lab9
Ostin Molina
2022-05-07
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summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00## Warning: package 'tidyverse' was built under R version 4.1.3## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.6 v dplyr 1.0.7
## v tidyr 1.2.0 v stringr 1.4.0
## v readr 2.1.2 v forcats 0.5.1## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()## Warning: package 'lubridate' was built under R version 4.1.3##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union## Warning: package 'car' was built under R version 4.1.3## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
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## recode## The following object is masked from 'package:purrr':
##
## some## Warning: package 'tseries' was built under R version 4.1.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo##
## Attaching package: 'aTSA'## The following objects are masked from 'package:tseries':
##
## adf.test, kpss.test, pp.test## The following object is masked from 'package:graphics':
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## identify##
## Attaching package: 'forecast'## The following object is masked from 'package:aTSA':
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## forecast## Warning: package 'vars' was built under R version 4.1.3## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
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## select## Loading required package: strucchange## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
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## as.Date, as.Date.numeric## Loading required package: sandwich##
## Attaching package: 'strucchange'## The following object is masked from 'package:stringr':
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## boundary## Loading required package: lmtest##
## Attaching package: 'vars'## The following object is masked from 'package:aTSA':
##
## arch.test## Warning: package 'mFilter' was built under R version 4.1.3## Warning: package 'dynlm' was built under R version 4.1.3## Warning: package 'readxl' was built under R version 4.1.3## [1] "Year" "Quarter" "tiempo" "DPI" "GDP" "PCE" "CP"
## [8] "DIVIDEND"## [1] "tbl_df" "tbl" "data.frame"
## AIC(n) HQ(n) SC(n) FPE(n)
## 6 3 1 6## 1 2 3 4 5
## AIC(n) -1.855753e+01 -1.856794e+01 -1.872222e+01 -1.871195e+01 -1.876550e+01
## HQ(n) -1.848511e+01 -1.845930e+01 -1.857737e+01 -1.853089e+01 -1.854823e+01
## SC(n) -1.837928e+01 -1.830056e+01 -1.836571e+01 -1.826632e+01 -1.823075e+01
## FPE(n) 8.721332e-09 8.631923e-09 7.399231e-09 7.477904e-09 7.091277e-09
## 6 7 8
## AIC(n) -1.879237e+01 -1.874658e+01 -1.874820e+01
## HQ(n) -1.853888e+01 -1.845688e+01 -1.842229e+01
## SC(n) -1.816848e+01 -1.803357e+01 -1.794607e+01
## FPE(n) 6.907847e-09 7.237794e-09 7.234190e-09##
## VAR Estimation Results:
## =========================
## Endogenous variables: PCE, DPI
## Deterministic variables: const
## Sample size: 133
## Log Likelihood: 876.289
## Roots of the characteristic polynomial:
## 0.9987 0.6775 0.4343 0.4343 0.4321 0.4321
## Call:
## VAR(y = datos1, p = 3, type = "const", exogen = NULL)
##
##
## Estimation results for equation PCE:
## ====================================
## PCE = PCE.l1 + DPI.l1 + PCE.l2 + DPI.l2 + PCE.l3 + DPI.l3 + const
##
## Estimate Std. Error t value Pr(>|t|)
## PCE.l1 0.776760 0.105025 7.396 1.73e-11 ***
## DPI.l1 0.431260 0.111393 3.872 0.000173 ***
## PCE.l2 0.008803 0.117820 0.075 0.940558
## DPI.l2 -0.259850 0.133200 -1.951 0.053297 .
## PCE.l3 -0.051678 0.095506 -0.541 0.589395
## DPI.l3 0.103407 0.110735 0.934 0.352179
## const -0.028137 0.024918 -1.129 0.260963
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.01073 on 126 degrees of freedom
## Multiple R-Squared: 0.9993, Adjusted R-squared: 0.9992
## F-statistic: 2.818e+04 on 6 and 126 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation DPI:
## ====================================
## DPI = PCE.l1 + DPI.l1 + PCE.l2 + DPI.l2 + PCE.l3 + DPI.l3 + const
##
## Estimate Std. Error t value Pr(>|t|)
## PCE.l1 0.21003 0.09432 2.227 0.0277 *
## DPI.l1 0.83352 0.10004 8.332 1.15e-13 ***
## PCE.l2 0.04421 0.10581 0.418 0.6768
## DPI.l2 0.24143 0.11963 2.018 0.0457 *
## PCE.l3 -0.12637 0.08577 -1.473 0.1432
## DPI.l3 -0.20835 0.09945 -2.095 0.0382 *
## const 0.03307 0.02238 1.478 0.1419
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.009638 on 126 degrees of freedom
## Multiple R-Squared: 0.9994, Adjusted R-squared: 0.9993
## F-statistic: 3.244e+04 on 6 and 126 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## PCE DPI
## PCE 1.152e-04 5.887e-05
## DPI 5.887e-05 9.288e-05
##
## Correlation matrix of residuals:
## PCE DPI
## PCE 1.0000 0.5692
## DPI 0.5692 1.0000## PCE DPI
## 1 -2.690958e-02 -5.110853e-03
## 2 -3.852546e-03 6.234045e-04
## 3 1.664360e-02 9.162285e-03
## 4 6.035827e-03 -8.835974e-03
## 5 -4.276020e-03 -7.427321e-03
## 6 -3.023379e-02 -8.379138e-03
## 7 -8.217265e-03 1.112910e-02
## 8 -1.179868e-02 2.566674e-03
## 9 -7.966736e-03 7.166392e-03
## 10 5.211906e-02 1.387731e-02
## 11 -1.341815e-02 -1.887648e-03
## 12 2.440824e-03 3.277811e-02
## 13 -1.513620e-02 -3.313745e-02
## 14 6.190768e-04 2.715024e-03
## 15 -5.348381e-03 -2.550211e-02
## 16 1.044199e-02 -4.476189e-03
## 17 -7.426049e-03 1.398669e-03
## 18 -5.179358e-03 -8.183421e-03
## 19 6.566826e-03 1.030462e-02
## 20 8.540921e-03 -2.797782e-03
## 21 1.548295e-02 1.936062e-02
## 22 -1.030522e-03 2.156576e-03
## 23 6.343558e-03 -1.041045e-02
## 24 -1.076616e-02 -1.470672e-02
## 25 -1.195108e-02 -1.646070e-02
## 26 8.610240e-04 -2.090404e-03
## 27 -6.702754e-03 7.031096e-03
## 28 7.555127e-05 6.562193e-03
## 29 8.542572e-03 1.227857e-02
## 30 1.226891e-03 1.204228e-02
## 31 8.258654e-03 7.651084e-03
## 32 5.073915e-03 1.151898e-04
## 33 -3.066012e-04 -9.026884e-04
## 34 -1.984279e-03 -8.830002e-03
## 35 2.144990e-03 -7.466940e-03
## 36 -3.070420e-03 -6.889657e-03
## 37 9.594790e-03 4.245500e-03
## 38 -5.933234e-03 -2.310897e-03
## 39 -4.325771e-04 -9.713120e-03
## 40 -1.401259e-04 -1.233067e-03
## 41 -1.339219e-02 -7.533312e-03
## 42 -1.621864e-02 -2.187067e-02
## 43 3.126538e-03 2.215694e-03
## 44 1.090094e-02 1.324253e-02
## 45 3.563767e-03 2.020308e-03
## 46 -1.019523e-03 3.297378e-03
## 47 8.108993e-03 7.145731e-03
## 48 -1.119136e-02 2.541427e-04
## 49 -4.580259e-03 -8.092247e-03
## 50 2.294802e-03 1.295275e-03
## 51 -6.514007e-03 5.147787e-03
## 52 -1.251704e-02 -1.157294e-02
## 53 -9.293120e-03 -6.975420e-03
## 54 -1.891140e-03 -3.650439e-03
## 55 6.766878e-03 8.323346e-03
## 56 1.915917e-03 -2.674041e-03
## 57 1.312412e-02 7.233119e-03
## 58 -6.944628e-04 4.034917e-04
## 59 3.386557e-03 -1.375338e-03
## 60 -3.115398e-03 -1.956857e-03
## 61 -3.351005e-04 4.306877e-03
## 62 -3.357689e-03 -8.947575e-04
## 63 -5.665659e-05 8.852383e-05
## 64 3.346169e-04 5.619492e-03
## 65 4.551459e-03 2.062048e-04
## 66 1.100448e-02 8.729518e-03
## 67 1.507471e-02 7.135056e-03
## 68 4.552199e-03 3.382975e-03
## 69 1.353521e-03 -1.059650e-02
## 70 6.380324e-03 8.516387e-03
## 71 -1.197646e-03 3.315888e-03
## 72 1.857895e-02 5.142736e-03
## 73 1.118428e-02 1.579111e-02
## 74 -3.412891e-03 1.459234e-03
## 75 -7.753107e-03 -1.051057e-02
## 76 3.526238e-03 2.401627e-03
## 77 -2.924595e-05 -2.094098e-03
## 78 7.005480e-03 -4.503975e-03
## 79 1.221957e-03 3.174100e-03
## 80 4.061213e-04 -4.262140e-03
## 81 1.573838e-03 -4.887655e-03
## 82 1.092725e-02 1.418781e-02
## 83 5.369613e-03 6.730711e-03
## 84 -6.507664e-03 4.860290e-03
## 85 -7.308899e-03 -3.936356e-03
## 86 -8.626511e-03 2.903107e-03
## 87 -5.422667e-03 2.333813e-03
## 88 6.834643e-03 -1.431110e-03
## 89 -2.920334e-03 -1.080499e-03
## 90 -6.118100e-03 -2.506485e-03
## 91 7.443045e-03 -2.646923e-03
## 92 6.295117e-03 -5.892069e-04
## 93 -1.074697e-02 -1.350477e-02
## 94 1.675715e-02 9.146936e-03
## 95 5.614036e-03 2.399111e-03
## 96 -4.580881e-04 -6.851829e-03
## 97 4.701701e-03 5.959534e-03
## 98 -2.505754e-03 4.794420e-03
## 99 -4.837431e-04 8.975728e-03
## 100 7.267372e-03 8.022682e-03
## 101 2.747036e-02 1.263426e-02
## 102 6.793070e-04 3.622352e-03
## 103 -1.322221e-03 -1.569052e-02
## 104 1.462580e-03 -8.722905e-03
## 105 6.115277e-03 -1.095836e-02
## 106 -1.609797e-02 -1.970819e-02
## 107 -9.474540e-03 -3.614311e-03
## 108 -2.489878e-03 2.937727e-03
## 109 -1.019409e-02 -2.039103e-02
## 110 -3.932455e-03 -3.471393e-04
## 111 3.659767e-02 1.457088e-02
## 112 -1.578326e-02 2.244390e-04
## 113 1.363679e-03 -2.927348e-03
## 114 8.203946e-03 1.235671e-02
## 115 -3.320907e-03 2.951082e-05
## 116 1.043221e-04 -5.617373e-04
## 117 -3.120153e-03 5.410798e-03
## 118 -1.032363e-02 4.705361e-03
## 119 -3.411758e-03 -3.072167e-04
## 120 2.969669e-03 3.112525e-03
## 121 7.238856e-03 7.912421e-03
## 122 -6.412966e-03 -3.522318e-03
## 123 1.720992e-03 1.105828e-02
## 124 -7.105584e-03 -6.439168e-04
## 125 -2.226063e-03 -1.632325e-03
## 126 -1.149609e-03 -4.389892e-04
## 127 -1.725216e-02 -7.924685e-03
## 128 -5.031781e-03 4.668867e-03
## 129 -4.798773e-03 1.056880e-03
## 130 -3.583165e-03 -8.410492e-03
## 131 -2.666811e-02 -2.948056e-02
## 132 7.022005e-03 5.751531e-03
## 133 1.033948e-02 1.465282e-02
## Augmented Dickey-Fuller Test
## alternative: stationary
##
## Type 1: no drift no trend
## lag ADF p.value
## [1,] 0 -11.60 0.01
## [2,] 1 -8.53 0.01
## [3,] 2 -6.96 0.01
## [4,] 3 -6.61 0.01
## [5,] 4 -6.08 0.01
## Type 2: with drift no trend
## lag ADF p.value
## [1,] 0 -11.56 0.01
## [2,] 1 -8.50 0.01
## [3,] 2 -6.93 0.01
## [4,] 3 -6.58 0.01
## [5,] 4 -6.06 0.01
## Type 3: with drift and trend
## lag ADF p.value
## [1,] 0 -11.52 0.01
## [2,] 1 -8.48 0.01
## [3,] 2 -6.90 0.01
## [4,] 3 -6.56 0.01
## [5,] 4 -6.04 0.01
## ----
## Note: in fact, p.value = 0.01 means p.value <= 0.01## Augmented Dickey-Fuller Test
## alternative: stationary
##
## Type 1: no drift no trend
## lag ADF p.value
## [1,] 0 -10.86 0.01
## [2,] 1 -7.19 0.01
## [3,] 2 -6.19 0.01
## [4,] 3 -6.18 0.01
## [5,] 4 -6.41 0.01
## Type 2: with drift no trend
## lag ADF p.value
## [1,] 0 -10.82 0.01
## [2,] 1 -7.16 0.01
## [3,] 2 -6.16 0.01
## [4,] 3 -6.16 0.01
## [5,] 4 -6.38 0.01
## Type 3: with drift and trend
## lag ADF p.value
## [1,] 0 -10.78 0.01
## [2,] 1 -7.13 0.01
## [3,] 2 -6.14 0.01
## [4,] 3 -6.14 0.01
## [5,] 4 -6.36 0.01
## ----
## Note: in fact, p.value = 0.01 means p.value <= 0.01##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.030697 -0.005832 -0.000346 0.005442 0.050779
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.148e-04 1.849e-03 0.441 0.660
## z.lag.1 -1.051e+00 1.240e-01 -8.475 5.04e-14 ***
## tt -8.757e-06 2.403e-05 -0.364 0.716
## z.diff.lag 5.109e-02 8.675e-02 0.589 0.557
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01039 on 127 degrees of freedom
## Multiple R-squared: 0.4998, Adjusted R-squared: 0.488
## F-statistic: 42.3 on 3 and 127 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -8.4751 23.9641 35.9146
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.99 -3.43 -3.13
## phi2 6.22 4.75 4.07
## phi3 8.43 6.49 5.47## tau3 phi2 phi3
## statistic -8.475097 23.96407 35.91462## 1pct 5pct 10pct
## tau3 -3.99 -3.43 -3.13
## phi2 6.22 4.75 4.07
## phi3 8.43 6.49 5.47##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.034260 -0.004486 -0.000077 0.005815 0.031944
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.529e-04 1.698e-03 -0.090 0.928
## z.lag.1 -8.835e-01 1.240e-01 -7.127 6.83e-11 ***
## tt 3.012e-06 2.207e-05 0.136 0.892
## z.diff.lag -7.443e-02 8.933e-02 -0.833 0.406
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.009553 on 127 degrees of freedom
## Multiple R-squared: 0.4759, Adjusted R-squared: 0.4636
## F-statistic: 38.45 on 3 and 127 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -7.1272 16.9641 25.43
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.99 -3.43 -3.13
## phi2 6.22 4.75 4.07
## phi3 8.43 6.49 5.47## tau3 phi2 phi3
## statistic -7.127248 16.9641 25.43001## 1pct 5pct 10pct
## tau3 -3.99 -3.43 -3.13
## phi2 6.22 4.75 4.07
## phi3 8.43 6.49 5.47##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.030151 -0.006004 -0.000159 0.005671 0.051303
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0002280 0.0009049 0.252 0.802
## z.lag.1 -1.0494964 0.1235253 -8.496 4.3e-14 ***
## z.diff.lag 0.0506692 0.0864443 0.586 0.559
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01036 on 128 degrees of freedom
## Multiple R-squared: 0.4993, Adjusted R-squared: 0.4914
## F-statistic: 63.81 on 2 and 128 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -8.4962 36.1244
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.46 -2.88 -2.57
## phi1 6.52 4.63 3.81##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.034421 -0.004389 -0.000085 0.005833 0.031778
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.888e-05 8.315e-04 0.059 0.953
## z.lag.1 -8.838e-01 1.235e-01 -7.158 5.67e-11 ***
## z.diff.lag -7.429e-02 8.898e-02 -0.835 0.405
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.009516 on 128 degrees of freedom
## Multiple R-squared: 0.4759, Adjusted R-squared: 0.4677
## F-statistic: 58.11 on 2 and 128 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -7.1578 25.6334
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.46 -2.88 -2.57
## phi1 6.52 4.63 3.81##
## ###############################################
## # 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
## -0.029920 -0.005774 0.000076 0.005894 0.051530
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -1.04950 0.12308 -8.527 3.46e-14 ***
## z.diff.lag 0.05095 0.08612 0.592 0.555
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01032 on 129 degrees of freedom
## Multiple R-squared: 0.499, Adjusted R-squared: 0.4913
## F-statistic: 64.25 on 2 and 129 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -8.5272
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62##
## ###############################################
## # 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
## -0.034371 -0.004340 -0.000036 0.005881 0.031828
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.88388 0.12297 -7.188 4.73e-11 ***
## z.diff.lag -0.07420 0.08862 -0.837 0.404
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.009479 on 129 degrees of freedom
## Multiple R-squared: 0.4759, Adjusted R-squared: 0.4678
## F-statistic: 58.56 on 2 and 129 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -7.1877
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62##
## ########################################
## # Phillips and Ouliaris Unit Root Test #
## ########################################
##
## Test of type Pz
## detrending of series none
##
## Response PCE :
##
## Call:
## lm(formula = PCE ~ zr - 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.035593 -0.005006 0.000100 0.005352 0.053987
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## zrPCE 0.78931 0.05893 13.394 < 2e-16 ***
## zrDPI 0.21501 0.05979 3.596 0.000454 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01117 on 133 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 3.18e+07 on 2 and 133 DF, p-value: < 2.2e-16
##
##
## Response DPI :
##
## Call:
## lm(formula = DPI ~ zr - 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.035093 -0.004833 0.000136 0.005776 0.042633
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## zrPCE 0.06780 0.05341 1.27 0.206
## zrDPI 0.93239 0.05418 17.21 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01012 on 133 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 3.761e+07 on 2 and 133 DF, p-value: < 2.2e-16
##
##
##
## Value of test-statistic is: 50.7408
##
## Critical values of Pz are:
## 10pct 5pct 1pct
## critical values 33.9267 40.8217 55.1911##
## ########################################
## # Phillips and Ouliaris Unit Root Test #
## ########################################
##
## Test of type Pu
## detrending of series none
##
##
## Call:
## lm(formula = z[, 1] ~ z[, -1] - 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.064570 -0.006143 0.001245 0.008814 0.043063
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z[, -1] 1.0146094 0.0001865 5441 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01642 on 135 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 2.961e+07 on 1 and 135 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: 38.8218
##
## Critical values of Pu are:
## 10pct 5pct 1pct
## critical values 20.3933 25.9711 38.3413## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## [19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## [37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
## [55] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
## [73] 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
## [91] 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
## [109] 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
## [127] 127 128 129 130 131 132 133 134 135 136## DPI.ts PCE.ts tendencia
## 1 -2.510899e-02 -1.919049e-03 -8.635583e-14
## 2 -2.953340e-03 2.217372e-03 -2.170361e-14
## 3 1.784882e-02 1.129870e-02 -8.988726e-14
## 4 6.739032e-03 -7.589446e-03 1.878533e-14
## 5 -3.706020e-03 -6.416917e-03 6.538353e-16
## 6 -2.914558e-02 -6.450135e-03 -1.563895e-15
## 7 -7.404300e-03 1.257019e-02 1.072713e-14
## 8 -1.097711e-02 4.023027e-03 1.586251e-14
## 9 -8.215015e-03 6.726283e-03 2.984845e-14
## 10 5.195708e-02 1.359018e-02 6.911730e-15
## 11 -1.332322e-02 -1.719371e-03 1.641736e-14
## 12 2.395476e-03 3.269772e-02 -1.416905e-14
## 13 -1.276104e-02 -2.892714e-02 6.986769e-15
## 14 1.697488e-03 4.626656e-03 1.070690e-14
## 15 -2.862755e-03 -2.109599e-02 2.350813e-14
## 16 1.130998e-02 -2.937561e-03 3.296744e-14
## 17 -6.289420e-03 3.413502e-03 -1.169187e-14
## 18 -4.813219e-03 -7.534389e-03 -1.771087e-14
## 19 6.725819e-03 1.058646e-02 6.032383e-16
## 20 8.711987e-03 -2.494544e-03 1.155809e-15
## 21 1.516685e-02 1.880030e-02 -9.104782e-16
## 22 -5.301884e-04 3.043486e-03 1.816894e-15
## 23 6.851905e-03 -9.509333e-03 -3.815380e-15
## 24 -9.607165e-03 -1.265224e-02 1.689166e-14
## 25 -1.098136e-02 -1.474174e-02 1.024520e-14
## 26 1.510791e-03 -9.386031e-04 1.541471e-14
## 27 -6.638958e-03 7.144184e-03 7.534834e-15
## 28 -5.258384e-04 5.496147e-03 2.830119e-15
## 29 7.800106e-03 1.096245e-02 1.646498e-14
## 30 5.731200e-04 1.088338e-02 1.169841e-15
## 31 7.895301e-03 7.006991e-03 5.293849e-15
## 32 5.334324e-03 5.767996e-04 7.076760e-15
## 33 3.350332e-04 2.346975e-04 2.869805e-15
## 34 -8.241227e-04 -6.773464e-03 7.184017e-15
## 35 3.369390e-03 -5.296521e-03 -1.170313e-15
## 36 -1.849343e-03 -4.725130e-03 8.774923e-15
## 37 1.049930e-02 5.848863e-03 -7.992471e-15
## 38 -4.992293e-03 -6.429490e-04 1.900141e-14
## 39 8.221320e-05 -8.800583e-03 -1.929542e-15
## 40 4.335974e-04 -2.160625e-04 -5.028093e-17
## 41 -1.306822e-02 -6.959016e-03 2.085878e-15
## 42 -1.640072e-02 -2.219343e-02 -7.206078e-15
## 43 2.280164e-03 7.153777e-04 -4.168236e-15
## 44 9.637625e-03 1.100314e-02 1.260922e-14
## 45 1.583194e-03 -1.490533e-03 4.292467e-15
## 46 -3.100251e-03 -3.909998e-04 -6.758981e-15
## 47 6.486978e-03 4.270483e-03 1.335508e-15
## 48 -1.253617e-02 -2.129724e-03 -2.606939e-15
## 49 -5.949808e-03 -1.051996e-02 -1.208203e-14
## 50 1.107776e-03 -8.088938e-04 -1.053046e-15
## 51 -7.866667e-03 2.750010e-03 1.612908e-14
## 52 -1.406379e-02 -1.431478e-02 9.919864e-15
## 53 -1.116514e-02 -1.029384e-02 -9.541298e-15
## 54 -3.966318e-03 -7.328981e-03 -9.778574e-16
## 55 4.063324e-03 3.530922e-03 4.793565e-15
## 56 -1.013307e-03 -7.866497e-03 -1.014600e-14
## 57 9.857970e-03 1.443419e-03 -1.453510e-14
## 58 -3.448909e-03 -4.479146e-03 -1.817569e-14
## 59 5.496020e-04 -6.404235e-03 -1.165614e-14
## 60 -5.474114e-03 -6.138009e-03 -1.630511e-14
## 61 -2.756961e-03 1.379402e-05 1.670882e-14
## 62 -5.607955e-03 -4.883666e-03 2.767089e-15
## 63 -2.535010e-03 -4.304701e-03 5.574346e-15
## 64 -2.075325e-03 1.347536e-03 2.022614e-14
## 65 2.122959e-03 -4.098647e-03 1.851369e-14
## 66 8.550897e-03 4.380205e-03 -1.061233e-14
## 67 1.298568e-02 3.431958e-03 -3.583792e-16
## 68 2.772005e-03 2.273340e-04 1.122378e-14
## 69 1.204070e-04 -1.278237e-02 -5.575978e-15
## 70 5.502678e-03 6.960637e-03 -7.050823e-15
## 71 -1.534656e-03 2.718491e-03 3.882843e-16
## 72 1.809563e-02 4.285977e-03 1.426836e-14
## 73 1.121850e-02 1.585176e-02 2.484177e-15
## 74 -2.977705e-03 2.230663e-03 -6.028588e-15
## 75 -6.808790e-03 -8.836637e-03 -1.974582e-15
## 76 4.853054e-03 4.753592e-03 8.390239e-15
## 77 1.490202e-03 5.993348e-04 5.782798e-15
## 78 8.091731e-03 -2.578443e-03 -8.853107e-15
## 79 2.380293e-03 5.227412e-03 -3.954247e-15
## 80 1.555824e-03 -2.224133e-03 -1.065252e-15
## 81 2.644215e-03 -2.990263e-03 8.137091e-16
## 82 1.196199e-02 1.602203e-02 -2.101387e-14
## 83 6.656500e-03 9.011897e-03 -7.518214e-16
## 84 -5.299604e-03 7.001744e-03 -3.367784e-15
## 85 -5.562117e-03 -8.399423e-04 9.934337e-15
## 86 -6.779376e-03 6.177410e-03 4.473575e-15
## 87 -3.556430e-03 5.641977e-03 1.771264e-14
## 88 8.451690e-03 1.435329e-03 6.185291e-15
## 89 -1.490436e-03 1.454193e-03 1.495580e-14
## 90 -4.808515e-03 -1.850633e-04 1.965830e-14
## 91 8.782409e-03 -2.727145e-04 -7.320313e-15
## 92 7.506540e-03 1.558209e-03 5.385330e-15
## 93 -9.713619e-03 -1.167301e-02 1.147318e-14
## 94 1.751218e-02 1.048533e-02 4.276212e-16
## 95 6.787132e-03 4.478586e-03 1.655066e-14
## 96 8.560366e-05 -5.888060e-03 -1.764016e-14
## 97 5.607101e-03 7.564481e-03 -2.084591e-14
## 98 -1.347588e-03 6.847429e-03 -1.518753e-15
## 99 5.140640e-04 1.074448e-02 1.014278e-15
## 100 8.584682e-03 1.035780e-02 -8.896862e-15
## 101 2.890220e-02 1.517240e-02 1.814321e-14
## 102 2.667936e-03 7.147472e-03 -1.430597e-14
## 103 1.053923e-03 -1.147848e-02 -3.574194e-15
## 104 4.503151e-03 -3.333071e-03 -1.042140e-14
## 105 9.259451e-03 -5.384872e-03 1.215699e-15
## 106 -1.338467e-02 -1.489849e-02 -7.626269e-15
## 107 -7.451602e-03 -2.837360e-05 -4.667533e-15
## 108 -7.453413e-04 6.030161e-03 -1.883397e-14
## 109 -9.477315e-03 -1.912045e-02 -2.078141e-14
## 110 -4.285748e-03 -9.734010e-04 1.428721e-14
## 111 3.605626e-02 1.361116e-02 -1.708047e-14
## 112 -1.676034e-02 -1.507568e-03 -2.087086e-14
## 113 -1.127673e-04 -5.544554e-03 -3.996490e-14
## 114 7.702899e-03 1.146853e-02 1.315687e-14
## 115 -4.032877e-03 -1.232555e-03 -3.125034e-15
## 116 -6.937422e-04 -1.976417e-03 -9.178139e-15
## 117 -3.590305e-03 4.577387e-03 9.212465e-15
## 118 -1.080764e-02 3.847397e-03 1.682920e-14
## 119 -3.923225e-03 -1.213863e-03 5.574775e-15
## 120 2.388496e-03 2.082315e-03 1.050187e-14
## 121 6.568518e-03 6.724155e-03 -1.286042e-14
## 122 -6.995955e-03 -4.555748e-03 4.274434e-15
## 123 1.086457e-03 9.933475e-03 2.520453e-15
## 124 -7.130079e-03 -6.873386e-04 -1.627598e-15
## 125 -2.616445e-03 -2.324330e-03 6.583684e-15
## 126 -1.275868e-03 -6.628007e-04 9.582457e-15
## 127 -1.759389e-02 -8.530458e-03 1.569377e-15
## 128 -5.734114e-03 3.423885e-03 3.689129e-14
## 129 -5.484564e-03 -1.587806e-04 5.962706e-15
## 130 -4.997332e-03 -1.091730e-02 -3.318309e-15
## 131 -2.838075e-02 -3.251645e-02 -1.827679e-14
## 132 4.382402e-03 1.072469e-03 -1.052489e-14
## 133 7.681441e-03 9.941066e-03 -2.057109e-15
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.029661 -0.005469 -0.000092 0.005705 0.050719
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.889e-04 1.837e-03 0.484 0.629
## z.lag.1 -1.039e+00 1.236e-01 -8.403 7.49e-14 ***
## tt -1.014e-05 2.388e-05 -0.425 0.672
## z.diff.lag 4.455e-02 8.681e-02 0.513 0.609
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01033 on 127 degrees of freedom
## Multiple R-squared: 0.4973, Adjusted R-squared: 0.4854
## F-statistic: 41.88 on 3 and 127 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -8.403 23.5528 35.3081
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.99 -3.43 -3.13
## phi2 6.22 4.75 4.07
## phi3 8.43 6.49 5.47##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.032212 -0.004751 0.000097 0.005425 0.031915
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.652e-05 1.638e-03 -0.016 0.987
## z.lag.1 -9.069e-01 1.239e-01 -7.321 2.49e-11 ***
## tt 4.684e-07 2.129e-05 0.022 0.982
## z.diff.lag -6.301e-02 8.895e-02 -0.708 0.480
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.009212 on 127 degrees of freedom
## Multiple R-squared: 0.4839, Adjusted R-squared: 0.4717
## F-statistic: 39.69 on 3 and 127 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -7.3208 17.8798 26.8158
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.99 -3.43 -3.13
## phi2 6.22 4.75 4.07
## phi3 8.43 6.49 5.47##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.010e-14 -7.833e-15 8.750e-16 7.614e-15 3.590e-14
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.200e-15 2.494e-15 1.283 0.20169
## z.lag.1 -6.630e-01 1.019e-01 -6.509 1.59e-09 ***
## tt -3.677e-17 3.238e-17 -1.135 0.25834
## z.diff.lag -2.414e-01 7.561e-02 -3.192 0.00178 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.397e-14 on 127 degrees of freedom
## Multiple R-squared: 0.4727, Adjusted R-squared: 0.4603
## F-statistic: 37.96 on 3 and 127 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -6.5087 14.3936 21.5222
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.99 -3.43 -3.13
## phi2 6.22 4.75 4.07
## phi3 8.43 6.49 5.47## dlnPCE dlnDPI
## 1 -8.166007e-03 5.186159e-03
## 2 8.858848e-03 2.675018e-02
## 3 -1.394811e-02 1.119258e-02
## 4 -4.908224e-03 1.043509e-03
## 5 -2.459059e-03 -2.622343e-02
## 6 1.229856e-02 -4.787232e-03
## 7 -1.374145e-03 -1.078473e-02
## 8 -1.097248e-03 -5.374421e-03
## 9 9.486912e-03 5.875504e-02
## 10 -2.013505e-03 -1.339273e-02
## 11 3.320570e-02 9.138631e-03
## 12 -2.678918e-02 -8.217060e-03
## 13 -1.729457e-05 -2.643530e-03
## 14 -2.431881e-02 -1.599016e-03
## 15 -2.719484e-03 1.254376e-02
## 16 3.845466e-03 -8.711504e-03
## 17 -5.639674e-03 -4.004290e-03
## 18 1.209167e-02 1.928180e-03
## 19 -3.269558e-03 5.138173e-03
## 20 1.958452e-02 1.112868e-02
## 21 3.278887e-03 -2.894572e-03
## 22 -8.847991e-03 5.018631e-03
## 23 -1.087981e-02 -1.467518e-02
## 24 -1.363310e-02 -1.262453e-02
## 25 9.392781e-04 -5.557009e-04
## 26 6.625288e-03 -9.563448e-03
## 27 4.005248e-03 -6.998896e-04
## 28 1.104672e-02 7.177909e-03
## 29 9.529851e-03 9.902886e-05
## 30 5.990860e-03 1.010004e-02
## 31 2.521373e-04 6.317886e-03
## 32 -5.618322e-04 1.205354e-03
## 33 -6.805774e-03 8.284066e-04
## 34 -5.376477e-03 3.254723e-03
## 35 -4.999638e-03 -3.317600e-03
## 36 6.042506e-03 9.387223e-03
## 37 -6.728030e-04 -8.207535e-03
## 38 -9.487969e-03 -2.279839e-03
## 39 1.852133e-03 -3.459969e-03
## 40 -7.282253e-03 -1.608684e-02
## 41 -2.153244e-02 -1.736870e-02
## 42 3.390163e-03 7.036913e-04
## 43 1.196075e-02 8.859322e-03
## 44 -7.984690e-04 1.721866e-03
## 45 3.810090e-03 -3.081308e-03
## 46 9.194433e-03 7.141270e-03
## 47 4.635668e-04 -1.338845e-02
## 48 -9.555713e-03 -4.025416e-03
## 49 2.498491e-03 2.579422e-03
## 50 3.166273e-03 -6.025760e-03
## 51 -1.321832e-02 -9.391420e-03
## 52 -7.157111e-03 -7.742277e-03
## 53 -4.694705e-03 -1.420202e-04
## 54 6.759757e-03 8.127571e-03
## 55 -4.534000e-03 2.770864e-03
## 56 7.860039e-03 1.316148e-02
## 57 2.349877e-03 -2.123784e-03
## 58 -1.540421e-04 2.425242e-03
## 59 6.717268e-04 -5.436796e-03
## 60 4.742871e-03 -1.845451e-03
## 61 -1.028380e-03 -4.185981e-03
## 62 -1.098005e-03 -6.510381e-04
## 63 5.101365e-03 2.928945e-04
## 64 -1.027673e-03 5.642664e-03
## 65 8.476396e-03 1.090973e-02
## 66 7.280053e-03 1.516938e-02
## 67 4.894163e-03 3.648788e-03
## 68 -8.356548e-03 6.430680e-04
## 69 1.293679e-02 4.192790e-03
## 70 4.307570e-03 -3.003082e-03
## 71 4.890966e-03 1.734712e-02
## 72 1.682080e-02 7.427093e-03
## 73 1.230498e-03 -3.923781e-03
## 74 -8.439848e-03 -7.858990e-03
## 75 3.983028e-03 2.401200e-03
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Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.