Zeitreihenanalyse - Übung 10
From StatWiki
Exercise
Fit an AR model of order 1 to the growth rates of the quarterly GDP and plot its spectral density.
Exercise
Fit an ARMA(1,2) model to the growth rates of the quarterly GDP
GDPC1 <- readdataSK("GDPC1.txt","table")
GDP <- ts(data=GDPC1[,2])
d <- diff(log(GDP),k=-1); n <- length(d)
m <- floor(n/2)
d.dm <- d-mean(d) # d is demeaned
ms = c(outer(0:4, 0:4, function(p,q) { apply(cbind(p,q), 1, function(row) {
p = row[1]; q = row[2]
arima(d.dm,order=c(p,0,q),include.mean=FALSE,transform.pars=TRUE)
}) }))
ms[sort(sapply(ms, function(x) x$aic),index.return=TRUE)$ix[1:3]]
#[[1]]Call: arima(x = d.dm, order = c(p, 0, q), include.mean = FALSE, transform.pars = TRUE)
Coefficients:
ar1 ar2 ar3 ma1 ma2 1.6593 -1.2884 0.2198 -1.4039 1.000s.e. 0.0635 0.0931 0.0629 0.0158 0.018
sigma^2 estimated as 7.708e-05: log likelihood = 813.21, aic = -1614.43
[[2]]
Call: arima(x = d.dm, order = c(p, 0, q), include.mean = FALSE, transform.pars = TRUE)
Coefficients:
ar1 ar2 ar3 ma1 ma2 ma3 1.7645 -1.4404 0.3213 -1.5128 1.1518 -0.1081s.e. 0.1984 0.2874 0.1920 0.2027 0.2831 0.2008
sigma^2 estimated as 7.701e-05: log likelihood = 813.35, aic = -1612.71
[[3]]
Call: arima(x = d.dm, order = c(p, 0, q), include.mean = FALSE, transform.pars = TRUE)
Coefficients:
ar1 ar2 ar3 ar4 ma1 ma2 1.7117 -1.2048 0.0595 0.0967 -1.4504 0.9497s.e. 0.0726 0.1346 0.1298 0.0664 0.0385 0.0389
sigma^2 estimated as 7.828e-05: log likelihood = 813.09, aic = -1612.18
Data for validation
V1 V2 1 1947-01-01 1570.5 2 1947-04-01 1568.7 3 1947-07-01 1568.0 4 1947-10-01 1590.9 5 1948-01-01 1616.1 6 1948-04-01 1644.6 7 1948-07-01 1654.1 8 1948-10-01 1658.0 9 1949-01-01 1633.2 10 1949-04-01 1628.4 11 1949-07-01 1646.7 12 1949-10-01 1629.9 13 1950-01-01 1696.8 14 1950-04-01 1747.3 15 1950-07-01 1815.8 16 1950-10-01 1848.9 17 1951-01-01 1871.3 18 1951-04-01 1903.1 19 1951-07-01 1941.1 20 1951-10-01 1944.4 21 1952-01-01 1964.7 22 1952-04-01 1966.0 23 1952-07-01 1978.8 24 1952-10-01 2043.8 25 1953-01-01 2082.3 26 1953-04-01 2098.1 27 1953-07-01 2085.4 28 1953-10-01 2052.5 29 1954-01-01 2042.4 30 1954-04-01 2044.3 31 1954-07-01 2066.9 32 1954-10-01 2107.8 33 1955-01-01 2168.5 34 1955-04-01 2204.0 35 1955-07-01 2233.4 36 1955-10-01 2245.3 37 1956-01-01 2234.8 38 1956-04-01 2252.5 39 1956-07-01 2249.8 40 1956-10-01 2286.5 41 1957-01-01 2300.3 42 1957-04-01 2294.6 43 1957-07-01 2317.0 44 1957-10-01 2292.5 45 1958-01-01 2230.2 46 1958-04-01 2243.4 47 1958-07-01 2295.2 48 1958-10-01 2348.0 49 1959-01-01 2392.9 50 1959-04-01 2455.8 51 1959-07-01 2453.9 52 1959-10-01 2462.6 53 1960-01-01 2517.4 54 1960-04-01 2504.8 55 1960-07-01 2508.7 56 1960-10-01 2476.2 57 1961-01-01 2491.2 58 1961-04-01 2538.0 59 1961-07-01 2579.1 60 1961-10-01 2631.8 61 1962-01-01 2679.1 62 1962-04-01 2708.4 63 1962-07-01 2733.3 64 1962-10-01 2740.0 65 1963-01-01 2775.9 66 1963-04-01 2810.6 67 1963-07-01 2863.5 68 1963-10-01 2885.8 69 1964-01-01 2950.5 70 1964-04-01 2984.8 71 1964-07-01 3025.5 72 1964-10-01 3033.6 73 1965-01-01 3108.2 74 1965-04-01 3150.2 75 1965-07-01 3214.1 76 1965-10-01 3291.8 77 1966-01-01 3372.3 78 1966-04-01 3384.0 79 1966-07-01 3406.3 80 1966-10-01 3433.7 81 1967-01-01 3464.1 82 1967-04-01 3464.3 83 1967-07-01 3491.8 84 1967-10-01 3518.2 85 1968-01-01 3590.7 86 1968-04-01 3651.6 87 1968-07-01 3676.5 88 1968-10-01 3692.0 89 1969-01-01 3750.2 90 1969-04-01 3760.9 91 1969-07-01 3784.2 92 1969-10-01 3766.3 93 1970-01-01 3760.0 94 1970-04-01 3767.1 95 1970-07-01 3800.5 96 1970-10-01 3759.8 97 1971-01-01 3864.1 98 1971-04-01 3885.9 99 1971-07-01 3916.7 100 1971-10-01 3927.9 101 1972-01-01 3997.7 102 1972-04-01 4092.1 103 1972-07-01 4131.1 104 1972-10-01 4198.7 105 1973-01-01 4305.3 106 1973-04-01 4355.1 107 1973-07-01 4331.9 108 1973-10-01 4373.3 109 1974-01-01 4335.4 110 1974-04-01 4347.9 111 1974-07-01 4305.8 112 1974-10-01 4288.9 113 1975-01-01 4237.6 114 1975-04-01 4268.6 115 1975-07-01 4340.9 116 1975-10-01 4397.8 117 1976-01-01 4496.8 118 1976-04-01 4530.3 119 1976-07-01 4552.0 120 1976-10-01 4584.6 121 1977-01-01 4640.0 122 1977-04-01 4731.1 123 1977-07-01 4815.8 124 1977-10-01 4815.3 125 1978-01-01 4830.8 126 1978-04-01 5021.2 127 1978-07-01 5070.7 128 1978-10-01 5137.4 129 1979-01-01 5147.4 130 1979-04-01 5152.3 131 1979-07-01 5189.4 132 1979-10-01 5204.7 133 1980-01-01 5221.3 134 1980-04-01 5115.9 135 1980-07-01 5107.4 136 1980-10-01 5202.1 137 1981-01-01 5307.5 138 1981-04-01 5266.1 139 1981-07-01 5329.8 140 1981-10-01 5263.4 141 1982-01-01 5177.1 142 1982-04-01 5204.9 143 1982-07-01 5185.2 144 1982-10-01 5189.8 145 1983-01-01 5253.8 146 1983-04-01 5372.3 147 1983-07-01 5478.4 148 1983-10-01 5590.5 149 1984-01-01 5699.8 150 1984-04-01 5797.9 151 1984-07-01 5854.3 152 1984-10-01 5902.4 153 1985-01-01 5956.9 154 1985-04-01 6007.8 155 1985-07-01 6101.7 156 1985-10-01 6148.6 157 1986-01-01 6207.4 158 1986-04-01 6232.0 159 1986-07-01 6291.7 160 1986-10-01 6323.4 161 1987-01-01 6365.0 162 1987-04-01 6435.0 163 1987-07-01 6493.4 164 1987-10-01 6606.8 165 1988-01-01 6639.1 166 1988-04-01 6723.5 167 1988-07-01 6759.4 168 1988-10-01 6848.6 169 1989-01-01 6918.1 170 1989-04-01 6963.5 171 1989-07-01 7013.1 172 1989-10-01 7030.9 173 1990-01-01 7112.1 174 1990-04-01 7130.3 175 1990-07-01 7130.8 176 1990-10-01 7076.9 177 1991-01-01 7040.8 178 1991-04-01 7086.5 179 1991-07-01 7120.7 180 1991-10-01 7154.1 181 1992-01-01 7228.2 182 1992-04-01 7297.9 183 1992-07-01 7369.5 184 1992-10-01 7450.7 185 1993-01-01 7459.7 186 1993-04-01 7497.5 187 1993-07-01 7536.0 188 1993-10-01 7637.4 189 1994-01-01 7715.1 190 1994-04-01 7815.7 191 1994-07-01 7859.5 192 1994-10-01 7951.6 193 1995-01-01 7973.7 194 1995-04-01 7988.0 195 1995-07-01 8053.1 196 1995-10-01 8112.0 197 1996-01-01 8169.2 198 1996-04-01 8303.1 199 1996-07-01 8372.7 200 1996-10-01 8470.6 201 1997-01-01 8536.1 202 1997-04-01 8665.8 203 1997-07-01 8773.7 204 1997-10-01 8838.4 205 1998-01-01 8936.2 206 1998-04-01 8995.3 207 1998-07-01 9098.9 208 1998-10-01 9237.1 209 1999-01-01 9315.5 210 1999-04-01 9392.6 211 1999-07-01 9502.2 212 1999-10-01 9671.1 213 2000-01-01 9695.6 214 2000-04-01 9847.9 215 2000-07-01 9836.6 216 2000-10-01 9887.7 217 2001-01-01 9875.6 218 2001-04-01 9905.9 219 2001-07-01 9871.1 220 2001-10-01 9910.0 221 2002-01-01 9977.3 222 2002-04-01 10031.6 223 2002-07-01 10090.7 224 2002-10-01 10095.8 225 2003-01-01 10126.0 226 2003-04-01 10212.7 227 2003-07-01 10398.7 228 2003-10-01 10467.0 229 2004-01-01 10543.6 230 2004-04-01 10634.2 231 2004-07-01 10728.7 232 2004-10-01 10796.4 233 2005-01-01 10875.8 234 2005-04-01 10946.1 235 2005-07-01 11050.0 236 2005-10-01 11086.1 237 2006-01-01 11217.3 238 2006-04-01 11291.7 239 2006-07-01 11314.1 240 2006-10-01 11356.4 241 2007-01-01 11357.8 242 2007-04-01 11491.4 243 2007-07-01 11625.7 244 2007-10-01 11620.7 245 2008-01-01 11646.0 246 2008-04-01 11727.4 247 2008-07-01 11712.3
