[R-sig-finance] Puzzled in arch estimation

[Ajay Narottam Shah]

I have attached a time-series r. I find that I am able to use the
garch() function in the tseries package to estimate a GARCH(1,1)
model. But it fails to get convergence for the GARCH(1,0) -- i.e.,
ARCH(1) -- model. I seem to think that the latter is actually a simple
likelihood function and it's much easier to get convergence for it.

There's a mysterious statement towards the end of the time-series
chapter of the MASS book which says that the garch() function requires
the series to be mean 0 (a statement which I didn't find in the
documentation of tseries). So I also did this one more way: To first
estimate an AR(1) model, and focus on the residuals. Once again, I get
the same pathology: GARCH(1,1) works but ARCH(1) does not.

I fed the same series to stata and it estimates AR(1)-ARCH(1) easily,
so this doesn't seem to be a pathological case of bad
data. Difficulties in convergence can, of course, always come about in
realworld data. I wondered if I'm missing something fundamental.

Here's some code which illustrates my problem --

library(tseries)
# take the definition of `r' ahead and then say

m.ar1 <- arima(r, order=c(1,0,0))
m.garch11 <- garch(m.ar1$residual, order=c(1,1)) # Seems to be okay
# BUT
m.arch1 <- garch(m.ar1$residual, order=c(1,0))
# breaks.

Alternatively, equally, one can do:

m.garch11 <- garch(r, order=c(1,1)) # Seems to be okay
# BUT
m.arch1 <- garch(r, order=c(1,0))
# breaks.

    -ans.

r <- c(0, 0.579142, 1.03736, -0.208672, -0.765883, 0.281692,
-0.397706, 0.328364, -0.125584, -0.193477, -0.0610791, -0.990004,
-0.71914, -0.829374, -2.08766, 0.756307, -0.637729, 0.134032, 1.63858,
-0.627174, 0.169323, -1.11391, -1.08862, -1.46264, -1.14154,
-0.446539, -3.38369, -1.61522, 1.17325, -1.00522, -0.578756,
-0.677731, -1.83069, -1.39811, -1.74083, 2.51195, -1.13877, -2.06056,
0.169783, 1.98911, 1.26197, -1.07611, 0.325627, 1.42208, 2.21524,
-1.28735, -1.10025, 0.235853, 1.10524, -0.555269, -0.104693,
-0.088162, 0.123343, 0.204409, 1.67633, 0.0161745, 0.5192, 1.87783,
-0.864954, -0.660769, -0.0564514, -0.844007, -0.492193, -0.705106,
-0.557051, -1.71258, -0.0664624, -0.614921, 1.09121, 0.214559,
-0.438513, -0.32201, -1.32279, -0.970354, -0.571795, 0.0379108,
-1.36068, -1.72062, -0.461166, 1.93922, 1.87047, 0.218172, 2.45879,
5.45718, 2.66156, -1.85931, 0.679358, 5.04796, 5.24155, -1.41465,
0.864773, 2.36954, -0.548473, -2.23819, -0.166255, -2.10307, 2.44766,
0.383161, 0.570884, -0.705994, -0.0057834, -3.45401, 0.69873,
-0.063715, 0.40676, -0.44536, -0.989944, -1.36045, 0.0988081, 1.61739,
-0.10033, -0.940164, -2.0354, -1.57128, 1.93312, -0.985401, -0.222106,
0.329964, 1.76344, 2.34919, -1.21275, 0.959598, 0.848386, 1.01093,
-0.249911, 2.07488, -0.297048, 0.0197712, -0.398818, 0.681907,
1.37138, 1.16532, 3.48685, 2.29011, 0.893023, -2.21592, -1.0093,
4.39966, -2.14394, 0.250645, -0.469434, -0.358823, 2.08695, -0.512225,
-1.11659, -2.85231, 0.46674, 1.40263, -1.6371, -1.09721, 0.874134,
1.58375, 0.94534, 1.12451, -1.16305, -2.86807, -0.833724, 0.568613,
-0.382739, 0.740059, -1.86052, -0.18797, 3.14841, -1.28442, 0.636933,
1.72372, -0.291713, 0.67605, 1.48735, 0.319893, 0.695452, 0.14971,
1.80418, 0.388463, 2.33975, -0.897786, -0.288935, -1.1847, 0.124064,
-1.03658, -0.923538, -1.67069, -0.705635, 0.636449, -0.444643,
-1.16541, -0.814853, -1.83491, 0.738011, 0.458506, 0.953355, -1.34203,
-0.196747, 0.990823, -0.739901, 0.369263, -0.910496, 2.24238,
0.955673, 0.0527268, 0.570173, -3.02393, -2.10133, -0.633178,
-1.08236, -1.65647, -1.86058, 2.73012, -0.612611, -0.356596,
-0.062947, 0.311442, 1.25523, -0.895673, -0.12806, -0.554569,
-0.752702, -0.582504, -1.60638, -2.68886, 0.172043, 2.21104, 0.297798,
1.04623, -0.363052, 0.557391, 1.21563, -0.119828, 0.305617, 0.769626,
-1.32803, 0.30639, 1.07178, -0.519918, -1.78013, -1.26352, -0.984705,
-0.208016, -0.869041, -1.89919, 0.924764, 2.3627, -1.69055,
-0.0746883, -0.841788, 0.00722487, 0.245336, -1.24108, -1.26723,
-0.345814, -0.81799, -1.21966, -2.27452, -3.38817, -0.0114423,
0.0937883, 2.67338, 1.14764, -1.85919, 0.639173, -0.558492,
-0.0784384, 0.327911, 2.65603, 3.44349, -1.96603, 0.447127, -0.113197,
-1.02026, -1.86312, -0.28745, -1.84221, -0.966311, -1.71615, 0.955527,
1.10826, -0.484987, 1.23165, 0.623006, -0.834164, 0.551664, 1.08322,
-0.718242, -2.36401, -0.77759, -2.26618, 0.226714, 0.377107, -3.13461,
-0.436373, 0.585825, -1.2202, -1.32789, -2.66419, 1.77069, 0.740183,
0.0618475, -0.681191, 4.1304, -1.18008, -0.318427, 2.70967, 0.408714,
1.12908, 0.0209183, 2.72803, -0.269478, 0.232157, 3.0907, -1.40264,
4.40068, -1.33935, 0.494971, -0.414102, 0.107724, 1.90888, 1.04031,
2.45243, 0.0356952, 0.873102, 5.17076, -3.15939, -0.760762, -2.50171,
-1.70327, 2.73174, -0.121642, 2.33087, 1.24574, -0.451202, -1.70538,
-2.7731, -2.54589, 1.05954, 0.437318, 0.543972, 1.13535, 0.270374,
1.14478, 0.827591, 0.114819, 0.725794, 1.0495, -1.91509, 1.10306,
-0.868513, -1.15811, -2.74004, 0.139835, 0.284245, 2.43691, 5.94418,
4.5823, 0.429739, 0.862927, 1.38657, -0.499968, -4.40244, -2.50635,
2.08831, -0.719394, 0.336984, 0.233351, -0.772132, -1.16236, 0.261053,
0.623762, -0.28777, 0.0802815, -0.132263, -8.84046, 0.190874, 3.25022,
0.83961, -0.959419, -1.01412, 3.89917, -2.15347, 0.499568, -1.00663,
1.15454, 1.98046, 2.42401, -0.0754575, 1.05593, -0.360108, 0.205935,
-0.374743, -0.748997, 2.09618, -1.00985, -2.22284, 0.276995,
-0.382263, 0.919733, -0.0664326, -1.22742, -0.912367, 1.02283,
0.321089, 0.324831, 0.228659, 0.00475817, -0.845742, -0.461717,
-0.338018, -0.660004, -0.116925, 0.126662, 1.08465, 1.21585, 1.32809,
0.822934, 1.11138, 0.0782563, -0.354945, -0.750907, 0.598401, 2.15042,
1.44702, 1.38239, -0.582526, 0.802297, 1.82725, 0, -0.1251, -0.402241,
0.138588, 0.569655, 0.540751, 0.124046, 1.92635, 0.67284, 1.85695,
-0.66042, 0.0987248, -0.527662, -0.951024, 3.14631, 0.210042,
-1.46736, -2.82809, -0.312184, -0.0295814, -0.135341, -1.39791,
0.705659, 2.3127, -0.0624831, -1.24949, -0.28732, 0.729361, 0.636465,
1.95096, 0.888388, 1.45, 1.80306, 1.54323, -1.81852, -1.00531,
0.111319, -0.789856, -0.308859, -1.35088, -2.17762, -1.74217, 1.47129,
-1.40356, -1.7977, -1.40148, 0.648943, 1.43528, -2.93111, -2.64789,
-0.027153, 1.1207, 1.55875, 0.215683, 1.05844, 0.780069, 0.112175,
-0.432134, -0.0216558, -0.996896, -0.162007, -0.0745238, -0.523228,
-2.21533, -0.456261, -1.76317, 0.335841, 1.11442, 0.949288, 0.426497,
0.85646, -0.168926, -0.813049, 1.76508, 2.52396, -0.568844, -1.66028,
1.09687, 1.54393, 0.805579, 0.879127, -1.1214, -0.435006, -1.56798,
-1.31104, -1.40426, -8.19628, 6.95738, -1.98433, -0.115247, 0.570326,
-0.478118, -0.37397, -0.570569, -0.831509, 0.696509, -2.67677,
-2.18641, 0.249103, -1.48915, -2.19767, 0.736262, 1.05953, -2.46615,
2.95712, 0.606645, 2.89805, -2.20224, 0.846062, -0.276371, 0.0873574,
-1.85567, -0.540127, 0.248127, -2.48401, -1.24238, 0.179898,
-0.876837, 1.5116, 2.2703, 1.0717, -0.341103, 1.83509, 2.21184,
0.322857, -0.0616421, 0.690114, 1.63988, -1.91819, 1.95525, 0.16662,
0.461383, 0.500495, -1.15166, 0.30071, -2.30368, -2.31445, -3.72083,
0.330844, -0.15526, -0.795093, 0.820151, 1.93053, -0.571796,
0.0938805, -2.00032, -0.560848, -2.41025, -1.93916, -0.365825,
2.32056, 1.35566, -0.13833, -0.751342, 0.838461, 0.158669, -0.158669,
-1.2785, -0.499325, -0.23492, 1.85382, 1.74448, -0.287799, 0.875962,
-0.391724, 1.59245, 0.444731, 2.14139, 0.936674, 1.41941, 3.46963,
-3.21071, 2.6766, -0.827325, -0.175536, 1.65528, -1.23083, -0.281229,
-0.509143, 1.19469, -0.657852, 1.83391, 0.221805, 0.343054, 1.29831,
-0.289539, 2.30189, -1.53312, 0.956018, -1.36855, -0.70927, 2.92919,
0.632722, 1.3772, 1.15652, 0.0589499, 1.81869, -1.43216, -2.80223,
3.96121, -0.769763, 1.07602, -0.235815, 0.46283, -0.160921, -2.39888,
-0.704617, -0.808336, -1.51875, 0.374255, 0.71415, 2.20098, 0.248604,
-1.32598, -0.934026, -0.107673, -2.44718, -3.42747, 2.21905, -0.76725,
0.87, 0.173987, 1.7278, -1.33632, 0.0355129, -0.320071, -1.66117,
-1.22986, -1.42167, -1.1596, -0.888097, -3.29448, 1.39277, -0.669613,
-3.31631, -2.53823, 2.69413, -3.28434, -0.161102, 1.01424, -5.75916,
-0.733486, 7.04203, -2.10599, -4.59051, -3.68605, -0.523979, 3.68855,
2.56989, -0.840296, 2.64234, -0.788051, 0.0636977, -2.40057, -2.12593,
1.84834, 0.798028, 2.08157, 1.77414, 1.96792, -1.62513, 0.310607,
0.417796, 3.30588, -0.309227, -2.39112, -1.21476, 0.0207125, -3.29486,
-1.54223, -2.28101, 1.97078, 2.221, -0.561364, -0.128755, -2.76495,
0.0220726, 0.137844, -0.519281, -1.13631, -1.55821, -1.40383,
-0.741345, 1.40274, -0.938758, -1.11135, -2.62019, 0.700287, 3.56218,
-1.53702, 0.507216, 1.39749, 0.634524, -3.20189, 0.352403, -2.16324,
0.9481, 0.467747, 2.3411, 2.34956, 1.43815, 0.404758, 0.419658,
-0.852199, 2.28556, 0.0325857, -0.686539, -0.482298, -0.932807,
-0.439048, -0.0501407, 1.16345, 2.93636, 0.0160449, -0.756908,
-2.12392, -0.380512, -7.35853, 0.592946, 3.31426, -3.05447, 0.135529,
-1.57876, -2.30563, 3.22861, -0.940931, 0.459661, -0.987588, -2.75026,
0.357959, 0.705979, 3.3565, -0.43276, -0.925131, -0.192065, -0.409368,
-0.586867, -0.0971345, -0.279789, 0.999978, 1.39527, 2.7971, 0.467304,
0.0172657, 0.333219, -0.51754, -1.38165, 0.542165, 1.73486, -1.14359,
0.0462267, -0.940282, -1.15547, -0.686678, -2.07666, -1.46621,
-0.197129, 0.847359, -0.134606, 0.549519, -0.50055, 1.37355, 2.00784,
0.924542, 0.415315, 0.912293, 0.645759, -0.738351, -2.17139, 0.766242,
-2.53314, 0.594436, 2.50663, 0.105036, 0.16317, 0.279102, 2.15408,
-0.821688, 3.08046, -1.75994, 0.738011, 0.782739, 1.04156, 2.29382,
2.80961, 3.63583, -0.450485, -2.16926, -0.337549, -0.673298, -2.16519,
1.12815, -2.22588, 4.5585, -1.05497, -0.76042, 2.23839, -1.68193,
1.15548, -2.73314, -0.956536, 2.2511, -1.34244, -0.362474, -2.13739,
0.896136, 3.68368, 0.0625163, 1.05684, -1.63137, 0.454677, 1.05294,
0.453025, 0.292345, -2.32635, -0.441293, 0.838887, -0.350428,
-1.38224, 4.17226, 3.45535, 3.4874, -1.01766, 1.26454, 1.66, 0.581275,
0.0463564, -1.80042, 1.22407, 0.121122, -1.95578, 0.709625, 1.30666,
-1.09475, -0.240198, 0.249606, 0.931676, -0.950493, -0.746096,
-1.30241, 1.27396, 2.19923, -1.36355, -5.01828, 1.25763, 0.666588,
-1.0432, -2.67676, 0.482025, -0.396497, -2.6137, 7.5394, -7.70989,
2.74898, 0.150807, 0.125499, -1.51648, 0.0356479, -5.29562, 1.29612,
2.41884, 1.19294, -0.764518, 3.80016, 1.1046, 2.65198, 1.51198,
2.90225, 1.5147, 0.458037, 2.83575, 1.49131, -1.16087, 0.713655,
1.7177, -1.13756, -1.82039, 0.500556, 0.744012, -2.15193, -3.9566,
-0.915812, 4.5902, -0.753516, 0.120056, 1.0169, 1.60583, 2.04806,
-1.34494, -0.0515952, -1.79653, -1.3223, -0.569549, 2.43769, 2.42645,
-0.102063, 2.28406, 0.993139, -1.75709, -0.998134, -0.36467, 1.28315,
-0.0755192, -0.302648, -0.379603, 1.23057, 2.66891, 0.890154,
0.197187, 0.0281379, 0.796626, 4.77643, 0.462683, 1.0314, -1.31559,
0.495847, 1.8962, -2.61997, 1.9173, 0.673028, -0.464314, -1.25887,
-1.23674, 0.779486, 0.423313, -1.1799, -1.58095, -0.353446, 3.16709,
-0.233989, -0.492407, 0.828123, -1.36495, 0.42285, -0.441939,
-1.35701, 1.38755, 1.048, 2.95141, -1.35509, 0.170858, 1.64891,
0.941021, -0.798755, 2.2242, 1.06384, 0.359143, -0.747904, -0.0921104,
-2.50143, -0.0654355, 1.10303, -0.501182, 1.16792, -0.185953,
-0.416069, -1.48827, 0.302341, -1.72424, 0.6271, -0.136152, -0.535363,
2.61976, 0.829612, 1.01415, -1.62402, -0.74766, 2.58742, -0.155565,
-0.703053, -2.22672, 0.425386, 1.05023, 5.3848, 0.644288, 0.320594,
-0.0101083, 0.835533, 0.593039, -3.42292, -0.724491, 2.30013,
-1.65818, -1.6022, 1.35764, -1.64121, -0.83435, -0.208794, -3.14516,
-3.13785, -4.27351, 4.78148, -0.436321, 0.781019, 2.0546, 0.369402,
0.116754, 1.29698, 0.0359881, -1.16173, -0.79306, -0.363911,
-0.405905, 0.883496, -0.176076, 0.979146, 1.4223, 0.977323, -0.644532,
-1.07391, -0.615765, 0.911432, 1.43697, 0.647366, 1.73729, 0.15928,
-0.450795, 0.61673, -0.543771, -0.840502, -2.08083, 0.225028, 1.29738,
-0.0281789, 0.221694, -0.0527398, 4.13367, 0.447805, -1.99169,
-1.86094, 0.702783, 2.34031, 0.277327, 7.27706, 2.87865, -2.65281,
1.35684, -0.26618, 1.21064, -3.77215, 3.2718, -0.209476, 0.0832267,
-0.689477, -0.304509, 1.73687, -2.08602, 1.21056, -0.432874, -1.70004,
1.09709, -0.299719, -3.36407, 0.213199, 2.45431, 0.62149, 0.11571,
2.27736, 1.58519, 1.60485, 1.26735, 2.58436, -0.657051, -2.43409,
0.500931, 1.79548, -1.40469, 2.05694, -0.82748, -2.48306, 2.07685,
-1.25203, 0.704926, -4.01256, 3.43909, -0.94743, -2.41917, 1.94355,
0.840403, -2.1609, -1.21356, -2.67791, -2.65865, 0.406043, 3.3293,
-3.63928, -0.359113, 2.09785, -2.30363, 1.03429, -0.421389, 0.360844,
-0.662011, -0.56311, -1.36781, 0.411335, -7.20226, 0.457603, 1.26751,
6.92613, 3.52386, 0.719661, -1.98617, -4.76089, -5.07164, -2.01172,
-0.698646, 0.758707, -1.97249, -2.07837, 5.48509, -1.34597, -0.733149,
-5.33703, -1.31347, 4.78471, 2.98636, -4.11545, 0.984116, -1.1234,
-4.394, -1.6813, 1.2742, 0.583249, 0.366623, -1.40115, -1.98336,
-2.79906, -0.69993, 0.934852, 0.946233, 2.19589, 2.76077, 2.54541,
2.61271, -2.3046, 2.94005, 1.09885, 1.21359, 0.603066, 2.30141,
0.242251, -1.8435, -0.522049, 0.181286, 0.67691, 2.19338, 1.44153,
0.555585, -2.14276, 0.884125, -1.08431, -1.4057, 0.182384, 1.07377,
1.50897, -1.41037, 1.60451, 1.06768, 0.971249, -0.607985, 0.0527287,
-0.52523, 0.58781, 0.969895, -0.703548, -0.847533, -2.01385, -1.12481,
-1.88353, -0.811193, -1.91042, -5.85803, 2.33637, -2.29843, 1.49082,
-0.318132, -0.0712504, -0.451179, 0.379878, -0.802824, -0.204561,
-0.589501, 2.62024, -0.0483173, -1.26828, -1.30746, 0.544007, 2.51385,
-0.746425, 1.2336, 0.894336, 0.795948, 0.350529, 0.0649117, -0.411821,
-0.828764, -0.157075, 0.60139, 1.31046, 2.38507, 0.035014, 0.49588,
0.306077, 0.712855, 0.433527, 0.772918, -0.786652, -0.747905,
-1.96338, -4.53615, -2.79652, 1.9475, -0.97653, -4.88484, 2.03993,
-1.9255, 1.9255, -2.04388, 0.413704, 0.810609, 1.22492, -1.01064,
0.0194571, -1.38701, -2.26244, -3.03606, 0.361274, -2.476, -0.110535,
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0.884108, 1.80656, 2.02422, 0.553187, 0.47356, 0.699823, 0.240623,
0.831379, 0.654346, -1.60385, -1.13777, 2.18759, 2.1244, 0.830793,
0.153996, 0.979195, 0.0681458, 2.66113, -0.289164, 0.756309, 1.04701,
0.780985, -3.10219, 3.63845, 1.66263, 0.055942, 1.14918, 1.41997,
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1.05179, 2.59112, 0.0512643, 0.72094, 0.280958, -1.7706, 0.0273386,
1.78205, 0.657203, 0.502618, 0.206228, 1.46372, 0.710945, -0.172936,
1.30972, 1.2703, 0.594222, -0.495876, 1.58265, 1.55527, 1.99408,
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2.66662, 0.170031, -1.34271, 0.920911, 0.940259, -1.9203, -2.27832,
1.80923, -2.19933, -3.69341, -3.00988, 4.25984, 3.04641, -2.20827,
-1.05216, -1.85315, -2.27743, 2.96301, -0.976102, 1.6025, 2.53355,
0.00265855, 0.569953, -0.328321, 1.48993, -0.00261291, 0.341711,
-0.190275, -3.08124, -0.304504, -2.42852, 0.724611, -1.91517,
-1.18225, 1.93495)

-- 
Ajay Shah                                      http://www.mayin.org/ajayshah  
ajayshah at mayin.org                             http://ajayshahblog.blogspot.com
<*(:-? - wizard who doesn't know the answer.