Identify Optimal Lag Order Selection for (Augmented) Dickey-Fuller Tests
adf_lag_select.Rdadf_lag_select() runs a series of (Augmented) Dickey-Fuller
tests and returns information that may (or may not) be useful in identify
a potential lag order for unit root tests.
Value
adf_lag_select() returns a list of length 3. The first element
in the list is a data frame of a series of (Augmented) Dickey-Fuller tests
for no-drift, no-trend. The second is a data frame of a series of (Augmented)
Dickey-Fuller tests for drift, no trend. The third is a data frame of a series
of (Augmented) Dickey-Fuller tests for a drift and trend. Each data frame has
the following columns communicating the following information.
The lag order
The (A)DF statistic for the lag order.
The Akaike information criterion for the model.
Schwartz' (Bayesian) criteron for the model.
The absolute value of the last lagged first difference in the model.
The "modified" Akaike information criterion for the model.
The "modified" Schwarz' (Bayesian) criterion for the model.
A note indicating if the lag was suggested by Schwert (1989) or Said and Dickey (1984)
Details
This function removes missing values from the vector before calculating test statistics.
The lower bound lag order suggested by Schwert (1989) and the default suggested
by Said and Dickey (1984) do not meaningfully separate from each other until
the length of the series reaches 127. Under those conditions, if the note
column returned by this function for a finite series does not identify the
Said and Dickey (1984) default, but identifies the Schwert (1989) lower
bound, interpret the latter as the former.
Examples
x <- head(tbills$tb3m, 500)
adf_lag_select(x)
#> [[1]]
#> lag tau AIC BIC abs_llfd mAIC mBIC
#> 1 0 2.0896816 -2031.526 -2023.101 NA -6.915188 -6.915188
#> 2 1 1.5224557 -2055.447 -2042.815 5.37390603 -6.971305 -6.962850
#> 3 2 1.2410477 -2054.325 -2037.490 2.43091641 -6.977366 -6.960430
#> 4 3 1.0213490 -2050.905 -2029.873 1.56819885 -6.978832 -6.953389
#> 5 4 1.1244779 -2044.968 -2019.740 1.09046482 -6.975191 -6.941214
#> 6 5 0.8945364 -2042.605 -2013.187 2.13833855 -6.978810 -6.936274
#> 7 6 1.1006935 -2040.181 -2006.577 1.87420498 -6.982269 -6.931148
#> 8 7 1.2993100 -2038.238 -2000.452 2.27338367 -6.986733 -6.926999
#> 9 8 1.2182212 -2033.691 -1991.727 1.28923464 -6.985927 -6.917553
#> 10 9 1.4680644 -2034.073 -1987.934 1.43944228 -6.995166 -6.918126
#> 11 10 1.4208201 -2027.125 -1976.816 0.06730902 -6.989459 -6.903726
#> 12 11 1.6119787 -2023.307 -1968.833 1.50539765 -6.990146 -6.895692
#> 13 12 1.9039005 -2024.156 -1965.520 1.50426284 -7.000426 -6.897225
#> 14 13 2.2413755 -2025.662 -1962.869 1.58458569 -7.012110 -6.900133
#> 15 14 2.0280381 -2020.490 -1953.544 0.94201841 -7.010039 -6.889259
#> 16 15 2.0153462 -2013.278 -1942.183 0.12503851 -7.003761 -6.874151
#> 17 16 1.8750131 -2014.282 -1939.042 0.70052179 -7.014476 -6.876007
#> 18 17 2.1973872 -2030.811 -1951.430 0.05759803 -7.057429 -6.910074
#> note
#> 1 <NA>
#> 2 <NA>
#> 3 <NA>
#> 4 <NA>
#> 5 <NA>
#> 6 Schwert (1989) lower bound
#> 7 <NA>
#> 8 Said and Dickey (1984) default
#> 9 <NA>
#> 10 <NA>
#> 11 <NA>
#> 12 <NA>
#> 13 <NA>
#> 14 <NA>
#> 15 <NA>
#> 16 <NA>
#> 17 <NA>
#> 18 Schwert (1989) upper bound
#>
#> [[2]]
#> lag tau AIC BIC abs_llfd mAIC mBIC
#> 1 0 1.3482375 -2029.936 -2017.298 NA -6.915902 -6.915902
#> 2 1 0.6443310 -2053.458 -2036.615 5.33242816 -6.971324 -6.962869
#> 3 2 0.3298184 -2052.340 -2031.297 2.42925494 -6.977393 -6.960457
#> 4 3 0.1185905 -2048.976 -2023.737 1.58514688 -6.978957 -6.953514
#> 5 4 0.2507231 -2042.995 -2013.563 1.06865218 -6.975238 -6.941261
#> 6 5 -0.0213418 -2040.740 -2007.120 2.16162433 -6.979049 -6.936513
#> 7 6 0.1958805 -2038.226 -2000.421 1.84563012 -6.982349 -6.931227
#> 8 7 0.4572120 -2036.238 -1994.253 2.26127393 -6.986733 -6.926999
#> 9 8 0.3090882 -2031.709 -1985.548 1.29458331 -6.985958 -6.917585
#> 10 9 0.4972708 -2032.073 -1981.740 1.42934568 -6.995168 -6.918127
#> 11 10 0.4781685 -2025.125 -1970.625 0.06950695 -6.989460 -6.903727
#> 12 11 0.6653122 -2021.318 -1962.653 1.50684469 -6.990165 -6.895712
#> 13 12 0.8837657 -2022.209 -1959.385 1.51732816 -7.000521 -6.897319
#> 14 13 1.1359101 -2023.801 -1956.822 1.61140779 -7.012363 -6.900386
#> 15 14 0.9780633 -2018.571 -1947.440 0.90907911 -7.010185 -6.889406
#> 16 15 0.9861440 -2011.367 -1936.090 0.15353906 -7.003923 -6.874313
#> 17 16 1.0082698 -2012.423 -1933.003 0.73144003 -7.014735 -6.876267
#> 18 17 1.0927102 -2028.930 -1945.371 0.02711476 -7.057647 -6.910292
#> note
#> 1 <NA>
#> 2 <NA>
#> 3 <NA>
#> 4 <NA>
#> 5 <NA>
#> 6 Schwert (1989) lower bound
#> 7 <NA>
#> 8 Said and Dickey (1984) default
#> 9 <NA>
#> 10 <NA>
#> 11 <NA>
#> 12 <NA>
#> 13 <NA>
#> 14 <NA>
#> 15 <NA>
#> 16 <NA>
#> 17 <NA>
#> 18 Schwert (1989) upper bound
#>
#> [[3]]
#> lag tau AIC BIC abs_llfd mAIC mBIC
#> 1 0 -2.426949 -2040.999 -2024.148 NA -6.915902 -6.915902
#> 2 1 -2.431819 -2061.744 -2040.691 5.19930082 -6.971324 -6.962869
#> 3 2 -2.636012 -2060.955 -2035.704 2.38841959 -6.977393 -6.960457
#> 4 3 -2.926802 -2059.004 -2029.558 1.59187943 -6.978957 -6.953514
#> 5 4 -2.873455 -2053.123 -2019.486 1.05401272 -6.975238 -6.941261
#> 6 5 -3.125903 -2051.782 -2013.959 2.18917693 -6.979049 -6.936513
#> 7 6 -2.888941 -2048.215 -2006.209 1.81488949 -6.982349 -6.931227
#> 8 7 -2.810820 -2046.640 -2000.457 2.28004951 -6.986733 -6.926999
#> 9 8 -2.777149 -2041.239 -1990.882 1.26012365 -6.985958 -6.917585
#> 10 9 -2.422055 -2039.649 -1985.122 1.45478325 -6.995168 -6.918127
#> 11 10 -2.517194 -2033.328 -1974.635 0.03138362 -6.989460 -6.903727
#> 12 11 -2.346064 -2028.951 -1966.097 1.56158019 -6.990165 -6.895712
#> 13 12 -2.013863 -2028.311 -1961.299 1.59050853 -7.000521 -6.897319
#> 14 13 -1.689410 -2028.660 -1957.495 1.69896031 -7.012363 -6.900386
#> 15 14 -1.860517 -2024.038 -1948.723 0.80878246 -7.010185 -6.889406
#> 16 15 -1.880276 -2017.012 -1937.553 0.24539439 -7.003923 -6.874313
#> 17 16 -2.236949 -2020.632 -1937.032 0.85327346 -7.014735 -6.876267
#> 18 17 -1.673499 -2033.637 -1945.900 0.08384766 -7.057647 -6.910292
#> note
#> 1 <NA>
#> 2 <NA>
#> 3 <NA>
#> 4 <NA>
#> 5 <NA>
#> 6 Schwert (1989) lower bound
#> 7 <NA>
#> 8 Said and Dickey (1984) default
#> 9 <NA>
#> 10 <NA>
#> 11 <NA>
#> 12 <NA>
#> 13 <NA>
#> 14 <NA>
#> 15 <NA>
#> 16 <NA>
#> 17 <NA>
#> 18 Schwert (1989) upper bound
#>