Recursive Augmented Dickey-Fuller Test

radf returns the recursive univariate and panel Augmented Dickey-Fuller test statistics.

Usage

radf(data, minw = NULL, lag = 0L)

Arguments

data: A univariate or multivariate numeric time series object, a numeric vector or matrix, or a data.frame. A column may have leading and/or trailing NA values (an uneven/unbalanced panel where series enter or exit the sample at different times) – those periods are filled with NA in badf/bsadf and excluded from that series' adf/sadf/ gsadf. Interior NA values (a gap in the middle of a series) are not supported. When any series is padded this way, the panel statistic (bsadf_panel/gsadf_panel) is not available and is returned as NA, with a warning.
minw: A positive integer. The minimum window size (default = \((0.01 + 1.8/\sqrt(T))T\), where T denotes the sample size).
lag: A non-negative integer. The lag length of the Augmented Dickey-Fuller regression (default = 0L).

Value

A list that contains the unit root test statistics (sequence):

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

And attributes:

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

The radf() function is vectorized, i.e., it can handle multiple series at once, to improve efficiency. This property also enables the computation of panel statistics internally as a by-product of the univariate estimations with minimal additional cost incurred.

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.

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.

Examples

# \donttest{
# 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)
# }