STAT 6555 - HWK 2

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library(astsa)

A

trend <- time(jj) - 1970
Q <- factor(cycle(jj))

reg1 <- lm(log(jj) ~ 0 + trend + Q, na.action = NULL)

summary(reg1)

Call:
lm(formula = log(jj) ~ 0 + trend + Q, na.action = NULL)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.29318 -0.09062 -0.01180  0.08460  0.27644 

Coefficients:
      Estimate Std. Error t value Pr(>|t|)    
trend 0.167172   0.002259   74.00   <2e-16 ***
Q1    1.052793   0.027359   38.48   <2e-16 ***
Q2    1.080916   0.027365   39.50   <2e-16 ***
Q3    1.151024   0.027383   42.03   <2e-16 ***
Q4    0.882266   0.027412   32.19   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1254 on 79 degrees of freedom
Multiple R-squared:  0.9935,    Adjusted R-squared:  0.9931 
F-statistic:  2407 on 5 and 79 DF,  p-value: < 2.2e-16

B.

reg2 <- lm (log(jj) ~ trend + Q, na.action = NULL)

summary(reg2)

Call:
lm(formula = log(jj) ~ trend + Q, na.action = NULL)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.29318 -0.09062 -0.01180  0.08460  0.27644 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.052793   0.027359  38.480  < 2e-16 ***
trend        0.167172   0.002259  73.999  < 2e-16 ***
Q2           0.028123   0.038696   0.727   0.4695    
Q3           0.098231   0.038708   2.538   0.0131 *  
Q4          -0.170527   0.038729  -4.403 3.31e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1254 on 79 degrees of freedom
Multiple R-squared:  0.9859,    Adjusted R-squared:  0.9852 
F-statistic:  1379 on 4 and 79 DF,  p-value: < 2.2e-16

C.

The rersdiduals do not look like a sample from the white noise

par(mfrow = c(1,2))
plot(log(jj), main = "DATA & FITTED DATA")
lines(fitted(reg1), col = "green")

plot(log(jj) - fitted(reg1), main = "RESIDUALS")

acf(log(jj) - fitted(reg1))

pacf(log(jj) - fitted(reg1))

2.3

#set.seed(2)
#n <- 100
#delta <- 0.01
#time <- 1:n
#par(mfrow <- c(3,2))
 # for (k in 1:6){w = rnorn(100, 0.01, 1)
 # x = c() for (t in 1:100){x[t] = delta * t + sum (w[1:6])}
 # mu = delta*time
  #fit = lm(x ~ 0 + time)
  #plot(time, x, type = "l", main = "RANDOM WALK")
  #lines(time, fitted(fit), col = "red")
 # lines(time, mu, col = "blue")}

par(mfcol = c(3,2)) # set up graphics
for (i in 1:6){
x = ts(cumsum(rnorm(100,.01,1))) # the data
reg = lm(x~0+time(x), na.action=NULL) # the regression
plot(x) # plot data
lines(.01*time(x), col="red", lty="dashed") # plot mean
abline(reg, col="blue") } # plot regression line

2.11

A

there seemed to havce been a steady increase till the year 2008, where there was a drop, then again an increase in the yer 2010. This doesnt show stationarity in both the oil and gas.

op <- par(mfrow = c(2,1), mar = c(2, 3, 1.5, 0.5))
plot(oil)
plot(gas)

B

Here, the transformed data seems stationary apart from the years 2006 and 2009 for gas prices and oil prices respectively

plot(diff(log(oil)), main = "OIL")

plot(diff(log(gas)), main = "GAS")

C

We see that the ACFs are statiinary ACF & PACF of gas

acf(diff(log(gas)))

pacf(diff(log(gas)))

ACF & PACF of oil

acf(diff(log(oil)))

pacf(diff(log(oil)))

D

CCF

LagReg(diff(log(oil)), diff(log(gas)))

INPUT: diff(log(oil)) OUTPUT: diff(log(gas))   L = 3 3    M = 40 

The coefficients beta(0), beta(1), beta(2) ... beta(M/2-1) are 

0.7389142 -0.05024009 -0.05080066 -0.04530582 0.05385858 0.05575409 0.1340516 
-0.07575214 0.01748974 -0.004864297 0.1062629 -0.0358188 -0.06984526 0.01365599 
0.0006313248 -0.3463913 -0.1356426 -0.173927 0.1685202 -0.09426999 


The coefficients beta(0), beta(-1), beta(-2) ... beta(-M/2+1) are 

0.7389142 -0.06497907 0.08110308 0.0459882 -0.1847163 -0.0893233 0.01940072 
0.02234675 -0.0255585 -0.08277468 -0.02098733 0.01429463 0.0195192 -0.09625142 
0.01409666 -0.1008326 0.185693 -0.02386474 0.1263648 -0.09945544 


The positive lags, at which the coefficients are large
in absolute value, and the coefficients themselves, are: 
      lag s       beta(s)
 [1,]     0  0.7389141905
 [2,]     1 -0.0502400882
 [3,]     2 -0.0508006645
 [4,]     3 -0.0453058163
 [5,]     4  0.0538585755
 [6,]     5  0.0557540884
 [7,]     6  0.1340515851
 [8,]     7 -0.0757521415
 [9,]     8  0.0174897367
[10,]     9 -0.0048642965
[11,]    10  0.1062628842
[12,]    11 -0.0358187959
[13,]    12 -0.0698452575
[14,]    13  0.0136559900
[15,]    14  0.0006313248
[16,]    15 -0.3463912684
[17,]    16 -0.1356425857
[18,]    17 -0.1739269705
[19,]    18  0.1685202170
[20,]    19 -0.0942699873

The prediction equation is
diff(log(gas))(t) = alpha + sum_s[ beta(s)*diff(log(oil))(t-s) ], where alpha = 0.001471305
MSE = 0.004046668
$betas
        S             b
 [1,] -19 -0.0994554387
 [2,] -18  0.1263647889
 [3,] -17 -0.0238647413
 [4,] -16  0.1856930148
 [5,] -15 -0.1008326050
 [6,] -14  0.0140966591
 [7,] -13 -0.0962514202
 [8,] -12  0.0195192047
 [9,] -11  0.0142946341
[10,] -10 -0.0209873268
[11,]  -9 -0.0827746773
[12,]  -8 -0.0255585032
[13,]  -7  0.0223467542
[14,]  -6  0.0194007235
[15,]  -5 -0.0893233037
[16,]  -4 -0.1847163391
[17,]  -3  0.0459881997
[18,]  -2  0.0811030756
[19,]  -1 -0.0649790681
[20,]   0  0.7389141905
[21,]   1 -0.0502400882
[22,]   2 -0.0508006645
[23,]   3 -0.0453058163
[24,]   4  0.0538585755
[25,]   5  0.0557540884
[26,]   6  0.1340515851
[27,]   7 -0.0757521415
[28,]   8  0.0174897367
[29,]   9 -0.0048642965
[30,]  10  0.1062628842
[31,]  11 -0.0358187959
[32,]  12 -0.0698452575
[33,]  13  0.0136559900
[34,]  14  0.0006313248
[35,]  15 -0.3463912684
[36,]  16 -0.1356425857
[37,]  17 -0.1739269705
[38,]  18  0.1685202170
[39,]  19 -0.0942699873

$fit
Time Series:
Start = c(2000, 22) 
End = c(2010, 25) 
Frequency = 52 
                output           fit        resids
2000.404  4.545592e-02 -3.075057e-02  0.0762064865
2000.423  5.695009e-02  2.751910e-02  0.0294309913
2000.442 -4.843580e-03  2.877303e-02 -0.0336166072
2000.462  6.915251e-02 -7.633500e-03  0.0767860064
2000.481 -3.041102e-02 -2.276372e-02 -0.0076472991
2000.500  3.829360e-02 -1.690583e-02  0.0551994311
2000.519 -2.933040e-02  6.891847e-02 -0.0982488736
2000.538  1.139252e-02  1.517611e-02 -0.0037835904
2000.558 -1.529365e-01 -2.710173e-02 -0.1258347550
2000.577  9.482744e-02 -8.883651e-03  0.1037110884
2000.596 -3.529358e-02  4.885139e-02 -0.0841449660
2000.615 -9.058533e-02  5.878124e-02 -0.1493665744
2000.635  6.076957e-02 -4.422331e-02  0.1049928822
2000.654 -3.695951e-02 -4.411158e-03 -0.0325483512
2000.673  5.977066e-02  3.705858e-02  0.0227120890
2000.692  1.454736e-02  1.967572e-02 -0.0051283560
2000.712  5.912221e-02  7.390817e-03  0.0517313925
2000.731  7.439508e-02 -3.358456e-02  0.1079796390
2000.750 -4.426689e-02  1.086484e-03 -0.0453533761
2000.769  3.379078e-03  1.122124e-02 -0.0078421631
2000.788 -8.045075e-02  3.164190e-02 -0.1120926536
2000.808 -4.313939e-02 -1.268678e-01  0.0837284062
2000.827  9.570367e-02 -1.589853e-02  0.1116021995
2000.846  2.545634e-02  6.840237e-02 -0.0429460338
2000.865  4.751488e-02  4.543582e-02  0.0020790515
2000.885 -6.832878e-02  1.344059e-02 -0.0817693685
2000.904 -6.844567e-03 -3.856070e-02  0.0317161358
2000.923  6.549780e-03  2.656322e-02 -0.0200134381
2000.942  2.999727e-02  6.297703e-02 -0.0329797610
2000.962 -9.809552e-02  2.015171e-02 -0.1182472349
2000.981 -1.663760e-01 -9.493524e-02 -0.0714407229
2001.000 -3.574858e-02 -1.257315e-01  0.0899829273
2001.019 -1.121020e-02 -1.594976e-02  0.0047395641
2001.038  2.352336e-02 -2.031094e-02  0.0438343011
2001.058  6.610873e-02 -2.884103e-02  0.0949497565
2001.077  7.577214e-02  1.379521e-02  0.0619769394
2001.096 -1.846417e-03  5.641703e-02 -0.0582634439
2001.115 -4.131256e-03  3.748067e-02 -0.0416119273
2001.135 -1.105274e-02  1.698426e-02 -0.0280370057
2001.154  4.448628e-02 -8.721900e-02  0.1317052754
2001.173 -4.718423e-02  2.489212e-02 -0.0720763445
2001.192 -5.222431e-02 -4.855783e-03 -0.0473685220
2001.212 -8.024998e-03 -2.413477e-02  0.0161097679
2001.231  1.032238e-02 -1.690985e-02  0.0272322276
2001.250 -3.425310e-02 -8.621572e-03 -0.0256315313
2001.269  2.858261e-02 -1.987033e-02  0.0484529388
2001.288  2.984471e-02  5.355484e-02 -0.0237101296
2001.308  8.689793e-02  4.008763e-02  0.0468103023
2001.327  8.307342e-02  3.524362e-02  0.0478297986
2001.346  1.774775e-02  3.257551e-02 -0.0148277544
2001.365 -7.722682e-03  1.869413e-03 -0.0095920952
2001.385  2.609793e-02 -5.641701e-02  0.0825149383
2001.404 -2.425968e-02 -1.546404e-04 -0.0241050347
2001.423 -1.051083e-01 -9.041584e-03 -0.0960667512
2001.442  7.349542e-02  3.877210e-02  0.0347233268
2001.462 -1.203648e-01 -9.902764e-03 -0.1104620331
2001.481 -8.644919e-02 -2.955349e-03 -0.0834938392
2001.500 -3.578190e-02 -6.520656e-03 -0.0292612415
2001.519 -5.006819e-02  7.097986e-02 -0.1210480546
2001.538 -6.454042e-02 -5.381055e-02 -0.0107298723
2001.558  1.521143e-02  3.749978e-03  0.0114614508
2001.577  2.839156e-02  1.649380e-02  0.0118977614
2001.596 -2.831660e-02  3.006126e-02 -0.0583778691
2001.615  4.671078e-02 -6.070398e-02  0.1074147615
2001.635  3.104387e-02  1.903336e-02  0.0120105143
2001.654  5.506820e-02  9.223391e-03  0.0458448062
2001.673  2.271026e-02  2.258430e-02  0.0001259596
2001.692 -8.918734e-03 -1.366748e-02  0.0047487456
2001.712  5.821224e-02 -9.865196e-03  0.0680774330
2001.731 -2.121922e-02 -4.582795e-02  0.0246087332
2001.750  4.536534e-02  3.972056e-02  0.0056447782
2001.769 -7.685851e-02  2.553913e-02 -0.1023976456
2001.788 -2.040784e-01 -1.209924e-02 -0.1919791071
2001.808  1.839852e-02 -1.655768e-01  0.1839753065
2001.827 -4.667948e-02  4.614892e-02 -0.0928283945
2001.846 -6.426352e-02  3.250554e-02 -0.0967690581
2001.865  5.802925e-03  1.418633e-03  0.0043842912
2001.885 -7.014978e-02 -3.022667e-02 -0.0399231083
2001.904  4.801566e-04 -1.605980e-02  0.0165399545
2001.923 -5.510785e-02 -3.613073e-02 -0.0189771201
2001.942 -3.489903e-02 -2.162596e-02 -0.0132730711
2001.962  2.698611e-02 -8.115188e-02  0.1081379950
2001.981 -1.141171e-03  4.119369e-02 -0.0423348636
2002.000 -3.754954e-02 -4.231497e-03 -0.0333180404
2002.019  6.596319e-02 -2.363494e-02  0.0895981251
2002.038  7.730116e-02  2.793505e-02  0.0493661087
2002.058  1.223445e-02  3.996722e-02 -0.0277327721
2002.077 -1.209277e-02 -4.198093e-03 -0.0078946763
2002.096 -9.236418e-02  6.623240e-02 -0.1585965823
2002.115  3.812871e-02 -4.611340e-02  0.0842421092
2002.135  1.165430e-02  4.852309e-02 -0.0368687896
2002.154  6.447001e-03  1.472310e-02 -0.0082760972
2002.173  4.561659e-02  5.632195e-02 -0.0107053557
2002.192 -4.495582e-02  4.928794e-02 -0.0942437675
2002.212  2.217434e-02 -2.751707e-02  0.0496914120
2002.231  1.417839e-01  4.927072e-02  0.0925131948
2002.250  1.112519e-01  1.172507e-01 -0.0059988206
2002.269  2.117707e-02  2.832726e-02 -0.0071501966
2002.288 -1.173263e-02  7.829375e-03 -0.0195620091
2002.308  5.626387e-02  1.228707e-02  0.0439768035
2002.327 -4.126246e-02  3.956176e-02 -0.0808242192
2002.346  8.772699e-03 -5.757969e-02  0.0663523889
2002.365 -1.529360e-02 -7.534047e-03 -0.0077595540
2002.385 -4.928401e-04  3.848745e-02 -0.0389802874
2002.404 -5.410222e-02  6.266067e-02 -0.1167628840
2002.423  2.925760e-02  4.623790e-03  0.0246338054
2002.442 -4.212241e-04  4.290328e-02 -0.0433245077
2002.462 -4.141845e-02 -7.454069e-02  0.0331222418
2002.481  3.332466e-02 -5.961340e-02  0.0929380667
2002.500 -2.097566e-03  1.880975e-03 -0.0039785409
2002.519  2.405431e-02 -8.696501e-03  0.0327508131
2002.538  1.664736e-02 -4.773859e-03  0.0214212232
2002.558  1.031279e-02 -1.713680e-02  0.0274495910
2002.577 -4.337112e-03 -2.316326e-02  0.0188261525
2002.596  6.525592e-02 -2.293965e-02  0.0881955624
2002.615 -2.746945e-02  3.786167e-03 -0.0312556166
2002.635  2.051923e-02 -6.651199e-03  0.0271704309
2002.654 -3.403987e-02  5.937380e-03 -0.0399772497
2002.673  1.346848e-02 -4.656192e-03  0.0181246744
2002.692  7.430729e-03  2.840659e-02 -0.0209758566
2002.712  8.890780e-03  3.640742e-02 -0.0275166431
2002.731 -5.074386e-02 -4.412095e-02 -0.0066229178
2002.750  4.050614e-02 -4.595722e-03  0.0451018640
2002.769  1.843962e-02  5.682124e-02 -0.0383816171
2002.788  1.840558e-02  2.519133e-02 -0.0067857485
2002.808  1.822013e-02  4.790628e-02 -0.0296861545
2002.827  8.403411e-03 -3.170642e-02  0.0401098275
2002.846  3.722304e-02 -3.852395e-02  0.0757469877
2002.865 -3.851316e-02  2.600282e-03 -0.0411134390
2002.885 -2.927188e-03 -3.235106e-02  0.0294238764
2002.904  1.450285e-02 -2.499364e-02  0.0394964902
2002.923 -1.054060e-01 -2.319385e-02 -0.0822121455
2002.942 -1.931422e-02 -1.442018e-02 -0.0048940391
2002.962 -2.998439e-02  5.682621e-02 -0.0868105969
2002.981  1.962075e-02 -3.892349e-02  0.0585442379
2003.000  5.641862e-02 -2.445273e-02  0.0808713534
2003.019  8.425955e-02  8.291729e-03  0.0759678255
2003.038  7.630062e-02  6.620551e-02  0.0100951095
2003.058 -3.625468e-02  5.054979e-02 -0.0868044699
2003.077 -3.514965e-02 -2.778713e-02 -0.0073625188
2003.096  3.200479e-02 -3.567976e-02  0.0676845554
2003.115  8.730469e-03  5.037567e-02 -0.0416451981
2003.135  6.718565e-02  4.405704e-02  0.0231286080
2003.154  6.746313e-02  1.252517e-03  0.0662106172
2003.173  7.310717e-03  3.389304e-02 -0.0265823221
2003.192 -4.170395e-02  4.726500e-02 -0.0889689507
2003.212  3.732792e-02  6.073393e-02 -0.0234060054
2003.231  3.323086e-02  1.836115e-02  0.0148697130
2003.250 -1.062334e-02 -7.352100e-03 -0.0032712428
2003.269 -1.482532e-01 -2.577950e-02 -0.1224736889
2003.288 -4.599063e-03 -1.386253e-01  0.1340262089
2003.308 -4.206412e-02  2.428703e-02 -0.0663511506
2003.327 -5.556038e-02 -5.284453e-02 -0.0027158430
2003.346  2.412944e-02 -6.773670e-02  0.0918661387
2003.365 -2.070534e-02  1.237563e-02 -0.0330809670
2003.385 -1.112579e-01 -1.465135e-02 -0.0966065729
2003.404  1.783177e-03 -1.087191e-01  0.1105022996
2003.423  7.513345e-02  9.820904e-03  0.0653125463
2003.442  1.910568e-02  4.743321e-02 -0.0283275240
2003.462 -1.851078e-03  1.647956e-02 -0.0183306360
2003.481  4.709668e-02 -3.965098e-02  0.0867476670
2003.500  2.089399e-02  9.401796e-04  0.0199538141
2003.519 -7.568518e-02  1.342267e-02 -0.0891078489
2003.538 -3.330518e-03 -1.046939e-02  0.0071388747
2003.558  6.472215e-02  1.621991e-03  0.0631001579
2003.577  7.859936e-02  7.339805e-02  0.0052013124
2003.596 -2.613173e-02  2.899542e-02 -0.0551271554
2003.615 -9.494178e-03  8.008949e-02 -0.0895836706
2003.635  1.756415e-02 -2.156154e-02  0.0391256861
2003.654  7.548326e-02  9.877777e-03  0.0656054881
2003.673  4.350655e-02  3.490360e-02  0.0086029558
2003.692  6.524306e-02  1.833567e-02  0.0469073879
2003.712 -2.592494e-02  1.854019e-02 -0.0444651261
2003.731 -1.259951e-01 -1.754917e-02 -0.1084459792
2003.750  1.612368e-02 -9.899214e-02  0.1151158236
2003.769 -5.598162e-02  7.644639e-03 -0.0636262603
2003.788  4.378502e-02 -4.248430e-02  0.0862693205
2003.808 -6.141372e-02 -4.736039e-03 -0.0566776837
2003.827  3.871157e-02  3.540972e-02  0.0033018567
2003.846  1.159214e-02  4.324976e-02 -0.0316576202
2003.865 -4.898117e-02  1.016273e-02 -0.0591438961
2003.885 -2.308065e-02 -4.849661e-02  0.0254159538
2003.904 -2.299448e-02 -4.094447e-02  0.0179499863
2003.923  7.581830e-02  3.961136e-02  0.0362069374
2003.942  4.970185e-02  4.747815e-02  0.0022237055
2003.962 -6.001845e-02  1.603707e-02 -0.0760555198
2003.981 -2.968138e-02 -6.958316e-02  0.0399017799
2004.000  8.909057e-03  9.158657e-03 -0.0002496000
2004.019  4.827148e-02  6.009438e-02 -0.0118229010
2004.038 -1.502413e-02  5.219274e-02 -0.0672168785
2004.058  5.295783e-02 -1.064857e-02  0.0636063922
2004.077  4.676301e-02  3.442494e-02  0.0123380724
2004.096  5.493684e-03  6.961124e-03 -0.0014674402
2004.115  4.566137e-02  2.580607e-02  0.0198553070
2004.135 -4.251259e-02 -4.097339e-03 -0.0384152510
2004.154  1.763841e-02 -5.955486e-02  0.0771932661
2004.173  1.186893e-02 -5.725264e-03  0.0175941970
2004.192  6.400396e-02  3.732799e-02  0.0266759689
2004.212 -1.296800e-02  6.092599e-02 -0.0738939881
2004.231  1.397695e-02 -1.893071e-02  0.0329076544
2004.250 -4.310504e-02 -2.119585e-02 -0.0219091830
2004.269  6.224594e-02  4.087619e-03  0.0581583200
2004.288 -6.279342e-03  4.716111e-02 -0.0534404543
2004.308 -2.190490e-02 -2.473364e-02  0.0028287469
2004.327 -2.535149e-02 -5.759333e-02  0.0322418366
2004.346  6.587075e-02  1.269174e-02  0.0531790079
2004.365 -5.290782e-03  4.177785e-02 -0.0470686341
2004.385  6.899168e-02 -5.544445e-03  0.0745361259
2004.404  8.957120e-02 -1.710138e-02  0.1066725737
2004.423  3.336640e-02  1.402433e-02  0.0193420703
2004.442  1.406773e-02  3.545193e-02 -0.0213842021
2004.462 -3.353871e-02  1.519889e-02 -0.0487376018
2004.481 -8.719588e-02  9.477532e-03 -0.0966734090
2004.500 -6.363575e-02 -4.531574e-02 -0.0183200129
2004.519 -6.048565e-03 -4.694004e-02  0.0408914729
2004.538  1.641225e-02  3.655350e-03  0.0127569023
2004.558 -2.062397e-02  1.315768e-02 -0.0337816491
2004.577  1.081952e-01 -2.746833e-02  0.1356635768
2004.596  7.131566e-05  5.247016e-02 -0.0523988439
2004.615 -5.296116e-02  2.040576e-02 -0.0733669200
2004.635  3.586057e-03  2.265920e-02 -0.0190731451
2004.654 -1.116731e-02 -2.415762e-03 -0.0087515523
2004.673  2.858001e-02  8.306954e-03  0.0202730586
2004.692  2.773810e-02  2.056910e-02  0.0071690016
2004.712 -5.633495e-02  2.676690e-02 -0.0831018478
2004.731 -1.994710e-02 -7.042351e-02  0.0504764110
2004.750  2.174700e-02 -2.383034e-02  0.0455773462
2004.769  4.236632e-02  1.206684e-02  0.0302994792
2004.788  5.792600e-02  4.181297e-02  0.0161130235
2004.808  2.140269e-02  7.804738e-02 -0.0566446833
2004.827  2.239580e-02  3.017216e-02 -0.0077763544
2004.846  2.291544e-02  2.269865e-02  0.0002167846
2004.865 -1.520402e-02  3.042577e-02 -0.0456297943
2004.885 -2.689813e-02 -1.003058e-02 -0.0168675516
2004.904 -5.107707e-02 -1.762536e-02 -0.0334517063
2004.923 -2.096440e-02 -7.317951e-02  0.0522151095
2004.942 -2.585796e-03 -2.307015e-02  0.0204843500
2004.962  2.847871e-02 -1.727313e-02  0.0457518390
2004.981 -8.198759e-02  2.286791e-02 -0.1048555018
2005.000 -1.425200e-01 -6.264104e-02 -0.0798789211
2005.019  4.774244e-02 -6.180955e-02  0.1095519928
2005.038  1.474816e-02  3.371794e-02 -0.0189697801
2005.058 -5.744802e-02  4.285228e-02 -0.1003002959
2005.077  1.190140e-01 -5.364159e-02  0.1726555451
2005.096  4.949001e-02 -6.694481e-03  0.0561844876
2005.115  1.929674e-02 -5.711505e-04  0.0198678933
2005.135  5.464426e-02 -1.755885e-02  0.0722031016
2005.154 -4.880914e-02  2.755183e-03 -0.0515643229
2005.173 -5.040859e-02 -3.893312e-02 -0.0114754694
2005.192  2.070584e-02 -1.916153e-02  0.0398673726
2005.212  2.159634e-02  6.224271e-02 -0.0406463735
2005.231  6.497432e-02  1.011489e-01 -0.0361745850
2005.250  6.599065e-02  3.617443e-02  0.0298162179
2005.269  1.809125e-02 -9.322298e-03  0.0274135526
2005.288  3.466109e-02  3.721309e-02 -0.0025519997
2005.308  1.097878e-02  6.106311e-03  0.0048724698
2005.327  8.049102e-03  5.549851e-02 -0.0474494085
2005.346 -7.910938e-02  2.950040e-03 -0.0820594212
2005.365  6.275916e-02 -5.993359e-02  0.1226927472
2005.385 -2.378044e-02  2.245025e-02 -0.0462306921
2005.404 -5.537241e-02 -1.164285e-02 -0.0437295603
2005.423 -6.749736e-03 -4.570255e-02  0.0389528170
2005.442 -2.086820e-02 -8.326843e-03 -0.0125413598
2005.462  1.385309e-02 -3.179048e-02  0.0456435620
2005.481  6.445528e-02  4.194331e-02  0.0225119681
2005.500  3.930516e-03  4.659489e-02 -0.0426643751
2005.519  3.080728e-02 -3.976373e-02  0.0705710070
2005.538  3.572227e-02  2.728485e-03  0.0329937829
2005.558 -2.084364e-02  4.536946e-03 -0.0253805911
2005.577  7.649472e-02 -1.758724e-02  0.0940819540
2005.596 -4.696710e-02  4.810513e-02 -0.0950722322
2005.615 -1.716023e-02 -2.220896e-02  0.0050487279
2005.635  3.120968e-02 -1.525882e-02  0.0464685003
2005.654  6.682283e-02  3.968080e-02  0.0271420278
2005.673  7.885741e-02  5.484051e-02  0.0240168970
2005.692  2.158346e-02  5.182416e-02 -0.0302407048
2005.712 -1.699051e-02 -1.215050e-02 -0.0048400095
2005.731  3.733587e-01  2.471962e-02  0.3486390848
2005.750 -2.249456e-01  4.848517e-02 -0.2734307322
2005.769 -1.043075e-01 -4.912378e-02 -0.0551837549
2005.788  4.074130e-02 -2.343715e-02  0.0641784500
2005.808  6.750422e-02  1.129434e-02  0.0562098768
2005.827 -1.083793e-01 -2.143932e-02 -0.0869400171
2005.846 -1.010543e-01 -4.079747e-02 -0.0602568148
2005.865 -7.186778e-02 -1.294045e-02 -0.0589273278
2005.885 -5.952157e-02 -2.146818e-02 -0.0380533926
2005.904 -1.062840e-02  2.081243e-03 -0.0127096398
2005.923 -2.492039e-02 -6.890715e-03 -0.0180296709
2005.942 -3.208129e-02 -1.604348e-02 -0.0160378174
2005.962  1.753573e-02 -5.169976e-02  0.0692354869
2005.981  1.330667e-02 -1.292392e-02  0.0262305975
2006.000  6.031545e-02 -3.794920e-04  0.0606949441
2006.019  3.583470e-02  9.198552e-03  0.0266361448
2006.038 -4.457528e-02 -1.589600e-02 -0.0286792768
2006.058  5.373713e-02 -2.428791e-02  0.0780250456
2006.077  8.865535e-02  3.606090e-02  0.0525944478
2006.096 -4.053301e-02  4.991646e-02 -0.0904494655
2006.115  1.482809e-02 -1.116383e-02  0.0259919209
2006.135 -4.778513e-02  4.666056e-02 -0.0944456842
2006.154 -1.771536e-02  9.263942e-03 -0.0269793042
2006.173 -1.033550e-01  7.686876e-03 -0.1110418766
2006.192 -4.170999e-02 -2.973426e-02 -0.0119757335
2006.212  6.427272e-02 -1.736772e-02  0.0816404402
2006.231  6.101031e-02  2.690091e-02  0.0341094012
2006.250  1.232529e-02  4.976699e-02 -0.0374416989
2006.269  9.989328e-02 -1.626511e-02  0.1161583932
2006.288 -1.196564e-02  2.513074e-02 -0.0370963827
2006.308  6.797670e-02 -4.761756e-02  0.1155942637
2006.327  4.784740e-02  5.167171e-02 -0.0038243078
2006.346  6.007670e-02  1.611840e-02  0.0439582998
2006.365  7.932374e-02  2.318615e-02  0.0561375900
2006.385 -8.695528e-02 -1.641949e-03 -0.0853133296
2006.404  1.801247e-04 -3.674785e-02  0.0369279707
2006.423 -8.778417e-03  5.014386e-03 -0.0137928026
2006.442 -6.366548e-02  1.315911e-02 -0.0768245894
2006.462  1.736767e-02 -4.037426e-02  0.0577419280
2006.481  4.441692e-02  5.002093e-02 -0.0056040056
2006.500  4.850562e-03  4.168924e-02 -0.0368386798
2006.519 -5.569844e-02  1.620471e-02 -0.0719031474
2006.538  9.521158e-03 -3.077078e-02  0.0402919348
2006.558  7.281191e-02 -3.510456e-03  0.0763223627
2006.577  2.826578e-02  2.635475e-02  0.0019110265
2006.596 -5.085109e-03  3.323235e-02 -0.0383174555
2006.615  1.248546e-02 -3.007179e-02  0.0425572490
2006.635  1.953506e-02 -1.936914e-02  0.0389041974
2006.654  3.551384e-02 -3.855971e-02  0.0740735477
2006.673 -9.012102e-02  1.755480e-02 -0.1076758259
2006.692 -7.994761e-02  6.450214e-03 -0.0863978212
2006.712 -5.266166e-02 -4.870101e-02 -0.0039606504
2006.731 -4.866993e-02  8.340917e-03 -0.0570108442
2006.750 -8.675357e-02 -1.663017e-02 -0.0701233972
2006.769 -2.601603e-02 -7.335429e-03 -0.0186806001
2006.788 -5.088776e-02 -4.103159e-02 -0.0098561671
 [ reached getOption("max.print") -- omitted 191 rows ]