Regresi dengan Peubah Lag
Kenia
14/9/2022
##Regresi Dengan Peubah Lag #Data Preparation #PACKAGE
library(dLagM)## 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)
library(MLmetrics)##
## 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(readxl)
library(readr)
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(knitr)
library(caTools)
library(ggplot2)
library(hrbrthemes)## NOTE: Either Arial Narrow or Roboto Condensed fonts are required to use these themes.## Please use hrbrthemes::import_roboto_condensed() to install Roboto Condensed and## if Arial Narrow is not on your system, please see https://bit.ly/arialnarrowData
Data yang digunakan adalah kumpulan data pemeriksaan suhu dari program data transportasi Departemen Transportasi Alaska yang berasal dari situs web kaggle https://www.kaggle.com/datasets/erikjamesmason/akdot-tdp-temperature-data-probes?select=TDP_2002_entire.csv. Variabel yang akan digunakan untuk analisis adalah OBSERVATION_TIME, BATTERY_VOLTAGE, dan REF_TEMP dengan jumlah amatan 91,026.
Input Data
data <- read_csv("C:/Users/ASUS/OneDrive/Documents/STK SMT 5/Tugas/Individu/MPDW/P4/TDP_2002_entire (1).csv")## Rows: 5271 Columns: 24
## -- Column specification --------------------------------------------------------
## Delimiter: ","
## chr (1): OBSERVATION_TIME
## dbl (22): SITE_NUMBER, REF_TEMP, AMBIENT_AIR_TEMP, IN_PAVEMENT_TEMP, INTERNA...
## lgl (1): TIMEZONE_FLAG
##
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.knitr::kable(head(data), align="l")| SITE_NUMBER | OBSERVATION_TIME | REF_TEMP | AMBIENT_AIR_TEMP | IN_PAVEMENT_TEMP | INTERNAL_TEMP | BATTERY_VOLTAGE | TMR_PAV | TMR_SUB_0 | TMR_SUB_3 | TMR_SUB_6 | TMR_SUB_9 | TMR_SUB_12 | TMR_SUB_18 | TMR_SUB_24 | TMR_SUB_30 | TMR_SUB_36 | TMR_SUB_42 | TMR_SUB_48 | TMR_SUB_54 | TMR_SUB_60 | TMR_SUB_66 | TMR_SUB_72 | TIMEZONE_FLAG |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 110 | 2002-04-16-19-00-00 | 49.36 | 35.45 | 32 | 32 | 12.75 | 75.40 | 78.70 | 81.00 | 83.00 | 84.30 | 85.70 | 86.40 | 87.40 | 88.50 | 89.10 | 89.80 | 90.50 | 91.10 | 91.70 | 92.20 | 93.00 | NA |
| 110 | 2002-04-16-20-00-00 | 56.15 | 34.99 | 32 | 32 | 12.76 | 33.32 | 49.20 | 58.37 | 63.12 | 66.61 | 69.47 | 71.70 | 73.60 | 75.10 | 76.20 | 77.40 | 77.90 | 79.00 | 79.70 | 80.50 | 81.00 | NA |
| 110 | 2002-04-16-21-00-00 | 43.97 | 36.09 | 32 | 32 | 12.72 | 53.76 | 62.26 | 67.21 | 71.20 | 73.70 | 75.70 | 77.30 | 78.90 | 79.90 | 81.20 | 81.80 | 82.60 | 83.40 | 84.00 | 84.60 | 85.40 | NA |
| 110 | 2002-04-16-22-00-00 | 43.52 | 36.38 | 32 | 32 | 13.58 | 39.76 | 30.97 | 30.90 | 30.55 | 30.41 | 30.41 | 30.48 | 30.69 | 31.59 | 31.86 | 32.21 | 32.41 | 32.61 | 33.02 | 33.69 | 34.02 | NA |
| 110 | 2002-04-16-23-00-00 | 48.02 | 37.47 | 32 | 32 | 13.59 | 42.89 | 30.98 | 30.90 | 30.62 | 30.41 | 30.34 | 30.41 | 30.69 | 31.53 | 31.87 | 32.21 | 32.34 | 32.69 | 33.02 | 33.62 | 34.02 | NA |
| 110 | 2002-04-17-00-00-00 | 52.60 | 36.91 | 32 | 32 | 13.52 | 43.14 | 30.98 | 30.84 | 30.63 | 30.42 | 30.35 | 30.42 | 30.70 | 31.39 | 31.87 | 32.21 | 32.35 | 32.69 | 33.09 | 33.63 | 34.03 | NA |
str(data)## spec_tbl_df [5,271 x 24] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ SITE_NUMBER : num [1:5271] 110 110 110 110 110 110 110 110 110 110 ...
## $ OBSERVATION_TIME: chr [1:5271] "2002-04-16-19-00-00" "2002-04-16-20-00-00" "2002-04-16-21-00-00" "2002-04-16-22-00-00" ...
## $ REF_TEMP : num [1:5271] 49.4 56.1 44 43.5 48 ...
## $ AMBIENT_AIR_TEMP: num [1:5271] 35.5 35 36.1 36.4 37.5 ...
## $ IN_PAVEMENT_TEMP: num [1:5271] 32 32 32 32 32 32 32 32 32 32 ...
## $ INTERNAL_TEMP : num [1:5271] 32 32 32 32 32 32 32 32 32 32 ...
## $ BATTERY_VOLTAGE : num [1:5271] 12.8 12.8 12.7 13.6 13.6 ...
## $ TMR_PAV : num [1:5271] 75.4 33.3 53.8 39.8 42.9 ...
## $ TMR_SUB_0 : num [1:5271] 78.7 49.2 62.3 31 31 ...
## $ TMR_SUB_3 : num [1:5271] 81 58.4 67.2 30.9 30.9 ...
## $ TMR_SUB_6 : num [1:5271] 83 63.1 71.2 30.6 30.6 ...
## $ TMR_SUB_9 : num [1:5271] 84.3 66.6 73.7 30.4 30.4 ...
## $ TMR_SUB_12 : num [1:5271] 85.7 69.5 75.7 30.4 30.3 ...
## $ TMR_SUB_18 : num [1:5271] 86.4 71.7 77.3 30.5 30.4 ...
## $ TMR_SUB_24 : num [1:5271] 87.4 73.6 78.9 30.7 30.7 ...
## $ TMR_SUB_30 : num [1:5271] 88.5 75.1 79.9 31.6 31.5 ...
## $ TMR_SUB_36 : num [1:5271] 89.1 76.2 81.2 31.9 31.9 ...
## $ TMR_SUB_42 : num [1:5271] 89.8 77.4 81.8 32.2 32.2 ...
## $ TMR_SUB_48 : num [1:5271] 90.5 77.9 82.6 32.4 32.3 ...
## $ TMR_SUB_54 : num [1:5271] 91.1 79 83.4 32.6 32.7 ...
## $ TMR_SUB_60 : num [1:5271] 91.7 79.7 84 33 33 ...
## $ TMR_SUB_66 : num [1:5271] 92.2 80.5 84.6 33.7 33.6 ...
## $ TMR_SUB_72 : num [1:5271] 93 81 85.4 34 34 ...
## $ TIMEZONE_FLAG : logi [1:5271] NA NA NA NA NA NA ...
## - attr(*, "spec")=
## .. cols(
## .. SITE_NUMBER = col_double(),
## .. OBSERVATION_TIME = col_character(),
## .. REF_TEMP = col_double(),
## .. AMBIENT_AIR_TEMP = col_double(),
## .. IN_PAVEMENT_TEMP = col_double(),
## .. INTERNAL_TEMP = col_double(),
## .. BATTERY_VOLTAGE = col_double(),
## .. TMR_PAV = col_double(),
## .. TMR_SUB_0 = col_double(),
## .. TMR_SUB_3 = col_double(),
## .. TMR_SUB_6 = col_double(),
## .. TMR_SUB_9 = col_double(),
## .. TMR_SUB_12 = col_double(),
## .. TMR_SUB_18 = col_double(),
## .. TMR_SUB_24 = col_double(),
## .. TMR_SUB_30 = col_double(),
## .. TMR_SUB_36 = col_double(),
## .. TMR_SUB_42 = col_double(),
## .. TMR_SUB_48 = col_double(),
## .. TMR_SUB_54 = col_double(),
## .. TMR_SUB_60 = col_double(),
## .. TMR_SUB_66 = col_double(),
## .. TMR_SUB_72 = col_double(),
## .. TIMEZONE_FLAG = col_logical()
## .. )
## - attr(*, "problems")=<externalptr>dim(data)## [1] 5271 24data$OBSERVATION_TIME <- as.Date(data$OBSERVATION_TIME,"%y/%m/%d")
t<-data$OBSERVATION_TIME
Xt<-data$BATTERY_VOLTAGE
Yt<-data$REF_TEMP
datareg1<-cbind(t, Xt, Yt)
datareg <- as.data.frame(datareg1)Split Data dan Membuat data menjadi time series.
Dilakukan splitting data dengan data train dengan jumlah amatan 80% dari jumlah seluruh amatan yaitu 4.216 dan data test yaitu 20% dari jumlah seluruh amatan yaitu 1.055 amatan.
#Split data
train<-data[1:4216,]
test<-data[4217:5271,]
#data time series
train.ts<-ts(train)
test.ts<-ts(test)
data.ts<-ts(data)Exploratory Data Analysis
Korelasi Peubah total_vaccinations (X) dan total_deaths (Y)
cor(Xt, Yt)## [1] -0.9820873Scatter Plot Peubah total_vaccinations (X) dan total_deaths (Y)
plot(Xt, Yt, pch = 20, col = "red", main = "Scatter Plot Ref Temp dan Battery Voltage")
Berdasarkan scatter plot terlihat bahwa hubungan antara Peubah
BATTERY_VOLTAGE (X) dan REF_TEMP (Y) memiliki hubungan linier negatif
dengan korelasi -0.9820873.
Model Regresi Linier Awal
model1 <- lm(data$REF_TEMP~data$BATTERY_VOLTAGE, data = data)
summary(model1)##
## Call:
## lm(formula = data$REF_TEMP ~ data$BATTERY_VOLTAGE, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -66.749 -1.060 -0.285 0.761 10.033
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1062.6632 2.6543 400.4 <2e-16 ***
## data$BATTERY_VOLTAGE -74.8384 0.1978 -378.3 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.419 on 5269 degrees of freedom
## Multiple R-squared: 0.9645, Adjusted R-squared: 0.9645
## F-statistic: 1.431e+05 on 1 and 5269 DF, p-value: < 2.2e-16Berdasarkan output diatas, dapat diperoleh model regresi linier data deret waktu yaitu: Yt^ = 1062.6632 - 74.8384 (Xt)
Uji t = dilakukan untuk menguji signifikansi peubah penjelas terhdap variabel dependen. Berdasarkan output, dapat diperoleh pada peubah penjelas BATTERY_VOLTAGE memiliki P-Value<0.05. Maka dapat disimpulkan bahwa peubah penjelas BATTERY_VOLTAGE berpengaruh signifikan pada taraf nyata 5%.
Nilai R-Squared pada model regresi linier deret waktu yaitu 96,45%, artinya keragaman Y yang mampu dijelaskan oleh peubah penjelas X adalah sebesar 96.45%.
Interpretasi Model Regresi
Nilai intersep sebesar 1062.6632 yang artinya jika peubah penjelas bernilai nol, maka dugaan nilai IPM sebesar 1062.6632.
Pengaruh peubah BATTERY_VOLTAGE terhadap REF_ _TEMP bernilai negatif sebesar - 74.8384, hal ini menunjukkan bahwa jika jumlah BATTERY_VOLTAGE berkurang satu maka dugaan jumlah REF_TEMP berkurang sebesar - 74.8384.
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.
model.koyck = dLagM::koyckDlm(x = train$BATTERY_VOLTAGE, y = train$REF_TEMP)
summary(model.koyck)##
## Call:
## "Y ~ (Intercept) + Y.1 + X.t"
##
## Residuals:
## Min 1Q Median 3Q Max
## -67.6074 -1.8022 -0.4625 1.1787 60.4005
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -513.17083 72.67834 -7.061 1.93e-12 ***
## Y.1 1.40996 0.06453 21.850 < 2e-16 ***
## X.t 36.46061 5.13679 7.098 1.48e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.53 on 4212 degrees of freedom
## Multiple R-Squared: 0.8213, Adjusted R-squared: 0.8212
## Wald test: 1.076e+04 on 2 and 4212 DF, p-value: < 2.2e-16
##
## Diagnostic tests:
## NULL
##
## alpha beta phi
## Geometric coefficients: 1251.748 36.46061 1.409963AIC(model.koyck)## [1] 26383.92BIC(model.koyck)## [1] 26409.31Ramalan KOYCK
(fore.koyck <- forecast(model = model.koyck, x=test$BATTERY_VOLTAGE, h=1055))## $forecasts
## [1] 6.472232e+01 6.446980e+01 6.338456e+01 6.148979e+01
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## [361] -3.079743e+54 -4.342326e+54 -6.122521e+54 -8.632530e+54
## [365] -1.217155e+55 -1.716144e+55 -2.419701e+55 -3.411690e+55
## [369] -4.810358e+55 -6.782429e+55 -9.562977e+55 -1.348345e+56
## [373] -1.901117e+56 -2.680505e+56 -3.779415e+56 -5.328837e+56
## [377] -7.513465e+56 -1.059371e+57 -1.493675e+57 -2.106027e+57
## [381] -2.969420e+57 -4.186774e+57 -5.903199e+57 -8.323295e+57
## [385] -1.173554e+58 -1.654668e+58 -2.333022e+58 -3.289476e+58
## [389] -4.638041e+58 -6.539468e+58 -9.220411e+58 -1.300044e+59
## [393] -1.833015e+59 -2.584484e+59 -3.644028e+59 -5.137946e+59
## [397] -7.244317e+59 -1.021422e+60 -1.440168e+60 -2.030584e+60
## [401] -2.863049e+60 -4.036795e+60 -5.691734e+60 -8.025136e+60
## [405] -1.131515e+61 -1.595395e+61 -2.249448e+61 -3.171640e+61
## [409] -4.471896e+61 -6.305210e+61 -8.890116e+61 -1.253474e+62
## [413] -1.767352e+62 -2.491902e+62 -3.513491e+62 -4.953894e+62
## [417] -6.984810e+62 -9.848326e+62 -1.388578e+63 -1.957844e+63
## [421] -2.760489e+63 -3.892188e+63 -5.487843e+63 -7.737659e+63
## [425] -1.090982e+64 -1.538244e+64 -2.168868e+64 -3.058025e+64
## [429] -4.311703e+64 -6.079344e+64 -8.571653e+64 -1.208572e+65
## [433] -1.704042e+65 -2.402637e+65 -3.387630e+65 -4.776435e+65
## [437] -6.734599e+65 -9.495538e+65 -1.338836e+66 -1.887710e+66
## [441] -2.661602e+66 -3.752762e+66 -5.291257e+66 -7.460479e+66
## [445] -1.051900e+67 -1.483141e+67 -2.091175e+67 -2.948480e+67
## [449] -4.157249e+67 -5.861569e+67 -8.264598e+67 -1.165278e+68
## [453] -1.643000e+68 -2.316569e+68 -3.266278e+68 -4.605333e+68
## [457] -6.493351e+68 -9.155388e+68 -1.290876e+69 -1.820088e+69
## [461] -2.566258e+69 -3.618330e+69 -5.101713e+69 -7.193229e+69
## [465] -1.014219e+70 -1.430012e+70 -2.016264e+70 -2.842859e+70
## [469] -4.008327e+70 -5.651595e+70 -7.968542e+70 -1.123535e+71
## [473] -1.584144e+71 -2.233585e+71 -3.149273e+71 -4.440360e+71
## [477] -6.260745e+71 -8.827422e+71 -1.244634e+72 -1.754889e+72
## [481] -2.474329e+72 -3.488714e+72 -4.918959e+72 -6.935552e+72
## [485] -9.778875e+72 -1.378786e+73 -1.944037e+73 -2.741022e+73
## [489] -3.864740e+73 -5.449143e+73 -7.683092e+73 -1.083288e+74
## [493] -1.527396e+74 -2.153573e+74 -3.036459e+74 -4.281297e+74
## [497] -6.036472e+74 -8.511205e+74 -1.200049e+75 -1.692025e+75
## [501] -2.385693e+75 -3.363740e+75 -4.742751e+75 -6.687106e+75
## [505] -9.428574e+75 -1.329395e+76 -1.874398e+76 -2.642832e+76
## [509] -3.726297e+76 -5.253943e+76 -7.407867e+76 -1.044482e+77
## [513] -1.472682e+77 -2.076427e+77 -2.927687e+77 -4.127931e+77
## [517] -5.820232e+77 -8.206315e+77 -1.157060e+78 -1.631413e+78
## [521] -2.300233e+78 -3.243244e+78 -4.572855e+78 -6.447559e+78
## [525] -9.090823e+78 -1.281773e+79 -1.807253e+79 -2.548160e+79
## [529] -3.592813e+79 -5.065735e+79 -7.142501e+79 -1.007067e+80
## [533] -1.419927e+80 -2.002045e+80 -2.822811e+80 -3.980060e+80
## [537] -5.611739e+80 -7.912347e+80 -1.115612e+81 -1.572972e+81
## [541] -2.217833e+81 -3.127064e+81 -4.409046e+81 -6.216594e+81
## [545] -8.765170e+81 -1.235857e+82 -1.742513e+82 -2.456880e+82
## [549] -3.464111e+82 -4.884270e+82 -6.886642e+82 -9.709913e+82
## [553] -1.369062e+83 -1.930328e+83 -2.721692e+83 -3.837486e+83
## [557] -5.410715e+83 -7.628910e+83 -1.075648e+84 -1.516625e+84
## [561] -2.138386e+84 -3.015046e+84 -4.251104e+84 -5.993902e+84
## [565] -8.451183e+84 -1.191586e+85 -1.680093e+85 -2.368869e+85
## [569] -3.340019e+85 -4.709305e+85 -6.639947e+85 -9.362083e+85
## [573] -1.320020e+86 -1.861179e+86 -2.624195e+86 -3.700019e+86
## [577] -5.216891e+86 -7.355626e+86 -1.037116e+87 -1.462296e+87
## [581] -2.061784e+87 -2.907040e+87 -4.098821e+87 -5.779188e+87
## [585] -8.148443e+87 -1.148901e+88 -1.619908e+88 -2.284011e+88
## [589] -3.220372e+88 -4.540607e+88 -6.402090e+88 -9.026713e+88
## [593] -1.272734e+89 -1.794508e+89 -2.530190e+89 -3.567476e+89
## [597] -5.030011e+89 -7.092132e+89 -9.999647e+89 -1.409914e+90
## [601] -1.987927e+90 -2.802904e+90 -3.951992e+90 -5.572165e+90
## [605] -7.856548e+90 -1.107745e+91 -1.561879e+91 -2.202193e+91
## [609] -3.105012e+91 -4.377953e+91 -6.172754e+91 -8.703357e+91
## [613] -1.227142e+92 -1.730225e+92 -2.439554e+92 -3.439681e+92
## [617] -4.849825e+92 -6.838076e+92 -9.641438e+92 -1.359407e+93
## [621] -1.916715e+93 -2.702498e+93 -3.810423e+93 -5.372558e+93
## [625] -7.575110e+93 -1.068063e+94 -1.505930e+94 -2.123306e+94
## [629] -2.993783e+94 -4.221125e+94 -5.951632e+94 -8.391584e+94
## [633] -1.183183e+95 -1.668244e+95 -2.352164e+95 -3.316465e+95
## [637] -4.676094e+95 -6.593122e+95 -9.296061e+95 -1.310711e+96
## [641] -1.848054e+96 -2.605689e+96 -3.673926e+96 -5.180101e+96
## [645] -7.303753e+96 -1.029803e+97 -1.451984e+97 -2.047244e+97
## [649] -2.886540e+97 -4.069915e+97 -5.738432e+97 -8.090979e+97
## [653] -1.140799e+98 -1.608484e+98 -2.267904e+98 -3.197662e+98
## [657] -4.508586e+98 -6.356942e+98 -8.963056e+98 -1.263758e+99
## [661] -1.781853e+99 -2.512347e+99 -3.542318e+99 -4.994539e+99
## [665] -7.042117e+99 -9.929128e+99 -1.399971e+100 -1.973908e+100
## [669] -2.783138e+100 -3.924122e+100 -5.532869e+100 -7.801143e+100
## [673] -1.099933e+101 -1.550865e+101 -2.186663e+101 -3.083115e+101
## [677] -4.347079e+101 -6.129223e+101 -8.641980e+101 -1.218488e+102
## [681] -1.718023e+102 -2.422350e+102 -3.415424e+102 -4.815624e+102
## [685] -6.789853e+102 -9.573445e+102 -1.349821e+103 -1.903198e+103
## [689] -2.683440e+103 -3.783552e+103 -5.334670e+103 -7.521690e+103
## [693] -1.060531e+104 -1.495310e+104 -2.108332e+104 -2.972671e+104
## [697] -4.191357e+104 -5.909661e+104 -8.332406e+104 -1.174839e+105
## [701] -1.656480e+105 -2.335576e+105 -3.293077e+105 -4.643118e+105
## [705] -6.546626e+105 -9.230504e+105 -1.301467e+106 -1.835021e+106
## [709] -2.587313e+106 -3.648017e+106 -5.143571e+106 -7.252246e+106
## [713] -1.022540e+107 -1.441744e+107 -2.032807e+107 -2.866183e+107
## [717] -4.041214e+107 -5.697964e+107 -8.033921e+107 -1.132754e+108
## [721] -1.597141e+108 -2.251911e+108 -3.175112e+108 -4.476791e+108
## [725] -6.312112e+108 -8.899847e+108 -1.254846e+109 -1.769287e+109
## [729] -2.494630e+109 -3.517337e+109 -4.959317e+109 -6.992455e+109
## [733] -9.859107e+109 -1.390098e+110 -1.959987e+110 -2.763511e+110
## [737] -3.896449e+110 -5.493851e+110 -7.746129e+110 -1.092176e+111
## [741] -1.539928e+111 -2.171242e+111 -3.061372e+111 -4.316423e+111
## [745] -6.085999e+111 -8.581036e+111 -1.209895e+112 -1.705907e+112
## [749] -2.405267e+112 -3.391339e+112 -4.781663e+112 -6.741971e+112
## [753] -9.505932e+112 -1.340302e+113 -1.889776e+113 -2.664516e+113
## [757] -3.756870e+113 -5.297049e+113 -7.468646e+113 -1.053052e+114
## [761] -1.484765e+114 -2.093464e+114 -2.951707e+114 -4.161799e+114
## [765] -5.867985e+114 -8.273645e+114 -1.166554e+115 -1.644798e+115
## [769] -2.319105e+115 -3.269853e+115 -4.610374e+115 -6.500459e+115
## [773] -9.165409e+115 -1.292289e+116 -1.822081e+116 -2.569067e+116
## [777] -3.622291e+116 -5.107297e+116 -7.201103e+116 -1.015329e+117
## [781] -1.431577e+117 -2.018471e+117 -2.845971e+117 -4.012715e+117
## [785] -5.657781e+117 -7.977265e+117 -1.124765e+118 -1.585878e+118
## [789] -2.236030e+118 -3.152720e+118 -4.445220e+118 -6.267598e+118
## [793] -8.837085e+118 -1.245997e+119 -1.756810e+119 -2.477038e+119
## [797] -3.492532e+119 -4.924343e+119 -6.943144e+119 -9.789579e+119
## [801] -1.380295e+120 -1.946165e+120 -2.744022e+120 -3.868971e+120
## [805] -5.455107e+120 -7.691502e+120 -1.084474e+121 -1.529068e+121
## [809] -2.155930e+121 -3.039783e+121 -4.285983e+121 -6.043080e+121
## [813] -8.520521e+121 -1.201362e+122 -1.693877e+122 -2.388305e+122
## [817] -3.367422e+122 -4.747943e+122 -6.694426e+122 -9.438895e+122
## [821] -1.330850e+123 -1.876450e+123 -2.645725e+123 -3.730376e+123
## [825] -5.259694e+123 -7.415976e+123 -1.045626e+124 -1.474294e+124
## [829] -2.078700e+124 -2.930892e+124 -4.132450e+124 -5.826603e+124
## [833] -8.215298e+124 -1.158327e+125 -1.633199e+125 -2.302751e+125
## [837] -3.246794e+125 -4.577861e+125 -6.454617e+125 -9.100774e+125
## [841] -1.283176e+126 -1.809231e+126 -2.550950e+126 -3.596746e+126
## [845] -5.071280e+126 -7.150320e+126 -1.008169e+127 -1.421481e+127
## [849] -2.004237e+127 -2.825901e+127 -3.984417e+127 -5.617882e+127
## [853] -7.921008e+127 -1.116833e+128 -1.574694e+128 -2.220261e+128
## [857] -3.130487e+128 -4.413872e+128 -6.223399e+128 -8.774765e+128
## [861] -1.237210e+129 -1.744421e+129 -2.459569e+129 -3.467903e+129
## [865] -4.889616e+129 -6.894180e+129 -9.720542e+129 -1.370561e+130
## [869] -1.932441e+130 -2.724671e+130 -3.841686e+130 -5.416637e+130
## [873] -7.637261e+130 -1.076826e+131 -1.518285e+131 -2.140727e+131
## [877] -3.018346e+131 -4.255758e+131 -6.000463e+131 -8.460434e+131
## [881] -1.192890e+132 -1.681932e+132 -2.371462e+132 -3.343675e+132
## [885] -4.714460e+132 -6.647216e+132 -9.372331e+132 -1.321464e+133
## [889] -1.863217e+133 -2.627067e+133 -3.704069e+133 -5.222602e+133
## [893] -7.363678e+133 -1.038252e+134 -1.463897e+134 -2.064041e+134
## [897] -2.910223e+134 -4.103307e+134 -5.785514e+134 -8.157363e+134
## [901] -1.150158e+135 -1.621681e+135 -2.286511e+135 -3.223897e+135
## [905] -4.545577e+135 -6.409098e+135 -9.036594e+135 -1.274127e+136
## [909] -1.796472e+136 -2.532960e+136 -3.571381e+136 -5.035517e+136
## [913] -7.099895e+136 -1.001059e+137 -1.411457e+137 -1.990103e+137
## [917] -2.805972e+137 -3.956318e+137 -5.578264e+137 -7.865149e+137
## [921] -1.108957e+138 -1.563589e+138 -2.204604e+138 -3.108410e+138
## [925] -4.382745e+138 -6.179511e+138 -8.712884e+138 -1.228485e+139
## [929] -1.732119e+139 -2.442224e+139 -3.443447e+139 -4.855134e+139
## [933] -6.845562e+139 -9.651992e+139 -1.360896e+140 -1.918813e+140
## [937] -2.705456e+140 -3.814594e+140 -5.378439e+140 -7.583402e+140
## [941] -1.069232e+141 -1.507578e+141 -2.125630e+141 -2.997061e+141
## [945] -4.225746e+141 -5.958147e+141 -8.400770e+141 -1.184478e+142
## [949] -1.670070e+142 -2.354738e+142 -3.320095e+142 -4.681213e+142
## [953] -6.600339e+142 -9.306237e+142 -1.312145e+143 -1.850077e+143
## [957] -2.608541e+143 -3.677947e+143 -5.185771e+143 -7.311748e+143
## [961] -1.030930e+144 -1.453573e+144 -2.049485e+144 -2.889699e+144
## [965] -4.074371e+144 -5.744714e+144 -8.099836e+144 -1.142047e+145
## [969] -1.610245e+145 -2.270387e+145 -3.201162e+145 -4.513522e+145
## [973] -6.363901e+145 -8.972867e+145 -1.265141e+146 -1.783803e+146
## [977] -2.515097e+146 -3.546195e+146 -5.000006e+146 -7.049826e+146
## [981] -9.939997e+146 -1.401503e+147 -1.976068e+147 -2.786184e+147
## [985] -3.928418e+147 -5.538926e+147 -7.809683e+147 -1.101137e+148
## [989] -1.552563e+148 -2.189056e+148 -3.086490e+148 -4.351838e+148
## [993] -6.135932e+148 -8.651440e+148 -1.219821e+149 -1.719904e+149
## [997] -2.425001e+149 -3.419163e+149 -4.820895e+149 -6.797286e+149
## [1001] -9.583925e+149 -1.351298e+150 -1.905281e+150 -2.686377e+150
## [1005] -3.787693e+150 -5.340509e+150 -7.529923e+150 -1.061692e+151
## [1009] -1.496946e+151 -2.110640e+151 -2.975925e+151 -4.195945e+151
## [1013] -5.916130e+151 -8.341527e+151 -1.176125e+152 -1.658293e+152
## [1017] -2.338132e+152 -3.296681e+152 -4.648200e+152 -6.553792e+152
## [1021] -9.240608e+152 -1.302892e+153 -1.837030e+153 -2.590145e+153
## [1025] -3.652010e+153 -5.149201e+153 -7.260185e+153 -1.023660e+154
## [1029] -1.443323e+154 -2.035032e+154 -2.869321e+154 -4.045638e+154
## [1033] -5.704201e+154 -8.042715e+154 -1.133993e+155 -1.598889e+155
## [1037] -2.254376e+155 -3.178587e+155 -4.481692e+155 -6.319022e+155
## [1041] -8.909590e+155 -1.256220e+156 -1.771224e+156 -2.497361e+156
## [1045] -3.521187e+156 -4.964745e+156 -7.000110e+156 -9.869899e+156
## [1049] -1.391620e+157 -1.962133e+157 -2.766536e+157 -3.900714e+157
## [1053] -5.499864e+157 -7.754608e+157 -1.093371e+158
##
## $call
## forecast.koyckDlm(model = model.koyck, x = test$BATTERY_VOLTAGE,
## h = 1055)
##
## attr(,"class")
## [1] "forecast.koyckDlm" "dLagM"MAPE testing dan akurasi Data Training
#mape data testing
mape.koyck <- MAPE(fore.koyck$forecasts, test$REF_TEMP)
#akurasi data training
mape_train <- dLagM::GoF(model.koyck)["MAPE"]
c("MAPE_testing" = mape.koyck, "MAPE_training" = mape_train)## $MAPE_testing
## [1] 7.067076e+153
##
## $MAPE_training.MAPE
## [1] 0.0487201Regression with Distributed Lag
Regression with Distributed Lag (lag=2) -> estimasi parameter menggunakan least square
model.dlm = dLagM::dlm(x = train$BATTERY_VOLTAGE, y = train$REF_TEMP , q = 2)
summary(model.dlm)##
## Call:
## lm(formula = model.formula, data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -66.858 -0.977 -0.269 0.735 10.976
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1058.7185 2.4999 423.508 <2e-16 ***
## x.t -84.9375 0.6298 -134.859 <2e-16 ***
## x.1 0.4987 0.9359 0.533 0.594
## x.2 9.8943 0.6287 15.737 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.017 on 4210 degrees of freedom
## Multiple R-squared: 0.9762, Adjusted R-squared: 0.9762
## F-statistic: 5.768e+04 on 3 and 4210 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 17876.94 17908.67AIC(model.dlm)## [1] 17876.94BIC(model.dlm)## [1] 17908.67ramalan
(fore.dlm <- forecast(model = model.dlm, x=test$BATTERY_VOLTAGE, h=1055))## $forecasts
## [1] 64.73170 63.99124 65.89286 66.83120 68.32708 75.01317 81.57040
## [8] 84.13647 85.87311 86.31175 86.85931 85.90601 52.68641 51.28108
## [15] 54.30043 52.80455 52.06409 50.56821 48.97838 47.48749 47.69534
## [22] 48.74260 51.28574 53.71997 55.95631 56.49390 57.89083 57.78192
## [29] 58.43341 74.56655 72.67412 68.25606 66.77015 66.22757 64.73170
## [36] 64.84061 64.18912 67.59161 71.06811 79.14615 82.94739 86.17991
## [43] 87.35901 88.55308 87.49584 84.75482 84.86872 83.46680 81.77802
## [50] 80.28713 78.79623 75.60659 73.27630 71.13890 71.45069 58.15751
## [57] 57.38792 55.57848 53.99862 50.15748 48.68155 46.63811 45.15220
## [64] 42.91088 42.27435 42.57616 42.67510 42.67510 42.67510 41.82573
## [71] 41.83072 43.62841 48.71469 55.28189 59.74459 61.47126 59.16389
## [78] 58.02766 57.38116 58.33447 57.57905 54.93696 53.35211 50.26141
## [85] 47.08174 44.94933 51.30569 51.56761 50.87501 50.02564 50.88000
## [92] 50.97396 50.87501 52.57377 53.41317 53.21030 51.41260 51.42258
## [99] 52.46984 53.31423 52.36092 54.81509 35.36344 36.03068 40.00012
## [106] 44.13808 54.10777 60.34822 63.36790 66.79830 64.57990 64.09516
## [113] 64.29305 64.29305 62.59430 60.90552 56.86650 53.69182 51.65835
## [120] 48.67158 46.44023 45.15220 43.76025 43.96811 44.16600 44.16600
## [127] 45.01537 45.85976 46.60521 44.80253 43.01481 40.67454 39.18863
## [134] 37.79668 36.30579 35.66427 35.01777 33.42295 33.53186 32.03100
## [141] 32.04097 32.23885 33.08823 34.78199 36.37183 40.41085 48.68179
## [148] 53.23346 48.81661 43.99603 41.86860 39.83015 39.29256 38.74500
## [155] 37.15018 35.56034 34.91883 33.42295 31.83311 32.04097 30.54010
## [162] 29.70070 29.90357 29.15314 29.15813 30.10644 30.95083 58.87629
## [169] 113.82220 57.57170 53.99772 64.36408 65.74107 69.48326 73.50732
## [176] 72.13830 69.94982 68.35998 66.86909 65.37820 63.03793 62.40140
## [183] 60.15509 59.41961 58.02268 57.28222 57.48509 56.73466 57.58902
## [190] 56.83360 68.63090 68.66003 66.42546 66.43045 66.52939 65.68001
## [197] 66.53438 65.77896 66.53438 69.17646 71.61068 76.39515 79.46590
## [204] 79.70168 78.45154 78.35759 76.75778 75.06900 73.57811 72.93659
## [211] 69.74196 68.16210 68.56784 67.91635 67.07196 68.87464 68.11424
## [218] 66.22259 64.63275 62.29248 63.35470 64.49592 66.94012 68.52497
## [225] 70.76629 72.25220 72.79477 71.74253 69.94982 67.51061 66.87408
## [232] 64.62777 65.59104 65.03351 64.93955 64.18912 61.64598 61.75988
## [239] 62.05671 62.90609 67.14798 69.57223 75.00818 78.07395 80.75891
## [246] 82.89132 82.48059 82.18376 77.08751 74.56930 74.32854 73.78098
## [253] 73.88491 71.43573 70.60131 69.20437 54.02453 54.31217 56.94251
## [260] 57.78690 61.08048 64.35909 64.79275 64.39199 65.14243 66.83619
## [267] 65.87790 40.20374 39.60290 42.57616 42.67510 41.82573 41.83072
## [274] 41.92966 41.92966 42.77903 42.77405 42.67510 43.52448 43.51949
## [281] 45.96868 53.59810 54.10577 54.05967 54.80512 56.39994 54.59227
## [288] 52.70561 50.36534 48.87944 49.18624 50.23350 49.37914 49.28518
## [295] 46.83600 46.85095 48.84653 50.53531 48.62870 46.74204 44.40177
## [302] 42.06649 42.37828 49.47011 57.07459 60.48505 72.31027 71.74076
## [309] 72.80475 74.48854 75.88049 75.67263 75.47475 74.62537 73.78098
## [316] 73.03553 72.29009 69.84589 69.11042 68.56286 68.66679 67.91635
## [323] 66.22259 66.33150 66.52939 68.22814 69.06754 71.41280 77.24452
## [330] 60.77466 57.62868 56.12604 55.59344 53.44607 49.31310 47.93610
## [337] 45.04329 41.86362 40.58058 39.28758 38.64606 38.84893 38.09850
## [344] 38.10348 39.05180 38.19744 37.25411 37.35804 39.15573 39.14576
## [351] 42.34537 46.57231 52.09723 71.95262 72.83910 70.45451 72.80475
## [358] 75.33791 76.72488 78.11683 78.75835 76.85672 74.21963 73.58310
## [365] 70.48741 69.75692 68.45893 67.71847 67.07196 67.17589 68.12421
## [372] 67.26985 66.32652 66.43045 66.52939 68.22814 67.36879 68.02527
## [379] 66.42047 68.03025 69.91692 84.14844 85.56454 84.72192 85.36842
## [386] 81.86699 78.39049 75.40871 73.27630 71.13890 69.75194 68.35998
## [393] 67.71847 67.07196 66.32652 66.43045 64.83064 66.53936 65.87790
## [400] 64.83562 65.78893 65.03351 66.63830 66.72727 67.37876 65.67503
## [407] 66.43543 64.08021 63.14685 62.59929 61.00446 60.26400 58.76812
## [414] 57.17829 55.68740 55.89525 55.24376 54.39937 54.50330 55.45162
## [421] 56.29601 59.58958 61.16945 65.85996 69.02965 71.81355 70.54846
## [428] 68.45893 68.56784 67.91635 66.22259 61.23525 62.31243 62.90110
## [435] 61.95278 63.65652 63.74549 64.39698 66.09074 66.83120 68.32708
## [442] 69.06754 68.86467 67.91635 69.62009 68.85968 67.81741 67.92134
## [449] 68.86966 68.01530 66.22259 65.48213 63.98625 64.09516 59.19680
## [456] 56.67859 55.58845 54.19650 52.70561 53.76284 53.95574 53.85680
## [463] 53.00742 53.01241 53.96073 53.95574 56.40493 57.23934 57.78690
## [470] 57.68297 56.73466 55.89027 56.84357 57.78690 58.53235 58.42842
## [477] 32.84821 32.99781 35.11671 35.12170 35.22064 35.22064 36.07002
## [484] 35.21565 36.82045 37.75879 37.55592 38.30635 39.15074 40.74557
## [491] 42.33540 42.12754 41.92966 41.92966 41.08028 41.93464 42.87798
## [498] 44.47280 45.21326 47.55851 52.54086 49.66599 55.88230 59.53674
## [505] 59.57462 61.72199 62.45747 63.00503 62.90110 62.80216 62.80216
## [512] 62.80216 62.80216 61.95278 62.80714 63.75047 62.79717 63.55259
## [519] 62.79717 62.70321 62.80216 61.95278 61.10839 58.66420 57.07935
## [526] 56.53677 55.04089 47.50543 45.20007 46.95488 45.54797 45.45900
## [533] 43.95814 45.66686 45.85477 46.50627 47.35065 48.09610 47.99217
## [540] 48.74260 51.28574 55.41872 56.79571 56.29102 57.79189 56.08317
## [547] 54.19650 52.70561 53.76284 54.80512 52.15306 50.37033 54.07463
## [554] 53.40319 51.31366 49.72382 48.23293 45.04329 43.56237 41.41999
## [561] 39.93408 38.54213 37.05124 72.08349 72.92630 68.86467 70.46448
## [568] 73.00263 72.78979 74.19171 74.18174 71.43573 68.90256 65.81685
## [575] 61.88674 62.30744 61.10341 61.96275 63.85440 62.04674 60.16007
## [582] 59.51856 60.57080 63.21289 63.09898 64.50091 65.34031 63.43869
## [589] 62.50034 65.25134 67.03407 65.87790 64.83562 64.93955 66.73725
## [596] 67.57665 66.52440 66.43045 63.98126 62.29747 60.05615 57.72086
## [603] 56.33390 55.79133 55.99420 56.09314 56.09314 56.09314 56.94251
## [610] 59.48565 61.07050 59.91433 61.42018 69.15353 57.86888 57.04323
## [617] 57.48010 57.48509 58.43341 58.42842 59.17885 57.47512 55.68740
## [624] 55.89525 54.39439 53.55499 52.90848 53.86179 78.58763 76.64533
## [631] 72.08722 71.44570 69.94982 69.20936 67.71348 66.12365 62.93400
## [638] 62.30246 62.70321 61.10341 60.26400 60.46688 59.71644 58.02268
## [645] 58.98097 61.72199 64.15622 68.94068 71.16206 75.64970 77.02171
## [652] 64.52682 63.54937 62.39143 62.50533 62.80216 63.65153 65.34530
## [659] 67.78451 65.02354 64.74167 65.03850 66.73725 65.02852 63.14186
## [666] 60.80159 58.46631 58.77810 58.22555 57.38116 57.48509 56.73466
## [673] 56.73964 55.98921 55.99420 56.09314 56.09314 56.09314 57.79189
## [680] 57.78192 59.28278 60.12219 61.61806 59.81040 59.62249 58.97100
## [687] 58.12661 59.07991 57.47512 57.38615 58.43341 57.57905 57.48509
## [694] 56.73466 56.73964 55.13983 55.14981 55.34769 56.19707 66.38459
## [701] 64.52706 60.80159 58.46631 55.38060 54.84799 52.70062 51.11578
## [708] 49.72382 47.38356 46.74703 46.19946 46.30339 48.95046 54.88113
## [715] 62.19378 67.40193 69.02467 72.56399 69.69410 66.66622 66.12863
## [722] 65.58107 63.98625 62.39641 48.16489 47.59817 49.28518 49.38412
## [729] 48.53475 48.53973 47.78930 48.64366 49.58699 51.18182 51.07290
## [736] 52.57377 51.71442 50.67214 49.92670 49.18125 50.13455 49.37914
## [743] 49.28518 47.68537 45.99659 46.20445 44.70359 53.20731 53.35533
## [750] 52.36591 50.66716 49.82775 49.18125 48.43580 46.84098 46.94990
## [757] 45.44903 43.76025 42.26936 40.77847 40.13695 38.64107 37.90061
## [764] 38.10348 37.35305 37.35804 39.15573 40.84451 42.33540 42.97692
## [771] 43.62342 43.51949 76.54619 78.89985 79.27300 80.64999 79.29593
## [778] 79.10304 77.50323 75.81445 76.02231 73.67207 71.98827 69.74695
## [785] 68.26104 68.56784 66.21760 65.38319 64.83562 63.24080 63.34972
## [792] 63.54760 65.24635 66.93513 70.12478 71.60570 75.44683 76.07339
## [799] 75.57369 75.47475 76.32412 76.31913 76.22019 75.37082 73.67705
## [806] 72.93659 69.74196 69.86085 67.70849 65.17533 63.78836 62.39641
## [813] 61.75490 59.40964 59.52354 59.82037 64.06725 66.59044 74.57452
## [820] 80.17346 81.69726 83.53782 85.77416 56.58361 58.15508 59.81040
## [827] 57.92374 57.28222 57.48509 57.58403 55.88528 56.74463 56.08815
## [834] 55.14482 56.09813 61.28833 65.40635 66.48651 69.37933 70.01087
## [841] 69.61012 68.66180 68.66679 67.06698 64.52882 63.04292 60.80159
## [848] 59.31569 59.62249 59.82037 58.12162 57.28222 57.48509 56.73466
## [855] 55.89027 55.14482 53.55000 54.50829 53.85181 54.60723 56.39994
## [862] 60.53790 62.01383 62.35852 62.15565 63.75546 62.89611 61.85384
## [869] 61.10839 58.66420 57.07935 56.53677 40.60151 41.64457 43.51949
## [876] 43.42055 43.42055 43.42055 42.57118 44.27491 44.36388 44.16600
## [883] 44.16600 43.31662 43.32161 44.26993 44.26494 44.16600 45.01537
## [890] 44.16101 44.91643 45.85976 47.45458 50.74317 52.22409 51.81835
## [897] 50.77109 49.92670 49.18125 47.58643 46.84597 47.04884 47.14778
## [904] 47.14778 47.14778 47.14778 46.29841 46.30339 45.55296 44.70857
## [911] 43.11375 42.37329 41.72679 41.83072 42.77903 44.47280 46.06263
## [918] 47.55353 47.34567 47.99716 47.14280 47.89822 47.99217 47.04385
## [925] 47.04884 47.14778 47.14778 47.14778 47.14778 45.44903 46.30838
## [932] 45.65190 44.70857 49.90875 57.62216 56.98362 56.94251 60.33503
## [939] 62.76427 64.90166 66.28863 65.13245 63.24080 62.50034 61.00446
## [946] 59.41463 58.77311 58.12661 57.38116 56.63571 55.89027 55.99420
## [953] 55.24376 53.55000 54.50829 53.85181 53.75786 53.85680 56.40493
## [960] 57.23934 57.78690 59.38173 60.97156 62.46245 63.10397 62.05172
## [967] 61.10839 60.36295 60.46688 40.18081 40.30048 40.97635 41.83570
## [974] 41.17922 41.93464 42.02860 42.77903 44.47280 46.06263 48.40290
## [981] 50.73818 51.27577 60.31709 58.46454 56.53677 55.89027 55.99420
## [988] 56.09314 55.24376 55.24875 54.49832 53.65393 54.60723 55.55056
## [995] 57.14539 60.43397 62.76427 69.14854 72.20932 72.24721 70.14771
## [1002] 69.20936 69.41223 67.81242 66.12365 64.63275 62.29248 42.12032
## [1009] 42.53682 45.76082 44.90646 45.66188 47.45458 47.34567 47.14778
## [1016] 51.39466 54.76723 55.10195 54.70119 52.05412 50.37033 49.82775
## [1023] 49.18125 48.43580 47.69036 46.94491 47.04884 47.14778 47.14778
## [1030] 46.29841 45.45402 45.55795 44.80751 45.66188 46.60521 46.50128
## [1037] 48.10109 54.03674 56.35208 57.34327 57.03647 56.83859 55.98921
## [1044] 54.29545 52.70561 52.91347 52.26198 50.56821 50.67713 50.87501
## [1051] 50.87501 50.87501 50.87501 50.87501 50.02564
##
## $call
## forecast.dlm(model = model.dlm, x = test$BATTERY_VOLTAGE, h = 1055)
##
## attr(,"class")
## [1] "forecast.dlm" "dLagM"MAPE testing dan akurasi Data Training
#mape data testing
mape.dlm <- MAPE(fore.dlm$forecasts, test$REF_TEMP)
#akurasi data training
mape_train <- GoF(model.dlm)["MAPE"]
c("MAPE_testing" = mape.dlm, "MAPE_training" = mape_train)## $MAPE_testing
## [1] 0.01844561
##
## $MAPE_training.MAPE
## [1] 0.0218475Lag Optimum
#penentuan lag optimum
finiteDLMauto(formula = REF_TEMP ~ BATTERY_VOLTAGE,
data = data.frame(train), q.min = 1, q.max = 4 ,
model.type = "dlm", error.type = "AIC", trace = TRUE) ##q max lag maksimum## q - k MASE AIC BIC GMRAE MBRAE R.Adj.Sq Ljung-Box
## 4 4 0.58721 16262.01 16306.43 0.79579 -0.70979 0.98377 0
## 3 3 0.59809 16394.75 16432.83 0.82436 0.34545 0.98327 0
## 2 2 0.61965 17876.94 17908.67 0.84677 0.56818 0.97623 0
## 1 1 0.65283 18694.23 18719.62 0.89583 1.72210 0.97116 0#model dlm dengan lag optimum
model.dlm2 = dLagM::dlm(x = train$BATTERY_VOLTAGE,y = train$REF_TEMP , q = 4) #terdapat lag yang tidak signifikan sehingga dapat dikurangi jumlah lagnya
summary(model.dlm2)##
## Call:
## lm(formula = model.formula, data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.8121 -0.9438 -0.2332 0.6889 9.4896
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1053.8877 2.1431 491.767 < 2e-16 ***
## x.t -84.8815 0.5423 -156.508 < 2e-16 ***
## x.1 2.1844 0.7920 2.758 0.00584 **
## x.2 1.4913 0.7744 1.926 0.05418 .
## x.3 1.2520 0.7742 1.617 0.10591
## x.4 5.7705 0.5227 11.039 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.666 on 4206 degrees of freedom
## Multiple R-squared: 0.9838, Adjusted R-squared: 0.9838
## F-statistic: 5.106e+04 on 5 and 4206 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 16262.01 16306.43AIC(model.dlm2)## [1] 16262.01BIC(model.dlm2)## [1] 16306.43ramalan
(fore.dlm2 <- forecast(model = model.dlm2, x=test$BATTERY_VOLTAGE, h=1055))## $forecasts
## [1] 64.46877 63.81900 65.69624 66.59902 68.37291 75.13750 81.59552
## [8] 84.61398 86.73817 86.90000 87.17052 86.01656 52.73406 51.83302
## [15] 51.56432 50.46435 51.94967 50.43164 48.87535 47.37917 47.53543
## [22] 48.55452 51.21957 53.80098 56.22464 56.86792 58.28829 58.01901
## [29] 58.65237 74.67527 72.43229 69.63366 67.73580 65.90405 64.41106
## [36] 64.66782 63.97676 67.47661 70.91482 79.26847 83.24208 86.94691
## [43] 88.10473 89.04446 87.77100 84.90301 84.84300 83.08722 81.52855
## [50] 80.07754 78.47847 75.29717 73.00837 70.72756 71.00332 57.73540
## [57] 57.44675 54.48506 53.09004 49.88510 48.43430 46.26197 44.83771
## [64] 42.69325 42.09277 42.35750 42.52539 42.71102 42.76873 41.91991
## [71] 41.94176 43.65430 48.71603 55.40337 60.20699 62.31254 60.01350
## [78] 58.62688 57.44594 58.18344 57.45562 54.98633 53.41433 50.06231
## [85] 46.87952 44.67825 50.91064 51.08337 51.24736 50.48401 50.95074
## [92] 50.94381 50.94142 52.68423 53.43165 53.37998 51.64240 51.55816
## [99] 52.37909 53.23111 52.46094 55.00180 35.35820 36.61950 38.65844
## [106] 42.95876 54.32019 60.69128 64.40364 67.98043 65.30639 64.75127
## [113] 64.42997 64.16649 62.58427 60.93032 56.75976 53.52858 51.28453
## [120] 48.19246 46.11673 44.81267 43.42666 43.76855 43.99653 44.13698
## [127] 45.10121 45.92818 46.74024 44.99333 43.25425 40.71109 39.07615
## [134] 37.60740 36.13625 35.55911 34.90241 33.38199 33.56852 31.97094
## [141] 32.09737 32.24261 33.11646 34.90766 36.54669 40.70474 48.97110
## [148] 53.63054 49.77707 45.11716 42.08742 39.38492 38.93980 38.48365
## [155] 37.03345 35.58006 34.87498 33.31176 31.81318 32.01463 30.42957
## [162] 29.76489 29.93197 29.12311 29.27288 30.19432 31.03381 59.06567
## [169] 113.49040 58.88164 61.34215 63.72726 62.29636 69.96233 73.83164
## [176] 72.48548 70.55711 68.56696 66.66684 65.12546 62.79298 62.17997
## [183] 59.84056 59.22516 57.77975 57.08480 57.32210 56.57095 57.56954
## [190] 56.77149 68.67436 68.42865 67.32586 67.23013 66.43717 65.60088
## [197] 66.52924 65.67350 66.54176 69.12646 71.54728 76.57509 79.69928
## [204] 80.16057 78.98202 78.59264 76.66658 74.96745 73.40104 72.65078
## [211] 69.44764 67.99275 68.22402 67.51281 66.94170 68.79150 67.92643
## [218] 66.29104 64.68468 62.10885 63.13577 64.14793 66.81059 68.58837
## [225] 70.97617 72.48318 73.04541 71.99195 70.10310 67.48732 66.68868
## [232] 64.29156 65.37379 64.73351 64.83570 64.16240 61.59261 61.73076
## [239] 61.78802 62.73210 67.12745 69.54976 75.33885 78.41616 81.29357
## [246] 83.43223 82.85304 82.52740 77.16612 74.57762 73.88382 73.17671
## [253] 73.59726 71.25136 70.53830 68.96495 53.78244 54.39108 55.59109
## [260] 56.75883 61.15602 64.43648 65.06804 64.87876 65.43176 66.86421
## [267] 65.89908 40.41412 40.15278 40.51913 40.96736 41.86221 41.94176
## [274] 41.95667 41.96919 42.87571 42.85387 42.83895 43.67525 43.59570
## [281] 46.12723 53.68852 54.23830 54.89349 55.41975 56.54876 54.72231
## [288] 52.96831 50.41263 48.71999 48.94887 49.98048 49.30798 49.43032
## [295] 46.88626 46.90661 48.70668 50.39819 48.80016 47.09135 44.47797
## [302] 41.93651 42.18723 49.17546 56.85073 60.95202 73.34065 72.36411
## [309] 74.10491 75.26069 76.00432 75.89324 75.66526 74.67599 73.73361
## [316] 72.92155 72.12202 69.68255 68.98441 68.27240 68.40442 67.75615
## [323] 66.15059 66.26690 66.30924 68.08962 69.01016 71.50493 77.34116
## [330] 60.88809 58.55701 55.24988 54.36713 53.03613 49.09569 47.79536
## [337] 44.61362 41.57127 40.33423 38.90543 38.41103 38.71856 38.02511
## [344] 38.17488 39.09632 38.23818 37.45400 37.47823 39.14559 39.17213
## [351] 42.59527 46.72693 52.38436 72.47838 73.25395 72.47618 74.28838
## [358] 75.35934 76.83129 78.40293 78.96756 77.02010 74.36198 73.48059
## [365] 70.11925 69.52569 68.09519 67.41276 66.85896 66.97846 67.97012
## [372] 67.16968 66.38550 66.40974 66.37947 68.14732 67.31253 68.15336
## [379] 66.42376 68.04727 69.77623 84.09991 85.48674 85.89790 86.36679
## [386] 81.92875 78.47802 75.15956 72.75251 70.61215 69.30569 67.96487
## [393] 67.40024 66.80125 66.12964 66.29433 64.68184 66.49338 65.68841
## [400] 64.85665 65.83259 64.87396 66.64874 66.66516 67.43896 65.75215
## [407] 66.51433 63.96335 63.13248 62.45314 60.77212 60.16754 58.59181
## [414] 57.03552 55.53933 55.69559 55.01705 54.33053 54.48270 55.35895
## [421] 56.25615 59.67236 61.25518 66.17451 69.30109 72.26364 71.07727
## [428] 68.94552 68.72322 67.68593 66.09289 61.17400 62.19623 62.34661
## [435] 61.67341 63.72660 63.64012 64.47163 66.18008 66.85488 68.48832
## [442] 69.19579 69.01619 68.06972 69.66126 68.72597 67.88169 67.95111
## [449] 68.71195 67.91152 66.27852 65.47579 63.78464 63.92599 58.99085
## [456] 56.65821 55.23100 53.69692 52.45659 53.57708 53.72551 53.85104
## [463] 53.10512 53.06926 53.93299 53.92366 56.51290 57.28367 58.00819
## [470] 57.93387 56.88451 55.98731 56.81518 57.66959 58.55187 58.56030
## [477] 33.01070 33.59578 33.13666 33.53411 35.28017 35.29269 36.19921
## [484] 35.32855 37.03311 37.84063 37.74378 38.61034 39.30939 40.91255
## [491] 42.53906 42.39533 42.28275 42.14230 41.17808 42.04874 42.89062
## [498] 44.56402 45.39942 47.82397 52.75367 49.90349 56.57480 59.59182
## [505] 59.92528 62.46319 62.71984 63.25873 63.12671 62.92616 62.85594
## [512] 62.79823 62.79823 61.94942 62.82007 63.66196 62.78891 63.68984
## [519] 62.76387 62.72561 62.78571 61.89171 61.12244 58.61275 57.00809
## [526] 56.31792 54.76723 47.38465 45.19255 46.32386 44.87722 45.46290
## [533] 43.95569 45.66434 45.76589 46.60992 47.52726 48.22391 48.17463
## [540] 48.93831 51.39269 55.49861 57.02977 56.81625 58.24834 56.19345
## [547] 54.39427 52.74512 53.57708 54.57432 52.13157 50.58745 54.00091
## [554] 53.07440 51.53712 49.96342 48.12100 44.88200 43.44202 41.13936
## [561] 39.70258 38.34923 36.87809 71.95119 72.07469 71.58185 72.86665
## [568] 72.99099 72.83793 74.46578 74.26912 71.51974 69.01378 65.61338
## [575] 61.53898 61.91852 60.51866 61.70458 63.69872 61.96753 60.38664
## [582] 59.52860 60.33871 63.01868 63.06617 64.76424 65.47410 63.55169
## [589] 62.70661 65.17679 66.79114 65.98183 65.14518 64.98378 66.59343
## [596] 67.46879 66.62600 66.60789 63.94843 62.27115 59.87083 57.45730
## [603] 56.06810 55.46068 55.72303 55.93610 56.06403 56.12173 56.97055
## [610] 59.49515 61.11233 60.16257 61.75695 69.16936 57.80545 57.98787
## [617] 57.10483 56.77010 58.38399 58.37466 59.26627 57.53428 55.80771
## [624] 55.86871 54.16824 53.50356 52.82183 53.73244 78.46909 76.19330
## [631] 74.15206 72.95597 69.66160 69.01184 67.49381 65.93752 62.74370
## [638] 62.09484 62.31678 60.79956 60.23777 60.34714 59.53828 57.99042
## [645] 58.95554 61.52249 64.07124 69.15675 71.43213 76.15934 77.43293
## [652] 65.03256 64.21149 61.52441 61.66472 62.52985 63.47393 65.32283
## [659] 67.81068 65.15636 65.09440 64.98617 66.54825 64.98004 63.29627
## [666] 60.79830 58.25684 58.50756 57.85646 57.24016 57.45003 56.62865
## [673] 56.72072 55.94452 55.97889 56.05151 56.06403 56.12173 57.81936
## [680] 57.77567 59.44348 60.22357 61.75412 59.97284 59.85878 58.95704
## [687] 58.03970 59.04068 57.34864 57.44764 58.37147 57.46814 57.59048
## [694] 56.74406 56.72072 55.09571 55.15191 55.23945 56.11330 66.39265
## [701] 64.41799 61.72375 59.06471 55.11230 54.54857 52.29430 50.90031
## [708] 49.53444 47.15677 46.60147 45.95969 46.14942 48.89641 54.84281
## [715] 62.34221 67.94537 69.94394 73.50148 70.19409 67.19711 66.22285
## [722] 65.18965 63.73946 62.28606 47.99994 47.63503 48.05086 48.39402
## [729] 48.53871 48.61826 47.78435 48.66753 49.56712 51.24052 51.22710
## [736] 52.82468 51.84943 50.87723 50.04013 49.12518 50.08098 49.29546
## [743] 49.37261 47.73508 46.03595 46.16717 44.52440 53.19670 53.12350
## [750] 52.99940 51.29198 49.90980 49.11266 48.32564 46.79270 46.92152
## [757] 45.32394 43.75274 42.24404 40.64496 40.01011 38.50460 37.85483
## [764] 38.03443 37.28328 37.43305 39.20330 40.86976 42.55159 43.30185
## [771] 43.95854 43.78133 76.74229 78.36661 81.90583 82.96122 79.70610
## [778] 79.46240 77.46612 75.70929 75.84051 73.34893 71.85728 69.51467
## [785] 67.94996 68.23654 65.87289 65.28776 64.62094 62.99762 63.24186
## [792] 63.34191 65.12229 66.89164 70.21339 71.76878 75.76906 76.31334
## [799] 75.96107 75.76815 76.31592 76.23637 76.22146 75.36012 73.62663
## [806] 72.83642 69.50534 69.69038 67.33151 64.95838 63.60184 62.03020
## [813] 61.46557 59.16895 59.38985 59.56252 63.90186 66.51220 74.86026
## [820] 80.47619 82.39451 84.47272 86.24421 56.83271 59.01761 57.57267
## [827] 56.14147 57.30310 57.26440 57.41976 55.85006 56.80027 55.95944
## [834] 55.14259 56.13105 61.17183 65.34016 66.88428 70.02846 70.35124
## [841] 69.95618 68.92696 68.70547 66.96504 64.47480 62.93024 60.49726
## [848] 59.04795 59.33454 59.51733 58.01786 57.32814 57.37981 56.57095
## [855] 55.87190 55.11755 53.46920 54.44684 53.67623 54.61472 56.40831
## [862] 60.54860 62.15238 62.80019 62.57051 63.93966 62.91923 62.00473
## [869] 61.16763 58.55505 57.00809 56.31792 40.33737 41.81428 42.20372
## [876] 42.48439 43.56827 43.51056 42.66175 44.38122 44.35245 44.33514
## [883] 44.36780 43.40358 43.42542 44.28915 44.27983 44.32262 45.15891
## [890] 44.23055 45.08630 45.91566 47.53135 50.91320 52.42340 52.23732
## [897] 51.19318 50.11035 49.18288 47.53453 46.81454 46.93644 47.03409
## [904] 47.16202 47.21973 47.21973 46.37091 46.39276 45.55885 44.74440
## [911] 43.14123 42.36354 41.63662 41.75612 42.74778 44.49379 46.19053
## [918] 47.80212 47.64587 48.32440 47.31329 48.05363 48.03418 47.12527
## [925] 47.19229 47.14950 47.16202 47.21973 47.21973 45.52210 46.41460
## [932] 45.57377 44.75692 49.98946 57.46747 57.25162 57.94880 60.86331
## [939] 62.78812 65.19686 66.67644 65.47082 63.55453 62.56616 60.81731
## [946] 59.26102 58.61365 57.89925 57.22764 56.54351 55.80168 55.90866
## [953] 55.14498 53.53942 54.50454 53.67623 53.76591 53.88371 56.38497
## [960] 57.22596 58.00819 59.63151 61.08490 62.63879 63.33135 62.29041
## [967] 61.30808 60.36809 60.35966 40.07323 40.66770 39.38570 40.57868
## [974] 41.12277 42.00355 42.09951 42.88823 44.60920 46.19053 48.65094
## [981] 51.01928 51.61738 60.73479 58.57129 57.41648 56.42391 55.85096
## [988] 55.99380 55.21521 55.29476 54.46086 53.64640 54.58968 55.44409
## [995] 57.17519 60.55703 62.91605 69.49865 72.50893 72.88268 70.83028
## [1002] 69.49852 69.30685 67.59147 66.06545 64.49904 62.05115 41.91539
## [1009] 42.62482 43.98453 43.58747 45.82813 47.50631 47.40253 47.41788
## [1016] 51.57922 54.74985 55.43672 55.29263 52.39266 50.51722 49.69913
## [1023] 48.93954 48.32564 47.64151 46.89968 47.00666 47.09180 47.16202
## [1030] 46.37091 45.54394 45.58070 44.75932 45.70020 46.59979 46.57555
## [1037] 48.30346 54.13125 56.43726 57.93993 57.64845 57.17713 56.13016
## [1044] 54.33896 52.69993 52.78596 52.04972 50.51438 50.68839 50.73074
## [1051] 50.81349 50.92890 50.92890 50.92890 50.08008
##
## $call
## forecast.dlm(model = model.dlm2, x = test$BATTERY_VOLTAGE, h = 1055)
##
## attr(,"class")
## [1] "forecast.dlm" "dLagM"#akurasi testing
mape.dlm2 <- MAPE(fore.dlm2$forecasts, test$REF_TEMP)
#akurasi data training
mape_train <- GoF(model.dlm2)["MAPE"]
c("MAPE_testing" = mape.dlm2, "MAPE_training" = mape_train)## $MAPE_testing
## [1] 0.01853903
##
## $MAPE_training.MAPE
## [1] 0.02076887Model Autoregressive / Dynamic Regression
Apabila peubah dependen dipengaruhi oleh peubah independen pada waktu sekarang, serta dipengaruhii juga oleh peubah dependen itu sendiri pada satu waktu yang lalu maka model tersebut disebut autoregressive (Gujarati, 2004)
#MODEL AUTOREGRESSIVE
#library(dLagM)
model.ardl = ardlDlm(x = train$BATTERY_VOLTAGE, y = train$REF_TEMP, p = 1 , q = 1) #p:lag x, q:lag y
#model untuk p=1, q=1: yt=b0+b1yt-1+b2xt+b3xt-1
#model untuk p=2, q=3: yt=b0+b1yt-1+b2yt-2+b3xt+b4xt-1+b5xt-2
summary(model.ardl)##
## Time series regression with "ts" data:
## Start = 2, End = 4216
##
## Call:
## dynlm(formula = as.formula(model.text), data = data, start = 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.819 -0.577 -0.051 0.476 48.212
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 259.785996 9.549597 27.20 <2e-16 ***
## X.t -75.674529 0.433500 -174.57 <2e-16 ***
## X.1 57.414829 0.677442 84.75 <2e-16 ***
## Y.1 0.747451 0.008771 85.22 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.346 on 4211 degrees of freedom
## Multiple R-squared: 0.9894, Adjusted R-squared: 0.9894
## F-statistic: 1.313e+05 on 3 and 4211 DF, p-value: < 2.2e-16AIC(model.ardl)## [1] 14471.32BIC(model.ardl)## [1] 14503.05Ramalan Autoregressive
ramalan
(fore.ardl <- forecast(model = model.dlm2, x=test$BATTERY_VOLTAGE, h=1055))## $forecasts
## [1] 64.46877 63.81900 65.69624 66.59902 68.37291 75.13750 81.59552
## [8] 84.61398 86.73817 86.90000 87.17052 86.01656 52.73406 51.83302
## [15] 51.56432 50.46435 51.94967 50.43164 48.87535 47.37917 47.53543
## [22] 48.55452 51.21957 53.80098 56.22464 56.86792 58.28829 58.01901
## [29] 58.65237 74.67527 72.43229 69.63366 67.73580 65.90405 64.41106
## [36] 64.66782 63.97676 67.47661 70.91482 79.26847 83.24208 86.94691
## [43] 88.10473 89.04446 87.77100 84.90301 84.84300 83.08722 81.52855
## [50] 80.07754 78.47847 75.29717 73.00837 70.72756 71.00332 57.73540
## [57] 57.44675 54.48506 53.09004 49.88510 48.43430 46.26197 44.83771
## [64] 42.69325 42.09277 42.35750 42.52539 42.71102 42.76873 41.91991
## [71] 41.94176 43.65430 48.71603 55.40337 60.20699 62.31254 60.01350
## [78] 58.62688 57.44594 58.18344 57.45562 54.98633 53.41433 50.06231
## [85] 46.87952 44.67825 50.91064 51.08337 51.24736 50.48401 50.95074
## [92] 50.94381 50.94142 52.68423 53.43165 53.37998 51.64240 51.55816
## [99] 52.37909 53.23111 52.46094 55.00180 35.35820 36.61950 38.65844
## [106] 42.95876 54.32019 60.69128 64.40364 67.98043 65.30639 64.75127
## [113] 64.42997 64.16649 62.58427 60.93032 56.75976 53.52858 51.28453
## [120] 48.19246 46.11673 44.81267 43.42666 43.76855 43.99653 44.13698
## [127] 45.10121 45.92818 46.74024 44.99333 43.25425 40.71109 39.07615
## [134] 37.60740 36.13625 35.55911 34.90241 33.38199 33.56852 31.97094
## [141] 32.09737 32.24261 33.11646 34.90766 36.54669 40.70474 48.97110
## [148] 53.63054 49.77707 45.11716 42.08742 39.38492 38.93980 38.48365
## [155] 37.03345 35.58006 34.87498 33.31176 31.81318 32.01463 30.42957
## [162] 29.76489 29.93197 29.12311 29.27288 30.19432 31.03381 59.06567
## [169] 113.49040 58.88164 61.34215 63.72726 62.29636 69.96233 73.83164
## [176] 72.48548 70.55711 68.56696 66.66684 65.12546 62.79298 62.17997
## [183] 59.84056 59.22516 57.77975 57.08480 57.32210 56.57095 57.56954
## [190] 56.77149 68.67436 68.42865 67.32586 67.23013 66.43717 65.60088
## [197] 66.52924 65.67350 66.54176 69.12646 71.54728 76.57509 79.69928
## [204] 80.16057 78.98202 78.59264 76.66658 74.96745 73.40104 72.65078
## [211] 69.44764 67.99275 68.22402 67.51281 66.94170 68.79150 67.92643
## [218] 66.29104 64.68468 62.10885 63.13577 64.14793 66.81059 68.58837
## [225] 70.97617 72.48318 73.04541 71.99195 70.10310 67.48732 66.68868
## [232] 64.29156 65.37379 64.73351 64.83570 64.16240 61.59261 61.73076
## [239] 61.78802 62.73210 67.12745 69.54976 75.33885 78.41616 81.29357
## [246] 83.43223 82.85304 82.52740 77.16612 74.57762 73.88382 73.17671
## [253] 73.59726 71.25136 70.53830 68.96495 53.78244 54.39108 55.59109
## [260] 56.75883 61.15602 64.43648 65.06804 64.87876 65.43176 66.86421
## [267] 65.89908 40.41412 40.15278 40.51913 40.96736 41.86221 41.94176
## [274] 41.95667 41.96919 42.87571 42.85387 42.83895 43.67525 43.59570
## [281] 46.12723 53.68852 54.23830 54.89349 55.41975 56.54876 54.72231
## [288] 52.96831 50.41263 48.71999 48.94887 49.98048 49.30798 49.43032
## [295] 46.88626 46.90661 48.70668 50.39819 48.80016 47.09135 44.47797
## [302] 41.93651 42.18723 49.17546 56.85073 60.95202 73.34065 72.36411
## [309] 74.10491 75.26069 76.00432 75.89324 75.66526 74.67599 73.73361
## [316] 72.92155 72.12202 69.68255 68.98441 68.27240 68.40442 67.75615
## [323] 66.15059 66.26690 66.30924 68.08962 69.01016 71.50493 77.34116
## [330] 60.88809 58.55701 55.24988 54.36713 53.03613 49.09569 47.79536
## [337] 44.61362 41.57127 40.33423 38.90543 38.41103 38.71856 38.02511
## [344] 38.17488 39.09632 38.23818 37.45400 37.47823 39.14559 39.17213
## [351] 42.59527 46.72693 52.38436 72.47838 73.25395 72.47618 74.28838
## [358] 75.35934 76.83129 78.40293 78.96756 77.02010 74.36198 73.48059
## [365] 70.11925 69.52569 68.09519 67.41276 66.85896 66.97846 67.97012
## [372] 67.16968 66.38550 66.40974 66.37947 68.14732 67.31253 68.15336
## [379] 66.42376 68.04727 69.77623 84.09991 85.48674 85.89790 86.36679
## [386] 81.92875 78.47802 75.15956 72.75251 70.61215 69.30569 67.96487
## [393] 67.40024 66.80125 66.12964 66.29433 64.68184 66.49338 65.68841
## [400] 64.85665 65.83259 64.87396 66.64874 66.66516 67.43896 65.75215
## [407] 66.51433 63.96335 63.13248 62.45314 60.77212 60.16754 58.59181
## [414] 57.03552 55.53933 55.69559 55.01705 54.33053 54.48270 55.35895
## [421] 56.25615 59.67236 61.25518 66.17451 69.30109 72.26364 71.07727
## [428] 68.94552 68.72322 67.68593 66.09289 61.17400 62.19623 62.34661
## [435] 61.67341 63.72660 63.64012 64.47163 66.18008 66.85488 68.48832
## [442] 69.19579 69.01619 68.06972 69.66126 68.72597 67.88169 67.95111
## [449] 68.71195 67.91152 66.27852 65.47579 63.78464 63.92599 58.99085
## [456] 56.65821 55.23100 53.69692 52.45659 53.57708 53.72551 53.85104
## [463] 53.10512 53.06926 53.93299 53.92366 56.51290 57.28367 58.00819
## [470] 57.93387 56.88451 55.98731 56.81518 57.66959 58.55187 58.56030
## [477] 33.01070 33.59578 33.13666 33.53411 35.28017 35.29269 36.19921
## [484] 35.32855 37.03311 37.84063 37.74378 38.61034 39.30939 40.91255
## [491] 42.53906 42.39533 42.28275 42.14230 41.17808 42.04874 42.89062
## [498] 44.56402 45.39942 47.82397 52.75367 49.90349 56.57480 59.59182
## [505] 59.92528 62.46319 62.71984 63.25873 63.12671 62.92616 62.85594
## [512] 62.79823 62.79823 61.94942 62.82007 63.66196 62.78891 63.68984
## [519] 62.76387 62.72561 62.78571 61.89171 61.12244 58.61275 57.00809
## [526] 56.31792 54.76723 47.38465 45.19255 46.32386 44.87722 45.46290
## [533] 43.95569 45.66434 45.76589 46.60992 47.52726 48.22391 48.17463
## [540] 48.93831 51.39269 55.49861 57.02977 56.81625 58.24834 56.19345
## [547] 54.39427 52.74512 53.57708 54.57432 52.13157 50.58745 54.00091
## [554] 53.07440 51.53712 49.96342 48.12100 44.88200 43.44202 41.13936
## [561] 39.70258 38.34923 36.87809 71.95119 72.07469 71.58185 72.86665
## [568] 72.99099 72.83793 74.46578 74.26912 71.51974 69.01378 65.61338
## [575] 61.53898 61.91852 60.51866 61.70458 63.69872 61.96753 60.38664
## [582] 59.52860 60.33871 63.01868 63.06617 64.76424 65.47410 63.55169
## [589] 62.70661 65.17679 66.79114 65.98183 65.14518 64.98378 66.59343
## [596] 67.46879 66.62600 66.60789 63.94843 62.27115 59.87083 57.45730
## [603] 56.06810 55.46068 55.72303 55.93610 56.06403 56.12173 56.97055
## [610] 59.49515 61.11233 60.16257 61.75695 69.16936 57.80545 57.98787
## [617] 57.10483 56.77010 58.38399 58.37466 59.26627 57.53428 55.80771
## [624] 55.86871 54.16824 53.50356 52.82183 53.73244 78.46909 76.19330
## [631] 74.15206 72.95597 69.66160 69.01184 67.49381 65.93752 62.74370
## [638] 62.09484 62.31678 60.79956 60.23777 60.34714 59.53828 57.99042
## [645] 58.95554 61.52249 64.07124 69.15675 71.43213 76.15934 77.43293
## [652] 65.03256 64.21149 61.52441 61.66472 62.52985 63.47393 65.32283
## [659] 67.81068 65.15636 65.09440 64.98617 66.54825 64.98004 63.29627
## [666] 60.79830 58.25684 58.50756 57.85646 57.24016 57.45003 56.62865
## [673] 56.72072 55.94452 55.97889 56.05151 56.06403 56.12173 57.81936
## [680] 57.77567 59.44348 60.22357 61.75412 59.97284 59.85878 58.95704
## [687] 58.03970 59.04068 57.34864 57.44764 58.37147 57.46814 57.59048
## [694] 56.74406 56.72072 55.09571 55.15191 55.23945 56.11330 66.39265
## [701] 64.41799 61.72375 59.06471 55.11230 54.54857 52.29430 50.90031
## [708] 49.53444 47.15677 46.60147 45.95969 46.14942 48.89641 54.84281
## [715] 62.34221 67.94537 69.94394 73.50148 70.19409 67.19711 66.22285
## [722] 65.18965 63.73946 62.28606 47.99994 47.63503 48.05086 48.39402
## [729] 48.53871 48.61826 47.78435 48.66753 49.56712 51.24052 51.22710
## [736] 52.82468 51.84943 50.87723 50.04013 49.12518 50.08098 49.29546
## [743] 49.37261 47.73508 46.03595 46.16717 44.52440 53.19670 53.12350
## [750] 52.99940 51.29198 49.90980 49.11266 48.32564 46.79270 46.92152
## [757] 45.32394 43.75274 42.24404 40.64496 40.01011 38.50460 37.85483
## [764] 38.03443 37.28328 37.43305 39.20330 40.86976 42.55159 43.30185
## [771] 43.95854 43.78133 76.74229 78.36661 81.90583 82.96122 79.70610
## [778] 79.46240 77.46612 75.70929 75.84051 73.34893 71.85728 69.51467
## [785] 67.94996 68.23654 65.87289 65.28776 64.62094 62.99762 63.24186
## [792] 63.34191 65.12229 66.89164 70.21339 71.76878 75.76906 76.31334
## [799] 75.96107 75.76815 76.31592 76.23637 76.22146 75.36012 73.62663
## [806] 72.83642 69.50534 69.69038 67.33151 64.95838 63.60184 62.03020
## [813] 61.46557 59.16895 59.38985 59.56252 63.90186 66.51220 74.86026
## [820] 80.47619 82.39451 84.47272 86.24421 56.83271 59.01761 57.57267
## [827] 56.14147 57.30310 57.26440 57.41976 55.85006 56.80027 55.95944
## [834] 55.14259 56.13105 61.17183 65.34016 66.88428 70.02846 70.35124
## [841] 69.95618 68.92696 68.70547 66.96504 64.47480 62.93024 60.49726
## [848] 59.04795 59.33454 59.51733 58.01786 57.32814 57.37981 56.57095
## [855] 55.87190 55.11755 53.46920 54.44684 53.67623 54.61472 56.40831
## [862] 60.54860 62.15238 62.80019 62.57051 63.93966 62.91923 62.00473
## [869] 61.16763 58.55505 57.00809 56.31792 40.33737 41.81428 42.20372
## [876] 42.48439 43.56827 43.51056 42.66175 44.38122 44.35245 44.33514
## [883] 44.36780 43.40358 43.42542 44.28915 44.27983 44.32262 45.15891
## [890] 44.23055 45.08630 45.91566 47.53135 50.91320 52.42340 52.23732
## [897] 51.19318 50.11035 49.18288 47.53453 46.81454 46.93644 47.03409
## [904] 47.16202 47.21973 47.21973 46.37091 46.39276 45.55885 44.74440
## [911] 43.14123 42.36354 41.63662 41.75612 42.74778 44.49379 46.19053
## [918] 47.80212 47.64587 48.32440 47.31329 48.05363 48.03418 47.12527
## [925] 47.19229 47.14950 47.16202 47.21973 47.21973 45.52210 46.41460
## [932] 45.57377 44.75692 49.98946 57.46747 57.25162 57.94880 60.86331
## [939] 62.78812 65.19686 66.67644 65.47082 63.55453 62.56616 60.81731
## [946] 59.26102 58.61365 57.89925 57.22764 56.54351 55.80168 55.90866
## [953] 55.14498 53.53942 54.50454 53.67623 53.76591 53.88371 56.38497
## [960] 57.22596 58.00819 59.63151 61.08490 62.63879 63.33135 62.29041
## [967] 61.30808 60.36809 60.35966 40.07323 40.66770 39.38570 40.57868
## [974] 41.12277 42.00355 42.09951 42.88823 44.60920 46.19053 48.65094
## [981] 51.01928 51.61738 60.73479 58.57129 57.41648 56.42391 55.85096
## [988] 55.99380 55.21521 55.29476 54.46086 53.64640 54.58968 55.44409
## [995] 57.17519 60.55703 62.91605 69.49865 72.50893 72.88268 70.83028
## [1002] 69.49852 69.30685 67.59147 66.06545 64.49904 62.05115 41.91539
## [1009] 42.62482 43.98453 43.58747 45.82813 47.50631 47.40253 47.41788
## [1016] 51.57922 54.74985 55.43672 55.29263 52.39266 50.51722 49.69913
## [1023] 48.93954 48.32564 47.64151 46.89968 47.00666 47.09180 47.16202
## [1030] 46.37091 45.54394 45.58070 44.75932 45.70020 46.59979 46.57555
## [1037] 48.30346 54.13125 56.43726 57.93993 57.64845 57.17713 56.13016
## [1044] 54.33896 52.69993 52.78596 52.04972 50.51438 50.68839 50.73074
## [1051] 50.81349 50.92890 50.92890 50.92890 50.08008
##
## $call
## forecast.dlm(model = model.dlm2, x = test$BATTERY_VOLTAGE, h = 1055)
##
## attr(,"class")
## [1] "forecast.dlm" "dLagM"MAPE testing dan akurasi Data Training
#akurasi testing
mape.ardl <- MAPE(fore.ardl$forecasts, test$REF_TEMP) #data testing
#akurasi data training
mape_train <- GoF(model.ardl)["MAPE"]
c("MAPE_testing" = mape.ardl, "MAPE_training" = mape_train)## $MAPE_testing
## [1] 0.01853903
##
## $MAPE_training.MAPE
## [1] 0.01269811Penentuan lag optimum
ardlBoundOrders(data = data.frame(train), ic="AIC", formula = REF_TEMP ~ BATTERY_VOLTAGE ) ## $p
## BATTERY_VOLTAGE
## 1 15
##
## $q
## [1] 15
##
## $Stat.table
## q = 1 q = 2 q = 3 q = 4 q = 5 q = 6 q = 7 q = 8
## p = 1 14388.70 13674.87 11953.76 11934.56 11928.94 11923.08 11912.05 11902.66
## p = 2 13713.53 13653.23 11955.28 11936.08 11929.41 11924.10 11913.66 11904.51
## p = 3 11957.68 11957.68 11947.68 11932.06 11926.50 11909.16 11901.70 11894.76
## p = 4 11927.24 11928.32 11928.32 11927.57 11922.67 11906.66 11891.16 11885.79
## p = 5 11916.71 11918.63 11919.99 11919.99 11920.26 11903.41 11889.24 11871.27
## p = 6 11904.99 11906.98 11899.34 11901.33 11901.33 11900.90 11886.52 11869.65
## p = 7 11886.54 11888.51 11882.63 11881.00 11882.99 11882.99 11882.29 11864.13
## p = 8 11868.91 11870.72 11866.55 11865.77 11861.82 11863.81 11863.81 11865.77
## p = 9 11869.95 11871.85 11866.83 11865.42 11860.39 11860.06 11860.40 11860.40
## p = 10 11869.03 11870.95 11865.80 11864.26 11859.12 11858.61 11853.15 11855.07
## p = 11 11855.08 11857.03 11852.54 11851.74 11847.88 11848.33 11844.89 11846.73
## p = 12 11859.21 11861.19 11855.61 11854.41 11850.06 11850.16 11846.02 11847.60
## p = 13 11865.64 11867.64 11861.25 11859.20 11853.67 11852.93 11846.99 11847.87
## p = 14 11864.69 11866.67 11859.54 11856.75 11849.86 11848.16 11840.73 11840.84
## p = 15 11863.80 11865.79 11858.87 11856.29 11849.79 11848.63 11842.17 11842.89
## q = 9 q = 10 q = 11 q = 12 q = 13 q = 14 q = 15
## p = 1 11893.50 11892.27 11884.93 11880.92 11875.90 11874.26 11868.14
## p = 2 11895.48 11894.26 11886.93 11882.92 11877.89 11876.26 11870.14
## p = 3 11887.15 11886.43 11879.91 11876.32 11871.38 11869.96 11863.97
## p = 4 11879.85 11879.48 11873.99 11870.88 11866.35 11864.92 11859.19
## p = 5 11867.80 11867.80 11863.51 11861.23 11857.10 11855.84 11850.16
## p = 6 11864.11 11864.28 11860.91 11859.06 11855.31 11854.23 11848.84
## p = 7 11859.56 11852.82 11850.56 11849.54 11846.22 11845.52 11840.60
## p = 8 11861.22 11854.55 11850.18 11849.58 11846.47 11845.90 11841.29
## p = 9 11862.23 11854.73 11850.73 11849.17 11846.71 11846.31 11841.96
## p = 10 11855.07 11852.07 11847.75 11846.56 11846.24 11845.85 11841.94
## p = 11 11847.62 11847.62 11849.61 11848.39 11848.12 11846.22 11842.95
## p = 12 11849.31 11848.42 11848.42 11850.39 11850.12 11848.21 11842.80
## p = 13 11848.95 11847.60 11849.53 11849.53 11835.43 11834.12 11827.98
## p = 14 11840.99 11837.31 11834.77 11831.19 11831.19 11826.27 11822.51
## p = 15 11843.80 11842.02 11842.37 11843.33 11824.47 11824.47 11821.02
##
## $min.Stat
## [1] 11821.02#PEMODELAN DLM dan ARDL dengan library dynlm
#library(dynlm)
#sama dengan model dlm p=1
cons_lm1 <- dynlm(REF_TEMP ~ BATTERY_VOLTAGE+L(BATTERY_VOLTAGE),data = train.ts)
#sama dengan model ardl p=0 q=1
cons_lm2 <- dynlm(REF_TEMP ~ BATTERY_VOLTAGE+L(REF_TEMP),data = train.ts)
#sama dengan ardl p=1 q=1
cons_lm3 <- dynlm(REF_TEMP ~ BATTERY_VOLTAGE+L(BATTERY_VOLTAGE)+L(REF_TEMP),data = train.ts)
#sama dengan dlm p=2
cons_lm4 <- dynlm(REF_TEMP ~ BATTERY_VOLTAGE+L(BATTERY_VOLTAGE)+L(BATTERY_VOLTAGE,2),data = train.ts)summary(cons_lm1)##
## Time series regression with "ts" data:
## Start = 2, End = 4216
##
## Call:
## dynlm(formula = REF_TEMP ~ BATTERY_VOLTAGE + L(BATTERY_VOLTAGE),
## data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -67.140 -1.045 -0.289 0.783 9.733
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1061.4948 2.7098 391.72 <2e-16 ***
## BATTERY_VOLTAGE -86.4626 0.6843 -126.35 <2e-16 ***
## L(BATTERY_VOLTAGE) 11.7100 0.6831 17.14 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.221 on 4212 degrees of freedom
## Multiple R-squared: 0.9712, Adjusted R-squared: 0.9712
## F-statistic: 7.096e+04 on 2 and 4212 DF, p-value: < 2.2e-16summary(cons_lm2)##
## Time series regression with "ts" data:
## Start = 2, End = 4216
##
## Call:
## dynlm(formula = REF_TEMP ~ BATTERY_VOLTAGE + L(REF_TEMP), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.542 -1.114 -0.270 0.838 10.981
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 903.047069 9.532103 94.74 <2e-16 ***
## BATTERY_VOLTAGE -63.636912 0.673633 -94.47 <2e-16 ***
## L(REF_TEMP) 0.158972 0.008813 18.04 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.213 on 4212 degrees of freedom
## Multiple R-squared: 0.9714, Adjusted R-squared: 0.9714
## F-statistic: 7.147e+04 on 2 and 4212 DF, p-value: < 2.2e-16summary(cons_lm3)##
## Time series regression with "ts" data:
## Start = 2, End = 4216
##
## Call:
## dynlm(formula = REF_TEMP ~ BATTERY_VOLTAGE + L(BATTERY_VOLTAGE) +
## L(REF_TEMP), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.819 -0.577 -0.051 0.476 48.212
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 259.785996 9.549597 27.20 <2e-16 ***
## BATTERY_VOLTAGE -75.674529 0.433500 -174.57 <2e-16 ***
## L(BATTERY_VOLTAGE) 57.414829 0.677442 84.75 <2e-16 ***
## L(REF_TEMP) 0.747451 0.008771 85.22 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.346 on 4211 degrees of freedom
## Multiple R-squared: 0.9894, Adjusted R-squared: 0.9894
## F-statistic: 1.313e+05 on 3 and 4211 DF, p-value: < 2.2e-16summary(cons_lm4)##
## Time series regression with "ts" data:
## Start = 3, End = 4216
##
## Call:
## dynlm(formula = REF_TEMP ~ BATTERY_VOLTAGE + L(BATTERY_VOLTAGE) +
## L(BATTERY_VOLTAGE, 2), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -66.858 -0.977 -0.269 0.735 10.976
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1058.7185 2.4999 423.508 <2e-16 ***
## BATTERY_VOLTAGE -84.9375 0.6298 -134.859 <2e-16 ***
## L(BATTERY_VOLTAGE) 0.4987 0.9359 0.533 0.594
## L(BATTERY_VOLTAGE, 2) 9.8943 0.6287 15.737 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.017 on 4210 degrees of freedom
## Multiple R-squared: 0.9762, Adjusted R-squared: 0.9762
## F-statistic: 5.768e+04 on 3 and 4210 DF, p-value: < 2.2e-16SSE
deviance(cons_lm1)## [1] 20781.08deviance(cons_lm2)## [1] 20636.79deviance(cons_lm3)## [1] 7626.971deviance(cons_lm4)## [1] 17123.24Diagnostik Model
Uji Non Autokorelasi
if(require("lmtest")) encomptest(cons_lm1, cons_lm2)## Encompassing test
##
## Model 1: REF_TEMP ~ BATTERY_VOLTAGE + L(BATTERY_VOLTAGE)
## Model 2: REF_TEMP ~ BATTERY_VOLTAGE + L(REF_TEMP)
## Model E: REF_TEMP ~ BATTERY_VOLTAGE + L(BATTERY_VOLTAGE) + L(REF_TEMP)
## Res.Df Df F Pr(>F)
## M1 vs. ME 4211 -1 7262.6 < 2.2e-16 ***
## M2 vs. ME 4211 -1 7183.0 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Diagnostik
Durbin Watson
dwtest(cons_lm1)##
## Durbin-Watson test
##
## data: cons_lm1
## DW = 0.58765, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm2)##
## Durbin-Watson test
##
## data: cons_lm2
## DW = 0.55408, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm3)##
## Durbin-Watson test
##
## data: cons_lm3
## DW = 2.0825, p-value = 0.996
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm4)##
## Durbin-Watson test
##
## data: cons_lm4
## DW = 0.64804, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0Uji Heterogenitas
bptest(cons_lm1)##
## studentized Breusch-Pagan test
##
## data: cons_lm1
## BP = 51.049, df = 2, p-value = 8.222e-12bptest(cons_lm2)##
## studentized Breusch-Pagan test
##
## data: cons_lm2
## BP = 417.76, df = 2, p-value < 2.2e-16bptest(cons_lm3)##
## studentized Breusch-Pagan test
##
## data: cons_lm3
## BP = 1072.9, df = 3, p-value < 2.2e-16Normalitas
shapiro.test(residuals(cons_lm1))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm1)
## W = 0.67637, p-value < 2.2e-16shapiro.test(residuals(cons_lm2))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm2)
## W = 0.76397, p-value < 2.2e-16shapiro.test(residuals(cons_lm3))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm3)
## W = 0.63256, p-value < 2.2e-16shapiro.test(residuals(cons_lm4))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm4)
## W = 0.73161, p-value < 2.2e-16Perbandingan Tiga Metode Penanganan Autokorelasi
Plot Perbandingan Data Aktual dengan Tiga Metode Penanganan Autokorelasi
par(mfrow=c(1,1))
plot(test$BATTERY_VOLTAGE, test$REF_TEMP, type="b", col="black")
points(test$BATTERY_VOLTAGE, fore.koyck$forecasts,col="red")
points(test$BATTERY_VOLTAGE, fore.dlm2$forecasts,col="blue")
points(test$BATTERY_VOLTAGE, fore.ardl$forecasts,col="green")
legend("topleft",c("aktual", "koyck","DLM", "autoregressive"), lty=1, col=c("black","red","blue","green"), cex=0.8)
Secara eksploratif, terlihat bahwa metode Distributel Lag Model
merupakan metode yang sesuai untuk peramalan karena memiliki tren data
yang paling mendekati pola data aktual dibandingkan dengan metode
Koyck.
Perbandingan Keakuratan Ramalan
#TABEL
akurasi <- matrix(c(mape.koyck, mape.dlm, mape.dlm2, mape.ardl))
row.names(akurasi)<- c("Koyck","DLM 1","DLM 2","Autoregressive")
colnames(akurasi) <- c("MAPE")
akurasi## MAPE
## Koyck 7.067076e+153
## DLM 1 1.844561e-02
## DLM 2 1.853903e-02
## Autoregressive 1.853903e-02Diagnostik Model
Uji Non Autokorelasi
bgtest(model.dlm2$model)##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: model.dlm2$model
## LM test = 2616.4, df = 1, p-value < 2.2e-16Uji Heterogenitas
bptest(model.dlm2$model)##
## studentized Breusch-Pagan test
##
## data: model.dlm2$model
## BP = 323.34, df = 5, p-value < 2.2e-16Diperoleh p-value =< 2.2e-16 < 0.05 Tolak H0, artinya cukup bukti untuk menyatakan bahwa terdapat autokorelasi pada model awal dengan taraf nyata 5%. Autokorelasi pada model masih belum berhasil ditangani, sehingga perlu dilakukan penanganan dengan metode lain.
Kesimpulan
Metode yang paling cocok untuk metode peramalan terbaik yaitu metode Distributed lag Model
Hasil uji diagnostik menunjukkan bahwa dengan metode Distributed lag Model autokorelasi pada model regresi deret waktu belum berhasil ditangani, sehingga perlu dilakukan uji lanjut atau penanganan dengan metode lain.