Model Regresi dengan Peubah Lag
Pendahuluan
Latar Belakang
Tekanan udara merupakan tenaga yang bekerja untuk menggerakkan massa udara dalam setiap satuan luas tertentu (Siswanti, 2011). Perubahan tekanan udara akan menyebabkan perubahan pada suhu udara dan curah hujan. Dengan demikian penyebaran curah hujan di seluruh permukaan bumi berhubungan sangat erat dengan sistem tekanan udara. Tekanan udara berkurang dengan bertambahnya ketinggian tempat.Menuut BMKG, Tekanan udara merupakan suatu tenaga yang bekerja untuk menggerakkan massa udara dalam setiap satuan luas tertentu, tenaga yang menggerakkan massa udara tersebut menekan searah gaya gravitasi bumi. Satuan tekanan udara adalah milibar (mb) atau Hecto Pascal (hPa). Tekanan udara dipengaruhi oleh temperature/suhu udara yang terjadi pada suatu tempat dan waktu, apabila temperatur udara tinggi maka volume molekul/partikel udara akan berkembang sehingga tekanan udara menjadi rendah dan berbanding sebaliknya. Tekanan udara juga merupakan salah satu parameter yang berkaitan erat dengan variasi pembentukan arah dan kecepatan angin.
Pada analisis ini, dilakukan analisis regresi pada data rata-rata tekanan udara terhadap rata-rata temperatur udara. Analisis regresi yang digunakan yaitu dengan model koyck, distributed lag, dan autoregressive model.
Data
Beberapa library yang digunakan pada analisis model regresi ini sebagai berikut:
library(dLagM) #bisa otomatis timeseries datanya## Loading required package: nardl## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Loading required package: dynlm## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(dynlm) #data harus timeseries
library(MLmetrics) #MAPE##
## Attaching package: 'MLmetrics'## The following object is masked from 'package:dLagM':
##
## MAPE## The following object is masked from 'package:base':
##
## Recalllibrary(lmtest)
library(car)## Loading required package: carDatalibrary(zoo)
library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:car':
##
## recode## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(readxl)
library(readr)Data yang digunakan merupakan data iklim harian di kota Delhi selama 3 tahun yaitu pada periode tahun 2013-2015yang berasal dari web kaggle: https://www.kaggle.com/datasets/sumanthvrao/daily-climate-time-series-data.
Peubah yang digunakan dalam model regresi adalah date,
meanpressure, dan meantemp dengan jumlah
amatan sebanyak 1095.
data <- read.csv("D:/SEMESTER 5/DailyDelhiClimateTrain.csv")
str(data)## 'data.frame': 1095 obs. of 5 variables:
## $ date : chr "2013-01-01" "2013-01-02" "2013-01-03" "2013-01-04" ...
## $ meantemp : num 10 7.4 7.17 8.67 6 ...
## $ humidity : num 84.5 92 87 71.3 86.8 ...
## $ wind_speed : num 0 2.98 4.63 1.23 3.7 ...
## $ meanpressure: num 1016 1018 1019 1017 1016 ...data## date meantemp humidity wind_speed meanpressure
## 1 2013-01-01 10.000000 84.50000 0.0000000 1015.6667
## 2 2013-01-02 7.400000 92.00000 2.9800000 1017.8000
## 3 2013-01-03 7.166667 87.00000 4.6333333 1018.6667
## 4 2013-01-04 8.666667 71.33333 1.2333333 1017.1667
## 5 2013-01-05 6.000000 86.83333 3.7000000 1016.5000
## 6 2013-01-06 7.000000 82.80000 1.4800000 1018.0000
## 7 2013-01-07 7.000000 78.60000 6.3000000 1020.0000
## 8 2013-01-08 8.857143 63.71429 7.1428571 1018.7143
## 9 2013-01-09 14.000000 51.25000 12.5000000 1017.0000
## 10 2013-01-10 11.000000 62.00000 7.4000000 1015.6667
## 11 2013-01-11 15.714286 51.28571 10.5714286 1016.1429
## 12 2013-01-12 14.000000 74.00000 13.2285714 1015.5714
## 13 2013-01-13 15.833333 75.16667 4.6333333 1013.3333
## 14 2013-01-14 12.833333 88.16667 0.6166667 1015.1667
## 15 2013-01-15 14.714286 71.85714 0.5285714 1015.8571
## 16 2013-01-16 13.833333 86.66667 0.0000000 1016.6667
## 17 2013-01-17 16.500000 80.83333 5.2500000 1015.8333
## 18 2013-01-18 13.833333 92.16667 8.9500000 1014.5000
## 19 2013-01-19 12.500000 76.66667 5.8833333 1021.6667
## 20 2013-01-20 11.285714 75.28571 8.4714286 1020.2857
## 21 2013-01-21 11.200000 77.00000 2.2200000 1021.0000
## 22 2013-01-22 9.500000 79.66667 3.0833333 1021.8000
## 23 2013-01-23 14.000000 60.16667 4.0166667 1020.5000
## 24 2013-01-24 13.833333 60.66667 6.1666667 1020.5000
## 25 2013-01-25 12.250000 67.00000 5.5500000 1020.7500
## 26 2013-01-26 12.666667 64.16667 6.8000000 1019.6667
## 27 2013-01-27 12.857143 65.57143 5.5571429 1018.1429
## 28 2013-01-28 14.833333 56.00000 3.7000000 1017.8333
## 29 2013-01-29 14.125000 65.50000 3.2375000 1016.6250
## 30 2013-01-30 14.714286 70.42857 1.0571429 1017.8571
## 31 2013-01-31 16.200000 65.60000 2.9600000 1018.4000
## 32 2013-02-01 16.000000 73.00000 2.2200000 1016.0000
## 33 2013-02-02 16.285714 77.57143 1.3285714 1017.1429
## 34 2013-02-03 18.000000 65.57143 1.8571429 1015.2857
## 35 2013-02-04 17.428571 74.28571 11.1142857 1014.5714
## 36 2013-02-05 16.625000 92.37500 9.7250000 1016.3750
## 37 2013-02-06 16.666667 71.33333 8.6333333 1018.6667
## 38 2013-02-07 15.600000 59.40000 10.7400000 1018.6000
## 39 2013-02-08 14.000000 70.42857 9.2571429 1017.1429
## 40 2013-02-09 15.428571 61.28571 9.2571429 1016.8571
## 41 2013-02-10 15.250000 71.50000 3.4750000 1017.1250
## 42 2013-02-11 15.875000 70.50000 5.3250000 1016.5000
## 43 2013-02-12 15.333333 70.33333 7.4166667 1017.5000
## 44 2013-02-13 16.285714 70.14286 6.0857143 1016.0000
## 45 2013-02-14 17.333333 63.83333 4.3333333 1014.1667
## 46 2013-02-15 19.166667 65.33333 10.1833333 1011.6667
## 47 2013-02-16 14.428571 92.71429 8.4857143 1008.0000
## 48 2013-02-17 13.666667 90.00000 0.0000000 1012.6667
## 49 2013-02-18 15.600000 78.40000 12.2200000 1016.2000
## 50 2013-02-19 15.857143 82.00000 5.8142857 1015.7143
## 51 2013-02-20 17.714286 74.71429 5.8142857 1017.0000
## 52 2013-02-21 20.000000 67.28571 6.6142857 1015.4286
## 53 2013-02-22 20.500000 65.62500 10.8750000 1016.0000
## 54 2013-02-23 17.428571 74.85714 9.2571429 1017.0000
## 55 2013-02-24 16.857143 78.85714 7.4000000 1018.8571
## 56 2013-02-25 16.875000 72.87500 4.6375000 1018.2500
## 57 2013-02-26 17.857143 70.00000 17.5875000 1015.1429
## 58 2013-02-27 20.800000 57.20000 6.6600000 1015.2000
## 59 2013-02-28 19.428571 52.85714 12.9571429 1017.4286
## 60 2013-03-01 17.333333 49.33333 24.0666667 1016.3333
## 61 2013-03-02 19.000000 54.00000 15.7250000 1016.2500
## 62 2013-03-03 19.333333 62.83333 8.6333333 1016.1667
## 63 2013-03-04 17.600000 71.00000 5.5600000 1015.8000
## 64 2013-03-05 20.875000 61.87500 4.1625000 1016.3750
## 65 2013-03-06 20.857143 65.28571 6.8714286 1015.7143
## 66 2013-03-07 23.428571 57.14286 8.7285714 1015.2857
## 67 2013-03-08 24.166667 44.83333 7.1000000 1014.8333
## 68 2013-03-09 25.428571 49.71429 5.2857143 1009.2857
## 69 2013-03-10 23.142857 57.57143 4.2285714 1008.0000
## 70 2013-03-11 24.000000 66.33333 0.9333333 1011.1667
## 71 2013-03-12 23.500000 62.50000 4.9333333 1011.5000
## 72 2013-03-13 21.500000 70.50000 5.5500000 1009.0000
## 73 2013-03-14 22.333333 61.16667 12.0333333 1013.1667
## 74 2013-03-15 24.166667 45.83333 7.7166667 1016.1667
## 75 2013-03-16 20.333333 67.66667 3.7000000 1016.1667
## 76 2013-03-17 22.666667 58.66667 8.9500000 1015.0000
## 77 2013-03-18 23.428571 58.14286 17.4571429 1009.4286
## 78 2013-03-19 22.500000 73.66667 10.4833333 1011.0000
## 79 2013-03-20 29.166667 36.33333 6.8000000 1009.5000
## 80 2013-03-21 23.833333 58.50000 10.5000000 1008.3333
## 81 2013-03-22 25.250000 50.25000 9.7125000 1006.3750
## 82 2013-03-23 27.375000 50.12500 9.9500000 1007.6250
## 83 2013-03-24 27.000000 48.75000 10.8875000 1010.2500
## 84 2013-03-25 23.500000 45.50000 15.9625000 1010.6250
## 85 2013-03-26 24.142857 44.57143 12.9571429 1008.8571
## 86 2013-03-27 21.000000 62.00000 1.8500000 1009.0000
## 87 2013-03-28 22.428571 62.71429 7.4142857 1009.5714
## 88 2013-03-29 21.250000 70.37500 5.5500000 1009.7500
## 89 2013-03-30 23.500000 54.75000 11.1125000 1008.6250
## 90 2013-03-31 23.200000 58.00000 6.6600000 1008.6000
## 91 2013-04-01 25.375000 45.50000 4.4000000 1008.5000
## 92 2013-04-02 25.166667 51.00000 8.6500000 1009.5000
## 93 2013-04-03 26.200000 45.60000 8.1400000 1009.0000
## 94 2013-04-04 24.600000 41.80000 11.1200000 1007.8000
## 95 2013-04-05 25.600000 31.00000 15.5600000 1007.0000
## 96 2013-04-06 25.857143 29.85714 11.9000000 1006.1429
## 97 2013-04-07 29.142857 23.28571 10.3142857 1005.0000
## 98 2013-04-08 28.714286 33.85714 5.3000000 1006.0000
## 99 2013-04-09 30.166667 30.50000 8.6500000 1005.3333
## 100 2013-04-10 30.000000 28.00000 6.1000000 1006.7143
## 101 2013-04-11 30.000000 24.20000 7.7800000 1006.4000
## 102 2013-04-12 28.857143 32.57143 6.3428571 1007.5714
## 103 2013-04-13 30.200000 29.20000 10.0000000 1008.4000
## 104 2013-04-14 28.250000 39.37500 6.4875000 1007.0000
## 105 2013-04-15 28.250000 41.37500 6.2500000 1003.8750
## 106 2013-04-16 32.125000 24.62500 10.4250000 1000.0000
## 107 2013-04-17 29.200000 24.20000 6.6600000 1002.2000
## 108 2013-04-18 30.285714 30.28571 4.7571429 1002.8571
## 109 2013-04-19 28.285714 31.28571 3.9714286 1002.5714
## 110 2013-04-20 30.625000 29.00000 7.6375000 1003.3750
## 111 2013-04-21 27.666667 38.66667 13.8833333 1006.8333
## 112 2013-04-22 27.375000 45.37500 7.6500000 1010.0000
## 113 2013-04-23 28.625000 44.12500 4.6250000 1009.8750
## 114 2013-04-24 30.285714 41.71429 2.1142857 1008.5714
## 115 2013-04-25 31.142857 38.28571 3.7000000 1007.7143
## 116 2013-04-26 29.875000 45.87500 6.7125000 1008.3750
## 117 2013-04-27 31.142857 31.42857 13.4857143 1007.0000
## 118 2013-04-28 30.571429 28.00000 12.9714286 1005.4286
## 119 2013-04-29 32.125000 26.37500 7.8750000 1004.8750
## 120 2013-04-30 31.142857 32.00000 7.9285714 1004.8571
## 121 2013-05-01 31.857143 15.85714 12.6857143 1002.8333
## 122 2013-05-02 29.833333 22.16667 11.4333333 1001.2000
## 123 2013-05-03 28.571429 31.57143 9.0000000 999.4286
## 124 2013-05-04 32.857143 31.42857 2.9142857 999.0000
## 125 2013-05-05 32.625000 31.12500 3.0125000 1000.6250
## 126 2013-05-06 32.750000 39.25000 3.7000000 1001.6250
## 127 2013-05-07 32.875000 33.25000 7.1750000 1002.0000
## 128 2013-05-08 34.500000 23.00000 9.2500000 1001.1667
## 129 2013-05-09 34.285714 26.00000 8.9857143 1000.8571
## 130 2013-05-10 34.000000 27.71429 9.5285714 1000.1429
## 131 2013-05-11 30.750000 30.37500 14.8125000 999.8750
## 132 2013-05-12 29.857143 40.14286 5.8285714 1003.7143
## 133 2013-05-13 31.714286 34.00000 3.9714286 1003.5714
## 134 2013-05-14 32.285714 34.28571 4.7714286 1001.5714
## 135 2013-05-15 33.000000 33.00000 3.2375000 999.8571
## 136 2013-05-16 33.000000 34.75000 7.1750000 998.5000
## 137 2013-05-17 32.833333 28.16667 9.8666667 1000.3333
## 138 2013-05-18 31.400000 42.20000 12.9666667 999.0000
## 139 2013-05-19 35.333333 22.33333 15.7500000 999.6667
## 140 2013-05-20 36.400000 24.20000 7.4000000 998.4000
## 141 2013-05-21 36.000000 19.00000 11.3714286 998.6667
## 142 2013-05-22 36.750000 22.12500 17.5875000 998.6250
## 143 2013-05-23 37.500000 23.33333 13.5666667 997.1667
## 144 2013-05-24 38.428571 27.42857 11.3857143 996.4286
## 145 2013-05-25 38.714286 22.42857 10.3142857 998.1429
## 146 2013-05-26 37.800000 21.20000 10.7400000 998.2000
## 147 2013-05-27 35.857143 31.57143 8.7285714 999.1429
## 148 2013-05-28 35.333333 29.00000 8.3333333 1000.1667
## 149 2013-05-29 34.142857 27.85714 5.5571429 999.4286
## 150 2013-05-30 32.200000 28.20000 5.5600000 999.6000
## 151 2013-05-31 33.625000 40.12500 10.6375000 998.7143
## 152 2013-06-01 32.000000 54.00000 13.4375000 998.7500
## 153 2013-06-02 32.400000 56.60000 14.2000000 1001.0000
## 154 2013-06-03 35.600000 47.00000 12.2400000 999.6000
## 155 2013-06-04 35.857143 42.57143 5.0285714 999.8571
## 156 2013-06-05 37.166667 36.50000 9.8666667 998.0000
## 157 2013-06-06 31.285714 61.71429 10.0428571 997.2857
## 158 2013-06-07 34.000000 49.25000 7.4125000 998.0000
## 159 2013-06-08 34.200000 57.40000 13.3400000 997.0000
## 160 2013-06-09 36.166667 40.00000 11.4166667 995.1667
## 161 2013-06-10 36.625000 42.75000 8.1000000 995.1250
## 162 2013-06-11 30.166667 61.66667 16.3500000 1000.0000
## 163 2013-06-12 34.142857 54.14286 7.4142857 998.0000
## 164 2013-06-13 29.833333 68.66667 9.8666667 998.6667
## 165 2013-06-14 30.142857 68.14286 7.9428571 997.4286
## 166 2013-06-15 30.714286 65.00000 13.2285714 997.8571
## 167 2013-06-16 27.000000 88.85714 8.4857143 996.4286
## 168 2013-06-17 26.875000 87.37500 8.3375000 994.7500
## 169 2013-06-18 28.400000 83.60000 5.1800000 996.4000
## 170 2013-06-19 29.857143 72.85714 4.2285714 999.0000
## 171 2013-06-20 33.000000 52.71429 4.7714286 997.1667
## 172 2013-06-21 34.833333 47.33333 5.8666667 995.3333
## 173 2013-06-22 35.600000 39.40000 10.7400000 996.2000
## 174 2013-06-23 35.166667 53.00000 8.3500000 995.6667
## 175 2013-06-24 33.142857 55.00000 13.2285714 996.2857
## 176 2013-06-25 30.571429 70.42857 11.1142857 999.1667
## 177 2013-06-26 30.666667 71.50000 6.4833333 999.0000
## 178 2013-06-27 31.428571 61.85714 7.9571429 996.7143
## 179 2013-06-28 31.500000 64.25000 8.8125000 996.0000
## 180 2013-06-29 33.250000 57.00000 13.8750000 995.2500
## 181 2013-06-30 32.833333 52.16667 10.5000000 997.1667
## 182 2013-07-01 33.857143 54.00000 8.7285714 996.4286
## 183 2013-07-02 33.142857 58.28571 9.8000000 996.0000
## 184 2013-07-03 31.571429 70.00000 6.3571429 997.5714
## 185 2013-07-04 32.375000 67.50000 9.2500000 997.0000
## 186 2013-07-05 32.800000 62.20000 12.9600000 997.8000
## 187 2013-07-06 31.000000 73.14286 11.3714286 1000.5714
## 188 2013-07-07 31.166667 77.33333 7.1000000 1000.1667
## 189 2013-07-08 29.833333 75.16667 6.4833333 997.5000
## 190 2013-07-09 29.000000 78.83333 8.0166667 996.8333
## 191 2013-07-10 29.750000 75.37500 6.4875000 995.7500
## 192 2013-07-11 32.500000 65.50000 7.1166667 997.3333
## 193 2013-07-12 28.875000 86.62500 5.5625000 1000.0000
## 194 2013-07-13 31.750000 70.25000 12.0625000 998.8750
## 195 2013-07-14 30.750000 71.62500 4.8125000 997.3750
## 196 2013-07-15 31.750000 73.25000 13.5375000 998.3750
## 197 2013-07-16 29.875000 83.87500 9.0000000 999.0000
## 198 2013-07-17 31.125000 78.37500 8.6500000 998.0000
## 199 2013-07-18 31.750000 76.00000 5.5500000 995.0000
## 200 2013-07-19 30.500000 73.50000 9.2666667 995.3333
## 201 2013-07-20 26.833333 90.66667 4.9333333 999.1667
## 202 2013-07-21 28.200000 88.00000 2.2400000 996.4000
## 203 2013-07-22 29.500000 80.33333 4.3333333 996.8333
## 204 2013-07-23 31.857143 70.71429 3.9714286 998.0000
## 205 2013-07-24 29.714286 84.14286 3.9714286 997.1429
## 206 2013-07-25 28.333333 84.50000 8.0166667 995.1667
## 207 2013-07-26 30.000000 73.85714 5.5714286 995.4286
## 208 2013-07-27 30.142857 79.00000 4.2285714 997.2857
## 209 2013-07-28 32.285714 67.42857 6.0857143 998.1429
## 210 2013-07-29 31.000000 77.42857 4.7714286 997.1429
## 211 2013-07-30 30.500000 75.66667 8.0166667 996.5000
## 212 2013-07-31 28.833333 78.50000 9.8666667 996.6667
## 213 2013-08-01 30.000000 73.50000 5.5500000 998.0000
## 214 2013-08-02 31.571429 66.42857 11.1142857 999.4286
## 215 2013-08-03 32.500000 62.33333 10.8166667 1000.8333
## 216 2013-08-04 32.500000 62.50000 5.1000000 993.2500
## 217 2013-08-05 29.500000 77.00000 6.7833333 1001.0000
## 218 2013-08-06 27.166667 90.66667 4.0166667 1002.1667
## 219 2013-08-07 28.375000 85.25000 3.2500000 1001.8750
## 220 2013-08-08 28.500000 84.00000 6.1666667 1000.5000
## 221 2013-08-09 27.166667 87.50000 3.7166667 1001.0000
## 222 2013-08-10 29.428571 79.85714 6.1000000 1000.3333
## 223 2013-08-11 30.000000 76.83333 6.8000000 1001.1667
## 224 2013-08-12 29.500000 81.50000 8.3500000 1001.0000
## 225 2013-08-13 30.750000 72.00000 11.1250000 999.2500
## 226 2013-08-14 29.666667 74.33333 9.8666667 999.8333
## 227 2013-08-15 27.714286 85.00000 8.2000000 1001.7143
## 228 2013-08-16 26.600000 92.00000 4.4600000 1000.8000
## 229 2013-08-17 27.428571 91.00000 14.2857143 999.4286
## 230 2013-08-18 28.333333 83.83333 1.2333333 1000.1667
## 231 2013-08-19 28.166667 84.66667 5.5500000 1000.5000
## 232 2013-08-20 27.375000 88.50000 5.3250000 999.0000
## 233 2013-08-21 28.333333 81.16667 10.3142857 999.2857
## 234 2013-08-22 29.166667 74.83333 6.4833333 1001.1667
## 235 2013-08-23 31.285714 73.14286 2.6428571 1001.4286
## 236 2013-08-24 32.000000 71.25000 18.5250000 1000.3333
## 237 2013-08-25 29.000000 90.75000 0.9250000 998.7500
## 238 2013-08-26 32.000000 69.87500 6.4750000 997.8571
## 239 2013-08-27 32.142857 57.28571 17.0714286 999.8571
## 240 2013-08-28 30.142857 60.71429 11.6428571 1003.7143
## 241 2013-08-29 31.500000 57.00000 9.2750000 1003.2500
## 242 2013-08-30 29.166667 73.00000 3.1000000 1003.5000
## 243 2013-08-31 29.000000 71.75000 4.6500000 1003.2500
## 244 2013-09-01 30.000000 65.20000 11.4800000 1003.2000
## 245 2013-09-02 31.857143 50.85714 15.3428571 1003.7143
## 246 2013-09-03 32.750000 45.50000 14.8000000 1001.5000
## 247 2013-09-04 31.714286 48.00000 14.5428571 1002.1667
## 248 2013-09-05 31.666667 46.00000 13.5666667 1001.5000
## 249 2013-09-06 30.571429 55.71429 10.0428571 1003.4286
## 250 2013-09-07 30.833333 51.83333 6.7833333 1004.1667
## 251 2013-09-08 28.000000 71.75000 2.3250000 1007.2500
## 252 2013-09-09 31.000000 57.50000 42.2200000 1007.0000
## 253 2013-09-10 29.666667 66.33333 3.7000000 1005.3333
## 254 2013-09-11 30.857143 61.14286 3.9714286 1005.5714
## 255 2013-09-12 31.166667 60.33333 2.7833333 1008.1667
## 256 2013-09-13 31.142857 67.14286 3.1714286 1007.1429
## 257 2013-09-14 30.500000 67.00000 2.7833333 1003.8333
## 258 2013-09-15 31.625000 56.37500 3.9375000 1001.3750
## 259 2013-09-16 29.666667 60.00000 7.1000000 1002.3333
## 260 2013-09-17 29.250000 56.50000 3.4750000 1002.8750
## 261 2013-09-18 29.142857 58.57143 5.5571429 1003.1429
## 262 2013-09-19 29.800000 61.60000 2.9600000 1001.8000
## 263 2013-09-20 28.666667 70.00000 9.5833333 1003.0000
## 264 2013-09-21 25.200000 89.00000 5.1800000 1003.0000
## 265 2013-09-22 28.333333 79.66667 3.0833333 1001.6667
## 266 2013-09-23 30.285714 68.00000 4.5000000 1001.0000
## 267 2013-09-24 30.750000 65.75000 5.7875000 1002.7500
## 268 2013-09-25 28.571429 75.00000 6.6142857 1005.4286
## 269 2013-09-26 28.200000 78.80000 4.0800000 1006.6000
## 270 2013-09-27 29.000000 71.25000 7.4125000 1005.6250
## 271 2013-09-28 30.000000 67.33333 1.2333333 1005.3333
## 272 2013-09-29 28.142857 79.85714 5.5571429 1003.8571
## 273 2013-09-30 26.857143 84.57143 4.2285714 1004.7143
## 274 2013-10-01 28.285714 68.71429 6.3714286 1007.7143
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## 285 2013-10-12 26.142857 82.57143 2.9142857 1008.2857
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## 334 2013-11-30 17.875000 69.62500 11.8125000 1015.8750
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## 365 2013-12-31 14.500000 89.37500 4.8625000 1020.5000
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## 372 2014-01-07 12.142857 72.28571 20.6000000 1017.7500
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## 383 2014-01-18 12.500000 94.25000 1.8500000 1020.2500
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## 385 2014-01-20 14.625000 83.50000 4.4125000 1021.3750
## 386 2014-01-21 13.571429 96.85714 7.1714286 1020.5714
## 387 2014-01-22 15.250000 96.12500 6.7125000 1019.8750
## 388 2014-01-23 15.625000 90.12500 6.7125000 1020.2500
## 389 2014-01-24 13.875000 88.87500 8.1125000 1019.2500
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## 394 2014-01-29 14.875000 81.87500 4.6250000 1018.6250
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## 494 2014-05-09 30.500000 39.62500 6.4875000 1000.4286
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## 498 2014-05-13 25.250000 65.75000 9.9625000 1008.3750
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## 500 2014-05-15 29.500000 39.87500 11.1250000 1004.2500
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## 507 2014-05-22 33.250000 33.37500 11.1125000 999.5000
## 508 2014-05-23 34.625000 32.75000 19.4500000 1000.0000
## 509 2014-05-24 31.500000 50.50000 6.7250000 1004.1250
## 510 2014-05-25 31.500000 43.25000 16.4375000 1005.5000
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## 519 2014-06-03 34.875000 33.62500 6.4875000 1000.0000
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## 891 2015-06-10 36.625000 32.28571 18.0500000 999.6250
## 892 2015-06-11 35.625000 34.75000 18.2875000 1000.0000
## 893 2015-06-12 35.875000 34.62500 12.7375000 998.5000
## 894 2015-06-13 31.125000 48.12500 10.1875000 998.8571
## 895 2015-06-14 27.000000 77.62500 3.9500000 1000.2857
## 896 2015-06-15 31.000000 60.75000 3.0125000 999.5714
## 897 2015-06-16 32.375000 52.12500 2.7875000 999.1429
## 898 2015-06-17 33.875000 49.75000 3.2500000 998.0000
## 899 2015-06-18 35.125000 45.12500 3.0125000 997.6250
## 900 2015-06-19 35.875000 46.75000 8.5750000 996.2500
## 901 2015-06-20 33.125000 48.50000 12.9750000 997.8750
## 902 2015-06-21 30.375000 63.62500 8.1125000 998.1250
## 903 2015-06-22 32.125000 59.50000 4.4000000 995.6250
## 904 2015-06-23 31.500000 61.62500 6.0125000 995.0000
## 905 2015-06-24 37.250000 63.87500 6.5000000 995.3750
## 906 2015-06-25 26.625000 82.75000 6.2625000 994.7500
## 907 2015-06-26 31.125000 54.25000 11.5625000 995.2500
## 908 2015-06-27 32.625000 48.25000 14.1125000 997.1250
## 909 2015-06-28 34.250000 47.50000 9.0375000 1000.2857
## 910 2015-06-29 31.125000 56.62500 11.5625000 1003.6250
## 911 2015-06-30 30.875000 58.62500 9.9625000 1002.6250
## 912 2015-07-01 32.000000 53.25000 4.1750000 1001.8750
## 913 2015-07-02 33.750000 45.87500 6.9500000 1001.1250
## 914 2015-07-03 33.000000 49.00000 14.3500000 999.6250
## 915 2015-07-04 34.125000 51.50000 16.9000000 997.5000
## 916 2015-07-05 35.714286 47.28571 14.0142857 995.4286
## 917 2015-07-06 27.875000 83.25000 9.2750000 997.8750
## 918 2015-07-07 28.125000 86.12500 1.8500000 998.1250
## 919 2015-07-08 31.250000 72.00000 2.7750000 998.6250
## 920 2015-07-09 29.625000 77.25000 2.5500000 998.6250
## 921 2015-07-10 26.625000 92.12500 6.0250000 998.7500
## 922 2015-07-11 25.500000 98.00000 3.2375000 999.3333
## 923 2015-07-12 25.500000 94.75000 7.4250000 998.6250
## 924 2015-07-13 29.875000 73.12500 4.8625000 1000.6250
## 925 2015-07-14 30.875000 67.87500 10.8750000 997.8571
## 926 2015-07-15 33.375000 52.87500 17.1375000 993.7500
## 927 2015-07-16 31.750000 61.37500 13.4375000 994.7500
## 928 2015-07-17 30.750000 75.62500 4.4000000 997.2500
## 929 2015-07-18 29.500000 78.87500 4.1750000 998.0000
## 930 2015-07-19 30.125000 70.00000 0.7000000 997.6250
## 931 2015-07-20 29.125000 78.00000 4.8625000 999.1250
## 932 2015-07-21 31.375000 69.25000 8.1250000 1000.0000
## 933 2015-07-22 32.250000 64.12500 7.8750000 1001.1250
## 934 2015-07-23 32.125000 64.87500 8.5750000 1001.7500
## 935 2015-07-24 32.000000 64.75000 6.7125000 1001.0000
## 936 2015-07-25 30.857143 71.00000 19.9125000 998.5714
## 937 2015-07-26 30.000000 71.62500 16.8875000 998.8750
## 938 2015-07-27 29.625000 69.00000 11.3375000 1000.2857
## 939 2015-07-28 29.500000 61.00000 11.5875000 1000.1250
## 940 2015-07-29 28.500000 68.12500 10.8750000 998.0000
## 941 2015-07-30 29.000000 67.75000 9.9625000 998.8750
## 942 2015-07-31 29.000000 71.00000 4.1750000 999.7500
## 943 2015-08-01 28.250000 71.75000 0.9250000 1002.7500
## 944 2015-08-02 29.625000 69.50000 2.5500000 1003.6250
## 945 2015-08-03 31.500000 58.62500 5.3250000 1001.8750
## 946 2015-08-04 29.428571 77.78571 4.7714286 1000.0714
## 947 2015-08-05 29.593750 79.65625 8.2218750 1000.2812
## 948 2015-08-06 29.500000 79.12500 3.0250000 998.0000
## 949 2015-08-07 29.250000 83.00000 2.3125000 1000.0000
## 950 2015-08-08 28.875000 84.87500 1.6250000 1002.0000
## 951 2015-08-09 27.375000 90.12500 3.0125000 1000.2500
## 952 2015-08-10 30.375000 77.00000 0.0000000 1000.0000
## 953 2015-08-11 28.375000 86.62500 0.4625000 1003.0000
## 954 2015-08-12 30.750000 74.25000 0.0000000 1003.1250
## 955 2015-08-13 32.000000 69.50000 0.4625000 1001.8750
## 956 2015-08-14 30.875000 72.62500 3.4750000 1002.0000
## 957 2015-08-15 28.500000 85.50000 0.0000000 1002.7500
## 958 2015-08-16 28.625000 82.62500 1.8500000 1002.8750
## 959 2015-08-17 30.750000 72.62500 0.7000000 1001.3750
## 960 2015-08-18 29.125000 72.87500 4.8750000 1002.5714
## 961 2015-08-19 31.250000 61.25000 33.3250000 1002.3750
## 962 2015-08-20 30.750000 58.62500 14.6000000 1001.3750
## 963 2015-08-21 29.375000 72.00000 8.5750000 1002.0000
## 964 2015-08-22 30.250000 65.37500 5.8000000 1000.8750
## 965 2015-08-23 29.875000 69.37500 5.5625000 1000.8571
## 966 2015-08-24 30.750000 65.62500 7.1875000 1001.7500
## 967 2015-08-25 32.000000 57.28571 10.0714286 1001.0000
## 968 2015-08-26 32.000000 61.00000 4.8625000 1001.1250
## 969 2015-08-27 32.500000 61.00000 5.3250000 1002.0000
## 970 2015-08-28 32.000000 63.50000 2.3125000 1002.2500
## 971 2015-08-29 32.250000 58.00000 5.8125000 1001.3750
## 972 2015-08-30 32.625000 56.50000 9.2750000 1001.3750
## 973 2015-08-31 31.857143 54.42857 13.4857143 1001.8333
## 974 2015-09-01 32.125000 47.62500 15.2750000 1000.8571
## 975 2015-09-02 31.875000 45.62500 12.7375000 1001.7500
## 976 2015-09-03 31.625000 49.12500 10.1875000 1005.5000
## 977 2015-09-04 32.000000 42.62500 11.3500000 1007.8750
## 978 2015-09-05 30.875000 47.25000 7.6375000 1007.1250
## 979 2015-09-06 31.250000 41.80000 7.6375000 1006.2500
## 980 2015-09-07 31.500000 46.37500 9.4875000 1005.7500
## 981 2015-09-08 31.625000 47.00000 11.8125000 1005.5000
## 982 2015-09-09 31.000000 47.87500 10.1875000 1005.6250
## 983 2015-09-10 31.250000 46.50000 8.5750000 1006.7500
## 984 2015-09-11 30.750000 49.75000 6.0125000 1006.2500
## 985 2015-09-12 32.142857 54.42857 3.1714286 1006.0000
## 986 2015-09-13 32.125000 55.25000 1.3875000 1005.8750
## 987 2015-09-14 31.875000 54.37500 2.5500000 1003.6250
## 988 2015-09-15 33.000000 55.00000 0.4625000 1003.2500
## 989 2015-09-16 32.375000 55.00000 1.4000000 1003.6250
## 990 2015-09-17 31.375000 58.37500 1.1625000 1004.3750
## 991 2015-09-18 31.000000 67.62500 7.4125000 1005.1250
## 992 2015-09-19 30.625000 74.25000 2.0875000 1003.6250
## 993 2015-09-20 29.142857 69.14286 5.5571429 1002.8571
## 994 2015-09-21 30.125000 64.50000 5.8000000 1002.5000
## 995 2015-09-22 30.250000 64.37500 10.1875000 1002.5000
## 996 2015-09-23 28.625000 61.25000 13.6750000 1006.3750
## 997 2015-09-24 28.250000 52.37500 11.5750000 1004.6250
## 998 2015-09-25 28.500000 49.37500 8.5750000 1003.7500
## 999 2015-09-26 29.250000 53.50000 6.2500000 1005.2500
## 1000 2015-09-27 28.714286 58.14286 2.9142857 1007.0000
## 1001 2015-09-28 28.250000 58.50000 3.9375000 1009.0000
## 1002 2015-09-29 29.000000 54.57143 9.5285714 1010.5714
## 1003 2015-09-30 29.000000 46.87500 8.3375000 1011.3750
## 1004 2015-10-01 28.125000 51.25000 5.5750000 1012.0000
## 1005 2015-10-02 28.285714 53.71429 14.5875000 1010.7500
## 1006 2015-10-03 30.000000 52.33333 18.7857143 1008.7143
## 1007 2015-10-04 29.000000 54.37500 3.0250000 1008.1250
## 1008 2015-10-05 28.875000 59.37500 1.3875000 1009.2500
## 1009 2015-10-06 28.375000 61.12500 4.6375000 1009.0000
## 1010 2015-10-07 28.625000 65.75000 6.4750000 1009.1250
## 1011 2015-10-08 28.375000 65.12500 4.4125000 1007.5000
## 1012 2015-10-09 28.500000 59.75000 6.0250000 1004.2500
## 1013 2015-10-10 28.500000 54.62500 6.7125000 1005.0000
## 1014 2015-10-11 28.571429 51.57143 6.8857143 1008.7143
## 1015 2015-10-12 29.250000 54.12500 3.2500000 1010.0000
## 1016 2015-10-13 29.500000 62.87500 3.7250000 1011.0000
## 1017 2015-10-14 28.125000 63.62500 4.8750000 1013.2500
## 1018 2015-10-15 27.500000 66.00000 0.4625000 1013.5000
## 1019 2015-10-16 27.875000 62.62500 0.9250000 1013.5000
## 1020 2015-10-17 28.000000 63.75000 3.7125000 1012.2500
## 1021 2015-10-18 26.857143 71.71429 11.1125000 1013.1250
## 1022 2015-10-19 28.142857 66.28571 3.4571429 1011.7143
## 1023 2015-10-20 27.714286 64.85714 2.9142857 1009.8571
## 1024 2015-10-21 26.500000 62.12500 2.0875000 1011.8750
## 1025 2015-10-22 24.750000 56.00000 4.4000000 1012.2500
## 1026 2015-10-23 24.000000 51.62500 4.8625000 1011.8750
## 1027 2015-10-24 24.875000 53.25000 1.4000000 1011.6250
## 1028 2015-10-25 26.375000 47.12500 5.5750000 1012.7500
## 1029 2015-10-26 25.625000 52.12500 5.5750000 1014.8750
## 1030 2015-10-27 24.750000 54.25000 3.4750000 1013.8750
## 1031 2015-10-28 20.875000 57.25000 7.8750000 1015.8750
## 1032 2015-10-29 22.125000 63.50000 1.8500000 1016.8750
## 1033 2015-10-30 22.375000 67.25000 1.6250000 1016.3750
## 1034 2015-10-31 22.375000 69.37500 1.1625000 1016.1250
## 1035 2015-11-01 22.875000 70.50000 0.9250000 1016.2500
## 1036 2015-11-02 23.375000 71.37500 0.4625000 1015.8750
## 1037 2015-11-03 24.000000 67.87500 0.4750000 1014.2500
## 1038 2015-11-04 23.750000 69.00000 0.9250000 1012.2500
## 1039 2015-11-05 22.125000 75.25000 5.1000000 1012.3750
## 1040 2015-11-06 22.875000 74.37500 2.3250000 1012.7500
## 1041 2015-11-07 21.875000 74.87500 1.1625000 1014.6250
## 1042 2015-11-08 21.875000 70.25000 1.8625000 1015.8750
## 1043 2015-11-09 21.750000 73.62500 0.7000000 1015.0000
## 1044 2015-11-10 22.750000 72.62500 0.7000000 1013.5000
## 1045 2015-11-11 21.875000 59.50000 4.6375000 1014.3750
## 1046 2015-11-12 21.875000 60.50000 5.7875000 1015.3750
## 1047 2015-11-13 22.375000 59.37500 5.3250000 1014.8750
## 1048 2015-11-14 22.375000 59.62500 3.4750000 1012.0000
## 1049 2015-11-15 22.500000 62.00000 0.0000000 1012.0000
## 1050 2015-11-16 21.875000 50.37500 2.7875000 1012.6250
## 1051 2015-11-17 19.875000 48.37500 5.1000000 1013.5000
## 1052 2015-11-18 18.500000 57.62500 4.4000000 1016.3750
## 1053 2015-11-19 18.500000 64.75000 0.9250000 1017.5000
## 1054 2015-11-20 18.500000 66.00000 0.4625000 1016.1250
## 1055 2015-11-21 18.750000 67.62500 1.3875000 1015.5000
## 1056 2015-11-22 18.625000 64.87500 0.4625000 1015.1250
## 1057 2015-11-23 17.000000 73.50000 0.0000000 1015.8750
## 1058 2015-11-24 18.500000 63.00000 1.6250000 1016.0000
## 1059 2015-11-25 19.375000 56.37500 5.7875000 1014.7500
## 1060 2015-11-26 20.000000 59.50000 0.9250000 1012.7500
## 1061 2015-11-27 18.500000 66.25000 2.5500000 1011.2500
## 1062 2015-11-28 18.750000 82.12500 1.1625000 1015.3750
## 1063 2015-11-29 18.125000 81.25000 1.1625000 1018.0000
## 1064 2015-11-30 19.500000 82.37500 0.9250000 1016.7500
## 1065 2015-12-01 19.250000 78.75000 1.6250000 1014.7500
## 1066 2015-12-02 18.125000 72.12500 2.0875000 1016.1250
## 1067 2015-12-03 17.625000 70.25000 7.1875000 1016.0000
## 1068 2015-12-04 17.625000 67.50000 4.6375000 1015.0000
## 1069 2015-12-05 17.500000 72.37500 0.9250000 1015.8750
## 1070 2015-12-06 17.125000 75.87500 1.4000000 1016.5000
## 1071 2015-12-07 17.625000 76.87500 2.3125000 1017.2500
## 1072 2015-12-08 18.428571 71.28571 1.0571429 1015.7143
## 1073 2015-12-09 18.375000 78.12500 3.4750000 1015.2500
## 1074 2015-12-10 19.000000 77.25000 2.0875000 1011.7500
## 1075 2015-12-11 17.250000 77.87500 5.1000000 1011.3750
## 1076 2015-12-12 13.250000 91.00000 4.4000000 1014.2500
## 1077 2015-12-13 12.875000 67.00000 3.4750000 1016.5000
## 1078 2015-12-14 13.250000 63.62500 7.4000000 1017.0000
## 1079 2015-12-15 13.125000 63.87500 5.3250000 1016.5000
## 1080 2015-12-16 13.000000 65.50000 1.1625000 1016.3750
## 1081 2015-12-17 12.250000 73.62500 0.9250000 1016.8750
## 1082 2015-12-18 12.875000 71.25000 4.4000000 1018.6250
## 1083 2015-12-19 12.375000 71.87500 3.4875000 1019.0000
## 1084 2015-12-20 11.750000 70.25000 1.1625000 1018.5000
## 1085 2015-12-21 12.625000 74.75000 1.3875000 1018.8750
## 1086 2015-12-22 12.000000 79.87500 0.7000000 1020.8750
## 1087 2015-12-23 12.500000 81.37500 3.4875000 1020.6250
## 1088 2015-12-24 11.250000 68.62500 6.0250000 1021.2500
## 1089 2015-12-25 11.500000 66.12500 5.5625000 1022.0000
## 1090 2015-12-26 12.750000 64.50000 6.4875000 1021.1250
## 1091 2015-12-27 15.375000 63.25000 7.8875000 1020.6250
## 1092 2015-12-28 17.125000 58.12500 10.8875000 1020.8750
## 1093 2015-12-29 16.375000 65.00000 7.4125000 1018.1250
## 1094 2015-12-30 15.500000 71.75000 2.1000000 1017.5000
## 1095 2015-12-31 15.000000 71.37500 2.0875000 1020.5000Peubah yang dijadikan sebagi peubah bebas (xt) adalah
meantemp (rata-rata temperatur udara) dan peubah responnya
(yt) adalah meanpressure (rata-rata tekanan udara)
t <- data$date
t <- tibble::num(1:1095)
xt <- data$meantemp
yt <- data$meanpressure
xt <- as.vector(xt)
yt <- as.vector(yt)data1 <- cbind(t, xt, yt)
data1 <- as.data.frame(data1)
str(data1)## 'data.frame': 1095 obs. of 3 variables:
## $ t : num 1 2 3 4 5 6 7 8 9 10 ...
## $ xt: num 10 7.4 7.17 8.67 6 ...
## $ yt: num 1016 1018 1019 1017 1016 ...data1## t xt yt
## 1 1 10.000000 1015.6667
## 2 2 7.400000 1017.8000
## 3 3 7.166667 1018.6667
## 4 4 8.666667 1017.1667
## 5 5 6.000000 1016.5000
## 6 6 7.000000 1018.0000
## 7 7 7.000000 1020.0000
## 8 8 8.857143 1018.7143
## 9 9 14.000000 1017.0000
## 10 10 11.000000 1015.6667
## 11 11 15.714286 1016.1429
## 12 12 14.000000 1015.5714
## 13 13 15.833333 1013.3333
## 14 14 12.833333 1015.1667
## 15 15 14.714286 1015.8571
## 16 16 13.833333 1016.6667
## 17 17 16.500000 1015.8333
## 18 18 13.833333 1014.5000
## 19 19 12.500000 1021.6667
## 20 20 11.285714 1020.2857
## 21 21 11.200000 1021.0000
## 22 22 9.500000 1021.8000
## 23 23 14.000000 1020.5000
## 24 24 13.833333 1020.5000
## 25 25 12.250000 1020.7500
## 26 26 12.666667 1019.6667
## 27 27 12.857143 1018.1429
## 28 28 14.833333 1017.8333
## 29 29 14.125000 1016.6250
## 30 30 14.714286 1017.8571
## 31 31 16.200000 1018.4000
## 32 32 16.000000 1016.0000
## 33 33 16.285714 1017.1429
## 34 34 18.000000 1015.2857
## 35 35 17.428571 1014.5714
## 36 36 16.625000 1016.3750
## 37 37 16.666667 1018.6667
## 38 38 15.600000 1018.6000
## 39 39 14.000000 1017.1429
## 40 40 15.428571 1016.8571
## 41 41 15.250000 1017.1250
## 42 42 15.875000 1016.5000
## 43 43 15.333333 1017.5000
## 44 44 16.285714 1016.0000
## 45 45 17.333333 1014.1667
## 46 46 19.166667 1011.6667
## 47 47 14.428571 1008.0000
## 48 48 13.666667 1012.6667
## 49 49 15.600000 1016.2000
## 50 50 15.857143 1015.7143
## 51 51 17.714286 1017.0000
## 52 52 20.000000 1015.4286
## 53 53 20.500000 1016.0000
## 54 54 17.428571 1017.0000
## 55 55 16.857143 1018.8571
## 56 56 16.875000 1018.2500
## 57 57 17.857143 1015.1429
## 58 58 20.800000 1015.2000
## 59 59 19.428571 1017.4286
## 60 60 17.333333 1016.3333
## 61 61 19.000000 1016.2500
## 62 62 19.333333 1016.1667
## 63 63 17.600000 1015.8000
## 64 64 20.875000 1016.3750
## 65 65 20.857143 1015.7143
## 66 66 23.428571 1015.2857
## 67 67 24.166667 1014.8333
## 68 68 25.428571 1009.2857
## 69 69 23.142857 1008.0000
## 70 70 24.000000 1011.1667
## 71 71 23.500000 1011.5000
## 72 72 21.500000 1009.0000
## 73 73 22.333333 1013.1667
## 74 74 24.166667 1016.1667
## 75 75 20.333333 1016.1667
## 76 76 22.666667 1015.0000
## 77 77 23.428571 1009.4286
## 78 78 22.500000 1011.0000
## 79 79 29.166667 1009.5000
## 80 80 23.833333 1008.3333
## 81 81 25.250000 1006.3750
## 82 82 27.375000 1007.6250
## 83 83 27.000000 1010.2500
## 84 84 23.500000 1010.6250
## 85 85 24.142857 1008.8571
## 86 86 21.000000 1009.0000
## 87 87 22.428571 1009.5714
## 88 88 21.250000 1009.7500
## 89 89 23.500000 1008.6250
## 90 90 23.200000 1008.6000
## 91 91 25.375000 1008.5000
## 92 92 25.166667 1009.5000
## 93 93 26.200000 1009.0000
## 94 94 24.600000 1007.8000
## 95 95 25.600000 1007.0000
## 96 96 25.857143 1006.1429
## 97 97 29.142857 1005.0000
## 98 98 28.714286 1006.0000
## 99 99 30.166667 1005.3333
## 100 100 30.000000 1006.7143
## 101 101 30.000000 1006.4000
## 102 102 28.857143 1007.5714
## 103 103 30.200000 1008.4000
## 104 104 28.250000 1007.0000
## 105 105 28.250000 1003.8750
## 106 106 32.125000 1000.0000
## 107 107 29.200000 1002.2000
## 108 108 30.285714 1002.8571
## 109 109 28.285714 1002.5714
## 110 110 30.625000 1003.3750
## 111 111 27.666667 1006.8333
## 112 112 27.375000 1010.0000
## 113 113 28.625000 1009.8750
## 114 114 30.285714 1008.5714
## 115 115 31.142857 1007.7143
## 116 116 29.875000 1008.3750
## 117 117 31.142857 1007.0000
## 118 118 30.571429 1005.4286
## 119 119 32.125000 1004.8750
## 120 120 31.142857 1004.8571
## 121 121 31.857143 1002.8333
## 122 122 29.833333 1001.2000
## 123 123 28.571429 999.4286
## 124 124 32.857143 999.0000
## 125 125 32.625000 1000.6250
## 126 126 32.750000 1001.6250
## 127 127 32.875000 1002.0000
## 128 128 34.500000 1001.1667
## 129 129 34.285714 1000.8571
## 130 130 34.000000 1000.1429
## 131 131 30.750000 999.8750
## 132 132 29.857143 1003.7143
## 133 133 31.714286 1003.5714
## 134 134 32.285714 1001.5714
## 135 135 33.000000 999.8571
## 136 136 33.000000 998.5000
## 137 137 32.833333 1000.3333
## 138 138 31.400000 999.0000
## 139 139 35.333333 999.6667
## 140 140 36.400000 998.4000
## 141 141 36.000000 998.6667
## 142 142 36.750000 998.6250
## 143 143 37.500000 997.1667
## 144 144 38.428571 996.4286
## 145 145 38.714286 998.1429
## 146 146 37.800000 998.2000
## 147 147 35.857143 999.1429
## 148 148 35.333333 1000.1667
## 149 149 34.142857 999.4286
## 150 150 32.200000 999.6000
## 151 151 33.625000 998.7143
## 152 152 32.000000 998.7500
## 153 153 32.400000 1001.0000
## 154 154 35.600000 999.6000
## 155 155 35.857143 999.8571
## 156 156 37.166667 998.0000
## 157 157 31.285714 997.2857
## 158 158 34.000000 998.0000
## 159 159 34.200000 997.0000
## 160 160 36.166667 995.1667
## 161 161 36.625000 995.1250
## 162 162 30.166667 1000.0000
## 163 163 34.142857 998.0000
## 164 164 29.833333 998.6667
## 165 165 30.142857 997.4286
## 166 166 30.714286 997.8571
## 167 167 27.000000 996.4286
## 168 168 26.875000 994.7500
## 169 169 28.400000 996.4000
## 170 170 29.857143 999.0000
## 171 171 33.000000 997.1667
## 172 172 34.833333 995.3333
## 173 173 35.600000 996.2000
## 174 174 35.166667 995.6667
## 175 175 33.142857 996.2857
## 176 176 30.571429 999.1667
## 177 177 30.666667 999.0000
## 178 178 31.428571 996.7143
## 179 179 31.500000 996.0000
## 180 180 33.250000 995.2500
## 181 181 32.833333 997.1667
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## 820 820 25.250000 1010.1429
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## 876 876 35.250000 1001.5000
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## 878 878 34.750000 1000.6250
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## 931 931 29.125000 999.1250
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## 935 935 32.000000 1001.0000
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## 999 999 29.250000 1005.2500
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## 1072 1072 18.428571 1015.7143
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## 1076 1076 13.250000 1014.2500
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## 1079 1079 13.125000 1016.5000
## 1080 1080 13.000000 1016.3750
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## 1082 1082 12.875000 1018.6250
## 1083 1083 12.375000 1019.0000
## 1084 1084 11.750000 1018.5000
## 1085 1085 12.625000 1018.8750
## 1086 1086 12.000000 1020.8750
## 1087 1087 12.500000 1020.6250
## 1088 1088 11.250000 1021.2500
## 1089 1089 11.500000 1022.0000
## 1090 1090 12.750000 1021.1250
## 1091 1091 15.375000 1020.6250
## 1092 1092 17.125000 1020.8750
## 1093 1093 16.375000 1018.1250
## 1094 1094 15.500000 1017.5000
## 1095 1095 15.000000 1020.5000Kemudian, data dibagi menjadi 2 yaitu data training dan data testing. Data training digunakan untuk menentukan model yang sesuai dengan keseluruhan data, sedangkan data testing digunakan untuk menguji performa dari model yang telah didapatkan. Data dibagi dengan perbandingan 80 : 20, yaitu dengan data training sebanyak 876 amatan (amatan 1 sampai 876) dan data testing sebanyak 219 amatan (amatan 877 sampai 1095).
#SPLIT DATA
train<-data1[1:876,]
test<-data1[877:1095,]
train <- as.data.frame(train)
test <- as.data.frame(test)#data time series
train.ts<-ts(train)
test.ts<-ts(test)
data.ts<-ts(data1)Eksplorasi Data
Plot Time Series
data.ts1 <- ts(yt)
plot(data.ts1, main = " Time Series Plot of Daily Delhi Climate", xlab = "Periode", ylab ="Mean Pressure")
points(data.ts1)
Berdasarkan plot time series di atas, dapat dilihat bahwa peubah mean
pressure atau rata-rata tekanan udara memiliki pola musiman.
#Time Series Plot
data.ts<-ts(xt)
plot(data.ts, main = "Time Series Plot of Daily Delhi Climate", xlab = "Period", ylab="Mean Temperature")
points(data.ts)
Berdasarkan plot time series di atas, dapat dilihat bahwa peubah mean temperature atau rata-rata temperatur udara memiliki pola musiman.
Korelasi Peubah Unique Visits (X) dan Page Loads (Y)
corrplot::corrplot(corr=cor(data1), method="number", type="upper")
cor(xt, yt)## [1] -0.8899641Scatter Plot Peubah Unique Visits (X) dan Page Loads (Y)
plot(xt, yt, pch = 20, col = "blue", main = "Scatter Plot Rata-Rata Tekanan Udara vs Rata-Rata Temperatur Udara")
Berdasarkan corrplot dan scatter plot di atas, dapat dilihat bahwa hubungan peubah Mean Temperature (xt) dan peubah Mean Pressure (yt) memiliki hubungan yang negatif kuat yaitu dengan nilai korelasi sebesar -0.8899641, artinya dengan kenaikan temperatur udara, tekanan udara cenderung menurun.
Model KOYCK
Metode Koyck didasarkan asumsi bahwa semakin jauh jarak lag peubah independen dari periode sekarang maka semakin kecil pengaruh peubah lag terhadap peubah dependen. Koyck mengusulkan suatu metode untuk menduga model dinamis distributed lag dengan mengasumsikan bahwa semua koefisien 𝛽 mempunyai tanda sama.
Model Koyck merupakan jenis paling umum dari model infinite distributed lag dan juga dikenal sebagai geometric lag.
Pemodelan Koyck
#MODEL KOYCK
model.koyck <- dLagM :: koyckDlm(x=train$xt , y =train$yt)
summary(model.koyck)##
## Call:
## "Y ~ (Intercept) + Y.1 + X.t"
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.65185 -1.04223 -0.02695 1.00772 6.61856
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 120.48015 17.79467 6.771 2.35e-11 ***
## Y.1 0.88306 0.01725 51.199 < 2e-16 ***
## X.t -0.10389 0.01786 -5.816 8.47e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.649 on 872 degrees of freedom
## Multiple R-Squared: 0.9535, Adjusted R-squared: 0.9534
## Wald test: 8907 on 2 and 872 DF, p-value: < 2.2e-16
##
## Diagnostic tests:
## NULL
##
## alpha beta phi
## Geometric coefficients: 1030.292 -0.1038871 0.8830621AIC dan BIC
AIC (Akaike’s Information Criteria) dan BIC (Bayesian Information Criteria) digunakan untuk mengukur kebaikan model. BIC memiliki perhitungan yang lebih kompleks. Kebaikan model dapat dilihat dari, semakin kecil nilai AIC/BIC, semakin baik suatu model.
AIC(model.koyck)## [1] 3363.836BIC(model.koyck)## [1] 3382.933Forecasting
#ramalan
(fore.koyck <- forecast(model = model.koyck, x=test$xt, h=nrow(test)))## $forecasts
## [1] 1001.3607 1001.1338 1000.8945 1000.9818 1000.8512 1001.2422 1001.3538
## [8] 1001.7641 1001.7887 1001.7325 1001.6049 1001.3235 1000.9192 1000.4452
## [15] 1000.1306 999.9566 999.7770 1000.1119 1000.8362 1001.0602 1001.1152
## [22] 1001.0079 1000.7833 1000.5070 1000.5488 1000.8713 1000.9744 1001.1303
## [29] 1000.6706 1001.3685 1001.5173 1001.4928 1001.3024 1001.4589 1001.6231
## [36] 1001.6512 1001.4942 1001.4335 1001.2630 1000.9474 1001.4830 1001.9301
## [43] 1002.0002 1002.2309 1002.7464 1003.3184 1003.8235 1003.8151 1003.7037
## [50] 1003.3457 1003.1983 1003.1721 1003.2788 1003.3081 1003.4378 1003.3186
## [57] 1003.1225 1002.9623 1002.8338 1002.8390 1002.9327 1003.0544 1003.1749
## [64] 1003.3851 1003.5188 1003.6369 1003.8191 1003.8372 1003.6583 1003.7156
## [71] 1003.7489 1003.7882 1003.8488 1003.9413 1004.1788 1004.0768 1004.1946
## [78] 1004.0519 1003.7960 1003.6868 1003.8372 1003.9570 1003.8421 1003.9094
## [85] 1003.7480 1003.6575 1003.7204 1003.6851 1003.6928 1003.6088 1003.4047
## [92] 1003.2244 1003.0133 1002.8789 1002.7342 1002.5674 1002.4999 1002.4125
## [99] 1002.3613 1002.3420 1002.2861 1002.3535 1002.3741 1002.3664 1002.3465
## [106] 1002.3939 1002.4098 1002.4758 1002.3893 1002.3148 1002.2750 1002.1230
## [113] 1002.0537 1002.0964 1002.1730 1002.2797 1002.5278 1002.6449 1002.7353
## [120] 1002.9840 1003.2425 1003.4449 1003.5456 1003.6903 1003.8662 1003.9437
## [127] 1004.0121 1004.1634 1004.2803 1004.2055 1004.2433 1004.2896 1004.3825
## [134] 1004.4385 1004.5140 1004.5677 1004.6150 1004.6495 1004.6094 1004.5480
## [141] 1004.6366 1004.7798 1004.8673 1004.9316 1005.1071 1005.1285 1005.1919
## [148] 1005.3741 1005.7167 1006.0972 1006.3423 1006.4030 1006.5344 1006.7414
## [155] 1007.3267 1007.7137 1008.0295 1008.3084 1008.5027 1008.6223 1008.6631
## [162] 1008.7250 1008.9485 1009.0680 1009.2773 1009.4622 1009.6385 1009.6903
## [169] 1009.8269 1009.9475 1010.0021 1010.0503 1010.0799 1010.1709 1010.4591
## [176] 1010.8564 1011.2073 1011.5171 1011.7647 1011.9964 1012.3698 1012.5436
## [183] 1012.6063 1012.5967 1012.7441 1012.8482 1013.0051 1013.0008 1013.0230
## [190] 1013.1595 1013.3319 1013.4842 1013.6316 1013.8008 1013.8983 1013.9008
## [197] 1013.9087 1013.8507 1013.9812 1014.5121 1015.0198 1015.4292 1015.8037
## [204] 1016.1475 1016.5289 1016.8008 1017.0928 1017.4156 1017.6098 1017.8462
## [211] 1018.0030 1018.2714 1018.4823 1018.5388 1018.3159 1017.9373 1017.6809
## [218] 1017.5454 1017.4777
##
## $call
## forecast.koyckDlm(model = model.koyck, x = test$xt, h = nrow(test))
##
## attr(,"class")
## [1] "forecast.koyckDlm" "dLagM"Akurasi
mape.koyck <- dLagM::GoF(model.koyck)["MAPE"]Regression with Distributed Lag
Pemodelan Regression with Distributed Lag
model.dlm = dLagM::dlm(x = train$xt,y = train$yt , q = 2)
summary(model.dlm)##
## Call:
## lm(formula = model.formula, data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.743 -2.220 0.230 2.417 7.405
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1031.20661 0.38456 2681.539 < 2e-16 ***
## x.t -0.53001 0.06855 -7.731 2.94e-14 ***
## x.1 -0.14692 0.08855 -1.659 0.09745 .
## x.2 -0.24428 0.06847 -3.568 0.00038 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.311 on 870 degrees of freedom
## Multiple R-squared: 0.8127, Adjusted R-squared: 0.812
## F-statistic: 1258 on 3 and 870 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 4579.104 4602.969AIC dan BIC
AIC(model.dlm)## [1] 4579.104BIC(model.dlm)## [1] 4602.969Akurasi
#akurasi data training
mape.dlm <- GoF(model.dlm)["MAPE"]Lag Optimum
#penentuan lag optimum
finiteDLMauto(formula = yt ~ xt,
data = data.frame(train), q.min = 1, q.max = 5 ,
model.type = "dlm", error.type = "AIC", trace = TRUE) ##q max lag maksimum## q - k MASE AIC BIC GMRAE MBRAE R.Adj.Sq Ljung-Box
## 5 5 1.97631 4534.450 4572.607 3.20129 0.79117 0.81857 0
## 4 4 1.98502 4549.724 4583.120 3.16957 0.55588 0.81627 0
## 3 3 2.00707 4564.009 4592.641 3.24695 5.51654 0.81419 0
## 2 2 2.01415 4579.104 4602.969 3.19890 0.63890 0.81202 0
## 1 1 2.01895 4596.848 4615.945 3.13677 0.73277 0.80920 0Pemodelan Lag Optimum
#model dlm dengan lag optimum
model.dlm2 = dLagM::dlm(x = train$xt,y = train$yt , q = 5) #terdapat lag yang tidak signifikan sehingga dapat dikurangi jumlah lagnya
summary(model.dlm2)##
## Call:
## lm(formula = model.formula, data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.7981 -2.2534 0.2189 2.3736 7.4943
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1031.59603 0.38341 2690.574 < 2e-16 ***
## x.t -0.48326 0.06856 -7.049 3.7e-12 ***
## x.1 -0.11436 0.08753 -1.306 0.19175
## x.2 -0.06154 0.08733 -0.705 0.48122
## x.3 -0.05114 0.08737 -0.585 0.55851
## x.4 -0.04800 0.08761 -0.548 0.58394
## x.5 -0.17893 0.06836 -2.617 0.00902 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.251 on 864 degrees of freedom
## Multiple R-squared: 0.8198, Adjusted R-squared: 0.8186
## F-statistic: 655.2 on 6 and 864 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 4534.45 4572.607AIC dan BIC
AIC(model.dlm2)## [1] 4534.45BIC(model.dlm2)## [1] 4572.607Akurasi
#akurasi data training
mape.dlm2 <- GoF(model.dlm2)["MAPE"]Model Autoregressive / Dynamic Regression
Apabila peubah dependen dipengaruhi oleh peubah independen pada waktu sekarang, serta dipengaruhii juga oleh peubah dependen itu sendiri pada satu waktu yang lalu maka model tersebut disebut autoregressive.
Pemodelan Model Autoregressive
#MODEL AUTOREGRESSIVE
#library(dLagM)
model.ardl = ardlDlm(x = train$xt, y = train$yt, p = 1 , q = 1) #p:lag x, q:lag y
#model untuk p=1, q=1: yt=b0+b1yt-1+b2xt+b3xt-1
#model untuk p=2, q=3: yt=b0+b1yt-1+b2yt-2+b3xt+b4xt-1+b5xt-2
summary(model.ardl)##
## Time series regression with "ts" data:
## Start = 2, End = 876
##
## Call:
## dynlm(formula = as.formula(model.text), data = data, start = 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.612 -1.092 0.026 1.013 6.117
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 134.59797 16.40353 8.205 8.22e-16 ***
## X.t -0.37987 0.03260 -11.654 < 2e-16 ***
## X.1 0.25680 0.03428 7.490 1.69e-13 ***
## Y.1 0.86954 0.01591 54.653 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.586 on 871 degrees of freedom
## Multiple R-squared: 0.957, Adjusted R-squared: 0.9569
## F-statistic: 6465 on 3 and 871 DF, p-value: < 2.2e-16AIC dan BIC
AIC(model.ardl)## [1] 3296.63BIC(model.ardl)## [1] 3320.501Ramalan
#ramalan
(fore.ardl <- forecast(model = model.ardl, x=test$xt, h=219))## $forecasts
## [1] 1001.6729 1001.0581 1000.6379 1001.4609 1000.6786 1002.3637 1001.7225
## [8] 1002.8823 1001.8858 1001.5690 1001.2012 1000.4567 999.6568 998.9192
## [15] 998.9465 999.0933 998.8692 1000.5429 1002.3455 1001.3342 1000.9596
## [22] 1000.4172 999.8559 999.4039 1000.2482 1001.3207 1000.8824 1001.1880
## [29] 999.1091 1002.8140 1001.5978 1001.1260 1000.4836 1001.5294 1001.7313
## [36] 1001.4153 1000.7646 1000.9331 1000.4597 999.7332 1002.4875 1002.7745
## [43] 1001.9011 1002.5614 1003.8579 1004.6423 1005.0354 1003.7153 1003.3110
## [50] 1002.2666 1002.6177 1002.8856 1003.3365 1003.1703 1003.5661 1002.7987
## [57] 1002.3769 1002.2822 1002.2153 1002.5592 1002.8903 1003.1006 1003.2347
## [64] 1003.6990 1003.6560 1003.7470 1004.1110 1003.7127 1003.0071 1003.6620
## [71] 1003.6367 1003.6928 1003.8124 1003.9947 1004.6267 1003.6515 1004.3336
## [78] 1003.5109 1002.9306 1003.1744 1003.9997 1004.0599 1003.3372 1003.8717
## [85] 1003.1119 1003.1869 1003.6461 1003.3599 1003.4781 1003.1522 1002.6188
## [92] 1002.4759 1002.1617 1002.2068 1002.0227 1001.7843 1001.9650 1001.8233
## [99] 1001.8637 1001.9297 1001.7804 1002.1742 1002.0853 1002.0093 1001.9600
## [106] 1002.1866 1002.1282 1002.3316 1001.8509 1001.7973 1001.8412 1001.3878
## [113] 1001.5198 1001.8540 1002.0302 1002.2296 1002.8698 1002.6727 1002.7060
## [120] 1003.3844 1003.6995 1003.7822 1003.6333 1003.9001 1004.1708 1004.0020
## [127] 1004.0479 1004.4202 1004.4581 1003.8812 1004.1996 1004.2672 1004.4838
## [134] 1004.4488 1004.5775 1004.5777 1004.6100 1004.6110 1004.3724 1004.2442
## [141] 1004.7193 1005.0167 1004.9723 1004.9826 1005.4578 1005.0890 1005.2614
## [148] 1005.7625 1006.5512 1007.0725 1007.0008 1006.5933 1006.9091 1007.3235
## [155] 1008.9311 1008.8591 1009.0225 1009.2288 1009.2182 1009.1475 1008.9770
## [162] 1009.0842 1009.7305 1009.5903 1010.0408 1010.1758 1010.3406 1010.0720
## [169] 1010.4276 1010.5121 1010.3957 1010.4228 1010.3989 1010.6477 1011.4632
## [176] 1012.1811 1012.4523 1012.6880 1012.7981 1013.0054 1013.7709 1013.4495
## [183] 1013.2227 1013.0129 1013.5607 1013.5569 1013.8552 1013.4318 1013.5116
## [190] 1013.9442 1014.2214 1014.3341 1014.4795 1014.7163 1014.6360 1014.3893
## [197] 1014.4015 1014.1610 1014.7770 1016.3829 1016.8944 1017.1005 1017.4235
## [204] 1017.7198 1018.2302 1018.2439 1018.6064 1019.0305 1018.9065 1019.2607
## [211] 1019.2183 1019.7847 1019.8612 1019.5171 1018.5417 1017.7029 1017.7078
## [218] 1017.8518 1017.9423
##
## $call
## forecast.ardlDlm(model = model.ardl, x = test$xt, h = 219)
##
## attr(,"class")
## [1] "forecast.ardlDlm" "dLagM"AKurasi
mape.ardl <- GoF(model.ardl)["MAPE"]#PEMODELAN DLM dan ARDL dengan library dynlm
#library(dynlm)
#sama dengan model dlm p=1
cons_lm1 <- dynlm(yt ~ xt+L(xt),data = train.ts)
#sama dengan model ardl p=0 q=1
cons_lm2 <- dynlm(yt ~ xt+L(yt),data = train.ts)
#sama dengan ardl p=1 q=1
cons_lm3 <- dynlm(yt ~ xt+L(xt)+L(yt),data = train.ts)
#sama dengan dlm p=2
cons_lm4 <- dynlm(yt ~ xt+L(xt)+L(xt,2),data = train.ts)summary(cons_lm1)##
## Time series regression with "ts" data:
## Start = 2, End = 876
##
## Call:
## dynlm(formula = yt ~ xt + L(xt), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.6727 -2.2683 0.2323 2.3889 7.4706
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1031.04429 0.38506 2677.622 < 2e-16 ***
## xt -0.55871 0.06822 -8.190 9.23e-16 ***
## L(xt) -0.35579 0.06815 -5.221 2.23e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.337 on 872 degrees of freedom
## Multiple R-squared: 0.8096, Adjusted R-squared: 0.8092
## F-statistic: 1854 on 2 and 872 DF, p-value: < 2.2e-16summary(cons_lm2)##
## Time series regression with "ts" data:
## Start = 2, End = 876
##
## Call:
## dynlm(formula = yt ~ xt + L(yt), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.5832 -1.0472 -0.0479 1.0470 6.2044
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 174.88826 15.97860 10.95 <2e-16 ***
## xt -0.16389 0.01567 -10.46 <2e-16 ***
## L(yt) 0.83058 0.01550 53.57 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.636 on 872 degrees of freedom
## Multiple R-squared: 0.9543, Adjusted R-squared: 0.9541
## F-statistic: 9095 on 2 and 872 DF, p-value: < 2.2e-16summary(cons_lm3)##
## Time series regression with "ts" data:
## Start = 2, End = 876
##
## Call:
## dynlm(formula = yt ~ xt + L(xt) + L(yt), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.612 -1.092 0.026 1.013 6.117
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 134.59797 16.40353 8.205 8.22e-16 ***
## xt -0.37987 0.03260 -11.654 < 2e-16 ***
## L(xt) 0.25680 0.03428 7.490 1.69e-13 ***
## L(yt) 0.86954 0.01591 54.653 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.586 on 871 degrees of freedom
## Multiple R-squared: 0.957, Adjusted R-squared: 0.9569
## F-statistic: 6465 on 3 and 871 DF, p-value: < 2.2e-16summary(cons_lm4)##
## Time series regression with "ts" data:
## Start = 3, End = 876
##
## Call:
## dynlm(formula = yt ~ xt + L(xt) + L(xt, 2), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.743 -2.220 0.230 2.417 7.405
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1031.20661 0.38456 2681.539 < 2e-16 ***
## xt -0.53001 0.06855 -7.731 2.94e-14 ***
## L(xt) -0.14692 0.08855 -1.659 0.09745 .
## L(xt, 2) -0.24428 0.06847 -3.568 0.00038 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.311 on 870 degrees of freedom
## Multiple R-squared: 0.8127, Adjusted R-squared: 0.812
## F-statistic: 1258 on 3 and 870 DF, p-value: < 2.2e-16SSE
deviance(cons_lm1)## [1] 9708.382deviance(cons_lm2)## [1] 2333.016deviance(cons_lm3)## [1] 2191.837deviance(cons_lm4)## [1] 9537.731Berdasarkan output di atas, model yang memiliki nilai SSE terendah yaitu cons_lm3, model tersebut merupakan model yang sama seperti ardl dengan p=1 q=1 # Diagnostik Model
Uji Non Autokorelasi
Hipotesis
H0: Tidak terdapat autokorelasi
H1: Terdapat autokorelasi
if(require("lmtest")) encomptest(cons_lm1, cons_lm2)## Encompassing test
##
## Model 1: yt ~ xt + L(xt)
## Model 2: yt ~ xt + L(yt)
## Model E: yt ~ xt + L(xt) + L(yt)
## Res.Df Df F Pr(>F)
## M1 vs. ME 871 -1 2986.951 < 2.2e-16 ***
## M2 vs. ME 871 -1 56.102 1.688e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#durbin watson
dwtest(cons_lm1)##
## Durbin-Watson test
##
## data: cons_lm1
## DW = 0.26376, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm2)##
## Durbin-Watson test
##
## data: cons_lm2
## DW = 1.6421, p-value = 4.156e-08
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm3)##
## Durbin-Watson test
##
## data: cons_lm3
## DW = 1.721, p-value = 1.404e-05
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm4)##
## Durbin-Watson test
##
## data: cons_lm4
## DW = 0.2637, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0Berdasarkan output di atas, pengujian non-autokorelasi dengan Durbin-Watson test semua model memiliki p-value < alpha, sehingga tolak H0. Artinya semua model terdapat autokorelasi.
Uji Heterogenitas
Hipotesis
H0: Tidak terdapat Heterogenitas
H1: Terdapat Heterogenitas
bptest(cons_lm1)##
## studentized Breusch-Pagan test
##
## data: cons_lm1
## BP = 15.011, df = 2, p-value = 0.00055bptest(cons_lm2)##
## studentized Breusch-Pagan test
##
## data: cons_lm2
## BP = 3.0001, df = 2, p-value = 0.2231bptest(cons_lm3)##
## studentized Breusch-Pagan test
##
## data: cons_lm3
## BP = 8.0233, df = 3, p-value = 0.04553bptest(cons_lm4)##
## studentized Breusch-Pagan test
##
## data: cons_lm4
## BP = 20.289, df = 3, p-value = 0.0001478Berdasarkan output di atas, pengujian heterogenitas dengan
Breusch-Pagan test hanya satu model yang memiliki p-value > alpha
yaitu model cons_lm2 yang artinya tidak terdapat
heterogenitas, dan model lainnya memiliki memiliki p-value < alpha
yang artinya terdapat heterogenitas.
Normalitas
Hipotesis
H0: Sisaan berdistribusi normal
H1: Sisaan tidak berdistribusi normal
shapiro.test(residuals(cons_lm1))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm1)
## W = 0.98982, p-value = 9.312e-06shapiro.test(residuals(cons_lm2))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm2)
## W = 0.99251, p-value = 0.0002126shapiro.test(residuals(cons_lm3))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm3)
## W = 0.99397, p-value = 0.001393shapiro.test(residuals(cons_lm4))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm4)
## W = 0.99029, p-value = 1.585e-05Berdasarkan output di atas, pengujian normalitas dengan Shapiro-Wilk normality test semua model memiliki p-value < alpha, sehingga tolak H0. Artinya semua model memiliki sisaan yang tidak berdistribusi normal.
Perbandingan Keakuratan Ramalan
#PERBANDINGAN
akurasi <- matrix(c(mape.koyck, mape.dlm, mape.dlm2, mape.ardl))
row.names(akurasi)<- c("Koyck","DLM 1","DLM 2","Autoregressive")
colnames(akurasi) <- c("MAPE")
akurasi## MAPE
## Koyck 0.001257333
## DLM 1 0.002665095
## DLM 2 0.002615808
## Autoregressive 0.001222942Simpulan
Berdasarkan perbangingan keakuratan ramalan, model yang terbaik yaitu model autoregressive karena model tersebut memiliki nilai MAPE terkecil.
Daftar Pustaka
Siswanti, K.Y. 2011. Model Fungsi Transfer Multivariat dan Aplikasinya untuk Meramalkan Curah Hujan Di Kota Yogyakarta. Skripsi. Yogyakarta : FMIPA Universitas Negeri Yogyakarta.