df<- WDI(country = "IN", indicator = c("nufus"= "SP.POP.TOTL", "gsyh"= "NY.GDP.MKTP.CD"), end = 2022)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.0 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors## # A tibble: 6 × 8
## variable type na na_pct unique min mean max
## <chr> <chr> <int> <dbl> <int> <dbl> <dbl> <dbl>
## 1 country chr 0 0 1 NA NA NA
## 2 iso2c chr 0 0 1 NA NA NA
## 3 iso3c chr 0 0 1 NA NA NA
## 4 year int 0 0 63 1960 1991 2.02e 3
## 5 nufus dbl 0 0 63 445954579 907933406. 1.42e 9
## 6 gsyh dbl 0 0 63 37029883876. 741932340366. 3.42e12## Warning in geom_smooth(binwidth = 39, colour = "red"): Ignoring unknown
## parameters: `binwidth`## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
ggplot(df, aes(kbgsyh)) + geom_histogram(binwidth = 39, colour= "red ", fill= "gray ") + theme_classic()
ARDL
ARDL Sınır Testi veya gecikmesi dağıtılmış otoregresif sınır testi, Mohammad Hashem Pesaran ve Yongcheol Shin tarafından 2001 yılında geliştirilen test, seviyelerinde durağan olmayan en az iki serinin durağan bir bileşimi olduğunu ifade eden eşbütünleşme kavramını test etmek amacıyla kullanılan modeldir. Özetle uzun ve kısa dönem nedensellik ilişkilerini yakalamaya yarayan modeldir. Bu eşbütünleşme testinde, diğer eşbütünleşme testlerinde olduğu gibi aralarındaki eşbütünleşme ilişkisi incelenen serilerin aynı dereceden durağan olmaları şartı bulunmamaktadır.
## To cite the ARDL package in publications:
##
## Use this reference to refer to the validity of the ARDL package.
##
## Natsiopoulos, Kleanthis, and Tzeremes, Nickolaos G. (2022). ARDL
## bounds test for cointegration: Replicating the Pesaran et al. (2001)
## results for the UK earnings equation using R. Journal of Applied
## Econometrics, 37(5), 1079-1090. https://doi.org/10.1002/jae.2919
##
## Use this reference to cite this specific version of the ARDL package.
##
## Kleanthis Natsiopoulos and Nickolaos Tzeremes (2023). ARDL: ARDL, ECM
## and Bounds-Test for Cointegration. R package version 0.2.4.
## https://CRAN.R-project.org/package=ARDL## Zorunlu paket yükleniyor: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## Zorunlu paket yükleniyor: strucchange## Zorunlu paket yükleniyor: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Zorunlu paket yükleniyor: sandwich##
## Attaching package: 'strucchange'## The following object is masked from 'package:stringr':
##
## boundary## Zorunlu paket yükleniyor: urca## Zorunlu paket yükleniyor: lmtest## Zorunlu paket yükleniyor: nardl## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Zorunlu paket yükleniyor: dynlm##
## Orders being calculated with max.p = 3 and max.q = 3 ...
##
## Autoregressive order: 4 and p-orders: 3
## ------------------------------------------------------
##
## Breusch-Godfrey Test for the autocorrelation in residuals:
##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: modelFull$model
## LM test = 0.0093592, df1 = 1, df2 = 49, p-value = 0.9233
##
## ------------------------------------------------------
##
## Ljung-Box Test for the autocorrelation in residuals:
##
## Box-Ljung test
##
## data: res
## X-squared = 0.0010806, df = 1, p-value = 0.9738
##
## ------------------------------------------------------
##
## Breusch-Pagan Test for the homoskedasticity of residuals:
##
## studentized Breusch-Pagan test
##
## data: modelFull$model
## BP = 32.084, df = 8, p-value = 8.995e-05
##
## The p-value of Breusch-Pagan test for the homoskedasticity of residuals: 8.995298e-05 < 0.05!
## ------------------------------------------------------
##
## Shapiro-Wilk test of normality of residuals:
##
## Shapiro-Wilk normality test
##
## data: modelFull$model$residual
## W = 0.89261, p-value = 8.154e-05
##
## The p-value of Shapiro-Wilk test normality of residuals: 8.153834e-05 < 0.05!
## ------------------------------------------------------
##
## PESARAN, SHIN AND SMITH (2001) COINTEGRATION TEST
##
## Observations: 62
## Number of Regressors (k): 1
## Case: 3
##
## ------------------------------------------------------
## - F-test -
## ------------------------------------------------------
## <------- I(0) ------------ I(1) ----->
## 10% critical value 4.175 4.93
## 5% critical value 5.13 5.98
## 1% critical value 7.32 8.435
##
##
## F-statistic = 7.32420366750023
##
## ------------------------------------------------------
##
##
## ------------------------------------------------------
##
## Ramsey's RESET Test for model specification:
##
## RESET test
##
## data: modelECM$model
## RESET = 6.5283, df1 = 2, df2 = 49, p-value = 0.003065
##
## the p-value of RESET test: 0.003065452 < 0.05!
## ------------------------------------------------------## ------------------------------------------------------
## Error Correction Model Output:
##
## Time series regression with "ts" data:
## Start = 4, End = 62
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.781e+11 -3.593e+10 -3.694e+09 2.990e+10 2.146e+11
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.490e+10 6.023e+10 0.911 0.3663
## ec.1 -1.677e-01 3.562e-02 -4.709 1.95e-05 ***
## dnufus.t -3.245e+04 4.455e+04 -0.728 0.4697
## dnufus.1 6.052e+04 8.660e+04 0.699 0.4878
## dnufus.2 -7.750e+04 5.444e+04 -1.424 0.1606
## dgsyh.1 -2.103e-01 1.253e-01 -1.678 0.0995 .
## dgsyh.2 -2.414e-01 1.441e-01 -1.675 0.1000
## dgsyh.3 -3.510e-01 1.638e-01 -2.143 0.0369 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.644e+10 on 51 degrees of freedom
## Multiple R-squared: 0.5411, Adjusted R-squared: 0.4782
## F-statistic: 8.592 on 7 and 51 DF, p-value: 6.418e-07
##
## ------------------------------------------------------
## Long-run coefficients:
## gsyh.1 nufus.1
## -0.1677445 1030.1792595
## ## $model
## $model$modelNull
## $model
##
## Time series regression with "ts" data:
## Start = 4, End = 62
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Coefficients:
## (Intercept) dnufus.t dnufus.1 dgsyh.1 dgsyh.2 dgsyh.3
## 3.477e+10 -1.275e+05 1.286e+05 5.443e-04 5.094e-02 -1.486e-02
##
##
## $order
## [1] 1 3
##
## $removed
## $removed$p
## $removed$p$ec
## [1] 0
##
##
##
## $formula
## dgsyh ~ +1 + dnufus
## <environment: 0x000001fe760deeb0>
##
## $data
## Time Series:
## Start = 1
## End = 62
## Frequency = 1
## gsyh nufus dgsyh dnufus
## 1 3.923244e+10 456351876 2202551908 10397297
## 2 4.216148e+10 467024193 2929046074 10672317
## 3 4.842192e+10 477933619 6260441601 10909426
## 4 5.648029e+10 489059309 8058366482 11125690
## 5 5.955485e+10 500114346 3074564635 11055037
## 6 4.586546e+10 510992617 -13689392542 10878271
## 7 5.013494e+10 521987069 4269480170 10994452
## 8 5.308546e+10 533431909 2950513667 11444840
## 9 5.844800e+10 545314670 5362539147 11882761
## 10 6.242248e+10 557501301 3974488037 12186631
## 11 6.735140e+10 569999178 4928921297 12497877
## 12 7.146319e+10 582837973 4111789479 12838795
## 13 8.551527e+10 596107483 14052075754 13269510
## 14 9.952590e+10 609721951 14010629531 13614468
## 15 9.847280e+10 623524219 -1053102659 13802268
## 16 1.027172e+11 637451448 4244368010 13927229
## 17 1.214866e+11 651685628 18769476975 14234180
## 18 1.373003e+11 666267760 15813653872 14582132
## 19 1.529917e+11 681248383 15691358480 14980623
## 20 1.863253e+11 696828385 33333691293 15580002
## 21 1.934914e+11 712869298 7166023359 16040913
## 22 2.007156e+11 729169466 7224256385 16300168
## 23 2.182621e+11 745826546 17546521582 16657080
## 24 2.121576e+11 762895156 -6104501236 17068610
## 25 2.325116e+11 780242084 20353909663 17346928
## 26 2.489860e+11 797878993 16474439200 17636909
## 27 2.790336e+11 815716125 30047590052 17837132
## 28 2.965897e+11 833729681 17556086804 18013556
## 29 2.960421e+11 852012673 -547617951 18282992
## 30 3.209790e+11 870452165 24936973475 18439492
## 31 2.701053e+11 888941756 -50873684541 18489591
## 32 2.882081e+11 907574049 18102728399 18632293
## 33 2.792956e+11 926351297 -8912421295 18777248
## 34 3.272756e+11 945261958 47979934547 18910661
## 35 3.602819e+11 964279129 33006326113 19017171
## 36 3.928969e+11 983281218 32614956561 19002089
## 37 4.158676e+11 1002335230 22970697388 19054012
## 38 4.213513e+11 1021434576 5483753632 19099346
## 39 4.588204e+11 1040500054 37469100113 19065478
## 40 4.683949e+11 1059633675 9574519918 19133621
## 41 4.854410e+11 1078970907 17046077283 19337232
## 42 5.149379e+11 1098313039 29496934336 19342132
## 43 6.076993e+11 1117415123 92761336562 19102084
## 44 7.091485e+11 1136264583 101449229380 18849460
## 45 8.203816e+11 1154638713 111233080695 18374130
## 46 9.402599e+11 1172373788 119878293284 17735075
## 47 1.216736e+12 1189691809 276476550048 17318021
## 48 1.198895e+12 1206734806 -17841299828 17042997
## 49 1.341888e+12 1223640160 142992877970 16905354
## 50 1.675616e+12 1240613620 333727502505 16973460
## 51 1.823052e+12 1257621191 147436310411 17007571
## 52 1.827638e+12 1274487215 4585760886 16866024
## 53 1.856722e+12 1291132063 29083916894 16644848
## 54 2.039126e+12 1307246509 182404971547 16114446
## 55 2.103588e+12 1322866505 64461880838 15619996
## 56 2.294797e+12 1338636340 191208525616 15769835
## 57 2.651474e+12 1354195680 356677377053 15559340
## 58 2.702930e+12 1369003306 51455378972 14807626
## 59 2.835606e+12 1383112050 132676614909 14108744
## 60 2.671595e+12 1396387127 -164010850629 13275077
## 61 3.150307e+12 1407563842 478711433155 11176715
## 62 3.416646e+12 1417173173 266338986911 9609331
##
## $call
## ardlDlm.default(formula = formula2, data = data.frame(data),
## p = (max.p - 1), q = (p[[vars[1]]] - 1), remove = removeP)
##
## attr(,"class")
## [1] "ardlDlm" "dLagM"
##
## $model$modelFull
## $model
##
## Time series regression with "ts" data:
## Start = 4, End = 62
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Coefficients:
## (Intercept) gsyh.1 nufus.1 dnufus.t dnufus.1 dnufus.2
## 5.490e+10 -1.677e-01 1.030e+03 -3.245e+04 6.052e+04 -7.750e+04
## dgsyh.1 dgsyh.2 dgsyh.3
## -2.103e-01 -2.414e-01 -3.510e-01
##
##
## $order
## [1] 2 3
##
## $removed
## $removed$p
## $removed$p$gsyh
## [1] 0 2
##
## $removed$p$nufus
## [1] 0 2
##
##
## $removed$q
## NULL
##
##
## $formula
## dgsyh ~ gsyh + nufus + dnufus
## <environment: 0x000001fe760deeb0>
##
## $data
## Time Series:
## Start = 1
## End = 62
## Frequency = 1
## gsyh nufus dgsyh dnufus
## 1 3.923244e+10 456351876 2202551908 10397297
## 2 4.216148e+10 467024193 2929046074 10672317
## 3 4.842192e+10 477933619 6260441601 10909426
## 4 5.648029e+10 489059309 8058366482 11125690
## 5 5.955485e+10 500114346 3074564635 11055037
## 6 4.586546e+10 510992617 -13689392542 10878271
## 7 5.013494e+10 521987069 4269480170 10994452
## 8 5.308546e+10 533431909 2950513667 11444840
## 9 5.844800e+10 545314670 5362539147 11882761
## 10 6.242248e+10 557501301 3974488037 12186631
## 11 6.735140e+10 569999178 4928921297 12497877
## 12 7.146319e+10 582837973 4111789479 12838795
## 13 8.551527e+10 596107483 14052075754 13269510
## 14 9.952590e+10 609721951 14010629531 13614468
## 15 9.847280e+10 623524219 -1053102659 13802268
## 16 1.027172e+11 637451448 4244368010 13927229
## 17 1.214866e+11 651685628 18769476975 14234180
## 18 1.373003e+11 666267760 15813653872 14582132
## 19 1.529917e+11 681248383 15691358480 14980623
## 20 1.863253e+11 696828385 33333691293 15580002
## 21 1.934914e+11 712869298 7166023359 16040913
## 22 2.007156e+11 729169466 7224256385 16300168
## 23 2.182621e+11 745826546 17546521582 16657080
## 24 2.121576e+11 762895156 -6104501236 17068610
## 25 2.325116e+11 780242084 20353909663 17346928
## 26 2.489860e+11 797878993 16474439200 17636909
## 27 2.790336e+11 815716125 30047590052 17837132
## 28 2.965897e+11 833729681 17556086804 18013556
## 29 2.960421e+11 852012673 -547617951 18282992
## 30 3.209790e+11 870452165 24936973475 18439492
## 31 2.701053e+11 888941756 -50873684541 18489591
## 32 2.882081e+11 907574049 18102728399 18632293
## 33 2.792956e+11 926351297 -8912421295 18777248
## 34 3.272756e+11 945261958 47979934547 18910661
## 35 3.602819e+11 964279129 33006326113 19017171
## 36 3.928969e+11 983281218 32614956561 19002089
## 37 4.158676e+11 1002335230 22970697388 19054012
## 38 4.213513e+11 1021434576 5483753632 19099346
## 39 4.588204e+11 1040500054 37469100113 19065478
## 40 4.683949e+11 1059633675 9574519918 19133621
## 41 4.854410e+11 1078970907 17046077283 19337232
## 42 5.149379e+11 1098313039 29496934336 19342132
## 43 6.076993e+11 1117415123 92761336562 19102084
## 44 7.091485e+11 1136264583 101449229380 18849460
## 45 8.203816e+11 1154638713 111233080695 18374130
## 46 9.402599e+11 1172373788 119878293284 17735075
## 47 1.216736e+12 1189691809 276476550048 17318021
## 48 1.198895e+12 1206734806 -17841299828 17042997
## 49 1.341888e+12 1223640160 142992877970 16905354
## 50 1.675616e+12 1240613620 333727502505 16973460
## 51 1.823052e+12 1257621191 147436310411 17007571
## 52 1.827638e+12 1274487215 4585760886 16866024
## 53 1.856722e+12 1291132063 29083916894 16644848
## 54 2.039126e+12 1307246509 182404971547 16114446
## 55 2.103588e+12 1322866505 64461880838 15619996
## 56 2.294797e+12 1338636340 191208525616 15769835
## 57 2.651474e+12 1354195680 356677377053 15559340
## 58 2.702930e+12 1369003306 51455378972 14807626
## 59 2.835606e+12 1383112050 132676614909 14108744
## 60 2.671595e+12 1396387127 -164010850629 13275077
## 61 3.150307e+12 1407563842 478711433155 11176715
## 62 3.416646e+12 1417173173 266338986911 9609331
##
## $call
## ardlDlm.default(formula = formula1, data = data.frame(data),
## p = (max.p - 1), q = (p[[vars[1]]] - 1), remove = removeP2)
##
## attr(,"class")
## [1] "ardlDlm" "dLagM"
##
##
## $F.stat
## [1] 7.324204
##
## $p
## gsyh nufus
## 1 4 3
##
## $k
## [1] 1
##
## $bg
##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: modelFull$model
## LM test = 0.0093592, df1 = 1, df2 = 49, p-value = 0.9233
##
##
## $lb
##
## Box-Ljung test
##
## data: res
## X-squared = 0.0010806, df = 1, p-value = 0.9738
##
##
## $bp
##
## studentized Breusch-Pagan test
##
## data: modelFull$model
## BP = 32.084, df = 8, p-value = 8.995e-05
##
##
## $sp
##
## Shapiro-Wilk normality test
##
## data: modelFull$model$residual
## W = 0.89261, p-value = 8.154e-05
##
##
## $ECM
## $ECM$EC.t
## [1] -2.763388e+12 -2.826001e+12 -2.886740e+12 -2.947008e+12 -3.011827e+12
## [6] -3.092323e+12 -3.155575e+12 -3.222911e+12 -3.290525e+12 -3.361393e+12
## [11] -3.433218e+12 -3.507954e+12 -3.575394e+12 -3.644995e+12 -3.730813e+12
## [16] -3.812101e+12 -3.880748e+12 -3.954489e+12 -4.030799e+12 -4.093147e+12
## [21] -4.184494e+12 -4.277375e+12 -4.362126e+12 -4.473055e+12 -4.559235e+12
## [26] -4.651075e+12 -4.730571e+12 -4.823643e+12 -4.936473e+12 -5.024780e+12
## [31] -5.189204e+12 -5.285529e+12 -5.409760e+12 -5.477917e+12 -5.561702e+12
## [36] -5.645785e+12 -5.739832e+12 -5.851644e+12 -5.931263e+12 -6.039195e+12
## [41] -6.140906e+12 -6.230196e+12 -6.254747e+12 -6.269059e+12 -6.270668e+12
## [46] -6.259708e+12 -6.089587e+12 -6.212096e+12 -6.172925e+12 -5.943437e+12
## [51] -5.900450e+12 -5.999445e+12 -6.072583e+12 -5.989143e+12 -6.020609e+12
## [56] -5.926248e+12 -5.665127e+12 -5.704610e+12 -5.658580e+12 -5.904118e+12
## [61] -5.494047e+12 -5.286722e+12
##
## $ECM$EC.model
##
## Time series regression with "ts" data:
## Start = 4, End = 62
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Coefficients:
## (Intercept) ec.1 dnufus.t dnufus.1 dnufus.2 dgsyh.1
## 5.490e+10 -1.677e-01 -3.245e+04 6.052e+04 -7.750e+04 -2.103e-01
## dgsyh.2 dgsyh.3
## -2.414e-01 -3.510e-01
##
##
## $ECM$EC.beta
## ec.1
## -0.1677445
##
## $ECM$EC.data
## gsyh nufus dgsyh dnufus ec
## 2 3.923244e+10 456351876 2202551908 10397297 -2.763388e+12
## 3 4.216148e+10 467024193 2929046074 10672317 -2.826001e+12
## 4 4.842192e+10 477933619 6260441601 10909426 -2.886740e+12
## 5 5.648029e+10 489059309 8058366482 11125690 -2.947008e+12
## 6 5.955485e+10 500114346 3074564635 11055037 -3.011827e+12
## 7 4.586546e+10 510992617 -13689392542 10878271 -3.092323e+12
## 8 5.013494e+10 521987069 4269480170 10994452 -3.155575e+12
## 9 5.308546e+10 533431909 2950513667 11444840 -3.222911e+12
## 10 5.844800e+10 545314670 5362539147 11882761 -3.290525e+12
## 11 6.242248e+10 557501301 3974488037 12186631 -3.361393e+12
## 12 6.735140e+10 569999178 4928921297 12497877 -3.433218e+12
## 13 7.146319e+10 582837973 4111789479 12838795 -3.507954e+12
## 14 8.551527e+10 596107483 14052075754 13269510 -3.575394e+12
## 15 9.952590e+10 609721951 14010629531 13614468 -3.644995e+12
## 16 9.847280e+10 623524219 -1053102659 13802268 -3.730813e+12
## 17 1.027172e+11 637451448 4244368010 13927229 -3.812101e+12
## 18 1.214866e+11 651685628 18769476975 14234180 -3.880748e+12
## 19 1.373003e+11 666267760 15813653872 14582132 -3.954489e+12
## 20 1.529917e+11 681248383 15691358480 14980623 -4.030799e+12
## 21 1.863253e+11 696828385 33333691293 15580002 -4.093147e+12
## 22 1.934914e+11 712869298 7166023359 16040913 -4.184494e+12
## 23 2.007156e+11 729169466 7224256385 16300168 -4.277375e+12
## 24 2.182621e+11 745826546 17546521582 16657080 -4.362126e+12
## 25 2.121576e+11 762895156 -6104501236 17068610 -4.473055e+12
## 26 2.325116e+11 780242084 20353909663 17346928 -4.559235e+12
## 27 2.489860e+11 797878993 16474439200 17636909 -4.651075e+12
## 28 2.790336e+11 815716125 30047590052 17837132 -4.730571e+12
## 29 2.965897e+11 833729681 17556086804 18013556 -4.823643e+12
## 30 2.960421e+11 852012673 -547617951 18282992 -4.936473e+12
## 31 3.209790e+11 870452165 24936973475 18439492 -5.024780e+12
## 32 2.701053e+11 888941756 -50873684541 18489591 -5.189204e+12
## 33 2.882081e+11 907574049 18102728399 18632293 -5.285529e+12
## 34 2.792956e+11 926351297 -8912421295 18777248 -5.409760e+12
## 35 3.272756e+11 945261958 47979934547 18910661 -5.477917e+12
## 36 3.602819e+11 964279129 33006326113 19017171 -5.561702e+12
## 37 3.928969e+11 983281218 32614956561 19002089 -5.645785e+12
## 38 4.158676e+11 1002335230 22970697388 19054012 -5.739832e+12
## 39 4.213513e+11 1021434576 5483753632 19099346 -5.851644e+12
## 40 4.588204e+11 1040500054 37469100113 19065478 -5.931263e+12
## 41 4.683949e+11 1059633675 9574519918 19133621 -6.039195e+12
## 42 4.854410e+11 1078970907 17046077283 19337232 -6.140906e+12
## 43 5.149379e+11 1098313039 29496934336 19342132 -6.230196e+12
## 44 6.076993e+11 1117415123 92761336562 19102084 -6.254747e+12
## 45 7.091485e+11 1136264583 101449229380 18849460 -6.269059e+12
## 46 8.203816e+11 1154638713 111233080695 18374130 -6.270668e+12
## 47 9.402599e+11 1172373788 119878293284 17735075 -6.259708e+12
## 48 1.216736e+12 1189691809 276476550048 17318021 -6.089587e+12
## 49 1.198895e+12 1206734806 -17841299828 17042997 -6.212096e+12
## 50 1.341888e+12 1223640160 142992877970 16905354 -6.172925e+12
## 51 1.675616e+12 1240613620 333727502505 16973460 -5.943437e+12
## 52 1.823052e+12 1257621191 147436310411 17007571 -5.900450e+12
## 53 1.827638e+12 1274487215 4585760886 16866024 -5.999445e+12
## 54 1.856722e+12 1291132063 29083916894 16644848 -6.072583e+12
## 55 2.039126e+12 1307246509 182404971547 16114446 -5.989143e+12
## 56 2.103588e+12 1322866505 64461880838 15619996 -6.020609e+12
## 57 2.294797e+12 1338636340 191208525616 15769835 -5.926248e+12
## 58 2.651474e+12 1354195680 356677377053 15559340 -5.665127e+12
## 59 2.702930e+12 1369003306 51455378972 14807626 -5.704610e+12
## 60 2.835606e+12 1383112050 132676614909 14108744 -5.658580e+12
## 61 2.671595e+12 1396387127 -164010850629 13275077 -5.904118e+12
## 62 3.150307e+12 1407563842 478711433155 11176715 -5.494047e+12
## 63 3.416646e+12 1417173173 266338986911 9609331 -5.286722e+12
##
##
## $ARDL.model
##
## Time series regression with "ts" data:
## Start = 4, End = 62
##
## Call:
## dynlm(formula = as.formula(model.text), data = data)
##
## Coefficients:
## (Intercept) gsyh.1 nufus.1 dnufus.t dnufus.1 dnufus.2
## 5.490e+10 -1.677e-01 1.030e+03 -3.245e+04 6.052e+04 -7.750e+04
## dgsyh.1 dgsyh.2 dgsyh.3
## -2.103e-01 -2.414e-01 -3.510e-01