# R/MacKinnonPValues.R In urca: Unit Root and Cointegration Tests for Time Series Data

```"punitroot" <-
function(q, N = Inf, trend = c("c", "nc", "ct", "ctt"),
statistic = c("t", "n"), na.rm = FALSE)
{   # A function implemented by Diethelm Wuertz

# Description:
#   Returns the cumulative probability for unit root distributions

# Arguments:
#   q - vector of quantiles
#   n.sample - a numerical values giving the number of observations
#       from which the test statistics are computed. The default
#       value is 0 which means that asymptotic cumulative probabilities
#       will be returned.
#   trend - a character string describing the regression type underlying
#       the computation of the statistics. Selections are
#       "nc" for a constant regression no intercept nor time trend,
#       "c" for a regression with an intercept but no trend component,
#       "ct" for a regression including intercept and trend.
#       The default value is "c".
#   statistic - a character string denoting the type of the test
#       statistic. The default choice is "t" for t-statistic, and
#       and the alternative choice is "n" for normalized statistic
#       also named as rho-statistic.
#   na.rm - a logical value. If set to TRUE, missing values will
#       be removed, the default is FALSE.

# Value:
#   A vector of probabilities for the unit root distribution.

# FUNCTION:

# Settings:
trend = match.arg(trend)
statistic = match.arg(statistic)
n.sample = N
if (N == Inf) n.sample = 0

# Remove any NA's in q:
if(any(is.na(q))) {
if(!na.rm) stop("NAs are not allowed when na.rm=FALSE")
else q = na.omit(q) }

# Settings - Will be Checked in Routine urcval:
if (statistic == "t") itt = 1
if (statistic == "n") itt = 2
if (trend == "nc")    itv = 1
if (trend == "c")     itv = 2
if (trend == "ct")    itv = 3
if (trend == "ctt")   itv = 4

# Calculate - Call "urcval":
result = 0 * q
for (i in 1:length(q)) {
result[i] = .urcval(arg = q[i], nobs = n.sample, niv = 1,
itt = itt, itv = itv, nc = 2) }

# Return Value:
result
}

"qunitroot" <-
function(p, N = Inf, trend = c("c", "nc", "ct", "ctt"),
statistic = c("t", "n"), na.rm = FALSE)
{   # A function implemented by Diethelm Wuertz

# Description:
#   Returns the quantile for unit root distributions

# Arguments:
#   q - vector of quantiles
#   n.sample - a numerical values giving the number of observations
#       from which the test statistics are computed. The default
#       value is 0 which means that asymptotic cumulative probabilities
#       will be returned.
#   trend - a character string describing the regression type underlying
#       the computation of the statistics. Selections are
#       "nc" for a constant regression no intercept nor time trend,
#       "c" for a regression with an intercept but no trend component,
#       "ct" for a regression including intercept and trend.
#       The default value is "c".
#   statistic - a character string denoting the type of the test
#       statistic. The default choice is "t" for t-statistic, and
#       and the alternative choice is "n" for normalized statistic
#       also named as rho-statistic.
#   na.rm - a logical value. If set to TRUE, missing values will
#       be removed, the default is FALSE.

# Value:
#   A vector of quantiles for the unit root distribution.

# FUNCTION:

# Settings:
trend = trend[1]
statistic = statistic[1]
n.sample = N
if (N == Inf) n.sample = 0

# Remove any NA's in p:
if (any(is.na(p))) {
if(!na.rm)
stop("NAs are not allowed when na.rm = FALSE")
else
p = na.omit(p)
}

# Settings - Will be Checked in Routine urcval:
if (statistic == "t") itt = 1
if (statistic == "n") itt = 2
if (trend == "nc")    itv = 1
if (trend == "c")     itv = 2
if (trend == "ct")    itv = 3
if (trend == "ctt")   itv = 4

# Calculate:
result = 0*p
for (i in 1:length(p)) {
result[i] = .urcval(arg = p[i], nobs = n.sample, niv = 1,
itt = itt, itv = itv, nc = 1) }

# Return Value:
result
}

"unitrootTable" <-
function(trend = c("c", "nc", "ct", "ctt"), statistic = c("t", "n"))
{   # A function implemented by Diethelm Wuertz

# Description:
#   Returns McKinnon's unitroot finite sample test table

# FUNCTION:

# Match Arguments:
trend = match.arg(trend)
statistic = match.arg(statistic)

# Set P Values and Sample Size:
p = c("0.010", "0.025", "0.050", "0.100",
"0.900", "0.950", "0.975", "0.990")
N = c(" 25", " 50", "100", "250", "500", "Inf")

# Create table:
table = NULL
for (n in N[-length(N)]) {
size = as.integer(n)
table = rbind(table, qunitroot(as.numeric(p), size, trend, statistic))
}
table = rbind(table, qunitroot(as.numeric(p), Inf, trend, statistic))

table = round(table, digits = 3)
rownames(table) = N
colnames(table) = p

attr(table, "control") <-
c(table = "unitroot", trend = trend, statistic = statistic)

# Return Value:
table
}

.strsplitUrcval =
function(x, sep = " ")
{   # A function implemented by Diethelm Wuertz

# Description:
#   Implements strsplit() function for SPlus compatibility

# FUNCTION:

# Split:
# if (exists("strsplit")) {
# R:
ans = strsplit(x = x , split = sep)
# } else {
#     # Splus:
#     ans = lapply(lapply(X = x, FUN = unpaste, sep = sep), unlist)
# }

# Return Value:
ans
}

".urcval" <-
function (arg, nobs = 0, niv = 1, itt = 1, itv = 1, nc = 1)
{   # A function implemented by Diethelm Wuertz

# Description:
#   Implements the unit root statists distribution

# Arguments:
#   arg - level of test (between .0001 and .9999) if nc = 1,
#       else test statistic if nc = 2
#   nobs - sample size (0 for asymptotic)
#   niv - number of integrated variables
#   itt - 1 or 2 for tau or z test
#   itv - 1, 2, 3, 4 for nc, c, ct, ctt
#   nc - 1 or 2 for critical value or P value

# Value:
#   val - critical value if nc = 1 (returned by routine),
#       else P value if nc = 2 (returned by routine)

# FUNCTION:

probs = .probsUrcval
cnorm = probs[, 2]
probs = probs[, 1]

# Read from appropriate urc Table:
# fnames = 'urc-1.tab' .... 'urc-12.tab'  (niv)
# Skip copyright line and groups of 222 lines as necessary
skip = 886*(itt-1) + 2*itt + (itv-1)*222

# Filename:
# root = paste(.tableDir(), "/.urc", sep = "")
# fname = paste(root, as.character(niv), ".tab", sep = "")

# Get Data:
TABLE = get(paste(".urc", as.character(niv), sep = ""))

# parms = scan(fname, what = "", skip = skip - 1, nlines = 1, quiet = TRUE)
parms = .strsplitUrcval(TABLE[skip], sep = " ")[[1]]
parms = parms[parms != ""]
nz = as.numeric(parms[2])
nreg = as.numeric(parms[3])
model = as.numeric(parms[4])
minsize = as.numeric(parms[5])

nvar = 4
if (model == 2 || model == 4) nvar = 3
nlines = 221
# scan(fname, skip = skip, nlines = 221, quiet = TRUE)
# beta = matrix(SCAN, byrow = TRUE, ncol = nvar+1)
beta = matrix(TABLE[(skip+1):(skip+nlines)], ncol = 1)
beta = unlist(apply(beta, 2, .strsplitUrcval))
beta = beta[beta != ""]
beta = matrix(as.numeric(beta), byrow = TRUE, nrow = nlines)
wght = t(beta[, nvar+1])
beta = t(beta[, 1:4])

# Check for Number of Observations:
if (nobs != 0 && nobs < minsize)
print("Warning: Specified sample size may be too small")

# Urcvals:
ans = NULL
for (i in 1:length(arg)) {
# Set size and stat and check for level
size = stat = arg[i]
# if (nc == 1)
#    stop("Level must be between .0001 and .9999")

# Calculate:
np = 9
cval = pval = 0.0
precrt = 2.0

# Call J. G. McKinnon's Fortran Subroutines:
if (nc == 1) {
if (min(size) < 0.0001 || max(size) > 0.9999) {
ans = c(ans, NA)
} else {
result = .Fortran("fcrit",
as.double(probs), as.double(cnorm), as.double(beta),
as.double(wght), as.double(cval), as.double(size),
as.double(precrt), as.integer(nobs), as.integer(model),
as.integer(nreg), as.integer(np), as.integer(0),
PACKAGE = "urca")
ans = c(ans, result[[5]])
}
}
if (nc == 2) {
result = .Fortran("fpval",
as.double(beta), as.double(cnorm), as.double(wght),
as.double(probs), as.double(pval), as.double(stat),
as.double(precrt), as.integer(nobs), as.integer(model),
as.integer(nreg), as.integer(np), as.integer(0),
PACKAGE = "urca")
ans = c(ans, result[[5]])
}
}

# Return Value:
ans
}

".probsUrcval" <-
structure(list(

V1 = c(1.0e-04, 2.0e-04, 5.0e-04, 0.001, 0.002, 0.003,
0.004, 0.005, 0.006, 0.007, 0.008, 0.009, 0.01, 0.015, 0.02,
0.025, 0.03, 0.035, 0.04, 0.045, 0.05, 0.055, 0.06, 0.065, 0.07,
0.075, 0.08, 0.085, 0.09, 0.095, 0.1, 0.105, 0.11, 0.115, 0.12,
0.125, 0.13, 0.135, 0.14, 0.145, 0.15, 0.155, 0.16, 0.165, 0.17,
0.175, 0.18, 0.185, 0.19, 0.195, 0.2, 0.205, 0.21, 0.215, 0.22,
0.225, 0.23, 0.235, 0.24, 0.245, 0.25, 0.255, 0.26, 0.265, 0.27,
0.275, 0.28, 0.285, 0.29, 0.295, 0.3, 0.305, 0.31, 0.315, 0.32,
0.325, 0.33, 0.335, 0.34, 0.345, 0.35, 0.355, 0.36, 0.365, 0.37,
0.375, 0.38, 0.385, 0.39, 0.395, 0.4, 0.405, 0.41, 0.415, 0.42,
0.425, 0.43, 0.435, 0.44, 0.445, 0.45, 0.455, 0.46, 0.465, 0.47,
0.475, 0.48, 0.485, 0.49, 0.495, 0.5, 0.505, 0.51, 0.515, 0.52,
0.525, 0.53, 0.535, 0.54, 0.545, 0.55, 0.555, 0.56, 0.565, 0.57,
0.575, 0.58, 0.585, 0.59, 0.595, 0.6, 0.605, 0.61, 0.615, 0.62,
0.625, 0.63, 0.635, 0.64, 0.645, 0.65, 0.655, 0.66, 0.665, 0.67,
0.675, 0.68, 0.685, 0.69, 0.695, 0.7, 0.705, 0.71, 0.715, 0.72,
0.725, 0.73, 0.735, 0.74, 0.745, 0.75, 0.755, 0.76, 0.765, 0.77,
0.775, 0.78, 0.785, 0.79, 0.795, 0.8, 0.805, 0.81, 0.815, 0.82,
0.825, 0.83, 0.835, 0.84, 0.845, 0.85, 0.855, 0.86, 0.865, 0.87,
0.875, 0.88, 0.885, 0.89, 0.895, 0.9, 0.905, 0.91, 0.915, 0.92,
0.925, 0.93, 0.935, 0.94, 0.945, 0.95, 0.955, 0.96, 0.965, 0.97,
0.975, 0.98, 0.985, 0.99, 0.991, 0.992, 0.993, 0.994, 0.995,
0.996, 0.997, 0.998, 0.999, 0.9995, 0.9998, 0.9999),

V2 = c(-3.71901649,
-3.5400838, -3.29052673, -3.09023231, -2.87816174, -2.74778139,
-2.65206981, -2.5758293, -2.51214433, -2.45726339, -2.40891555,
-2.36561813, -2.32634787, -2.17009038, -2.05374891, -1.95996398,
-1.88079361, -1.81191067, -1.75068607, -1.69539771, -1.64485363,
-1.59819314, -1.55477359, -1.51410189, -1.47579103, -1.43953147,
-1.40507156, -1.37220381, -1.34075503, -1.31057911, -1.28155157,
-1.25356544, -1.22652812, -1.20035886, -1.17498679, -1.15034938,
-1.12639113, -1.10306256, -1.08031934, -1.05812162, -1.03643339,
-1.01522203, -0.99445788, -0.97411388, -0.95416525, -0.93458929,
-0.91536509, -0.89647336, -0.8778963, -0.85961736, -0.84162123,
-0.82389363, -0.80642125, -0.78919165, -0.77219321, -0.75541503,
-0.73884685, -0.72247905, -0.70630256, -0.69030882, -0.67448975,
-0.65883769, -0.64334541, -0.62800601, -0.61281299, -0.59776013,
-0.58284151, -0.5680515, -0.55338472, -0.53883603, -0.52440051,
-0.51007346, -0.49585035, -0.48172685, -0.4676988, -0.45376219,
-0.43991317, -0.42614801, -0.41246313, -0.39885507, -0.38532047,
-0.37185609, -0.35845879, -0.34512553, -0.33185335, -0.31863936,
-0.30548079, -0.2923749, -0.27931903, -0.26631061, -0.2533471,
-0.24042603, -0.22754498, -0.21470157, -0.20189348, -0.18911843,
-0.17637416, -0.16365849, -0.15096922, -0.13830421, -0.12566135,
-0.11303854, -0.10043372, -0.08784484, -0.07526986, -0.06270678,
-0.05015358, -0.03760829, -0.02506891, -0.01253347, 0, 0.01253347,
0.02506891, 0.03760829, 0.05015358, 0.06270678, 0.07526986, 0.08784484,
0.10043372, 0.11303854, 0.12566135, 0.13830421, 0.15096922, 0.16365849,
0.17637416, 0.18911843, 0.20189348, 0.21470157, 0.22754498, 0.24042603,
0.2533471, 0.26631061, 0.27931903, 0.2923749, 0.30548079, 0.31863936,
0.33185335, 0.34512553, 0.35845879, 0.37185609, 0.38532047, 0.39885507,
0.41246313, 0.42614801, 0.43991317, 0.45376219, 0.4676988, 0.48172685,
0.49585035, 0.51007346, 0.52440051, 0.53883603, 0.55338472, 0.5680515,
0.58284151, 0.59776013, 0.61281299, 0.62800601, 0.64334541, 0.65883769,
0.67448975, 0.69030882, 0.70630256, 0.72247905, 0.73884685, 0.75541503,
0.77219321, 0.78919165, 0.80642125, 0.82389363, 0.84162123, 0.85961736,
0.8778963, 0.89647336, 0.91536509, 0.93458929, 0.95416525, 0.97411388,
0.99445788, 1.01522203, 1.03643339, 1.05812162, 1.08031934, 1.10306256,
1.12639113, 1.15034938, 1.17498679, 1.20035886, 1.22652812, 1.25356544,
1.28155157, 1.31057911, 1.34075503, 1.37220381, 1.40507156, 1.43953147,
1.47579103, 1.51410189, 1.55477359, 1.59819314, 1.64485363, 1.69539771,
1.75068607, 1.81191067, 1.88079361, 1.95996398, 2.05374891, 2.17009038,
2.32634787, 2.36561813, 2.40891555, 2.45726339, 2.51214433, 2.5758293,
2.65206981, 2.74778139, 2.87816174, 3.09023231, 3.29052673, 3.5400838,
3.71901649)),

.Names = c("V1", "V2"),

class = "data.frame",

row.names = c(
"1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13",
"14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24",
"25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35",
"36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46",
"47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57",
"58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68",
"69", "70", "71", "72", "73", "74", "75", "76", "77", "78", "79",
"80", "81", "82", "83", "84", "85", "86", "87", "88", "89", "90",
"91", "92", "93", "94", "95", "96", "97", "98", "99", "100",
"101", "102", "103", "104", "105", "106", "107", "108", "109",
"110", "111", "112", "113", "114", "115", "116", "117", "118",
"119", "120", "121", "122", "123", "124", "125", "126", "127",
"128", "129", "130", "131", "132", "133", "134", "135", "136",
"137", "138", "139", "140", "141", "142", "143", "144", "145",
"146", "147", "148", "149", "150", "151", "152", "153", "154",
"155", "156", "157", "158", "159", "160", "161", "162", "163",
"164", "165", "166", "167", "168", "169", "170", "171", "172",
"173", "174", "175", "176", "177", "178", "179", "180", "181",
"182", "183", "184", "185", "186", "187", "188", "189", "190",
"191", "192", "193", "194", "195", "196", "197", "198", "199",
"200", "201", "202", "203", "204", "205", "206", "207", "208",
"209", "210", "211", "212", "213", "214", "215", "216", "217",
"218", "219", "220", "221")
)

".urc1" <-
c("Copyright (C) James G. MacKinnon, 1995", "dfnc      0  1  2   20",
" -.38929681e+01 -.10711437e+02 -.55619955e+02  .33188192e-02",
" -.37185872e+01 -.95896921e+01 -.34166532e+02  .24951489e-02",
" -.34759164e+01 -.78746051e+01 -.17490657e+02  .15559156e-02",
" -.32842708e+01 -.64108912e+01 -.11983755e+02  .11445964e-02",
" -.30830457e+01 -.50567633e+01 -.68847143e+01  .84100765e-03",
" -.29598602e+01 -.42584716e+01 -.58142463e+01  .71049934e-03",
" -.28698825e+01 -.37289550e+01 -.58714971e+01  .62391151e-03",
" -.27977077e+01 -.34146427e+01 -.37615300e+01  .58693244e-03",
" -.27380050e+01 -.31208498e+01 -.30462883e+01  .52576407e-03",
" -.26868436e+01 -.28722476e+01 -.25438563e+01  .49052976e-03",
" -.26416852e+01 -.26793402e+01 -.18769783e+01  .46804316e-03",
" -.26012597e+01 -.25000004e+01 -.16307933e+01  .44346134e-03",
" -.25649446e+01 -.23127399e+01 -.20306605e+01  .43039003e-03",
" -.24206178e+01 -.17291886e+01 -.13466493e+01  .36467475e-03",
" -.23133304e+01 -.13423615e+01 -.13432257e+01  .32107164e-03",
" -.22273143e+01 -.10746264e+01 -.87624270e+00  .29789755e-03",
" -.21549047e+01 -.84657628e+00 -.10780188e+01  .27830583e-03",
" -.20921655e+01 -.67744316e+00 -.10430697e+01  .26027602e-03",
" -.20364584e+01 -.54192487e+00 -.96965194e+00  .25249134e-03",
" -.19864146e+01 -.41616890e+00 -.11334045e+01  .24079995e-03",
" -.19407684e+01 -.33025231e+00 -.67821426e+00  .23323022e-03",
" -.18988585e+01 -.22970773e+00 -.85640849e+00  .22075141e-03",
" -.18598488e+01 -.14639728e+00 -.10428806e+01  .21334955e-03",
" -.18233573e+01 -.89663803e-01 -.80855945e+00  .20963010e-03",
" -.17891398e+01 -.36466865e-01 -.63243896e+00  .20834232e-03",
" -.17567993e+01  .11402654e-01 -.51066497e+00  .20539933e-03",
" -.17262105e+01  .66220956e-01 -.63708003e+00  .19964762e-03",
" -.16969838e+01  .10236824e+00 -.46672787e+00  .19574132e-03",
" -.16690859e+01  .14265332e+00 -.45061418e+00  .18888062e-03",
" -.16424271e+01  .18701823e+00 -.66084335e+00  .18426555e-03",
" -.16167279e+01  .21626789e+00 -.64616991e+00  .18128089e-03",
" -.15920520e+01  .24778988e+00 -.63597502e+00  .17954902e-03",
" -.15682114e+01  .27323562e+00 -.61618157e+00  .17773495e-03",
" -.15452740e+01  .29991006e+00 -.60544565e+00  .17142168e-03",
" -.15230643e+01  .33148333e+00 -.76580637e+00  .16769202e-03",
" -.15014865e+01  .35136387e+00 -.69024691e+00  .16887147e-03",
" -.14805700e+01  .37478667e+00 -.72930388e+00  .16872218e-03",
" -.14602522e+01  .39420657e+00 -.70443601e+00  .16401731e-03",
" -.14404242e+01  .41028681e+00 -.64338518e+00  .16224607e-03",
" -.14210785e+01  .42119200e+00 -.55548400e+00  .16193196e-03",
" -.14022406e+01  .43747746e+00 -.57670820e+00  .16097849e-03",
" -.13837876e+01  .44575298e+00 -.43236279e+00  .15803832e-03",
" -.13657717e+01  .45528883e+00 -.35165569e+00  .15694908e-03",
" -.13481032e+01  .46306181e+00 -.31093184e+00  .15603528e-03",
" -.13309144e+01  .47972473e+00 -.39121260e+00  .15557033e-03",
" -.13139547e+01  .48814175e+00 -.38006723e+00  .15236727e-03",
" -.12973931e+01  .49859437e+00 -.35456698e+00  .14909593e-03",
" -.12811030e+01  .50420631e+00 -.25583170e+00  .14793470e-03",
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