exuber
Recursive Augmented Dickey-Fuller
Recursive Augmented Dickey-Fuller Test
radf radf(data, minw = NULL, lag = 0L)radf computes the recursive univariate and panel augmented Dickey-Fuller test statistics (ADF, SADF, GSADF and their backward sequences).
Arguments
| data | A univariate or multivariate numeric time series object, a numeric
vector or matrix, or a data.frame. A column may have leading or trailing
NA values, which describes an unbalanced panel in which series enter or
exit the sample at different times. Those periods are filled with NA in
badf and bsadf and excluded from the adf, sadf and
gsadf of that series. Interior NA values (a gap in the middle of
a series) are not supported. When any series is padded in this way, the panel
statistics (bsadf_panel and gsadf_panel) are not available, and
the function returns NA for them with a warning. |
| minw | A positive integer. The minimum window size (default = , where T denotes the sample size). |
| lag | A non-negative integer. The lag length of the Augmented Dickey-Fuller regression (default = 0L). |
Value
| adf | Augmented Dickey-Fuller |
| badf | Backward Augmented Dickey-Fuller |
| sadf | Supremum Augmented Dickey-Fuller |
| bsadf | Backward Supremum Augmented Dickey-Fuller |
| gsadf | Generalized Supremum Augmented Dickey-Fuller |
| bsadf_panel | Panel Backward Supremum Augmented Dickey-Fuller |
| gsadf_panel | Panel Generalized Supremum Augmented Dickey-Fuller |
| mat | The matrix used in the estimation. |
| index | The index parsed from the dataset. |
| lag | The lag used in the estimation. |
| n | The number of rows. |
| minw | The minimum window used in the estimation. |
| series_names | The series names. |
Details
radf() is vectorized: it handles several series at once. The panel statistics are computed as a by-product of the univariate estimations, at almost no additional cost.
Examples
These examples are copied from the package's own documentation and are run by R CMD check on every release.
The printed output (after #>) and the plots were produced by running them against the current package source.
# We will use simulated data that are stored as data
sim_data
#> # A tibble: 100 × 5
#> psy1 psy2 evans div blan
#> <sim> <sim> <sim> <sim> <sim>
#> 1 100 100 0.5 68.4 0.1
#> 2 90.3 102 0.563 66 0.0408
#> 3 93.4 110 0.583 78.9 0.121
#> 4 92.9 116 0.575 75.6 0.0195
#> 5 106 127 0.545 74.8 0.0216
#> 6 102 114 0.577 77.7 0.0117
#> 7 109 120 0.658 80.8 0.0265
#> 8 105 130 0.7 91.4 0.0238
#> 9 112 128 0.684 87.4 0.0332
#> 10 124 131 0.735 72.2 0.0342
#> # ℹ 90 more rows
rsim <- radf(sim_data)
str(rsim)
#> List of 7
#> $ adf : Named num [1:5] -2.46 -2.86 -5.83 -1.95 -5.15
#> ..- attr(*, "names")= chr [1:5] "psy1" "psy2" "evans" "div" ...
#> $ badf : num [1:81, 1:5] -2.31 -2.36 -2.49 -2.26 -1.63 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:5] "psy1" "psy2" "evans" "div" ...
#> $ sadf : Named num [1:5] 1.95 7.88 5.28 1.11 3.93
#> ..- attr(*, "names")= chr [1:5] "psy1" "psy2" "evans" "div" ...
#> $ bsadf : num [1:81, 1:5] -2.31 -2.36 -2.49 -2.26 -1.26 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:5] "psy1" "psy2" "evans" "div" ...
#> $ gsadf : Named num [1:5] 5.19 7.88 5.99 1.34 10.95
#> ..- attr(*, "names")= chr [1:5] "psy1" "psy2" "evans" "div" ...
#> $ bsadf_panel: num [1:81] -0.0702 -1.5266 -1.2379 -1.101 -0.7169 ...
#> $ gsadf_panel: num 2.41
#> - attr(*, "mat")= num [1:100, 1:5] 100 90.3 93.4 92.9 106.2 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:5] "psy1" "psy2" "evans" "div" ...
#> ..- attr(*, "index")= num [1:100] 1 2 3 4 5 6 7 8 9 10 ...
#> ..- attr(*, "series_names")= chr [1:5] "psy1" "psy2" "evans" "div" ...
#> - attr(*, "index")= num [1:100] 1 2 3 4 5 6 7 8 9 10 ...
#> - attr(*, "series_names")= chr [1:5] "psy1" "psy2" "evans" "div" ...
#> - attr(*, "minw")= num 19
#> - attr(*, "lag")= int 0
#> - attr(*, "n")= int 100
#> - attr(*, "valid_range")= num [1:2, 1:5] 1 100 1 100 1 100 1 100 1 100
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : chr [1:2] "start" "end"
#> .. ..$ : chr [1:5] "psy1" "psy2" "evans" "div" ...
#> - attr(*, "class")= chr [1:2] "radf_obj" "list"
# We would also use data that contain a Date column
sim_data_wdate
#> # A tibble: 100 × 6
#> psy1 psy2 evans div blan date
#> <sim> <sim> <sim> <sim> <sim> <date>
#> 1 100 100 0.5 68.4 0.1 2000-01-01
#> 2 90.3 102 0.563 66 0.0408 2000-02-01
#> 3 93.4 110 0.583 78.9 0.121 2000-03-01
#> 4 92.9 116 0.575 75.6 0.0195 2000-04-01
#> 5 106 127 0.545 74.8 0.0216 2000-05-01
#> 6 102 114 0.577 77.7 0.0117 2000-06-01
#> 7 109 120 0.658 80.8 0.0265 2000-07-01
#> 8 105 130 0.7 91.4 0.0238 2000-08-01
#> 9 112 128 0.684 87.4 0.0332 2000-09-01
#> 10 124 131 0.735 72.2 0.0342 2000-10-01
#> # ℹ 90 more rows
rsim_wdate <- radf(sim_data_wdate)
#> Using `date` as index variable.
tidy(rsim_wdate)
#> # A tibble: 5 × 4
#> id adf sadf gsadf
#> <fct> <dbl> <dbl> <dbl>
#> 1 psy1 -2.46 1.95 5.19
#> 2 psy2 -2.86 7.88 7.88
#> 3 evans -5.83 5.28 5.99
#> 4 div -1.95 1.11 1.34
#> 5 blan -5.15 3.93 11.0
augment(rsim_wdate)
#> # A tibble: 405 × 6
#> key index id data badf bsadf
#> <int> <date> <chr> <dbl> <dbl> <dbl>
#> 1 20 2001-08-01 psy1 104. -2.31 -2.31
#> 2 20 2001-08-01 psy2 161. -0.756 -0.756
#> 3 20 2001-08-01 evans 1.92 5.28 5.28
#> 4 20 2001-08-01 div 134. 0.184 0.184
#> 5 20 2001-08-01 blan 0.0585 -2.75 -2.75
#> 6 21 2001-09-01 psy1 110. -2.36 -2.36
#> 7 21 2001-09-01 psy2 170. -0.167 -0.167
#> 8 21 2001-09-01 evans 0.489 -2.73 -2.69
#> 9 21 2001-09-01 div 140. 0.288 0.288
#> 10 21 2001-09-01 blan 0.0438 -2.81 -2.70
#> # ℹ 395 more rows
tidy(rsim_wdate, panel = TRUE)
#> # A tibble: 1 × 1
#> gsadf_panel
#> <dbl>
#> 1 2.41
head(index(rsim_wdate))
#> [1] "2000-01-01" "2000-02-01" "2000-03-01" "2000-04-01" "2000-05-01"
#> [6] "2000-06-01"
# For lag = 1 and minimum window = 20
rsim_20 <- radf(sim_data, minw = 20, lag = 1)References
Phillips, P. C. B., Wu, Y., & Yu, J. (2011). Explosive Behavior in The 1990s Nasdaq: When Did Exuberance Escalate Asset Values? International Economic Review, 52(1), 201-226.
Phillips, P. C. B., Shi, S., & Yu, J. (2015). Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500. International Economic Review, 56(4), 1043-1078. 10.1111/iere.12132
Pavlidis, E., Yusupova, A., Paya, I., Peel, D., Martínez-García, E., Mack, A., & Grossman, V. (2016). Episodes of exuberance in housing markets: in search of the smoking gun. The Journal of Real Estate Finance and Economics, 53(4), 419-449. 10.1007/s11146-015-9531-2