structure(list(year = 1991:2015, Aa3 = c(11.7967532509252, 11.4555638363487,
13.1706280624658, 9.83853834721082, 11.0892774079976, 9.28558456688599,
8.37008645576346, 16.685201223273, 14.9208415784334, 12.5005737304688,
14.9006742778577, 9.53653243215462, 10.6907120554071, 13.3834204958197,
9.8151839406867, 13.2178794459293, 11.6116308379592, 11.5517068427906,
12.2147025125069, 11.5025536252741, 11.4172066671807, 12.803326094778,
15.5187240868284, 12.148594585218, 15.0073361045436), Bb = c(-3.18143519666869,
-4.39866028668509, 1.78033518645253, -1.09087811744935, 0.781504864298432,
-3.35258413204158, -0.147817393686718, 2.20858102713945, 2.78942101113926,
0.133688841044735, 7.54352335295978, -3.01163687673316, 4.76122905649298,
-0.067047827360323, 6.75503612812823, 4.59545579459801, -3.10992282189532,
5.19488285181458, -1.75941821116188, 3.67164104630711, -1.37833278441656,
0.889547512007415, -1.47006917494296, 2.96885387269044, -0.599857256084644
), Cc = c(-3.14888958162661, -5.09421300863669, 0.859087760125301,
-3.77697950592429, -2.35219581389364, -3.95249382467829, -3.33432632797512,
-1.20699309912482, -2.85922008621721, -3.713746771849, -1.33312677641961,
-2.46973133916438, -1.72655447645258, -3.11445919729557, -1.25910057594707,
-1.57561781314935, -4.75200348290639, 0.160156234390008, -0.626073828499617,
-1.68243433179146, -3.08619266129513, -2.68649754048611, -4.31190628871281,
-1.472913440597, -3.08940582665639), Dd = c(-1.37625014361211,
-5.05573658662682, -1.18101124482994, -2.52954173368564, -0.261439424402551,
-3.97714305204502, -1.98631268669575, 1.59101167566638, -3.05814029469207,
-5.33150060317094, -2.69995009478398, -2.56073069852939, -1.92038394703582,
-2.70067713120402, -0.0833998736213011, -3.31705501780788, -3.06175213982075,
-1.19264921300549, -2.02601964613968, -2.31430484547332, -1.1192687988281,
-1.61056051815255, -1.08186142865347, -2.30663057215071, -2.99631168141082
), medini = c(162L, 172L, 157L, 161L, 161L, 166L, 161L, 158L,
168L, 168L, 164L, 167L, 160L, 163L, 163L, 165L, 167L, 162L, 164L,
164L, 163L, 164L, 165L, 162L, 163L)), .Names = c("year", "Aa3",
"Bb", "Cc", "Dd", "medini"), class = "data.frame", row.names = c(NA,
-25L))

require(nlme)
m8 = gls(medini~Bb+Cc ,method="REML", control = list(maxIter=100),data=LDT )
plot(ACF(m8,resType="normalized"),alpha=0.05)
m8.1 <- update(m8, correlation=corARMA(form = ~ 1,p=1))
plot(ACF(m8.1,resType="normalized"),alpha=0.05)
m8.1.1 <- update(m8, correlation=corARMA(form = ~ 1,p=1,q=1))
plot(ACF(m8.1.1,resType="normalized"),alpha=0.05)
m8.2 <- update(m8, correlation=corARMA(form = ~ 1,p=2))
plot(ACF(m8.2,resType="normalized"),alpha=0.05)
m8.2.1 <- update(m8, correlation=corARMA(form = ~ 1,p=2, q=1))
plot(ACF(m8.2.1,resType="normalized"),alpha=0.05)
m8.2.2 <- update(m8, correlation=corARMA(form = ~ 1,p=2, q=2),control=glsControl(tolerance=1e-4,msVerbose=F))
plot(ACF(m8.2.2,resType="normalized"),alpha=0.05)
m8.3 <- update(m8, correlation=corARMA(form = ~ 1,p=3))

anova(m10,m10.1,m10.1.1,m10.2,m10.2.1,m10.2.2)

m13 = gls(medini~Bb+Cc+Dd  ,method="REML", data=LDT)
plot(ACF(m13,resType="normalized"),alpha=0.05)
m13.1 <- update(m13, correlation=corARMA(form = ~ 1,p=1))
plot(ACF(m13.1,resType="normalized"),alpha=0.05)
m13.1.1 <- update(m13, correlation=corARMA(form = ~ 1,p=1,q=1))
plot(ACF(m13.1.1,resType="normalized"),alpha=0.05)
m13.2 <- update(m13, correlation=corARMA(form = ~ 1,p=2))
plot(ACF(m13.2,resType="normalized"),alpha=0.05)
m13.2.1 <- update(m13, correlation=corARMA(form = ~ 1,p=2,q=1),control=lmeControl(opt="optim"))
plot(ACF(m13.2.1,resType="normalized"),alpha=0.05)
anova(m13,m13.1,m13.1.1,m13.2,m13.2.1)

m14.2.1 <- gls(medini~Aa3+Cc+Dd  ,method="REML", data=LDT, correlation=corARMA(form = ~ 1,p=2,q=1))
plot(ACF(m14.2.1,resType="normalized"),alpha=0.05)

m15 = gls(medini~Aa3+Bb+Cc+Dd ,method="REML", data=LDT)
plot(ACF(m15,resType="normalized"),alpha=0.05)
m15.1 <- update(m15, correlation=corARMA(form = ~ 1,p=1))
plot(ACF(m15.1,resType="normalized"),alpha=0.05)
m15.1.1 <- update(m15, correlation=corARMA(form = ~ 1,p=1,q=1))
plot(ACF(m15.1.1,resType="normalized"),alpha=0.05)
m15.2 <- update(m15, correlation=corARMA(form = ~ 1,p=2))
plot(ACF(m15.2,resType="normalized"),alpha=0.05)
m15.2.1 <- update(m15, correlation=corARMA(form = ~ 1,p=2,q=1))
plot(ACF(m15.2.1,resType="normalized"),alpha=0.05)
anova(m15,m15.1,m15.1.1,m15.2,m15.2.1)

m0 = gls(medini~1,method="ML", data=LDT)
m1 = gls(medini~Aa3,method="ML", data=LDT)
m2 = gls(medini~Bb,method="ML", data=LDT)
m3 = gls(medini~Cc,method="ML", data=LDT)
m4 = gls(medini~Dd,method="ML", data=LDT)
m5 = gls(medini~Aa3 + Bb ,method="ML", data=LDT)
m6 = gls(medini~Aa3 + Cc ,method="ML", data=LDT )
m7 = gls(medini~Aa3 + Dd ,method="ML",data=LDT )
m8 = gls(medini~Bb+Cc ,method="ML", control = list(maxIter=100),data=LDT )
m9 = gls(medini~Bb+Dd ,method="ML",data=LDT  )
m10.2.1 = gls(medini~Cc+Dd  ,method="ML",data=LDT,correlation=corARMA(form = ~ 1,p=2,q=1))
m11 = gls(medini~Aa3+Bb+Cc  ,method="ML",data=LDT)
m12 = gls(medini~Aa3+Bb+Dd  ,method="ML",data=LDT )

m13 = gls(medini~Bb+Cc+Dd  ,method="ML", data=LDT)
m13.2.1 <- update(m13, correlation=corARMA(form = ~ 1,p=2,q=1))
plot(ACF(m13.2.1,resType="normalized"),alpha=0.05)
m13.2.2 <- update(m13, correlation=corARMA(form = ~ 1,p=2,q=2),control=lmeControl(opt="optim"))
plot(ACF(m13.2.2,resType="normalized"),alpha=0.05)
m13.3 <- update(m13, correlation=corARMA(form = ~ 1,p=3))
plot(ACF(m13.3,resType="normalized"),alpha=0.05)

m14.2.1 <- gls(medini~Aa3+Cc+Dd,method="ML", data=LDT, correlation=corARMA(form = ~ 1,p=2,q=1),control=lmeControl(opt="optim"))

m15.2.1 <- gls(medini~Aa3+Bb+Cc+Dd ,method="ML", data=LDT, correlation=corARMA(form = ~ 1,p=2,q=1))
plot(ACF(m15.2.1,resType="normalized"),alpha=0.05)
m15.2.2 <- update(m15, correlation=corARMA(form = ~ 1,p=2,q=2),control=lmeControl(opt="optim"))
plot(ACF(m15.2.2,resType="normalized"),alpha=0.05)

anova(m0,mAa3,mBb,mCc,mDd,m5,m6,m7, m8,m9,m10.2.1,m11,m12,m13.2.2,m14.2.1, m15.2.2)