Dear all,
I am stuck with a problem that might be trivial for most of you (and
therefore is a bit embarrassing for me...):
I want to calculate a generalized least squares regression using two
time series (Y depending on X) with an autoregressive correlation
structure of order two (the data along time are given below). I use
'gls' from package 'nlme':
Calib.gls <- gls(Y~X, data=my.data,
correlation=corARMA(form=~Time,p=2,q=0), method="ML")
For reasons I do not understand, gls results in parameter estimate(s):
Phi1 Phi2
1.3066817 -0.3898277
Phi1 is larger than one... but how is this possible?
When I run the same regression with those parameters
Calib.gls <- gls(Y~X, data=my.data,
correlation=corARMA(value=c(1.3066817,-0.3898277),form=~Time,p=2,q=0,fixed=T),
method="ML")
I get the following error (as expected):
Error in corARMA(value = c(1.3066817, -0.3898277), form = ~Time, p = 2, :
Parameters in ARMA structure must be < 1 in absolute value
I did quite an extensive search on this strange result. The only thing I
found was an e-mail by Spencer Graves who suggested to shrink the
autoregressive parameters:
http://tolstoy.newcastle.edu.au/R/help/05/12/17416.html
But this sounds a bit like brute force to me.
What's wrong with the parameter estimation?
Any help would be highly appreciated!
Cheers, Christian
Time X Y
1 1873 -2.8950 156.4850
2 1874 -2.8675 156.2996
3 1875 -2.5850 156.1142
4 1876 -2.7500 155.4740
5 1877 -2.9525 154.8338
6 1878 -2.8425 156.0594
7 1879 -2.6100 157.2850
8 1880 -2.5550 157.2242
9 1881 -2.5450 157.1633
10 1882 -2.2375 158.1989
11 1883 -2.1825 159.2167
12 1884 -2.3575 160.2346
13 1885 -2.6950 160.9188
14 1886 -3.0025 162.6746
15 1887 -3.2450 161.0567
16 1888 -3.2300 159.4388
17 1889 -3.5525 158.9550
18 1890 -3.3375 157.3102
19 1891 -3.0575 156.8785
20 1892 -2.9150 154.2640
21 1893 -3.1250 152.9235
22 1894 -2.6475 152.4969
23 1895 -2.6225 151.1264
24 1896 -2.4800 150.9058
25 1897 -2.2825 151.7713
26 1898 -1.9725 152.5223
27 1899 -2.2050 151.2126
28 1900 -2.2225 153.0090
29 1901 -2.3850 152.0028
30 1902 -2.5500 153.5013
31 1903 -2.7250 154.7467
32 1904 -2.8350 156.6052
33 1905 -2.8925 157.2547
34 1906 -2.7625 158.1382
35 1907 -2.8950 159.0217
36 1908 -2.7850 159.9052
37 1909 -2.5875 157.1498
38 1910 -2.4025 156.6411
39 1911 -2.4825 156.1325
40 1912 -2.2050 155.6238
41 1913 -2.2700 158.2547
42 1914 -2.1475 159.1337
43 1915 -2.5125 159.1251
44 1916 -2.6450 161.1250
45 1917 -2.9700 158.5752
46 1918 -2.9100 156.0254
47 1919 -2.8500 153.4756
48 1920 -2.5525 154.3430
49 1921 -2.4425 155.4953
50 1922 -2.2900 156.6475
51 1923 -2.3200 157.7997
52 1924 -2.4075 160.5885
53 1925 -2.3300 160.3871
54 1926 -2.2275 161.6844
55 1927 -2.4725 160.1275
56 1928 -2.4050 156.8495
57 1929 -2.4550 155.8737
58 1930 -2.7650 156.7204
59 1931 -2.8375 156.9264
60 1932 -2.6025 156.8622
61 1933 -2.7850 158.0349
62 1934 -2.6425 160.3390
63 1935 -2.4750 162.1231
64 1936 -2.5775 162.2523
65 1937 -2.5225 162.3814
66 1938 -2.4900 156.1106
67 1939 -2.8625 154.4128
68 1940 -2.9775 154.4742
69 1941 -2.6400 154.5357
70 1942 -2.6925 153.9134
71 1943 -2.6250 154.1395
72 1944 -2.2500 155.8623
73 1945 -2.1150 154.9227
74 1946 -1.9875 152.7174
75 1947 -1.7175 154.1170
76 1948 -1.5450 154.3610
77 1949 -1.7300 154.3788
78 1950 -1.6025 157.3742
79 1951 -2.0350 158.5156
80 1952 -2.1750 159.6570
81 1953 -2.2150 159.6214
82 1954 -2.2800 159.5859
83 1955 -2.3825 159.3992
84 1956 -2.2525 159.2124
85 1957 -2.1775 159.0257
86 1958 -2.1800 158.8390
87 1959 -1.9800 157.9863
88 1960 -2.0825 157.1336
89 1961 -2.4000 156.2810
90 1962 -2.4250 155.4283
91 1963 -2.5900 154.8056
92 1964 -2.5500 154.1829
93 1965 -2.4700 153.8111
94 1966 -2.0950 153.9308
95 1967 -2.2675 153.3540
96 1968 -2.3675 153.7303
97 1969 -2.4875 155.9720
98 1970 -2.3150 157.2869
99 1971 -2.4525 159.7154
100 1972 -2.2550 159.0574
101 1973 -2.1025 158.7933
102 1974 -2.0250 157.7304
103 1975 -2.2000 156.6423
104 1976 -2.1225 154.8109
105 1977 -2.3350 153.9554
106 1978 -2.3650 153.5561
107 1979 -2.4400 153.9316
108 1980 -2.4825 154.3071
109 1981 -2.4150 156.0099
110 1982 -2.4750 156.2076
111 1983 -2.3875 155.6581
112 1984 -2.4025 155.1085
113 1985 -2.3425 155.2312
114 1986 -2.1300 152.8298
115 1987 -1.6550 151.7012
116 1988 -1.3775 150.5727
117 1989 -1.4125 148.7033
118 1990 -1.3150 147.1400
119 1991 -1.3600 147.5766
120 1992 -1.5225 148.0133
121 1993 -1.5050 149.6488
122 1994 -1.2525 151.8252
123 1995 -1.1700 151.1291
124 1996 -1.1675 150.4994
125 1997 -1.2700 149.4424
126 1998 -1.4000 148.3853
127 1999 -1.3325 148.3436
128 2000 -1.1625 148.3019
129 2001 -1.2175 146.5756
130 2002 -1.1950 144.8493
--
-----------------------------------------------
Oeschger Centre for Climate Change Research, Institute of Geography& Institute of Plant Sciences
University of Bern
http://www.stomatocysts.unibe.ch/kamenik
mailto: christian.kamenik at giub.unibe.ch
Postal address:
Dr. Christian Kamenik
Institute of Geography
Erlachstrasse 9a, Trakt 3
3012 Bern, Switzerland
Tel. +41 (0)31 631 5091
Fax +41 (0)31 631 43 38