1. Kết nối dữ liệu
library(readxl)
setwd("d:/DATA2020/arimaVSholtwiner")
dulieu <-read_excel("dubao.xlsx")
dulieu <-ts(dulieu,star=c(2010,10), frequency = 12)
head(dulieu)
## Month Quy Time Total Revenues Rev Rev2
## [1,] 1317427200 1317427200 88 0 0 0
## [2,] 1320105600 1320105600 79 0 0 0
## [3,] 1322697600 1322697600 18 0 0 0
## [4,] 1325376000 1325376000 36 0 0 0
## [5,] 1328054400 1328054400 27 0 0 0
## [6,] 1330560000 1330560000 61 0 0 0
2 . Tìm p d q thủ công
# Vẽ đồ thị
#Dữ liệu gốc theo thời gian
plot.ts(dulieu[,5])
#Dữ liệu sai phân
plot.ts(diff(dulieu[,5]))
# tìm d
library(urca)
summary(ur.df(dulieu[,5], type=c("none")))
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -239052 -5749 0 49009 351289
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.48435 0.10350 -4.680 9.03e-06 ***
## z.diff.lag -0.05695 0.10212 -0.558 0.578
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 98960 on 100 degrees of freedom
## Multiple R-squared: 0.2506, Adjusted R-squared: 0.2356
## F-statistic: 16.72 on 2 and 100 DF, p-value: 5.434e-07
##
##
## Value of test-statistic is: -4.6797
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62
summary(ur.pp(dulieu[,5], type=c("Z-tau"),model=c("constant")))
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -168378 -46998 -46511 24229 365030
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.700e+04 1.064e+04 4.416 2.53e-05 ***
## y.l1 2.503e-01 9.740e-02 2.570 0.0116 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 90290 on 101 degrees of freedom
## Multiple R-squared: 0.06136, Adjusted R-squared: 0.05207
## F-statistic: 6.603 on 1 and 101 DF, p-value: 0.01164
##
##
## Value of test-statistic, type: Z-tau is: -7.705
##
## aux. Z statistics
## Z-tau-mu 4.4195
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.4945 -2.889471 -2.581483
summary(ur.ers(dulieu[,5], type=c("DF-GLS"), model=c("constant")))
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -125932 -30398 -9319 36394 339604
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag -0.3254 0.1456 -2.235 0.027786 *
## yd.diff.lag1 -0.4052 0.1532 -2.645 0.009586 **
## yd.diff.lag2 -0.5702 0.1435 -3.975 0.000138 ***
## yd.diff.lag3 -0.3333 0.1240 -2.688 0.008504 **
## yd.diff.lag4 -0.1979 0.1040 -1.903 0.060106 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 89400 on 94 degrees of freedom
## Multiple R-squared: 0.4251, Adjusted R-squared: 0.3945
## F-statistic: 13.9 on 5 and 94 DF, p-value: 3.657e-10
##
##
## Value of test-statistic is: -2.235
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.59 -1.94 -1.62
summary(ur.kpss(dulieu[,5], type=c("mu")))
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: mu with 4 lags.
##
## Value of test-statistic is: 0.4193
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.347 0.463 0.574 0.739
# tim d dùng gói khác
library(fUnitRoots)
## Loading required package: timeDate
## Loading required package: timeSeries
## Loading required package: fBasics
##
## Attaching package: 'fUnitRoots'
## The following objects are masked from 'package:urca':
##
## punitroot, qunitroot, unitrootTable
adfTest(dulieu[,5], lags=12, type=(c("nc")))
##
## Title:
## Augmented Dickey-Fuller Test
##
## Test Results:
## PARAMETER:
## Lag Order: 12
## STATISTIC:
## Dickey-Fuller: -0.6379
## P VALUE:
## 0.4099
##
## Description:
## Mon Aug 03 17:59:52 2020 by user: Admin
adfTest(diff(dulieu[,5]), lags=12, type="nc")
## Warning in adfTest(diff(dulieu[, 5]), lags = 12, type = "nc"): p-value smaller
## than printed p-value
##
## Title:
## Augmented Dickey-Fuller Test
##
## Test Results:
## PARAMETER:
## Lag Order: 12
## STATISTIC:
## Dickey-Fuller: -4.1881
## P VALUE:
## 0.01
##
## Description:
## Mon Aug 03 17:59:52 2020 by user: Admin
# tìm p
pacf(dulieu[,5])
pacf(diff(dulieu[,5]))
# tìm q
acf(dulieu[,5])
acf(diff(dulieu[,5]))
# Tính xu hướng
library(pastecs)
trend.test(dulieu[,5])
## Warning in cor.test.default(x, time(x), alternative = "two.sided", method =
## "spearman"): Cannot compute exact p-value with ties
##
## Spearman's rank correlation rho
##
## data: dulieu[, 5] and time(dulieu[, 5])
## S = 128224, p-value = 0.001084
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## 0.3159939
trend.test(diff(dulieu[,5]))
## Warning in cor.test.default(x, time(x), alternative = "two.sided", method =
## "spearman"): Cannot compute exact p-value with ties
##
## Spearman's rank correlation rho
##
## data: diff(dulieu[, 5]) and time(diff(dulieu[, 5]))
## S = 189060, p-value = 0.7017
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## -0.03819874
# tính thời vụ
library(seastests)
summary(wo(dulieu[,5]))
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## Test used: WO
##
## Test statistic: 0
## P-value: 0.01088334 0.02202298 0.2371589
##
## The WO - test does not identify seasonality
isSeasonal(dulieu[,5])
## [1] FALSE
summary(wo(diff(dulieu[,5])))
## Test used: WO
##
## Test statistic: 0
## P-value: 1 0.0227325 0.2056103
##
## The WO - test does not identify seasonality
isSeasonal(diff(dulieu[,5]))
## [1] FALSE
3. Hồi quy arima
# thủ công
library(forecast)
hoiquy1 <- Arima(dulieu[,5], order=c(4,1,1), seasonal=c(1,1,1))
names(hoiquy1)
## [1] "coef" "sigma2" "var.coef" "mask" "loglik" "aic"
## [7] "arma" "residuals" "call" "series" "code" "n.cond"
## [13] "nobs" "model" "aicc" "bic" "x" "fitted"
uocluong <- fitted(hoiquy1)
hoiquy1
## Series: dulieu[, 5]
## ARIMA(4,1,1)(1,1,1)[12]
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1 sar1 sma1
## 0.0063 -0.3109 -0.0578 0.0540 -0.7425 0.1201 -0.9993
## s.e. 0.3125 0.2314 0.2337 0.2043 0.2906 0.1216 0.1539
##
## sigma^2 estimated as 6.899e+09: log likelihood=-1168.57
## AIC=2353.14 AICc=2354.89 BIC=2373.22
library(nlme)
##
## Attaching package: 'nlme'
## The following object is masked from 'package:forecast':
##
## getResponse
AIC(hoiquy1)
## [1] 2353.138
BIC(hoiquy1)
## [1] 2373.225
#library(Metrics)
library(MLmetrics)
##
## Attaching package: 'MLmetrics'
## The following object is masked from 'package:base':
##
## Recall
MSE(uocluong,dulieu[,5])
## [1] 5572246515
RMSE(uocluong,dulieu[,5])
## [1] 74647.48
MAE(uocluong,dulieu[,5])
## [1] 52623.9
MAPE(uocluong,dulieu[,5])
## [1] NaN
R2_Score(uocluong,dulieu[,5])
## [1] 0.3421931
library(staTools)
##
## Attaching package: 'staTools'
## The following objects are masked from 'package:MLmetrics':
##
## MAE, MAPE, MSE, RMSE
MPE(uocluong,dulieu[,5])
## [1] NaN
hoiquy2 <- auto.arima(dulieu[,5], ic="bic", trace=TRUE, test="kpss", seasonal=T)
##
## ARIMA(2,1,2)(1,0,1)[12] with drift : 2663.954
## ARIMA(0,1,0) with drift : 2697.711
## ARIMA(1,1,0)(1,0,0)[12] with drift : 2689.713
## ARIMA(0,1,1)(0,0,1)[12] with drift : 2654.613
## ARIMA(0,1,0) : 2693.109
## ARIMA(0,1,1) with drift : 2656.174
## ARIMA(0,1,1)(1,0,1)[12] with drift : 2658.302
## ARIMA(0,1,1)(0,0,2)[12] with drift : 2658.822
## ARIMA(0,1,1)(1,0,0)[12] with drift : 2653.998
## ARIMA(0,1,1)(2,0,0)[12] with drift : 2658.498
## ARIMA(0,1,1)(2,0,1)[12] with drift : 2663.227
## ARIMA(0,1,0)(1,0,0)[12] with drift : 2694.667
## ARIMA(1,1,1)(1,0,0)[12] with drift : 2657.035
## ARIMA(0,1,2)(1,0,0)[12] with drift : 2655.513
## ARIMA(1,1,2)(1,0,0)[12] with drift : 2658.094
## ARIMA(0,1,1)(1,0,0)[12] : 2649.602
## ARIMA(0,1,1) : 2651.779
## ARIMA(0,1,1)(2,0,0)[12] : 2654.079
## ARIMA(0,1,1)(1,0,1)[12] : 2653.861
## ARIMA(0,1,1)(0,0,1)[12] : 2650.254
## ARIMA(0,1,1)(2,0,1)[12] : 2658.817
## ARIMA(0,1,0)(1,0,0)[12] : 2690.065
## ARIMA(1,1,1)(1,0,0)[12] : 2652.692
## ARIMA(0,1,2)(1,0,0)[12] : 2651.206
## ARIMA(1,1,0)(1,0,0)[12] : 2685.118
## ARIMA(1,1,2)(1,0,0)[12] : 2653.748
##
## Best model: ARIMA(0,1,1)(1,0,0)[12]
summary(hoiquy2)
## Series: dulieu[, 5]
## ARIMA(0,1,1)(1,0,0)[12]
##
## Coefficients:
## ma1 sar1
## -0.8796 0.2483
## s.e. 0.0539 0.0928
##
## sigma^2 estimated as 7.591e+09: log likelihood=-1317.85
## AIC=2641.7 AICc=2641.94 BIC=2649.6
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 3842.122 85861.33 57673.92 NaN Inf 0.7763007 0.09615834
4. Hồi quy Holt-Winner
khongmua <-HoltWinters(dulieu[,5], gamma=F)
khongmua
## Holt-Winters exponential smoothing with trend and without seasonal component.
##
## Call:
## HoltWinters(x = dulieu[, 5], gamma = F)
##
## Smoothing parameters:
## alpha: 0.1165024
## beta : 0
## gamma: FALSE
##
## Coefficients:
## [,1]
## a 58202.72
## b 0.00
comua <-HoltWinters(dulieu[,5], seasonal = c("additive"))
comua
## Holt-Winters exponential smoothing with trend and additive seasonal component.
##
## Call:
## HoltWinters(x = dulieu[, 5], seasonal = c("additive"))
##
## Smoothing parameters:
## alpha: 0.1458954
## beta : 0.005783991
## gamma: 0.0815975
##
## Coefficients:
## [,1]
## a 73053.421
## b 1502.500
## s1 -26873.071
## s2 -25176.292
## s3 -35790.668
## s4 -15586.363
## s5 -41869.057
## s6 95379.805
## s7 75267.347
## s8 -50822.358
## s9 -1924.008
## s10 -14913.648
## s11 -5898.304
## s12 -9879.733
names(comua)
## [1] "fitted" "x" "alpha" "beta" "gamma"
## [6] "coefficients" "seasonal" "SSE" "call"
uocluong2 <- fitted(comua)
MSE(uocluong2,dulieu[,5])
## [1] 10754249398
RMSE(uocluong2,dulieu[,5])
## [1] 103702.7
MAE(uocluong2,dulieu[,5])
## [1] 71355.02
MAPE(uocluong2,dulieu[,5])
## [1] 991.8152
R2_Score(uocluong2,dulieu[,5])
## [1] -3.492237
MPE(uocluong2,dulieu[,5])
## [1] -766.4426
comua2 <- hw(dulieu[,5], seasonal = c("additive"))
summary(comua2)
##
## Forecast method: Holt-Winters' additive method
##
## Model Information:
## Holt-Winters' additive method
##
## Call:
## hw(y = dulieu[, 5], seasonal = c("additive"))
##
## Smoothing parameters:
## alpha = 0.1572
## beta = 0.003
## gamma = 1e-04
##
## Initial states:
## l = 1340.4399
## b = 3032.9358
## s = 19661.19 -29367 -12679.5 -22525.9 -25935.62 9676.476
## 13945.4 -40292.69 -62991.86 94276.35 87270.06 -31036.89
##
## sigma: 85646
##
## AIC AICc BIC
## 2862.102 2869.219 2907.057
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -8405.709 78782.87 59239.63 NaN Inf 0.7973755 0.06419114
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jun 2019 41690.998 -68068.77 151450.8 -126172.09 209554.1
## Jul 2019 51970.466 -59187.90 163128.8 -118031.59 221972.5
## Aug 2019 35715.461 -76875.58 148306.5 -136477.67 207908.6
## Sep 2019 85176.393 -28881.04 199233.8 -89259.40 259612.2
## Oct 2019 34913.733 -80643.45 150470.9 -141815.73 211643.2
## Nov 2019 153641.578 36551.64 270731.5 -25432.02 332715.2
## Dec 2019 161079.978 42424.69 279735.3 -20387.63 342547.6
## Jan 2020 4265.548 -115987.32 124518.4 -179645.34 188176.4
## Feb 2020 27390.880 -94491.40 149273.2 -159011.98 213793.7
## Mar 2020 82055.065 -41488.05 205598.2 -106887.83 270998.0
## Apr 2020 78215.761 -47019.23 203450.8 -113314.63 269746.2
## May 2020 43061.455 -83896.05 170019.0 -151103.29 237226.2
## Jun 2020 46884.185 -81827.86 175596.2 -149963.91 243732.3
## Jul 2020 57163.653 -73330.94 187658.2 -142410.60 256737.9
## Aug 2020 40908.649 -91397.92 173215.2 -161436.78 243254.1
## Sep 2020 90369.580 -43777.99 224517.2 -114791.43 295530.6
## Oct 2020 40106.921 -95910.29 176124.1 -167913.46 248127.3
## Nov 2020 158834.765 20919.67 296749.9 -52088.18 369757.7
## Dec 2020 166273.165 26432.32 306114.0 -47594.95 380141.3
## Jan 2021 9458.735 -132335.32 151252.8 -207396.56 226314.0
## Feb 2021 32584.068 -111190.30 176358.4 -187299.85 252468.0
## Mar 2021 87248.252 -58533.15 233029.7 -135705.16 310201.7
## Apr 2021 83408.949 -64405.84 231223.7 -142654.26 309472.2
## May 2021 48254.643 -101619.53 198128.8 -180958.12 277467.4
Dự báo
dubaoArima1 <- forecast(hoiquy1, h=19)
dubaoArima1
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jun 2019 77917.73 -34747.122 190582.6 -94388.29 250223.8
## Jul 2019 26232.26 -90278.371 142742.9 -151955.37 204419.9
## Aug 2019 31561.07 -85037.465 148159.6 -146761.00 209883.1
## Sep 2019 110121.18 -7223.791 227466.2 -69342.47 289584.8
## Oct 2019 56777.46 -65419.124 178974.0 -130106.09 243661.0
## Nov 2019 133119.44 7995.373 258243.5 -58241.31 324480.2
## Dec 2019 153138.95 26866.732 279411.2 -39977.74 346255.6
## Jan 2020 30107.54 -97626.608 157841.7 -165244.98 225460.1
## Feb 2020 43807.28 -86167.785 173782.3 -154972.43 242587.0
## Mar 2020 87181.87 -44889.482 219253.2 -114803.83 289167.6
## Apr 2020 73940.18 -59830.252 207710.6 -130644.04 278524.4
## May 2020 96988.51 -38480.913 232457.9 -110194.10 304171.1
## Jun 2020 70512.19 -73257.859 214282.2 -149365.13 290389.5
## Jul 2020 64015.03 -82660.949 210691.0 -160306.52 288336.6
## Aug 2020 52838.66 -95166.801 200844.1 -173516.16 279193.5
## Sep 2020 112841.20 -37260.745 262943.2 -116719.92 342402.3
## Oct 2020 63288.65 -89647.793 216225.1 -170607.46 297184.8
## Nov 2020 161535.99 6079.178 316992.8 -76214.69 399286.7
## Dec 2020 169870.65 12316.453 327424.8 -71087.70 410829.0
plot(dubaoArima1)
plot(hoiquy1$x,col="red")
lines(fitted(hoiquy1),col="blue")
dubaoArima2 <- forecast(hoiquy2, h=19)
dubaoArima2
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jun 2019 59461.46 -52196.51 171119.4 -111304.66 230227.6
## Jul 2019 82470.70 -29993.20 194934.6 -89527.99 254469.4
## Aug 2019 68890.75 -44373.34 182154.8 -104331.73 242113.2
## Sep 2019 48136.09 -65922.58 162194.8 -126301.60 222573.8
## Oct 2019 48136.09 -66711.67 162983.9 -127508.40 223780.6
## Nov 2019 56201.87 -59429.59 171833.3 -120641.19 233044.9
## Dec 2019 80895.08 -35514.81 197305.0 -97138.48 258928.6
## Jan 2020 50219.12 -66964.02 167402.3 -128997.03 229435.3
## Feb 2020 48136.09 -69815.23 166087.4 -132254.89 228527.1
## Mar 2020 60354.36 -58360.18 179068.9 -121203.86 241912.6
## Apr 2020 48136.09 -71336.79 167609.0 -134581.91 230854.1
## May 2020 99812.57 -20413.87 220039.0 -84057.90 283683.0
## Jun 2020 62901.57 -64177.50 189980.6 -131449.10 257252.2
## Jul 2020 68615.22 -59566.53 196797.0 -127421.85 264652.3
## Aug 2020 65243.05 -64031.98 194518.1 -132466.05 262952.1
## Sep 2020 60089.25 -70269.89 190448.4 -139277.84 259456.3
## Oct 2020 60089.25 -71345.05 191523.6 -140922.17 261100.7
## Nov 2020 62092.15 -70408.60 194592.9 -140550.26 264734.5
## Dec 2020 68223.97 -65334.71 201782.6 -136036.40 272484.3
plot(dubaoArima2)
dubaoKhongmua <- forecast(khongmua, h=19)
dubaoKhongmua
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jun 2019 58202.72 -57425.06 173830.5 -118634.7 235040.1
## Jul 2019 58202.72 -58207.11 174612.5 -119830.7 236236.2
## Aug 2019 58202.72 -58983.94 175389.4 -121018.8 237424.2
## Sep 2019 58202.72 -59755.66 176161.1 -122199.0 238604.5
## Oct 2019 58202.72 -60522.36 176927.8 -123371.6 239777.0
## Nov 2019 58202.72 -61284.14 177689.6 -124536.7 240942.1
## Dec 2019 58202.72 -62041.09 178446.5 -125694.3 242099.8
## Jan 2020 58202.72 -62793.31 179198.7 -126844.7 243250.2
## Feb 2020 58202.72 -63540.89 179946.3 -127988.1 244393.5
## Mar 2020 58202.72 -64283.90 180689.3 -129124.4 245529.8
## Apr 2020 58202.72 -65022.43 181427.9 -130253.9 246659.3
## May 2020 58202.72 -65756.56 182162.0 -131376.6 247782.1
## Jun 2020 58202.72 -66486.36 182891.8 -132492.8 248898.2
## Jul 2020 58202.72 -67211.92 183617.4 -133602.4 250007.9
## Aug 2020 58202.72 -67933.31 184338.7 -134705.7 251111.1
## Sep 2020 58202.72 -68650.60 185056.0 -135802.7 252208.1
## Oct 2020 58202.72 -69363.85 185769.3 -136893.5 253298.9
## Nov 2020 58202.72 -70073.13 186478.6 -137978.3 254383.7
## Dec 2020 58202.72 -70778.52 187184.0 -139057.1 255462.5
plot(dubaoKhongmua)
dubaocomua1 <- forecast(comua, h=19)
dubaocomua1
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jun 2019 47682.85 -66203.29 161569.0 -126490.964 221856.7
## Jul 2019 50882.13 -64223.60 165987.9 -125156.890 226921.1
## Aug 2019 41770.25 -74556.13 158096.6 -136135.591 219676.1
## Sep 2019 63477.06 -54071.08 181025.2 -116297.302 243251.4
## Oct 2019 38696.86 -80074.18 157467.9 -142947.768 220341.5
## Nov 2019 177448.23 57453.09 297443.4 -6068.499 360964.9
## Dec 2019 158838.27 37617.80 280058.7 -26552.433 344229.0
## Jan 2020 34251.06 -88196.00 156698.1 -153015.555 221517.7
## Feb 2020 84651.91 -39023.05 208326.9 -104492.620 273796.4
## Mar 2020 73164.77 -51739.43 198069.0 -117859.726 264189.3
## Apr 2020 83682.61 -42452.21 209817.4 -109223.951 276589.2
## May 2020 81203.68 -46163.17 208570.5 -113587.105 275994.5
## Jun 2020 65712.85 -64222.14 195647.8 -133005.565 264431.3
## Jul 2020 68912.13 -62245.23 200069.5 -131675.742 269500.0
## Aug 2020 59800.25 -72581.19 192181.7 -142659.698 262260.2
## Sep 2020 81507.05 -52100.22 215114.3 -122827.633 285841.7
## Oct 2020 56726.86 -78108.00 191561.7 -149485.259 262939.0
## Nov 2020 195478.22 59414.00 331542.4 -12614.052 403570.5
## Dec 2020 176868.26 39572.87 314163.7 -33106.917 386843.4
plot(dubaocomua1)
dubaocomua2 <- forecast(comua2, h=19)
dubaocomua2
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jun 2019 41690.998 -68068.77 151450.8 -126172.09 209554.1
## Jul 2019 51970.466 -59187.90 163128.8 -118031.59 221972.5
## Aug 2019 35715.461 -76875.58 148306.5 -136477.67 207908.6
## Sep 2019 85176.393 -28881.04 199233.8 -89259.40 259612.2
## Oct 2019 34913.733 -80643.45 150470.9 -141815.73 211643.2
## Nov 2019 153641.578 36551.64 270731.5 -25432.02 332715.2
## Dec 2019 161079.978 42424.69 279735.3 -20387.63 342547.6
## Jan 2020 4265.548 -115987.32 124518.4 -179645.34 188176.4
## Feb 2020 27390.880 -94491.40 149273.2 -159011.98 213793.7
## Mar 2020 82055.065 -41488.05 205598.2 -106887.83 270998.0
## Apr 2020 78215.761 -47019.23 203450.8 -113314.63 269746.2
## May 2020 43061.455 -83896.05 170019.0 -151103.29 237226.2
## Jun 2020 46884.185 -81827.86 175596.2 -149963.91 243732.3
## Jul 2020 57163.653 -73330.94 187658.2 -142410.60 256737.9
## Aug 2020 40908.649 -91397.92 173215.2 -161436.78 243254.1
## Sep 2020 90369.580 -43777.99 224517.2 -114791.43 295530.6
## Oct 2020 40106.921 -95910.29 176124.1 -167913.46 248127.3
## Nov 2020 158834.765 20919.67 296749.9 -52088.18 369757.7
## Dec 2020 166273.165 26432.32 306114.0 -47594.95 380141.3
plot(dubaocomua2)
