699 -0.5530998375 -0.0719700978
## [201] 0.1162479295 0.9584330444 0.6344896787 2.4637658099 2.2867046454
## [206] 1.5988556633 0.7653209481 0.3915332251 -0.0218611922 0.5574787959
## [211] 0.6001278409 2.0957927366 1.2982546155 1.5728132382 0.0805951955
## [216] -1.0094781239 -3.1290589551 -2.9867638935 -2.5487990772 -0.8746506343
## [221] -1.7204755510 -2.3373479869 -3.9397901303 -4.2603045521 -3.7080736007
## [226] -2.4567380560 -2.4451043371 -4.5475696207 -3.4437405213 -3.3531781238
## [231] -2.2477998694 -2.7793743188 -2.9892252870 -2.7065742281 -1.3646835008
## [236] 0.5205827432 0.1284297696 0.9535579764 1.4436000747 0.7192735976
## [241] 0.8655621589 -1.8247428875 -1.2940820209 -2.6010932672 -2.5683240349
## [246] -3.3390482543 -2.6056391336 -4.4232833523 -3.7565659797 -5.2443430811
## [251] -4.9963973684 -4.0655108800 -3.0676982101 -2.0284891531 -0.9220225427
## [256] -1.3180193115 -2.7850434151 -1.6722862864 -2.3760548989 -1.2871979057
## [261] -1.2457433091 -0.2704251019 0.4426094002 1.7244792000 1.6234544126
## [266] 1.2271504803 0.4637832128 0.8774865319 -0.1688721412 -0.7085067912
## [271] -0.9655544239 -0.4587798338 -1.6805074767 -0.4562603842 -1.2530770377
## [276] -0.4234566530 0.5792636344 2.0183639459 1.2335658487 2.4607872362
## [281] 0.5612596789 1.2593135541 0.8965377884 1.1050964502 -0.3891819897
## [286] -0.9852126937 -0.1110588970 0.2322458578 0.2510026152 -0.7146316233
## [291] -0.0134150381 0.2259188584 -0.0139370725 -0.1067440762 0.0047052158
## [296] 1.9459829310 1.1392060539yt_1_arma22## [1] -2.0296272586 0.1804874357 -1.0857429326 0.2019685297 0.5101006237
## [6] 0.3116647978 1.1440157679 0.4568971792 -0.3804875233 -0.8758133113
## [11] 0.3166261152 0.2548874061 0.2592079202 -0.3290331722 -0.2948120396
## [16] 0.8417548499 2.0860897066 2.3426969416 3.4797265438 1.9702862497
## [21] -0.2703838028 -1.6091794075 -2.9699033669 -4.6121759676 -3.5735246545
## [26] -4.6576056483 -3.2455887429 -4.7021051669 -3.2231197169 -1.3940059863
## [31] -1.1346987187 -0.1752041013 1.0623014400 2.1418761113 4.7392121372
## [36] 4.1182608009 4.0004548088 2.2502034531 3.0645576995 0.9645314951
## [41] 1.7489003118 0.3724604884 2.9537132225 1.8162605804 1.0974763535
## [46] 0.1760865572 -0.5446303408 -0.9525033432 -0.8123258962 -1.3227469686
## [51] -1.5334325506 -0.9672480418 -1.3288936550 -2.5250400524 -5.1130294931
## [56] -5.8037895789 -4.2935914351 -2.2360988083 0.4460497638 1.7472096231
## [61] 2.4006131137 0.7584947290 0.6515731377 1.2527039433 -1.8771638270
## [66] -1.8694819688 -2.5578881435 -1.1519209603 0.5748330869 1.1471366303
## [71] 1.8838444926 1.6757856446 0.6273297035 -0.9358028910 -1.3469021544
## [76] -2.0036326762 -2.3174267020 -1.7545802003 -1.5599728217 0.6442232795
## [81] -0.4340053617 -0.1765772798 -1.1300535322 -2.3487839887 -2.2931928545
## [86] -3.2830807993 -4.7019099638 -4.5753666098 -5.1642557266 -2.7481221530
## [91] -2.8782203654 -0.9930444704 -1.0689737305 -1.5783972995 -1.0380159333
## [96] -1.5332320899 -0.6261053110 0.0411088954 0.3721474367 2.2198607384
## [101] 2.0023547146 1.1884673403 1.3043018409 -0.7887107383 -2.0964309112
## [106] -3.5171926149 -4.3978707535 -4.2937125479 -2.1094795649 0.0003174271
## [111] 1.9226494154 0.9593493745 0.8134718138 0.3306846828 0.3997456277
## [116] 0.6752169718 -0.5407546124 -1.6978244943 -0.6312219023 -0.5972690490
## [121] 0.1183319718 0.2620479526 2.1022412464 2.4863522906 4.4575844054
## [126] 4.8757690067 4.3160857500 4.5533945371 2.5494245996 0.9087801371
## [131] -1.2175736136 -1.9406110437 -0.1972454851 0.2476564511 0.4017020994
## [136] 0.2225073455 0.5000164875 -0.5832769633 -1.3456109790 -3.9300614982
## [141] -4.9131646646 -5.8028221737 -5.2926716626 -3.0460358047 -1.3040226410
## [146] 0.2132688421 -0.0784369871 -0.0996436572 0.1260353647 -0.2660236350
## [151] 1.0782194035 1.7045666001 0.9758460554 0.2737953256 0.5401383054
## [156] -1.3278429554 -0.0870286339 -0.9200321168 3.0637048543 0.0366253987
## [161] 0.6159264510 -0.9848095514 1.0702410108 2.2519934840 1.2521472479
## [166] 3.2483253660 0.1560601148 0.2554054546 -1.3837918100 0.8997062858
## [171] 1.5437618975 3.2200970376 4.2428268660 4.8796814776 3.4944267802
## [176] 3.5338487343 1.9056374923 3.8243441222 2.6973660425 1.5586316888
## [181] 1.0537138077 0.4735564378 0.8667967201 -0.3227890170 -1.2601457680
## [186] -1.6767524636 -0.5606943256 -0.5724867409 -0.7927487057 -3.7823291437
## [191] -3.1600153700 -3.3339550694 -0.5223037166 1.3188603092 1.7841169179
## [196] 3.2771554059 2.4302864848 1.9737979026 0.3549837497 -0.5198143292
## [201] -0.6091253699 -0.5530998375 -0.0719700978 0.1162479295 0.9584330444
## [206] 0.6344896787 2.4637658099 2.2867046454 1.5988556633 0.7653209481
## [211] 0.3915332251 -0.0218611922 0.5574787959 0.6001278409 2.0957927366
## [216] 1.2982546155 1.5728132382 0.0805951955 -1.0094781239 -3.1290589551
## [221] -2.9867638935 -2.5487990772 -0.8746506343 -1.7204755510 -2.3373479869
## [226] -3.9397901303 -4.2603045521 -3.7080736007 -2.4567380560 -2.4451043371
## [231] -4.5475696207 -3.4437405213 -3.3531781238 -2.2477998694 -2.7793743188
## [236] -2.9892252870 -2.7065742281 -1.3646835008 0.5205827432 0.1284297696
## [241] 0.9535579764 1.4436000747 0.7192735976 0.8655621589 -1.8247428875
## [246] -1.2940820209 -2.6010932672 -2.5683240349 -3.3390482543 -2.6056391336
## [251] -4.4232833523 -3.7565659797 -5.2443430811 -4.9963973684 -4.0655108800
## [256] -3.0676982101 -2.0284891531 -0.9220225427 -1.3180193115 -2.7850434151
## [261] -1.6722862864 -2.3760548989 -1.2871979057 -1.2457433091 -0.2704251019
## [266] 0.4426094002 1.7244792000 1.6234544126 1.2271504803 0.4637832128
## [271] 0.8774865319 -0.1688721412 -0.7085067912 -0.9655544239 -0.4587798338
## [276] -1.6805074767 -0.4562603842 -1.2530770377 -0.4234566530 0.5792636344
## [281] 2.0183639459 1.2335658487 2.4607872362 0.5612596789 1.2593135541
## [286] 0.8965377884 1.1050964502 -0.3891819897 -0.9852126937 -0.1110588970
## [291] 0.2322458578 0.2510026152 -0.7146316233 -0.0134150381 0.2259188584
## [296] -0.0139370725 -0.1067440762# Perbandingan Yt dengan Yt-2
yt_arma22## [1] 0.2019685297 0.5101006237 0.3116647978 1.1440157679 0.4568971792
## [6] -0.3804875233 -0.8758133113 0.3166261152 0.2548874061 0.2592079202
## [11] -0.3290331722 -0.2948120396 0.8417548499 2.0860897066 2.3426969416
## [16] 3.4797265438 1.9702862497 -0.2703838028 -1.6091794075 -2.9699033669
## [21] -4.6121759676 -3.5735246545 -4.6576056483 -3.2455887429 -4.7021051669
## [26] -3.2231197169 -1.3940059863 -1.1346987187 -0.1752041013 1.0623014400
## [31] 2.1418761113 4.7392121372 4.1182608009 4.0004548088 2.2502034531
## [36] 3.0645576995 0.9645314951 1.7489003118 0.3724604884 2.9537132225
## [41] 1.8162605804 1.0974763535 0.1760865572 -0.5446303408 -0.9525033432
## [46] -0.8123258962 -1.3227469686 -1.5334325506 -0.9672480418 -1.3288936550
## [51] -2.5250400524 -5.1130294931 -5.8037895789 -4.2935914351 -2.2360988083
## [56] 0.4460497638 1.7472096231 2.4006131137 0.7584947290 0.6515731377
## [61] 1.2527039433 -1.8771638270 -1.8694819688 -2.5578881435 -1.1519209603
## [66] 0.5748330869 1.1471366303 1.8838444926 1.6757856446 0.6273297035
## [71] -0.9358028910 -1.3469021544 -2.0036326762 -2.3174267020 -1.7545802003
## [76] -1.5599728217 0.6442232795 -0.4340053617 -0.1765772798 -1.1300535322
## [81] -2.3487839887 -2.2931928545 -3.2830807993 -4.7019099638 -4.5753666098
## [86] -5.1642557266 -2.7481221530 -2.8782203654 -0.9930444704 -1.0689737305
## [91] -1.5783972995 -1.0380159333 -1.5332320899 -0.6261053110 0.0411088954
## [96] 0.3721474367 2.2198607384 2.0023547146 1.1884673403 1.3043018409
## [101] -0.7887107383 -2.0964309112 -3.5171926149 -4.3978707535 -4.2937125479
## [106] -2.1094795649 0.0003174271 1.9226494154 0.9593493745 0.8134718138
## [111] 0.3306846828 0.3997456277 0.6752169718 -0.5407546124 -1.6978244943
## [116] -0.6312219023 -0.5972690490 0.1183319718 0.2620479526 2.1022412464
## [121] 2.4863522906 4.4575844054 4.8757690067 4.3160857500 4.5533945371
## [126] 2.5494245996 0.9087801371 -1.2175736136 -1.9406110437 -0.1972454851
## [131] 0.2476564511 0.4017020994 0.2225073455 0.5000164875 -0.5832769633
## [136] -1.3456109790 -3.9300614982 -4.9131646646 -5.8028221737 -5.2926716626
## [141] -3.0460358047 -1.3040226410 0.2132688421 -0.0784369871 -0.0996436572
## [146] 0.1260353647 -0.2660236350 1.0782194035 1.7045666001 0.9758460554
## [151] 0.2737953256 0.5401383054 -1.3278429554 -0.0870286339 -0.9200321168
## [156] 3.0637048543 0.0366253987 0.6159264510 -0.9848095514 1.0702410108
## [161] 2.2519934840 1.2521472479 3.2483253660 0.1560601148 0.2554054546
## [166] -1.3837918100 0.8997062858 1.5437618975 3.2200970376 4.2428268660
## [171] 4.8796814776 3.4944267802 3.5338487343 1.9056374923 3.8243441222
## [176] 2.6973660425 1.5586316888 1.0537138077 0.4735564378 0.8667967201
## [181] -0.3227890170 -1.2601457680 -1.6767524636 -0.5606943256 -0.5724867409
## [186] -0.7927487057 -3.7823291437 -3.1600153700 -3.3339550694 -0.5223037166
## [191] 1.3188603092 1.7841169179 3.2771554059 2.4302864848 1.9737979026
## [196] 0.3549837497 -0.5198143292 -0.6091253699 -0.5530998375 -0.0719700978
## [201] 0.1162479295 0.9584330444 0.6344896787 2.4637658099 2.2867046454
## [206] 1.5988556633 0.7653209481 0.3915332251 -0.0218611922 0.5574787959
## [211] 0.6001278409 2.0957927366 1.2982546155 1.5728132382 0.0805951955
## [216] -1.0094781239 -3.1290589551 -2.9867638935 -2.5487990772 -0.8746506343
## [221] -1.7204755510 -2.3373479869 -3.9397901303 -4.2603045521 -3.7080736007
## [226] -2.4567380560 -2.4451043371 -4.5475696207 -3.4437405213 -3.3531781238
## [231] -2.2477998694 -2.7793743188 -2.9892252870 -2.7065742281 -1.3646835008
## [236] 0.5205827432 0.1284297696 0.9535579764 1.4436000747 0.7192735976
## [241] 0.8655621589 -1.8247428875 -1.2940820209 -2.6010932672 -2.5683240349
## [246] -3.3390482543 -2.6056391336 -4.4232833523 -3.7565659797 -5.2443430811
## [251] -4.9963973684 -4.0655108800 -3.0676982101 -2.0284891531 -0.9220225427
## [256] -1.3180193115 -2.7850434151 -1.6722862864 -2.3760548989 -1.2871979057
## [261] -1.2457433091 -0.2704251019 0.4426094002 1.7244792000 1.6234544126
## [266] 1.2271504803 0.4637832128 0.8774865319 -0.1688721412 -0.7085067912
## [271] -0.9655544239 -0.4587798338 -1.6805074767 -0.4562603842 -1.2530770377
## [276] -0.4234566530 0.5792636344 2.0183639459 1.2335658487 2.4607872362
## [281] 0.5612596789 1.2593135541 0.8965377884 1.1050964502 -0.3891819897
## [286] -0.9852126937 -0.1110588970 0.2322458578 0.2510026152 -0.7146316233
## [291] -0.0134150381 0.2259188584 -0.0139370725 -0.1067440762 0.0047052158
## [296] 1.9459829310 1.1392060539yt_2_arma22## [1] 0.1804874357 -1.0857429326 0.2019685297 0.5101006237 0.3116647978
## [6] 1.1440157679 0.4568971792 -0.3804875233 -0.8758133113 0.3166261152
## [11] 0.2548874061 0.2592079202 -0.3290331722 -0.2948120396 0.8417548499
## [16] 2.0860897066 2.3426969416 3.4797265438 1.9702862497 -0.2703838028
## [21] -1.6091794075 -2.9699033669 -4.6121759676 -3.5735246545 -4.6576056483
## [26] -3.2455887429 -4.7021051669 -3.2231197169 -1.3940059863 -1.1346987187
## [31] -0.1752041013 1.0623014400 2.1418761113 4.7392121372 4.1182608009
## [36] 4.0004548088 2.2502034531 3.0645576995 0.9645314951 1.7489003118
## [41] 0.3724604884 2.9537132225 1.8162605804 1.0974763535 0.1760865572
## [46] -0.5446303408 -0.9525033432 -0.8123258962 -1.3227469686 -1.5334325506
## [51] -0.9672480418 -1.3288936550 -2.5250400524 -5.1130294931 -5.8037895789
## [56] -4.2935914351 -2.2360988083 0.4460497638 1.7472096231 2.4006131137
## [61] 0.7584947290 0.6515731377 1.2527039433 -1.8771638270 -1.8694819688
## [66] -2.5578881435 -1.1519209603 0.5748330869 1.1471366303 1.8838444926
## [71] 1.6757856446 0.6273297035 -0.9358028910 -1.3469021544 -2.0036326762
## [76] -2.3174267020 -1.7545802003 -1.5599728217 0.6442232795 -0.4340053617
## [81] -0.1765772798 -1.1300535322 -2.3487839887 -2.2931928545 -3.2830807993
## [86] -4.7019099638 -4.5753666098 -5.1642557266 -2.7481221530 -2.8782203654
## [91] -0.9930444704 -1.0689737305 -1.5783972995 -1.0380159333 -1.5332320899
## [96] -0.6261053110 0.0411088954 0.3721474367 2.2198607384 2.0023547146
## [101] 1.1884673403 1.3043018409 -0.7887107383 -2.0964309112 -3.5171926149
## [106] -4.3978707535 -4.2937125479 -2.1094795649 0.0003174271 1.9226494154
## [111] 0.9593493745 0.8134718138 0.3306846828 0.3997456277 0.6752169718
## [116] -0.5407546124 -1.6978244943 -0.6312219023 -0.5972690490 0.1183319718
## [121] 0.2620479526 2.1022412464 2.4863522906 4.4575844054 4.8757690067
## [126] 4.3160857500 4.5533945371 2.5494245996 0.9087801371 -1.2175736136
## [131] -1.9406110437 -0.1972454851 0.2476564511 0.4017020994 0.2225073455
## [136] 0.5000164875 -0.5832769633 -1.3456109790 -3.9300614982 -4.9131646646
## [141] -5.8028221737 -5.2926716626 -3.0460358047 -1.3040226410 0.2132688421
## [146] -0.0784369871 -0.0996436572 0.1260353647 -0.2660236350 1.0782194035
## [151] 1.7045666001 0.9758460554 0.2737953256 0.5401383054 -1.3278429554
## [156] -0.0870286339 -0.9200321168 3.0637048543 0.0366253987 0.6159264510
## [161] -0.9848095514 1.0702410108 2.2519934840 1.2521472479 3.2483253660
## [166] 0.1560601148 0.2554054546 -1.3837918100 0.8997062858 1.5437618975
## [171] 3.2200970376 4.2428268660 4.8796814776 3.4944267802 3.5338487343
## [176] 1.9056374923 3.8243441222 2.6973660425 1.5586316888 1.0537138077
## [181] 0.4735564378 0.8667967201 -0.3227890170 -1.2601457680 -1.6767524636
## [186] -0.5606943256 -0.5724867409 -0.7927487057 -3.7823291437 -3.1600153700
## [191] -3.3339550694 -0.5223037166 1.3188603092 1.7841169179 3.2771554059
## [196] 2.4302864848 1.9737979026 0.3549837497 -0.5198143292 -0.6091253699
## [201] -0.5530998375 -0.0719700978 0.1162479295 0.9584330444 0.6344896787
## [206] 2.4637658099 2.2867046454 1.5988556633 0.7653209481 0.3915332251
## [211] -0.0218611922 0.5574787959 0.6001278409 2.0957927366 1.2982546155
## [216] 1.5728132382 0.0805951955 -1.0094781239 -3.1290589551 -2.9867638935
## [221] -2.5487990772 -0.8746506343 -1.7204755510 -2.3373479869 -3.9397901303
## [226] -4.2603045521 -3.7080736007 -2.4567380560 -2.4451043371 -4.5475696207
## [231] -3.4437405213 -3.3531781238 -2.2477998694 -2.7793743188 -2.9892252870
## [236] -2.7065742281 -1.3646835008 0.5205827432 0.1284297696 0.9535579764
## [241] 1.4436000747 0.7192735976 0.8655621589 -1.8247428875 -1.2940820209
## [246] -2.6010932672 -2.5683240349 -3.3390482543 -2.6056391336 -4.4232833523
## [251] -3.7565659797 -5.2443430811 -4.9963973684 -4.0655108800 -3.0676982101
## [256] -2.0284891531 -0.9220225427 -1.3180193115 -2.7850434151 -1.6722862864
## [261] -2.3760548989 -1.2871979057 -1.2457433091 -0.2704251019 0.4426094002
## [266] 1.7244792000 1.6234544126 1.2271504803 0.4637832128 0.8774865319
## [271] -0.1688721412 -0.7085067912 -0.9655544239 -0.4587798338 -1.6805074767
## [276] -0.4562603842 -1.2530770377 -0.4234566530 0.5792636344 2.0183639459
## [281] 1.2335658487 2.4607872362 0.5612596789 1.2593135541 0.8965377884
## [286] 1.1050964502 -0.3891819897 -0.9852126937 -0.1110588970 0.2322458578
## [291] 0.2510026152 -0.7146316233 -0.0134150381 0.2259188584 -0.0139370725
## [296] -0.1067440762 0.0047052158# Perbandingan Yt dengan Yt-3
yt_arma22## [1] 0.2019685297 0.5101006237 0.3116647978 1.1440157679 0.4568971792
## [6] -0.3804875233 -0.8758133113 0.3166261152 0.2548874061 0.2592079202
## [11] -0.3290331722 -0.2948120396 0.8417548499 2.0860897066 2.3426969416
## [16] 3.4797265438 1.9702862497 -0.2703838028 -1.6091794075 -2.9699033669
## [21] -4.6121759676 -3.5735246545 -4.6576056483 -3.2455887429 -4.7021051669
## [26] -3.2231197169 -1.3940059863 -1.1346987187 -0.1752041013 1.0623014400
## [31] 2.1418761113 4.7392121372 4.1182608009 4.0004548088 2.2502034531
## [36] 3.0645576995 0.9645314951 1.7489003118 0.3724604884 2.9537132225
## [41] 1.8162605804 1.0974763535 0.1760865572 -0.5446303408 -0.9525033432
## [46] -0.8123258962 -1.3227469686 -1.5334325506 -0.9672480418 -1.3288936550
## [51] -2.5250400524 -5.1130294931 -5.8037895789 -4.2935914351 -2.2360988083
## [56] 0.4460497638 1.7472096231 2.4006131137 0.7584947290 0.6515731377
## [61] 1.2527039433 -1.8771638270 -1.8694819688 -2.5578881435 -1.1519209603
## [66] 0.5748330869 1.1471366303 1.8838444926 1.6757856446 0.6273297035
## [71] -0.9358028910 -1.3469021544 -2.0036326762 -2.3174267020 -1.7545802003
## [76] -1.5599728217 0.6442232795 -0.4340053617 -0.1765772798 -1.1300535322
## [81] -2.3487839887 -2.2931928545 -3.2830807993 -4.7019099638 -4.5753666098
## [86] -5.1642557266 -2.7481221530 -2.8782203654 -0.9930444704 -1.0689737305
## [91] -1.5783972995 -1.0380159333 -1.5332320899 -0.6261053110 0.0411088954
## [96] 0.3721474367 2.2198607384 2.0023547146 1.1884673403 1.3043018409
## [101] -0.7887107383 -2.0964309112 -3.5171926149 -4.3978707535 -4.2937125479
## [106] -2.1094795649 0.0003174271 1.9226494154 0.9593493745 0.8134718138
## [111] 0.3306846828 0.3997456277 0.6752169718 -0.5407546124 -1.6978244943
## [116] -0.6312219023 -0.5972690490 0.1183319718 0.2620479526 2.1022412464
## [121] 2.4863522906 4.4575844054 4.8757690067 4.3160857500 4.5533945371
## [126] 2.5494245996 0.9087801371 -1.2175736136 -1.9406110437 -0.1972454851
## [131] 0.2476564511 0.4017020994 0.2225073455 0.5000164875 -0.5832769633
## [136] -1.3456109790 -3.9300614982 -4.9131646646 -5.8028221737 -5.2926716626
## [141] -3.0460358047 -1.3040226410 0.2132688421 -0.0784369871 -0.0996436572
## [146] 0.1260353647 -0.2660236350 1.0782194035 1.7045666001 0.9758460554
## [151] 0.2737953256 0.5401383054 -1.3278429554 -0.0870286339 -0.9200321168
## [156] 3.0637048543 0.0366253987 0.6159264510 -0.9848095514 1.0702410108
## [161] 2.2519934840 1.2521472479 3.2483253660 0.1560601148 0.2554054546
## [166] -1.3837918100 0.8997062858 1.5437618975 3.2200970376 4.2428268660
## [171] 4.8796814776 3.4944267802 3.5338487343 1.9056374923 3.8243441222
## [176] 2.6973660425 1.5586316888 1.0537138077 0.4735564378 0.8667967201
## [181] -0.3227890170 -1.2601457680 -1.6767524636 -0.5606943256 -0.5724867409
## [186] -0.7927487057 -3.7823291437 -3.1600153700 -3.3339550694 -0.5223037166
## [191] 1.3188603092 1.7841169179 3.2771554059 2.4302864848 1.9737979026
## [196] 0.3549837497 -0.5198143292 -0.6091253699 -0.5530998375 -0.0719700978
## [201] 0.1162479295 0.9584330444 0.6344896787 2.4637658099 2.2867046454
## [206] 1.5988556633 0.7653209481 0.3915332251 -0.0218611922 0.5574787959
## [211] 0.6001278409 2.0957927366 1.2982546155 1.5728132382 0.0805951955
## [216] -1.0094781239 -3.1290589551 -2.9867638935 -2.5487990772 -0.8746506343
## [221] -1.7204755510 -2.3373479869 -3.9397901303 -4.2603045521 -3.7080736007
## [226] -2.4567380560 -2.4451043371 -4.5475696207 -3.4437405213 -3.3531781238
## [231] -2.2477998694 -2.7793743188 -2.9892252870 -2.7065742281 -1.3646835008
## [236] 0.5205827432 0.1284297696 0.9535579764 1.4436000747 0.7192735976
## [241] 0.8655621589 -1.8247428875 -1.2940820209 -2.6010932672 -2.5683240349
## [246] -3.3390482543 -2.6056391336 -4.4232833523 -3.7565659797 -5.2443430811
## [251] -4.9963973684 -4.0655108800 -3.0676982101 -2.0284891531 -0.9220225427
## [256] -1.3180193115 -2.7850434151 -1.6722862864 -2.3760548989 -1.2871979057
## [261] -1.2457433091 -0.2704251019 0.4426094002 1.7244792000 1.6234544126
## [266] 1.2271504803 0.4637832128 0.8774865319 -0.1688721412 -0.7085067912
## [271] -0.9655544239 -0.4587798338 -1.6805074767 -0.4562603842 -1.2530770377
## [276] -0.4234566530 0.5792636344 2.0183639459 1.2335658487 2.4607872362
## [281] 0.5612596789 1.2593135541 0.8965377884 1.1050964502 -0.3891819897
## [286] -0.9852126937 -0.1110588970 0.2322458578 0.2510026152 -0.7146316233
## [291] -0.0134150381 0.2259188584 -0.0139370725 -0.1067440762 0.0047052158
## [296] 1.9459829310 1.1392060539yt_3_arma22## [1] -1.0857429326 0.2019685297 0.5101006237 0.3116647978 1.1440157679
## [6] 0.4568971792 -0.3804875233 -0.8758133113 0.3166261152 0.2548874061
## [11] 0.2592079202 -0.3290331722 -0.2948120396 0.8417548499 2.0860897066
## [16] 2.3426969416 3.4797265438 1.9702862497 -0.2703838028 -1.6091794075
## [21] -2.9699033669 -4.6121759676 -3.5735246545 -4.6576056483 -3.2455887429
## [26] -4.7021051669 -3.2231197169 -1.3940059863 -1.1346987187 -0.1752041013
## [31] 1.0623014400 2.1418761113 4.7392121372 4.1182608009 4.0004548088
## [36] 2.2502034531 3.0645576995 0.9645314951 1.7489003118 0.3724604884
## [41] 2.9537132225 1.8162605804 1.0974763535 0.1760865572 -0.5446303408
## [46] -0.9525033432 -0.8123258962 -1.3227469686 -1.5334325506 -0.9672480418
## [51] -1.3288936550 -2.5250400524 -5.1130294931 -5.8037895789 -4.2935914351
## [56] -2.2360988083 0.4460497638 1.7472096231 2.4006131137 0.7584947290
## [61] 0.6515731377 1.2527039433 -1.8771638270 -1.8694819688 -2.5578881435
## [66] -1.1519209603 0.5748330869 1.1471366303 1.8838444926 1.6757856446
## [71] 0.6273297035 -0.9358028910 -1.3469021544 -2.0036326762 -2.3174267020
## [76] -1.7545802003 -1.5599728217 0.6442232795 -0.4340053617 -0.1765772798
## [81] -1.1300535322 -2.3487839887 -2.2931928545 -3.2830807993 -4.7019099638
## [86] -4.5753666098 -5.1642557266 -2.7481221530 -2.8782203654 -0.9930444704
## [91] -1.0689737305 -1.5783972995 -1.0380159333 -1.5332320899 -0.6261053110
## [96] 0.0411088954 0.3721474367 2.2198607384 2.0023547146 1.1884673403
## [101] 1.3043018409 -0.7887107383 -2.0964309112 -3.5171926149 -4.3978707535
## [106] -4.2937125479 -2.1094795649 0.0003174271 1.9226494154 0.9593493745
## [111] 0.8134718138 0.3306846828 0.3997456277 0.6752169718 -0.5407546124
## [116] -1.6978244943 -0.6312219023 -0.5972690490 0.1183319718 0.2620479526
## [121] 2.1022412464 2.4863522906 4.4575844054 4.8757690067 4.3160857500
## [126] 4.5533945371 2.5494245996 0.9087801371 -1.2175736136 -1.9406110437
## [131] -0.1972454851 0.2476564511 0.4017020994 0.2225073455 0.5000164875
## [136] -0.5832769633 -1.3456109790 -3.9300614982 -4.9131646646 -5.8028221737
## [141] -5.2926716626 -3.0460358047 -1.3040226410 0.2132688421 -0.0784369871
## [146] -0.0996436572 0.1260353647 -0.2660236350 1.0782194035 1.7045666001
## [151] 0.9758460554 0.2737953256 0.5401383054 -1.3278429554 -0.0870286339
## [156] -0.9200321168 3.0637048543 0.0366253987 0.6159264510 -0.9848095514
## [161] 1.0702410108 2.2519934840 1.2521472479 3.2483253660 0.1560601148
## [166] 0.2554054546 -1.3837918100 0.8997062858 1.5437618975 3.2200970376
## [171] 4.2428268660 4.8796814776 3.4944267802 3.5338487343 1.9056374923
## [176] 3.8243441222 2.6973660425 1.5586316888 1.0537138077 0.4735564378
## [181] 0.8667967201 -0.3227890170 -1.2601457680 -1.6767524636 -0.5606943256
## [186] -0.5724867409 -0.7927487057 -3.7823291437 -3.1600153700 -3.3339550694
## [191] -0.5223037166 1.3188603092 1.7841169179 3.2771554059 2.4302864848
## [196] 1.9737979026 0.3549837497 -0.5198143292 -0.6091253699 -0.5530998375
## [201] -0.0719700978 0.1162479295 0.9584330444 0.6344896787 2.4637658099
## [206] 2.2867046454 1.5988556633 0.7653209481 0.3915332251 -0.0218611922
## [211] 0.5574787959 0.6001278409 2.0957927366 1.2982546155 1.5728132382
## [216] 0.0805951955 -1.0094781239 -3.1290589551 -2.9867638935 -2.5487990772
## [221] -0.8746506343 -1.7204755510 -2.3373479869 -3.9397901303 -4.2603045521
## [226] -3.7080736007 -2.4567380560 -2.4451043371 -4.5475696207 -3.4437405213
## [231] -3.3531781238 -2.2477998694 -2.7793743188 -2.9892252870 -2.7065742281
## [236] -1.3646835008 0.5205827432 0.1284297696 0.9535579764 1.4436000747
## [241] 0.7192735976 0.8655621589 -1.8247428875 -1.2940820209 -2.6010932672
## [246] -2.5683240349 -3.3390482543 -2.6056391336 -4.4232833523 -3.7565659797
## [251] -5.2443430811 -4.9963973684 -4.0655108800 -3.0676982101 -2.0284891531
## [256] -0.9220225427 -1.3180193115 -2.7850434151 -1.6722862864 -2.3760548989
## [261] -1.2871979057 -1.2457433091 -0.2704251019 0.4426094002 1.7244792000
## [266] 1.6234544126 1.2271504803 0.4637832128 0.8774865319 -0.1688721412
## [271] -0.7085067912 -0.9655544239 -0.4587798338 -1.6805074767 -0.4562603842
## [276] -1.2530770377 -0.4234566530 0.5792636344 2.0183639459 1.2335658487
## [281] 2.4607872362 0.5612596789 1.2593135541 0.8965377884 1.1050964502
## [286] -0.3891819897 -0.9852126937 -0.1110588970 0.2322458578 0.2510026152
## [291] -0.7146316233 -0.0134150381 0.2259188584 -0.0139370725 -0.1067440762
## [296] 0.0047052158 1.9459829310# Scatterplot Yt vs Yt-1
plot(arma22[-n], arma22[-1],
main="Scatterplot Yt vs Yt-1",
xlab="Yt-1", ylab="Yt")
# Scatterplot Yt vs Yt-2
plot(arma22[-c(n, n-1)], arma22[-c(1,2)],
main="Scatterplot Yt vs Yt-2",
xlab="Yt-2", ylab="Yt")
# Scatterplot Yt vs Yt-3
plot(arma22[-c(n, n-1, n-2)],
arma22[-c(1,2,3)],
main="Scatterplot Yt vs Yt-3",
xlab="Yt-3", ylab="Yt")
Autokorelasi dari data bangkitan
# hitung ACF dari data bangkitan
acf_values <- acf(arma22, plot=FALSE)
# tampilkan autokorelasi lag 1-3
acf_values$acf[2:4] ## [1] 0.6871620 0.4450373 0.2813706Autokorelasi dari empiris
library(stats)
# Fungsi teoretis: gunakan ARMAacf
acf_theory <- ARMAacf(ar=c(0.5,0.2), ma=c(0.4,0.6), lag.max=10)
acf_theory[2:4] ## 1 2 3
## 0.8591993 0.7491908 0.5464353Hasil ACF, PACF, dan EACF menunnjukkan bahwa hasil simulai model ARMA(2,2) itu stationer karena
ACF tails off
PACF cut off di lag 2
EACF menunjukkan pola sesuai dengan MA(2) yaitu segitiga nol berada pada ordo MA(2)