SARIMAX

Cargar las librerias

library(tseries)
library(forecast)
library(FitAR)
library(dynlm)
library(car)
library(urca)

FUNCIONES DE AYUDA

Función \(1\)

plotserie = function(data){
  par(mfrow = c(2,3))
  plot(data)
  stats::acf(data)
  stats::pacf(data)
  
  plot(diff(data))
  abline(h=2*sd(diff(data)), col = "red")
  abline(h=-2*sd(diff(data)), col = "red")
  stats::acf(diff(data))
  stats::pacf(diff(data))
}

función \(2\)

plotserieciclo = function(data, s) {
  par(mfrow = c(1,3))
  plot(diff(data, s))
  abline(h=2*sd(diff(data,s)), col = "red")
  abline(h=-2*sd(diff(data,s)), col = "red")
  stats::acf(diff(data,s))
  stats::pacf(diff(data,s))
}

Función \(3\)

plotresiduos = function(residuos, data) {
  par(mfrow = c(2,2))
  yfit = data - residuos
  plot(yfit, type="l", col="red", lty = 2)
  lines(data, col="blue")
  qqPlot(et)
  acf(et)
  pacf(et) 
}

Función \(4\)

ttest = function(modelo) {
  return(modelo$coef[which(modelo$coef!=0)] / sqrt(diag(modelo$var.coef)))
}

Función \(5\)

Lagtp = function(x, k){
  n = length(x)
  x1 = matrix(0, n)
  for (i in (k+1):n) {
    x1[i] = x[i-k]
  }
  return(x1)
}

Funcion \(6\)

Lagt = function(x, k){
  n = length(x)
  x1 = matrix(0, n, k)
  for (j in 1:k){
    for (i in (j+1):n) {
      x1[i,j] = x[i-j]
    }
  }
  return(x1)
}

plotserie(AirPassengers)

AirPassengers

##      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1949 112 118 132 129 121 135 148 148 136 119 104 118
## 1950 115 126 141 135 125 149 170 170 158 133 114 140
## 1951 145 150 178 163 172 178 199 199 184 162 146 166
## 1952 171 180 193 181 183 218 230 242 209 191 172 194
## 1953 196 196 236 235 229 243 264 272 237 211 180 201
## 1954 204 188 235 227 234 264 302 293 259 229 203 229
## 1955 242 233 267 269 270 315 364 347 312 274 237 278
## 1956 284 277 317 313 318 374 413 405 355 306 271 306
## 1957 315 301 356 348 355 422 465 467 404 347 305 336
## 1958 340 318 362 348 363 435 491 505 404 359 310 337
## 1959 360 342 406 396 420 472 548 559 463 407 362 405
## 1960 417 391 419 461 472 535 622 606 508 461 390 432

Lagtp(AirPassengers, 5)

##        [,1]
##   [1,]    0
##   [2,]    0
##   [3,]    0
##   [4,]    0
##   [5,]    0
##   [6,]  112
##   [7,]  118
##   [8,]  132
##   [9,]  129
##  [10,]  121
##  [11,]  135
##  [12,]  148
##  [13,]  148
##  [14,]  136
##  [15,]  119
##  [16,]  104
##  [17,]  118
##  [18,]  115
##  [19,]  126
##  [20,]  141
##  [21,]  135
##  [22,]  125
##  [23,]  149
##  [24,]  170
##  [25,]  170
##  [26,]  158
##  [27,]  133
##  [28,]  114
##  [29,]  140
##  [30,]  145
##  [31,]  150
##  [32,]  178
##  [33,]  163
##  [34,]  172
##  [35,]  178
##  [36,]  199
##  [37,]  199
##  [38,]  184
##  [39,]  162
##  [40,]  146
##  [41,]  166
##  [42,]  171
##  [43,]  180
##  [44,]  193
##  [45,]  181
##  [46,]  183
##  [47,]  218
##  [48,]  230
##  [49,]  242
##  [50,]  209
##  [51,]  191
##  [52,]  172
##  [53,]  194
##  [54,]  196
##  [55,]  196
##  [56,]  236
##  [57,]  235
##  [58,]  229
##  [59,]  243
##  [60,]  264
##  [61,]  272
##  [62,]  237
##  [63,]  211
##  [64,]  180
##  [65,]  201
##  [66,]  204
##  [67,]  188
##  [68,]  235
##  [69,]  227
##  [70,]  234
##  [71,]  264
##  [72,]  302
##  [73,]  293
##  [74,]  259
##  [75,]  229
##  [76,]  203
##  [77,]  229
##  [78,]  242
##  [79,]  233
##  [80,]  267
##  [81,]  269
##  [82,]  270
##  [83,]  315
##  [84,]  364
##  [85,]  347
##  [86,]  312
##  [87,]  274
##  [88,]  237
##  [89,]  278
##  [90,]  284
##  [91,]  277
##  [92,]  317
##  [93,]  313
##  [94,]  318
##  [95,]  374
##  [96,]  413
##  [97,]  405
##  [98,]  355
##  [99,]  306
## [100,]  271
## [101,]  306
## [102,]  315
## [103,]  301
## [104,]  356
## [105,]  348
## [106,]  355
## [107,]  422
## [108,]  465
## [109,]  467
## [110,]  404
## [111,]  347
## [112,]  305
## [113,]  336
## [114,]  340
## [115,]  318
## [116,]  362
## [117,]  348
## [118,]  363
## [119,]  435
## [120,]  491
## [121,]  505
## [122,]  404
## [123,]  359
## [124,]  310
## [125,]  337
## [126,]  360
## [127,]  342
## [128,]  406
## [129,]  396
## [130,]  420
## [131,]  472
## [132,]  548
## [133,]  559
## [134,]  463
## [135,]  407
## [136,]  362
## [137,]  405
## [138,]  417
## [139,]  391
## [140,]  419
## [141,]  461
## [142,]  472
## [143,]  535
## [144,]  622

Lagt(AirPassengers, 5)

##        [,1] [,2] [,3] [,4] [,5]
##   [1,]    0    0    0    0    0
##   [2,]  112    0    0    0    0
##   [3,]  118  112    0    0    0
##   [4,]  132  118  112    0    0
##   [5,]  129  132  118  112    0
##   [6,]  121  129  132  118  112
##   [7,]  135  121  129  132  118
##   [8,]  148  135  121  129  132
##   [9,]  148  148  135  121  129
##  [10,]  136  148  148  135  121
##  [11,]  119  136  148  148  135
##  [12,]  104  119  136  148  148
##  [13,]  118  104  119  136  148
##  [14,]  115  118  104  119  136
##  [15,]  126  115  118  104  119
##  [16,]  141  126  115  118  104
##  [17,]  135  141  126  115  118
##  [18,]  125  135  141  126  115
##  [19,]  149  125  135  141  126
##  [20,]  170  149  125  135  141
##  [21,]  170  170  149  125  135
##  [22,]  158  170  170  149  125
##  [23,]  133  158  170  170  149
##  [24,]  114  133  158  170  170
##  [25,]  140  114  133  158  170
##  [26,]  145  140  114  133  158
##  [27,]  150  145  140  114  133
##  [28,]  178  150  145  140  114
##  [29,]  163  178  150  145  140
##  [30,]  172  163  178  150  145
##  [31,]  178  172  163  178  150
##  [32,]  199  178  172  163  178
##  [33,]  199  199  178  172  163
##  [34,]  184  199  199  178  172
##  [35,]  162  184  199  199  178
##  [36,]  146  162  184  199  199
##  [37,]  166  146  162  184  199
##  [38,]  171  166  146  162  184
##  [39,]  180  171  166  146  162
##  [40,]  193  180  171  166  146
##  [41,]  181  193  180  171  166
##  [42,]  183  181  193  180  171
##  [43,]  218  183  181  193  180
##  [44,]  230  218  183  181  193
##  [45,]  242  230  218  183  181
##  [46,]  209  242  230  218  183
##  [47,]  191  209  242  230  218
##  [48,]  172  191  209  242  230
##  [49,]  194  172  191  209  242
##  [50,]  196  194  172  191  209
##  [51,]  196  196  194  172  191
##  [52,]  236  196  196  194  172
##  [53,]  235  236  196  196  194
##  [54,]  229  235  236  196  196
##  [55,]  243  229  235  236  196
##  [56,]  264  243  229  235  236
##  [57,]  272  264  243  229  235
##  [58,]  237  272  264  243  229
##  [59,]  211  237  272  264  243
##  [60,]  180  211  237  272  264
##  [61,]  201  180  211  237  272
##  [62,]  204  201  180  211  237
##  [63,]  188  204  201  180  211
##  [64,]  235  188  204  201  180
##  [65,]  227  235  188  204  201
##  [66,]  234  227  235  188  204
##  [67,]  264  234  227  235  188
##  [68,]  302  264  234  227  235
##  [69,]  293  302  264  234  227
##  [70,]  259  293  302  264  234
##  [71,]  229  259  293  302  264
##  [72,]  203  229  259  293  302
##  [73,]  229  203  229  259  293
##  [74,]  242  229  203  229  259
##  [75,]  233  242  229  203  229
##  [76,]  267  233  242  229  203
##  [77,]  269  267  233  242  229
##  [78,]  270  269  267  233  242
##  [79,]  315  270  269  267  233
##  [80,]  364  315  270  269  267
##  [81,]  347  364  315  270  269
##  [82,]  312  347  364  315  270
##  [83,]  274  312  347  364  315
##  [84,]  237  274  312  347  364
##  [85,]  278  237  274  312  347
##  [86,]  284  278  237  274  312
##  [87,]  277  284  278  237  274
##  [88,]  317  277  284  278  237
##  [89,]  313  317  277  284  278
##  [90,]  318  313  317  277  284
##  [91,]  374  318  313  317  277
##  [92,]  413  374  318  313  317
##  [93,]  405  413  374  318  313
##  [94,]  355  405  413  374  318
##  [95,]  306  355  405  413  374
##  [96,]  271  306  355  405  413
##  [97,]  306  271  306  355  405
##  [98,]  315  306  271  306  355
##  [99,]  301  315  306  271  306
## [100,]  356  301  315  306  271
## [101,]  348  356  301  315  306
## [102,]  355  348  356  301  315
## [103,]  422  355  348  356  301
## [104,]  465  422  355  348  356
## [105,]  467  465  422  355  348
## [106,]  404  467  465  422  355
## [107,]  347  404  467  465  422
## [108,]  305  347  404  467  465
## [109,]  336  305  347  404  467
## [110,]  340  336  305  347  404
## [111,]  318  340  336  305  347
## [112,]  362  318  340  336  305
## [113,]  348  362  318  340  336
## [114,]  363  348  362  318  340
## [115,]  435  363  348  362  318
## [116,]  491  435  363  348  362
## [117,]  505  491  435  363  348
## [118,]  404  505  491  435  363
## [119,]  359  404  505  491  435
## [120,]  310  359  404  505  491
## [121,]  337  310  359  404  505
## [122,]  360  337  310  359  404
## [123,]  342  360  337  310  359
## [124,]  406  342  360  337  310
## [125,]  396  406  342  360  337
## [126,]  420  396  406  342  360
## [127,]  472  420  396  406  342
## [128,]  548  472  420  396  406
## [129,]  559  548  472  420  396
## [130,]  463  559  548  472  420
## [131,]  407  463  559  548  472
## [132,]  362  407  463  559  548
## [133,]  405  362  407  463  559
## [134,]  417  405  362  407  463
## [135,]  391  417  405  362  407
## [136,]  419  391  417  405  362
## [137,]  461  419  391  417  405
## [138,]  472  461  419  391  417
## [139,]  535  472  461  419  391
## [140,]  622  535  472  461  419
## [141,]  606  622  535  472  461
## [142,]  508  606  622  535  472
## [143,]  461  508  606  622  535
## [144,]  390  461  508  606  622

FASE 1: IDENTIFICACION

rec = scan("recruit.dat")
soi=scan("soi.dat")

rec1<-ts(rec, start = c(1950,1), end = c(1986,9), frequency = 12) 
soi1<-ts(soi, start = c(1950,1), end = c(1986,9), frequency = 12)
length(rec1)

## [1] 441

xreg1 = soi1
xreg1

##             Jan        Feb        Mar        Apr        May        Jun
## 1950  0.3770000  0.2460000  0.3110000  0.1040000 -0.0160000  0.2350000
## 1951 -0.1580000  0.3660000  0.6070000 -0.3550000 -0.1800000  0.2680000
## 1952  0.7600000  0.8910000  0.6070000  0.5740000  0.0050000  0.4750000
## 1953  0.5300000  0.5300000  0.3770000 -0.2350000 -0.5850000 -0.1800000
## 1954  0.4100000  0.2240000  0.1480000 -0.4320000 -0.0930000 -0.2680000
## 1955  0.3440000 -0.0380000  0.2900000 -0.1260000 -0.3660000 -0.1150000
## 1956  0.6500000  0.6280000  0.1260000  0.1690000  0.1370000 -0.2570000
## 1957  0.1910000  1.0000000  0.4860000  0.4100000  0.1580000  0.1260000
## 1958  0.7050000  0.6390000  0.4540000  0.3110000  0.3550000 -0.1580000
## 1959  0.0820000  0.1480000  0.0600000 -0.1910000 -0.6070000 -0.5850000
## 1960  0.1690000  0.4320000  0.2020000 -0.3660000 -0.6610000  0.0930000
## 1961  0.6070000  0.1800000  0.0710000  0.2460000 -0.4320000  0.0600000
## 1962  0.1690000  0.3330000 -0.0050000 -0.0380000 -0.1260000 -0.4430000
## 1963  0.3110000  0.5960000  0.0050000  0.3880000 -0.5080001 -0.5520000
## 1964  0.3220000  0.1800000  0.1260000  0.0820000  0.1260000 -0.2130000
## 1965  0.7380000  0.4430000  0.5960000 -0.1370000 -0.4860000 -0.3770000
## 1966  0.3110000  0.3880000  0.3880000  0.1800000 -0.3330000  0.0490000
## 1967  0.3330000  0.3770000  0.0710000 -0.1580000 -0.5410000 -0.6830000
## 1968  0.1150000  0.4640000  0.1040000 -0.1800000 -0.6720000  0.1040000
## 1969  0.5300000  0.6610000  0.3550000 -0.3440000 -0.0380000  0.2350000
## 1970  0.7050000  0.3770000  0.5850000 -0.1260000 -0.2130000  0.1480000
## 1971  0.0820000  0.5740000  0.3550000 -0.2570000 -0.3770000 -0.3440000
## 1972  0.3660000  0.3660000  0.0380000 -0.2680000  0.3220000  0.0820000
## 1973  0.6610000  0.7160000  0.6280000  0.1910000  0.5300000  0.1800000
## 1974  0.1040000  0.2240000  0.4320000 -0.2130000 -0.9670000 -1.0000000
## 1975  0.3330000  0.3550000  0.3880000 -0.0600000 -0.2020000  0.0050000
## 1976  0.8030000  0.8360000  0.6500000  0.0050000 -0.3660000  0.0710000
## 1977  0.2350000 -0.0930000  0.4750000 -0.0820000 -0.6170000 -0.0930000
## 1978  0.5520000  0.6070000  0.4640000 -0.3010000 -0.7700000 -0.6500000
## 1979  0.0820000  0.6070000 -0.1580000 -0.4540000 -0.7810000 -0.3880000
## 1980  0.3990000  0.0270000  0.0160000 -0.3770000 -0.1800000 -0.0380000
## 1981  0.1690000  0.3990000  0.1580000 -0.5410000 -0.6280000  0.0270000
## 1982  0.4540000  0.3010000 -0.0050000 -0.0930000 -0.2240000 -0.2130000
## 1983  0.7700000  0.6070000 -0.1580000 -0.2350000 -0.2020000 -0.3330000
## 1984  0.5190000  0.5410000  0.3010000 -0.5740000 -0.3440000 -0.2790000
## 1985 -0.6070000 -0.5630000 -0.2350000 -0.2460000 -0.3990000 -0.3330000
## 1986  0.0490000  0.4540000  0.1580000 -0.4210000 -0.2680000 -0.3110000
##             Jul        Aug        Sep        Oct        Nov        Dec
## 1950  0.1370000  0.1910000 -0.0160000  0.2900000  0.0380000 -0.0160000
## 1951  0.0930000  0.0270000  0.2460000  0.2020000  0.4320000  0.6170000
## 1952  0.2020000 -0.0270000 -0.0380000  0.7160000  0.8360000  0.8910000
## 1953 -0.5300000 -0.4640000 -0.4430000  0.0490000  0.4540000  0.2570000
## 1954  0.1580000 -0.0600000 -0.3990000  0.2350000  0.3660000  0.2020000
## 1955 -0.3010000 -0.4860000 -0.1370000  0.7380000  0.3660000  0.3660000
## 1956  0.1690000 -0.0930000  0.4750000  0.6390000  0.5960000  0.7490000
## 1957  0.0600000  0.2460000  0.7380000  0.8030000  0.4210000  0.6170000
## 1958 -0.0380000  0.1150000  0.1370000  0.2570000  0.1150000  0.0380000
## 1959 -0.2680000 -0.0930000 -0.0930000  0.2570000 -0.0050000  0.2240000
## 1960 -0.7160000  0.1480000 -0.0930000  0.2790000  0.4320000 -0.1040000
## 1961 -0.3880000  0.2020000 -0.1040000  0.1910000  0.4750000  0.5520000
## 1962 -0.0160000  0.0270000  0.3330000  0.3550000  0.3440000  0.1150000
## 1963 -0.8580000 -0.5960000  0.0600000  0.0710000  0.2240000  0.2790000
## 1964 -0.2350000  0.1690000  0.3880000  0.5190000  0.1260000  0.4100000
## 1965  0.2680000 -0.1690000 -0.2130000 -0.1910000  0.3770000  0.1260000
## 1966 -0.0820000  0.1910000  0.3990000  0.0930000  0.0050000  0.3660000
## 1967 -0.6830000 -0.3440000 -0.3010000  0.2020000 -0.1260000  0.0820000
## 1968 -0.4860000  0.0930000  0.2790000  0.1040000  0.1800000  0.4750000
## 1969  0.4860000  0.1690000  0.3330000  0.1370000  0.1690000  0.3330000
## 1970 -0.1260000 -0.3440000 -0.5080001  0.2790000  0.0820000  0.3550000
## 1971 -0.6500000 -0.0930000 -0.1370000  0.1150000  0.7050000  0.3990000
## 1972  0.0820000  0.0600000  0.2680000  0.4210000  0.7700000  0.8030000
## 1973 -0.4640000  0.2790000  0.3550000  0.2020000  0.5520000  0.6170000
## 1974 -0.4320000 -0.6830000 -0.5080001 -0.1370000  0.0820000 -0.0600000
## 1975 -0.1150000  0.1370000  0.4540000  0.3880000  0.7380000  0.7700000
## 1976 -0.0050000 -0.4540000  0.1910000  0.4320000  0.6830000  0.3880000
## 1977 -0.0710000  0.4320000  0.4210000  0.4970000  0.4540000  0.5960000
## 1978 -0.6940000 -0.1370000 -0.4640000 -0.2460000  0.1690000 -0.2020000
## 1979  0.1800000  0.0600000 -0.5080001 -0.2680000  0.2240000  0.1150000
## 1980 -0.2020000  0.1370000  0.0930000 -0.2790000 -0.0380000  0.2350000
## 1981 -0.7380000 -0.9130000 -0.0270000  0.0710000 -0.1260000  0.0490000
## 1982 -0.3110000 -0.2350000 -0.3220000  0.3220000  0.0930000  0.1150000
## 1983 -0.1580000 -0.2240000 -0.3550000  0.0050000  0.4540000  0.4100000
## 1984 -0.7160000 -0.8690000 -0.5960000 -0.2900000 -0.4540000 -0.2460000
## 1985 -0.5300000 -0.0490000  0.1580000  0.1150000  0.3220000  0.1150000
## 1986 -0.1150000 -0.3220000 -0.3220000

Modelo 1

modelo1 = Arima(rec1, order = c(1,1,0),
                 season = list(order = c(0,1,1), 
                               freq = 12),
                 xreg = xreg1)

tt <- modelo1$coef[which(modelo1$coef!=0)]/sqrt(diag(modelo1$var.coef))
1 - pt(abs(tt),(modelo1$nobs - length(modelo1$coef[which(modelo1$coef!=0)])))

##          ar1         sma1         xreg 
## 7.194207e-10 0.000000e+00 3.154170e-01

Modelo 2

modelo2 = Arima(rec1, order = c(1,1,0),
                 season = list(order = c(0,1,1), 
                               freq = 12),
                 xreg = xreg1)

BIC(modelo2)

## [1] 3161.057

ttest(modelo2)

##         ar1        sma1        xreg 
##   6.1875444 -16.6469189   0.4809015

tt <- modelo2$coef[which(modelo2$coef!=0)]/sqrt(diag(modelo2$var.coef))
1 - pt(abs(tt),(modelo2$nobs - length(modelo2$coef[which(modelo2$coef!=0)])))

##          ar1         sma1         xreg 
## 7.194207e-10 0.000000e+00 3.154170e-01

et <- residuals(modelo2)
Box.test(et,lag=12,type="Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  et
## X-squared = 15.916, df = 12, p-value = 0.1951

tsdiag(modelo2, gof.lag=20 )

jarque.bera.test(et)

## 
##  Jarque Bera Test
## 
## data:  et
## X-squared = 107.18, df = 2, p-value < 2.2e-16

plotresiduos(et, rec1)

modelo 3: Soi rezagado

xreg2 = soi1
xlag = Lagt(xreg2, 6)
xlag# FUNCION ARRIBA 6

##              [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
##   [1,]  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
##   [2,]  0.3770000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
##   [3,]  0.2460000  0.3770000  0.0000000  0.0000000  0.0000000  0.0000000
##   [4,]  0.3110000  0.2460000  0.3770000  0.0000000  0.0000000  0.0000000
##   [5,]  0.1040000  0.3110000  0.2460000  0.3770000  0.0000000  0.0000000
##   [6,] -0.0160000  0.1040000  0.3110000  0.2460000  0.3770000  0.0000000
##   [7,]  0.2350000 -0.0160000  0.1040000  0.3110000  0.2460000  0.3770000
##   [8,]  0.1370000  0.2350000 -0.0160000  0.1040000  0.3110000  0.2460000
##   [9,]  0.1910000  0.1370000  0.2350000 -0.0160000  0.1040000  0.3110000
##  [10,] -0.0160000  0.1910000  0.1370000  0.2350000 -0.0160000  0.1040000
##  [11,]  0.2900000 -0.0160000  0.1910000  0.1370000  0.2350000 -0.0160000
##  [12,]  0.0380000  0.2900000 -0.0160000  0.1910000  0.1370000  0.2350000
##  [13,] -0.0160000  0.0380000  0.2900000 -0.0160000  0.1910000  0.1370000
##  [14,] -0.1580000 -0.0160000  0.0380000  0.2900000 -0.0160000  0.1910000
##  [15,]  0.3660000 -0.1580000 -0.0160000  0.0380000  0.2900000 -0.0160000
##  [16,]  0.6070000  0.3660000 -0.1580000 -0.0160000  0.0380000  0.2900000
##  [17,] -0.3550000  0.6070000  0.3660000 -0.1580000 -0.0160000  0.0380000
##  [18,] -0.1800000 -0.3550000  0.6070000  0.3660000 -0.1580000 -0.0160000
##  [19,]  0.2680000 -0.1800000 -0.3550000  0.6070000  0.3660000 -0.1580000
##  [20,]  0.0930000  0.2680000 -0.1800000 -0.3550000  0.6070000  0.3660000
##  [21,]  0.0270000  0.0930000  0.2680000 -0.1800000 -0.3550000  0.6070000
##  [22,]  0.2460000  0.0270000  0.0930000  0.2680000 -0.1800000 -0.3550000
##  [23,]  0.2020000  0.2460000  0.0270000  0.0930000  0.2680000 -0.1800000
##  [24,]  0.4320000  0.2020000  0.2460000  0.0270000  0.0930000  0.2680000
##  [25,]  0.6170000  0.4320000  0.2020000  0.2460000  0.0270000  0.0930000
##  [26,]  0.7600000  0.6170000  0.4320000  0.2020000  0.2460000  0.0270000
##  [27,]  0.8910000  0.7600000  0.6170000  0.4320000  0.2020000  0.2460000
##  [28,]  0.6070000  0.8910000  0.7600000  0.6170000  0.4320000  0.2020000
##  [29,]  0.5740000  0.6070000  0.8910000  0.7600000  0.6170000  0.4320000
##  [30,]  0.0050000  0.5740000  0.6070000  0.8910000  0.7600000  0.6170000
##  [31,]  0.4750000  0.0050000  0.5740000  0.6070000  0.8910000  0.7600000
##  [32,]  0.2020000  0.4750000  0.0050000  0.5740000  0.6070000  0.8910000
##  [33,] -0.0270000  0.2020000  0.4750000  0.0050000  0.5740000  0.6070000
##  [34,] -0.0380000 -0.0270000  0.2020000  0.4750000  0.0050000  0.5740000
##  [35,]  0.7160000 -0.0380000 -0.0270000  0.2020000  0.4750000  0.0050000
##  [36,]  0.8360000  0.7160000 -0.0380000 -0.0270000  0.2020000  0.4750000
##  [37,]  0.8910000  0.8360000  0.7160000 -0.0380000 -0.0270000  0.2020000
##  [38,]  0.5300000  0.8910000  0.8360000  0.7160000 -0.0380000 -0.0270000
##  [39,]  0.5300000  0.5300000  0.8910000  0.8360000  0.7160000 -0.0380000
##  [40,]  0.3770000  0.5300000  0.5300000  0.8910000  0.8360000  0.7160000
##  [41,] -0.2350000  0.3770000  0.5300000  0.5300000  0.8910000  0.8360000
##  [42,] -0.5850000 -0.2350000  0.3770000  0.5300000  0.5300000  0.8910000
##  [43,] -0.1800000 -0.5850000 -0.2350000  0.3770000  0.5300000  0.5300000
##  [44,] -0.5300000 -0.1800000 -0.5850000 -0.2350000  0.3770000  0.5300000
##  [45,] -0.4640000 -0.5300000 -0.1800000 -0.5850000 -0.2350000  0.3770000
##  [46,] -0.4430000 -0.4640000 -0.5300000 -0.1800000 -0.5850000 -0.2350000
##  [47,]  0.0490000 -0.4430000 -0.4640000 -0.5300000 -0.1800000 -0.5850000
##  [48,]  0.4540000  0.0490000 -0.4430000 -0.4640000 -0.5300000 -0.1800000
##  [49,]  0.2570000  0.4540000  0.0490000 -0.4430000 -0.4640000 -0.5300000
##  [50,]  0.4100000  0.2570000  0.4540000  0.0490000 -0.4430000 -0.4640000
##  [51,]  0.2240000  0.4100000  0.2570000  0.4540000  0.0490000 -0.4430000
##  [52,]  0.1480000  0.2240000  0.4100000  0.2570000  0.4540000  0.0490000
##  [53,] -0.4320000  0.1480000  0.2240000  0.4100000  0.2570000  0.4540000
##  [54,] -0.0930000 -0.4320000  0.1480000  0.2240000  0.4100000  0.2570000
##  [55,] -0.2680000 -0.0930000 -0.4320000  0.1480000  0.2240000  0.4100000
##  [56,]  0.1580000 -0.2680000 -0.0930000 -0.4320000  0.1480000  0.2240000
##  [57,] -0.0600000  0.1580000 -0.2680000 -0.0930000 -0.4320000  0.1480000
##  [58,] -0.3990000 -0.0600000  0.1580000 -0.2680000 -0.0930000 -0.4320000
##  [59,]  0.2350000 -0.3990000 -0.0600000  0.1580000 -0.2680000 -0.0930000
##  [60,]  0.3660000  0.2350000 -0.3990000 -0.0600000  0.1580000 -0.2680000
##  [61,]  0.2020000  0.3660000  0.2350000 -0.3990000 -0.0600000  0.1580000
##  [62,]  0.3440000  0.2020000  0.3660000  0.2350000 -0.3990000 -0.0600000
##  [63,] -0.0380000  0.3440000  0.2020000  0.3660000  0.2350000 -0.3990000
##  [64,]  0.2900000 -0.0380000  0.3440000  0.2020000  0.3660000  0.2350000
##  [65,] -0.1260000  0.2900000 -0.0380000  0.3440000  0.2020000  0.3660000
##  [66,] -0.3660000 -0.1260000  0.2900000 -0.0380000  0.3440000  0.2020000
##  [67,] -0.1150000 -0.3660000 -0.1260000  0.2900000 -0.0380000  0.3440000
##  [68,] -0.3010000 -0.1150000 -0.3660000 -0.1260000  0.2900000 -0.0380000
##  [69,] -0.4860000 -0.3010000 -0.1150000 -0.3660000 -0.1260000  0.2900000
##  [70,] -0.1370000 -0.4860000 -0.3010000 -0.1150000 -0.3660000 -0.1260000
##  [71,]  0.7380000 -0.1370000 -0.4860000 -0.3010000 -0.1150000 -0.3660000
##  [72,]  0.3660000  0.7380000 -0.1370000 -0.4860000 -0.3010000 -0.1150000
##  [73,]  0.3660000  0.3660000  0.7380000 -0.1370000 -0.4860000 -0.3010000
##  [74,]  0.6500000  0.3660000  0.3660000  0.7380000 -0.1370000 -0.4860000
##  [75,]  0.6280000  0.6500000  0.3660000  0.3660000  0.7380000 -0.1370000
##  [76,]  0.1260000  0.6280000  0.6500000  0.3660000  0.3660000  0.7380000
##  [77,]  0.1690000  0.1260000  0.6280000  0.6500000  0.3660000  0.3660000
##  [78,]  0.1370000  0.1690000  0.1260000  0.6280000  0.6500000  0.3660000
##  [79,] -0.2570000  0.1370000  0.1690000  0.1260000  0.6280000  0.6500000
##  [80,]  0.1690000 -0.2570000  0.1370000  0.1690000  0.1260000  0.6280000
##  [81,] -0.0930000  0.1690000 -0.2570000  0.1370000  0.1690000  0.1260000
##  [82,]  0.4750000 -0.0930000  0.1690000 -0.2570000  0.1370000  0.1690000
##  [83,]  0.6390000  0.4750000 -0.0930000  0.1690000 -0.2570000  0.1370000
##  [84,]  0.5960000  0.6390000  0.4750000 -0.0930000  0.1690000 -0.2570000
##  [85,]  0.7490000  0.5960000  0.6390000  0.4750000 -0.0930000  0.1690000
##  [86,]  0.1910000  0.7490000  0.5960000  0.6390000  0.4750000 -0.0930000
##  [87,]  1.0000000  0.1910000  0.7490000  0.5960000  0.6390000  0.4750000
##  [88,]  0.4860000  1.0000000  0.1910000  0.7490000  0.5960000  0.6390000
##  [89,]  0.4100000  0.4860000  1.0000000  0.1910000  0.7490000  0.5960000
##  [90,]  0.1580000  0.4100000  0.4860000  1.0000000  0.1910000  0.7490000
##  [91,]  0.1260000  0.1580000  0.4100000  0.4860000  1.0000000  0.1910000
##  [92,]  0.0600000  0.1260000  0.1580000  0.4100000  0.4860000  1.0000000
##  [93,]  0.2460000  0.0600000  0.1260000  0.1580000  0.4100000  0.4860000
##  [94,]  0.7380000  0.2460000  0.0600000  0.1260000  0.1580000  0.4100000
##  [95,]  0.8030000  0.7380000  0.2460000  0.0600000  0.1260000  0.1580000
##  [96,]  0.4210000  0.8030000  0.7380000  0.2460000  0.0600000  0.1260000
##  [97,]  0.6170000  0.4210000  0.8030000  0.7380000  0.2460000  0.0600000
##  [98,]  0.7050000  0.6170000  0.4210000  0.8030000  0.7380000  0.2460000
##  [99,]  0.6390000  0.7050000  0.6170000  0.4210000  0.8030000  0.7380000
## [100,]  0.4540000  0.6390000  0.7050000  0.6170000  0.4210000  0.8030000
## [101,]  0.3110000  0.4540000  0.6390000  0.7050000  0.6170000  0.4210000
## [102,]  0.3550000  0.3110000  0.4540000  0.6390000  0.7050000  0.6170000
## [103,] -0.1580000  0.3550000  0.3110000  0.4540000  0.6390000  0.7050000
## [104,] -0.0380000 -0.1580000  0.3550000  0.3110000  0.4540000  0.6390000
## [105,]  0.1150000 -0.0380000 -0.1580000  0.3550000  0.3110000  0.4540000
## [106,]  0.1370000  0.1150000 -0.0380000 -0.1580000  0.3550000  0.3110000
## [107,]  0.2570000  0.1370000  0.1150000 -0.0380000 -0.1580000  0.3550000
## [108,]  0.1150000  0.2570000  0.1370000  0.1150000 -0.0380000 -0.1580000
## [109,]  0.0380000  0.1150000  0.2570000  0.1370000  0.1150000 -0.0380000
## [110,]  0.0820000  0.0380000  0.1150000  0.2570000  0.1370000  0.1150000
## [111,]  0.1480000  0.0820000  0.0380000  0.1150000  0.2570000  0.1370000
## [112,]  0.0600000  0.1480000  0.0820000  0.0380000  0.1150000  0.2570000
## [113,] -0.1910000  0.0600000  0.1480000  0.0820000  0.0380000  0.1150000
## [114,] -0.6070000 -0.1910000  0.0600000  0.1480000  0.0820000  0.0380000
## [115,] -0.5850000 -0.6070000 -0.1910000  0.0600000  0.1480000  0.0820000
## [116,] -0.2680000 -0.5850000 -0.6070000 -0.1910000  0.0600000  0.1480000
## [117,] -0.0930000 -0.2680000 -0.5850000 -0.6070000 -0.1910000  0.0600000
## [118,] -0.0930000 -0.0930000 -0.2680000 -0.5850000 -0.6070000 -0.1910000
## [119,]  0.2570000 -0.0930000 -0.0930000 -0.2680000 -0.5850000 -0.6070000
## [120,] -0.0050000  0.2570000 -0.0930000 -0.0930000 -0.2680000 -0.5850000
## [121,]  0.2240000 -0.0050000  0.2570000 -0.0930000 -0.0930000 -0.2680000
## [122,]  0.1690000  0.2240000 -0.0050000  0.2570000 -0.0930000 -0.0930000
## [123,]  0.4320000  0.1690000  0.2240000 -0.0050000  0.2570000 -0.0930000
## [124,]  0.2020000  0.4320000  0.1690000  0.2240000 -0.0050000  0.2570000
## [125,] -0.3660000  0.2020000  0.4320000  0.1690000  0.2240000 -0.0050000
## [126,] -0.6610000 -0.3660000  0.2020000  0.4320000  0.1690000  0.2240000
## [127,]  0.0930000 -0.6610000 -0.3660000  0.2020000  0.4320000  0.1690000
## [128,] -0.7160000  0.0930000 -0.6610000 -0.3660000  0.2020000  0.4320000
## [129,]  0.1480000 -0.7160000  0.0930000 -0.6610000 -0.3660000  0.2020000
## [130,] -0.0930000  0.1480000 -0.7160000  0.0930000 -0.6610000 -0.3660000
## [131,]  0.2790000 -0.0930000  0.1480000 -0.7160000  0.0930000 -0.6610000
## [132,]  0.4320000  0.2790000 -0.0930000  0.1480000 -0.7160000  0.0930000
## [133,] -0.1040000  0.4320000  0.2790000 -0.0930000  0.1480000 -0.7160000
## [134,]  0.6070000 -0.1040000  0.4320000  0.2790000 -0.0930000  0.1480000
## [135,]  0.1800000  0.6070000 -0.1040000  0.4320000  0.2790000 -0.0930000
## [136,]  0.0710000  0.1800000  0.6070000 -0.1040000  0.4320000  0.2790000
## [137,]  0.2460000  0.0710000  0.1800000  0.6070000 -0.1040000  0.4320000
## [138,] -0.4320000  0.2460000  0.0710000  0.1800000  0.6070000 -0.1040000
## [139,]  0.0600000 -0.4320000  0.2460000  0.0710000  0.1800000  0.6070000
## [140,] -0.3880000  0.0600000 -0.4320000  0.2460000  0.0710000  0.1800000
## [141,]  0.2020000 -0.3880000  0.0600000 -0.4320000  0.2460000  0.0710000
## [142,] -0.1040000  0.2020000 -0.3880000  0.0600000 -0.4320000  0.2460000
## [143,]  0.1910000 -0.1040000  0.2020000 -0.3880000  0.0600000 -0.4320000
## [144,]  0.4750000  0.1910000 -0.1040000  0.2020000 -0.3880000  0.0600000
## [145,]  0.5520000  0.4750000  0.1910000 -0.1040000  0.2020000 -0.3880000
## [146,]  0.1690000  0.5520000  0.4750000  0.1910000 -0.1040000  0.2020000
## [147,]  0.3330000  0.1690000  0.5520000  0.4750000  0.1910000 -0.1040000
## [148,] -0.0050000  0.3330000  0.1690000  0.5520000  0.4750000  0.1910000
## [149,] -0.0380000 -0.0050000  0.3330000  0.1690000  0.5520000  0.4750000
## [150,] -0.1260000 -0.0380000 -0.0050000  0.3330000  0.1690000  0.5520000
## [151,] -0.4430000 -0.1260000 -0.0380000 -0.0050000  0.3330000  0.1690000
## [152,] -0.0160000 -0.4430000 -0.1260000 -0.0380000 -0.0050000  0.3330000
## [153,]  0.0270000 -0.0160000 -0.4430000 -0.1260000 -0.0380000 -0.0050000
## [154,]  0.3330000  0.0270000 -0.0160000 -0.4430000 -0.1260000 -0.0380000
## [155,]  0.3550000  0.3330000  0.0270000 -0.0160000 -0.4430000 -0.1260000
## [156,]  0.3440000  0.3550000  0.3330000  0.0270000 -0.0160000 -0.4430000
## [157,]  0.1150000  0.3440000  0.3550000  0.3330000  0.0270000 -0.0160000
## [158,]  0.3110000  0.1150000  0.3440000  0.3550000  0.3330000  0.0270000
## [159,]  0.5960000  0.3110000  0.1150000  0.3440000  0.3550000  0.3330000
## [160,]  0.0050000  0.5960000  0.3110000  0.1150000  0.3440000  0.3550000
## [161,]  0.3880000  0.0050000  0.5960000  0.3110000  0.1150000  0.3440000
## [162,] -0.5080001  0.3880000  0.0050000  0.5960000  0.3110000  0.1150000
## [163,] -0.5520000 -0.5080001  0.3880000  0.0050000  0.5960000  0.3110000
## [164,] -0.8580000 -0.5520000 -0.5080001  0.3880000  0.0050000  0.5960000
## [165,] -0.5960000 -0.8580000 -0.5520000 -0.5080001  0.3880000  0.0050000
## [166,]  0.0600000 -0.5960000 -0.8580000 -0.5520000 -0.5080001  0.3880000
## [167,]  0.0710000  0.0600000 -0.5960000 -0.8580000 -0.5520000 -0.5080001
## [168,]  0.2240000  0.0710000  0.0600000 -0.5960000 -0.8580000 -0.5520000
## [169,]  0.2790000  0.2240000  0.0710000  0.0600000 -0.5960000 -0.8580000
## [170,]  0.3220000  0.2790000  0.2240000  0.0710000  0.0600000 -0.5960000
## [171,]  0.1800000  0.3220000  0.2790000  0.2240000  0.0710000  0.0600000
## [172,]  0.1260000  0.1800000  0.3220000  0.2790000  0.2240000  0.0710000
## [173,]  0.0820000  0.1260000  0.1800000  0.3220000  0.2790000  0.2240000
## [174,]  0.1260000  0.0820000  0.1260000  0.1800000  0.3220000  0.2790000
## [175,] -0.2130000  0.1260000  0.0820000  0.1260000  0.1800000  0.3220000
## [176,] -0.2350000 -0.2130000  0.1260000  0.0820000  0.1260000  0.1800000
## [177,]  0.1690000 -0.2350000 -0.2130000  0.1260000  0.0820000  0.1260000
## [178,]  0.3880000  0.1690000 -0.2350000 -0.2130000  0.1260000  0.0820000
## [179,]  0.5190000  0.3880000  0.1690000 -0.2350000 -0.2130000  0.1260000
## [180,]  0.1260000  0.5190000  0.3880000  0.1690000 -0.2350000 -0.2130000
## [181,]  0.4100000  0.1260000  0.5190000  0.3880000  0.1690000 -0.2350000
## [182,]  0.7380000  0.4100000  0.1260000  0.5190000  0.3880000  0.1690000
## [183,]  0.4430000  0.7380000  0.4100000  0.1260000  0.5190000  0.3880000
## [184,]  0.5960000  0.4430000  0.7380000  0.4100000  0.1260000  0.5190000
## [185,] -0.1370000  0.5960000  0.4430000  0.7380000  0.4100000  0.1260000
## [186,] -0.4860000 -0.1370000  0.5960000  0.4430000  0.7380000  0.4100000
## [187,] -0.3770000 -0.4860000 -0.1370000  0.5960000  0.4430000  0.7380000
## [188,]  0.2680000 -0.3770000 -0.4860000 -0.1370000  0.5960000  0.4430000
## [189,] -0.1690000  0.2680000 -0.3770000 -0.4860000 -0.1370000  0.5960000
## [190,] -0.2130000 -0.1690000  0.2680000 -0.3770000 -0.4860000 -0.1370000
## [191,] -0.1910000 -0.2130000 -0.1690000  0.2680000 -0.3770000 -0.4860000
## [192,]  0.3770000 -0.1910000 -0.2130000 -0.1690000  0.2680000 -0.3770000
## [193,]  0.1260000  0.3770000 -0.1910000 -0.2130000 -0.1690000  0.2680000
## [194,]  0.3110000  0.1260000  0.3770000 -0.1910000 -0.2130000 -0.1690000
## [195,]  0.3880000  0.3110000  0.1260000  0.3770000 -0.1910000 -0.2130000
## [196,]  0.3880000  0.3880000  0.3110000  0.1260000  0.3770000 -0.1910000
## [197,]  0.1800000  0.3880000  0.3880000  0.3110000  0.1260000  0.3770000
## [198,] -0.3330000  0.1800000  0.3880000  0.3880000  0.3110000  0.1260000
## [199,]  0.0490000 -0.3330000  0.1800000  0.3880000  0.3880000  0.3110000
## [200,] -0.0820000  0.0490000 -0.3330000  0.1800000  0.3880000  0.3880000
## [201,]  0.1910000 -0.0820000  0.0490000 -0.3330000  0.1800000  0.3880000
## [202,]  0.3990000  0.1910000 -0.0820000  0.0490000 -0.3330000  0.1800000
## [203,]  0.0930000  0.3990000  0.1910000 -0.0820000  0.0490000 -0.3330000
## [204,]  0.0050000  0.0930000  0.3990000  0.1910000 -0.0820000  0.0490000
## [205,]  0.3660000  0.0050000  0.0930000  0.3990000  0.1910000 -0.0820000
## [206,]  0.3330000  0.3660000  0.0050000  0.0930000  0.3990000  0.1910000
## [207,]  0.3770000  0.3330000  0.3660000  0.0050000  0.0930000  0.3990000
## [208,]  0.0710000  0.3770000  0.3330000  0.3660000  0.0050000  0.0930000
## [209,] -0.1580000  0.0710000  0.3770000  0.3330000  0.3660000  0.0050000
## [210,] -0.5410000 -0.1580000  0.0710000  0.3770000  0.3330000  0.3660000
## [211,] -0.6830000 -0.5410000 -0.1580000  0.0710000  0.3770000  0.3330000
## [212,] -0.6830000 -0.6830000 -0.5410000 -0.1580000  0.0710000  0.3770000
## [213,] -0.3440000 -0.6830000 -0.6830000 -0.5410000 -0.1580000  0.0710000
## [214,] -0.3010000 -0.3440000 -0.6830000 -0.6830000 -0.5410000 -0.1580000
## [215,]  0.2020000 -0.3010000 -0.3440000 -0.6830000 -0.6830000 -0.5410000
## [216,] -0.1260000  0.2020000 -0.3010000 -0.3440000 -0.6830000 -0.6830000
## [217,]  0.0820000 -0.1260000  0.2020000 -0.3010000 -0.3440000 -0.6830000
## [218,]  0.1150000  0.0820000 -0.1260000  0.2020000 -0.3010000 -0.3440000
## [219,]  0.4640000  0.1150000  0.0820000 -0.1260000  0.2020000 -0.3010000
## [220,]  0.1040000  0.4640000  0.1150000  0.0820000 -0.1260000  0.2020000
## [221,] -0.1800000  0.1040000  0.4640000  0.1150000  0.0820000 -0.1260000
## [222,] -0.6720000 -0.1800000  0.1040000  0.4640000  0.1150000  0.0820000
## [223,]  0.1040000 -0.6720000 -0.1800000  0.1040000  0.4640000  0.1150000
## [224,] -0.4860000  0.1040000 -0.6720000 -0.1800000  0.1040000  0.4640000
## [225,]  0.0930000 -0.4860000  0.1040000 -0.6720000 -0.1800000  0.1040000
## [226,]  0.2790000  0.0930000 -0.4860000  0.1040000 -0.6720000 -0.1800000
## [227,]  0.1040000  0.2790000  0.0930000 -0.4860000  0.1040000 -0.6720000
## [228,]  0.1800000  0.1040000  0.2790000  0.0930000 -0.4860000  0.1040000
## [229,]  0.4750000  0.1800000  0.1040000  0.2790000  0.0930000 -0.4860000
## [230,]  0.5300000  0.4750000  0.1800000  0.1040000  0.2790000  0.0930000
## [231,]  0.6610000  0.5300000  0.4750000  0.1800000  0.1040000  0.2790000
## [232,]  0.3550000  0.6610000  0.5300000  0.4750000  0.1800000  0.1040000
## [233,] -0.3440000  0.3550000  0.6610000  0.5300000  0.4750000  0.1800000
## [234,] -0.0380000 -0.3440000  0.3550000  0.6610000  0.5300000  0.4750000
## [235,]  0.2350000 -0.0380000 -0.3440000  0.3550000  0.6610000  0.5300000
## [236,]  0.4860000  0.2350000 -0.0380000 -0.3440000  0.3550000  0.6610000
## [237,]  0.1690000  0.4860000  0.2350000 -0.0380000 -0.3440000  0.3550000
## [238,]  0.3330000  0.1690000  0.4860000  0.2350000 -0.0380000 -0.3440000
## [239,]  0.1370000  0.3330000  0.1690000  0.4860000  0.2350000 -0.0380000
## [240,]  0.1690000  0.1370000  0.3330000  0.1690000  0.4860000  0.2350000
## [241,]  0.3330000  0.1690000  0.1370000  0.3330000  0.1690000  0.4860000
## [242,]  0.7050000  0.3330000  0.1690000  0.1370000  0.3330000  0.1690000
## [243,]  0.3770000  0.7050000  0.3330000  0.1690000  0.1370000  0.3330000
## [244,]  0.5850000  0.3770000  0.7050000  0.3330000  0.1690000  0.1370000
## [245,] -0.1260000  0.5850000  0.3770000  0.7050000  0.3330000  0.1690000
## [246,] -0.2130000 -0.1260000  0.5850000  0.3770000  0.7050000  0.3330000
## [247,]  0.1480000 -0.2130000 -0.1260000  0.5850000  0.3770000  0.7050000
## [248,] -0.1260000  0.1480000 -0.2130000 -0.1260000  0.5850000  0.3770000
## [249,] -0.3440000 -0.1260000  0.1480000 -0.2130000 -0.1260000  0.5850000
## [250,] -0.5080001 -0.3440000 -0.1260000  0.1480000 -0.2130000 -0.1260000
## [251,]  0.2790000 -0.5080001 -0.3440000 -0.1260000  0.1480000 -0.2130000
## [252,]  0.0820000  0.2790000 -0.5080001 -0.3440000 -0.1260000  0.1480000
## [253,]  0.3550000  0.0820000  0.2790000 -0.5080001 -0.3440000 -0.1260000
## [254,]  0.0820000  0.3550000  0.0820000  0.2790000 -0.5080001 -0.3440000
## [255,]  0.5740000  0.0820000  0.3550000  0.0820000  0.2790000 -0.5080001
## [256,]  0.3550000  0.5740000  0.0820000  0.3550000  0.0820000  0.2790000
## [257,] -0.2570000  0.3550000  0.5740000  0.0820000  0.3550000  0.0820000
## [258,] -0.3770000 -0.2570000  0.3550000  0.5740000  0.0820000  0.3550000
## [259,] -0.3440000 -0.3770000 -0.2570000  0.3550000  0.5740000  0.0820000
## [260,] -0.6500000 -0.3440000 -0.3770000 -0.2570000  0.3550000  0.5740000
## [261,] -0.0930000 -0.6500000 -0.3440000 -0.3770000 -0.2570000  0.3550000
## [262,] -0.1370000 -0.0930000 -0.6500000 -0.3440000 -0.3770000 -0.2570000
## [263,]  0.1150000 -0.1370000 -0.0930000 -0.6500000 -0.3440000 -0.3770000
## [264,]  0.7050000  0.1150000 -0.1370000 -0.0930000 -0.6500000 -0.3440000
## [265,]  0.3990000  0.7050000  0.1150000 -0.1370000 -0.0930000 -0.6500000
## [266,]  0.3660000  0.3990000  0.7050000  0.1150000 -0.1370000 -0.0930000
## [267,]  0.3660000  0.3660000  0.3990000  0.7050000  0.1150000 -0.1370000
## [268,]  0.0380000  0.3660000  0.3660000  0.3990000  0.7050000  0.1150000
## [269,] -0.2680000  0.0380000  0.3660000  0.3660000  0.3990000  0.7050000
## [270,]  0.3220000 -0.2680000  0.0380000  0.3660000  0.3660000  0.3990000
## [271,]  0.0820000  0.3220000 -0.2680000  0.0380000  0.3660000  0.3660000
## [272,]  0.0820000  0.0820000  0.3220000 -0.2680000  0.0380000  0.3660000
## [273,]  0.0600000  0.0820000  0.0820000  0.3220000 -0.2680000  0.0380000
## [274,]  0.2680000  0.0600000  0.0820000  0.0820000  0.3220000 -0.2680000
## [275,]  0.4210000  0.2680000  0.0600000  0.0820000  0.0820000  0.3220000
## [276,]  0.7700000  0.4210000  0.2680000  0.0600000  0.0820000  0.0820000
## [277,]  0.8030000  0.7700000  0.4210000  0.2680000  0.0600000  0.0820000
## [278,]  0.6610000  0.8030000  0.7700000  0.4210000  0.2680000  0.0600000
## [279,]  0.7160000  0.6610000  0.8030000  0.7700000  0.4210000  0.2680000
## [280,]  0.6280000  0.7160000  0.6610000  0.8030000  0.7700000  0.4210000
## [281,]  0.1910000  0.6280000  0.7160000  0.6610000  0.8030000  0.7700000
## [282,]  0.5300000  0.1910000  0.6280000  0.7160000  0.6610000  0.8030000
## [283,]  0.1800000  0.5300000  0.1910000  0.6280000  0.7160000  0.6610000
## [284,] -0.4640000  0.1800000  0.5300000  0.1910000  0.6280000  0.7160000
## [285,]  0.2790000 -0.4640000  0.1800000  0.5300000  0.1910000  0.6280000
## [286,]  0.3550000  0.2790000 -0.4640000  0.1800000  0.5300000  0.1910000
## [287,]  0.2020000  0.3550000  0.2790000 -0.4640000  0.1800000  0.5300000
## [288,]  0.5520000  0.2020000  0.3550000  0.2790000 -0.4640000  0.1800000
## [289,]  0.6170000  0.5520000  0.2020000  0.3550000  0.2790000 -0.4640000
## [290,]  0.1040000  0.6170000  0.5520000  0.2020000  0.3550000  0.2790000
## [291,]  0.2240000  0.1040000  0.6170000  0.5520000  0.2020000  0.3550000
## [292,]  0.4320000  0.2240000  0.1040000  0.6170000  0.5520000  0.2020000
## [293,] -0.2130000  0.4320000  0.2240000  0.1040000  0.6170000  0.5520000
## [294,] -0.9670000 -0.2130000  0.4320000  0.2240000  0.1040000  0.6170000
## [295,] -1.0000000 -0.9670000 -0.2130000  0.4320000  0.2240000  0.1040000
## [296,] -0.4320000 -1.0000000 -0.9670000 -0.2130000  0.4320000  0.2240000
## [297,] -0.6830000 -0.4320000 -1.0000000 -0.9670000 -0.2130000  0.4320000
## [298,] -0.5080001 -0.6830000 -0.4320000 -1.0000000 -0.9670000 -0.2130000
## [299,] -0.1370000 -0.5080001 -0.6830000 -0.4320000 -1.0000000 -0.9670000
## [300,]  0.0820000 -0.1370000 -0.5080001 -0.6830000 -0.4320000 -1.0000000
## [301,] -0.0600000  0.0820000 -0.1370000 -0.5080001 -0.6830000 -0.4320000
## [302,]  0.3330000 -0.0600000  0.0820000 -0.1370000 -0.5080001 -0.6830000
## [303,]  0.3550000  0.3330000 -0.0600000  0.0820000 -0.1370000 -0.5080001
## [304,]  0.3880000  0.3550000  0.3330000 -0.0600000  0.0820000 -0.1370000
## [305,] -0.0600000  0.3880000  0.3550000  0.3330000 -0.0600000  0.0820000
## [306,] -0.2020000 -0.0600000  0.3880000  0.3550000  0.3330000 -0.0600000
## [307,]  0.0050000 -0.2020000 -0.0600000  0.3880000  0.3550000  0.3330000
## [308,] -0.1150000  0.0050000 -0.2020000 -0.0600000  0.3880000  0.3550000
## [309,]  0.1370000 -0.1150000  0.0050000 -0.2020000 -0.0600000  0.3880000
## [310,]  0.4540000  0.1370000 -0.1150000  0.0050000 -0.2020000 -0.0600000
## [311,]  0.3880000  0.4540000  0.1370000 -0.1150000  0.0050000 -0.2020000
## [312,]  0.7380000  0.3880000  0.4540000  0.1370000 -0.1150000  0.0050000
## [313,]  0.7700000  0.7380000  0.3880000  0.4540000  0.1370000 -0.1150000
## [314,]  0.8030000  0.7700000  0.7380000  0.3880000  0.4540000  0.1370000
## [315,]  0.8360000  0.8030000  0.7700000  0.7380000  0.3880000  0.4540000
## [316,]  0.6500000  0.8360000  0.8030000  0.7700000  0.7380000  0.3880000
## [317,]  0.0050000  0.6500000  0.8360000  0.8030000  0.7700000  0.7380000
## [318,] -0.3660000  0.0050000  0.6500000  0.8360000  0.8030000  0.7700000
## [319,]  0.0710000 -0.3660000  0.0050000  0.6500000  0.8360000  0.8030000
## [320,] -0.0050000  0.0710000 -0.3660000  0.0050000  0.6500000  0.8360000
## [321,] -0.4540000 -0.0050000  0.0710000 -0.3660000  0.0050000  0.6500000
## [322,]  0.1910000 -0.4540000 -0.0050000  0.0710000 -0.3660000  0.0050000
## [323,]  0.4320000  0.1910000 -0.4540000 -0.0050000  0.0710000 -0.3660000
## [324,]  0.6830000  0.4320000  0.1910000 -0.4540000 -0.0050000  0.0710000
## [325,]  0.3880000  0.6830000  0.4320000  0.1910000 -0.4540000 -0.0050000
## [326,]  0.2350000  0.3880000  0.6830000  0.4320000  0.1910000 -0.4540000
## [327,] -0.0930000  0.2350000  0.3880000  0.6830000  0.4320000  0.1910000
## [328,]  0.4750000 -0.0930000  0.2350000  0.3880000  0.6830000  0.4320000
## [329,] -0.0820000  0.4750000 -0.0930000  0.2350000  0.3880000  0.6830000
## [330,] -0.6170000 -0.0820000  0.4750000 -0.0930000  0.2350000  0.3880000
## [331,] -0.0930000 -0.6170000 -0.0820000  0.4750000 -0.0930000  0.2350000
## [332,] -0.0710000 -0.0930000 -0.6170000 -0.0820000  0.4750000 -0.0930000
## [333,]  0.4320000 -0.0710000 -0.0930000 -0.6170000 -0.0820000  0.4750000
## [334,]  0.4210000  0.4320000 -0.0710000 -0.0930000 -0.6170000 -0.0820000
## [335,]  0.4970000  0.4210000  0.4320000 -0.0710000 -0.0930000 -0.6170000
## [336,]  0.4540000  0.4970000  0.4210000  0.4320000 -0.0710000 -0.0930000
## [337,]  0.5960000  0.4540000  0.4970000  0.4210000  0.4320000 -0.0710000
## [338,]  0.5520000  0.5960000  0.4540000  0.4970000  0.4210000  0.4320000
## [339,]  0.6070000  0.5520000  0.5960000  0.4540000  0.4970000  0.4210000
## [340,]  0.4640000  0.6070000  0.5520000  0.5960000  0.4540000  0.4970000
## [341,] -0.3010000  0.4640000  0.6070000  0.5520000  0.5960000  0.4540000
## [342,] -0.7700000 -0.3010000  0.4640000  0.6070000  0.5520000  0.5960000
## [343,] -0.6500000 -0.7700000 -0.3010000  0.4640000  0.6070000  0.5520000
## [344,] -0.6940000 -0.6500000 -0.7700000 -0.3010000  0.4640000  0.6070000
## [345,] -0.1370000 -0.6940000 -0.6500000 -0.7700000 -0.3010000  0.4640000
## [346,] -0.4640000 -0.1370000 -0.6940000 -0.6500000 -0.7700000 -0.3010000
## [347,] -0.2460000 -0.4640000 -0.1370000 -0.6940000 -0.6500000 -0.7700000
## [348,]  0.1690000 -0.2460000 -0.4640000 -0.1370000 -0.6940000 -0.6500000
## [349,] -0.2020000  0.1690000 -0.2460000 -0.4640000 -0.1370000 -0.6940000
## [350,]  0.0820000 -0.2020000  0.1690000 -0.2460000 -0.4640000 -0.1370000
## [351,]  0.6070000  0.0820000 -0.2020000  0.1690000 -0.2460000 -0.4640000
## [352,] -0.1580000  0.6070000  0.0820000 -0.2020000  0.1690000 -0.2460000
## [353,] -0.4540000 -0.1580000  0.6070000  0.0820000 -0.2020000  0.1690000
## [354,] -0.7810000 -0.4540000 -0.1580000  0.6070000  0.0820000 -0.2020000
## [355,] -0.3880000 -0.7810000 -0.4540000 -0.1580000  0.6070000  0.0820000
## [356,]  0.1800000 -0.3880000 -0.7810000 -0.4540000 -0.1580000  0.6070000
## [357,]  0.0600000  0.1800000 -0.3880000 -0.7810000 -0.4540000 -0.1580000
## [358,] -0.5080001  0.0600000  0.1800000 -0.3880000 -0.7810000 -0.4540000
## [359,] -0.2680000 -0.5080001  0.0600000  0.1800000 -0.3880000 -0.7810000
## [360,]  0.2240000 -0.2680000 -0.5080001  0.0600000  0.1800000 -0.3880000
## [361,]  0.1150000  0.2240000 -0.2680000 -0.5080001  0.0600000  0.1800000
## [362,]  0.3990000  0.1150000  0.2240000 -0.2680000 -0.5080001  0.0600000
## [363,]  0.0270000  0.3990000  0.1150000  0.2240000 -0.2680000 -0.5080001
## [364,]  0.0160000  0.0270000  0.3990000  0.1150000  0.2240000 -0.2680000
## [365,] -0.3770000  0.0160000  0.0270000  0.3990000  0.1150000  0.2240000
## [366,] -0.1800000 -0.3770000  0.0160000  0.0270000  0.3990000  0.1150000
## [367,] -0.0380000 -0.1800000 -0.3770000  0.0160000  0.0270000  0.3990000
## [368,] -0.2020000 -0.0380000 -0.1800000 -0.3770000  0.0160000  0.0270000
## [369,]  0.1370000 -0.2020000 -0.0380000 -0.1800000 -0.3770000  0.0160000
## [370,]  0.0930000  0.1370000 -0.2020000 -0.0380000 -0.1800000 -0.3770000
## [371,] -0.2790000  0.0930000  0.1370000 -0.2020000 -0.0380000 -0.1800000
## [372,] -0.0380000 -0.2790000  0.0930000  0.1370000 -0.2020000 -0.0380000
## [373,]  0.2350000 -0.0380000 -0.2790000  0.0930000  0.1370000 -0.2020000
## [374,]  0.1690000  0.2350000 -0.0380000 -0.2790000  0.0930000  0.1370000
## [375,]  0.3990000  0.1690000  0.2350000 -0.0380000 -0.2790000  0.0930000
## [376,]  0.1580000  0.3990000  0.1690000  0.2350000 -0.0380000 -0.2790000
## [377,] -0.5410000  0.1580000  0.3990000  0.1690000  0.2350000 -0.0380000
## [378,] -0.6280000 -0.5410000  0.1580000  0.3990000  0.1690000  0.2350000
## [379,]  0.0270000 -0.6280000 -0.5410000  0.1580000  0.3990000  0.1690000
## [380,] -0.7380000  0.0270000 -0.6280000 -0.5410000  0.1580000  0.3990000
## [381,] -0.9130000 -0.7380000  0.0270000 -0.6280000 -0.5410000  0.1580000
## [382,] -0.0270000 -0.9130000 -0.7380000  0.0270000 -0.6280000 -0.5410000
## [383,]  0.0710000 -0.0270000 -0.9130000 -0.7380000  0.0270000 -0.6280000
## [384,] -0.1260000  0.0710000 -0.0270000 -0.9130000 -0.7380000  0.0270000
## [385,]  0.0490000 -0.1260000  0.0710000 -0.0270000 -0.9130000 -0.7380000
## [386,]  0.4540000  0.0490000 -0.1260000  0.0710000 -0.0270000 -0.9130000
## [387,]  0.3010000  0.4540000  0.0490000 -0.1260000  0.0710000 -0.0270000
## [388,] -0.0050000  0.3010000  0.4540000  0.0490000 -0.1260000  0.0710000
## [389,] -0.0930000 -0.0050000  0.3010000  0.4540000  0.0490000 -0.1260000
## [390,] -0.2240000 -0.0930000 -0.0050000  0.3010000  0.4540000  0.0490000
## [391,] -0.2130000 -0.2240000 -0.0930000 -0.0050000  0.3010000  0.4540000
## [392,] -0.3110000 -0.2130000 -0.2240000 -0.0930000 -0.0050000  0.3010000
## [393,] -0.2350000 -0.3110000 -0.2130000 -0.2240000 -0.0930000 -0.0050000
## [394,] -0.3220000 -0.2350000 -0.3110000 -0.2130000 -0.2240000 -0.0930000
## [395,]  0.3220000 -0.3220000 -0.2350000 -0.3110000 -0.2130000 -0.2240000
## [396,]  0.0930000  0.3220000 -0.3220000 -0.2350000 -0.3110000 -0.2130000
## [397,]  0.1150000  0.0930000  0.3220000 -0.3220000 -0.2350000 -0.3110000
## [398,]  0.7700000  0.1150000  0.0930000  0.3220000 -0.3220000 -0.2350000
## [399,]  0.6070000  0.7700000  0.1150000  0.0930000  0.3220000 -0.3220000
## [400,] -0.1580000  0.6070000  0.7700000  0.1150000  0.0930000  0.3220000
## [401,] -0.2350000 -0.1580000  0.6070000  0.7700000  0.1150000  0.0930000
## [402,] -0.2020000 -0.2350000 -0.1580000  0.6070000  0.7700000  0.1150000
## [403,] -0.3330000 -0.2020000 -0.2350000 -0.1580000  0.6070000  0.7700000
## [404,] -0.1580000 -0.3330000 -0.2020000 -0.2350000 -0.1580000  0.6070000
## [405,] -0.2240000 -0.1580000 -0.3330000 -0.2020000 -0.2350000 -0.1580000
## [406,] -0.3550000 -0.2240000 -0.1580000 -0.3330000 -0.2020000 -0.2350000
## [407,]  0.0050000 -0.3550000 -0.2240000 -0.1580000 -0.3330000 -0.2020000
## [408,]  0.4540000  0.0050000 -0.3550000 -0.2240000 -0.1580000 -0.3330000
## [409,]  0.4100000  0.4540000  0.0050000 -0.3550000 -0.2240000 -0.1580000
## [410,]  0.5190000  0.4100000  0.4540000  0.0050000 -0.3550000 -0.2240000
## [411,]  0.5410000  0.5190000  0.4100000  0.4540000  0.0050000 -0.3550000
## [412,]  0.3010000  0.5410000  0.5190000  0.4100000  0.4540000  0.0050000
## [413,] -0.5740000  0.3010000  0.5410000  0.5190000  0.4100000  0.4540000
## [414,] -0.3440000 -0.5740000  0.3010000  0.5410000  0.5190000  0.4100000
## [415,] -0.2790000 -0.3440000 -0.5740000  0.3010000  0.5410000  0.5190000
## [416,] -0.7160000 -0.2790000 -0.3440000 -0.5740000  0.3010000  0.5410000
## [417,] -0.8690000 -0.7160000 -0.2790000 -0.3440000 -0.5740000  0.3010000
## [418,] -0.5960000 -0.8690000 -0.7160000 -0.2790000 -0.3440000 -0.5740000
## [419,] -0.2900000 -0.5960000 -0.8690000 -0.7160000 -0.2790000 -0.3440000
## [420,] -0.4540000 -0.2900000 -0.5960000 -0.8690000 -0.7160000 -0.2790000
## [421,] -0.2460000 -0.4540000 -0.2900000 -0.5960000 -0.8690000 -0.7160000
## [422,] -0.6070000 -0.2460000 -0.4540000 -0.2900000 -0.5960000 -0.8690000
## [423,] -0.5630000 -0.6070000 -0.2460000 -0.4540000 -0.2900000 -0.5960000
## [424,] -0.2350000 -0.5630000 -0.6070000 -0.2460000 -0.4540000 -0.2900000
## [425,] -0.2460000 -0.2350000 -0.5630000 -0.6070000 -0.2460000 -0.4540000
## [426,] -0.3990000 -0.2460000 -0.2350000 -0.5630000 -0.6070000 -0.2460000
## [427,] -0.3330000 -0.3990000 -0.2460000 -0.2350000 -0.5630000 -0.6070000
## [428,] -0.5300000 -0.3330000 -0.3990000 -0.2460000 -0.2350000 -0.5630000
## [429,] -0.0490000 -0.5300000 -0.3330000 -0.3990000 -0.2460000 -0.2350000
## [430,]  0.1580000 -0.0490000 -0.5300000 -0.3330000 -0.3990000 -0.2460000
## [431,]  0.1150000  0.1580000 -0.0490000 -0.5300000 -0.3330000 -0.3990000
## [432,]  0.3220000  0.1150000  0.1580000 -0.0490000 -0.5300000 -0.3330000
## [433,]  0.1150000  0.3220000  0.1150000  0.1580000 -0.0490000 -0.5300000
## [434,]  0.0490000  0.1150000  0.3220000  0.1150000  0.1580000 -0.0490000
## [435,]  0.4540000  0.0490000  0.1150000  0.3220000  0.1150000  0.1580000
## [436,]  0.1580000  0.4540000  0.0490000  0.1150000  0.3220000  0.1150000
## [437,] -0.4210000  0.1580000  0.4540000  0.0490000  0.1150000  0.3220000
## [438,] -0.2680000 -0.4210000  0.1580000  0.4540000  0.0490000  0.1150000
## [439,] -0.3110000 -0.2680000 -0.4210000  0.1580000  0.4540000  0.0490000
## [440,] -0.1150000 -0.3110000 -0.2680000 -0.4210000  0.1580000  0.4540000
## [441,] -0.3220000 -0.1150000 -0.3110000 -0.2680000 -0.4210000  0.1580000

modelo3 = Arima(rec1, order = c(1,1,0),
                 season = list(order = c(0,1,1), 
                               freq = 12),
                 xreg = xlag)

BIC(modelo3)

## [1] 3048.068

ttest(modelo3)

##         ar1        sma1       xreg1       xreg2       xreg3       xreg4 
##   8.9540336 -29.7760354  -0.1545440   0.5851134   0.7293210   1.6797623 
##       xreg5       xreg6 
##  -6.3584169  -3.3403365

tt <- modelo3$coef[which(modelo3$coef!=0)]/sqrt(diag(modelo3$var.coef))
1 - pt(abs(tt),(modelo3$nobs - length(modelo3$coef[which(modelo3$coef!=0)])))

##          ar1         sma1        xreg1        xreg2        xreg3        xreg4 
## 0.000000e+00 0.000000e+00 4.386275e-01 2.793928e-01 2.331059e-01 4.687360e-02 
##        xreg5        xreg6 
## 2.662277e-10 4.557716e-04

et <- residuals(modelo3)
Box.test(et,lag=12,type="Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  et
## X-squared = 29.53, df = 12, p-value = 0.003284

tsdiag(modelo3, gof.lag=20)

jarque.bera.test(et)

## 
##  Jarque Bera Test
## 
## data:  et
## X-squared = 838.83, df = 2, p-value < 2.2e-16

plotresiduos(et, rec1)

modelo 4: SOi rezagado hace 6 periodos

library(quantmod)

## Loading required package: xts

## Loading required package: TTR

## Version 0.4-0 included new data defaults. See ?getSymbols.

x1<-ts(Lagtp(soi1,6),frequency = 12)


modelo4 = Arima(rec1, order = c(1,1,0),
                 season = list(order = c(0,1,1), 
                               freq = 12),
                 xreg =  Lag(soi1,6))

modelo4

## Series: rec1 
## Regression with ARIMA(1,1,0)(0,1,1)[12] errors 
## 
## Coefficients:
##          ar1     sma1    xreg
##       0.2867  -1.0000  0.5953
## s.e.  0.0463   0.0601  1.2379
## 
## sigma^2 estimated as 81.21:  log likelihood=-1568.41
## AIC=3144.82   AICc=3144.91   BIC=3161.06

BIC(modelo4)   # 3162.614

## [1] 3161.057

ttest(modelo4)

##         ar1        sma1        xreg 
##   6.1875444 -16.6469189   0.4809015

tt <- modelo4$coef[which(modelo4$coef!=0)]/sqrt(diag(modelo4$var.coef))
1 - pt(abs(tt),(modelo4$nobs - length(modelo4$coef[which(modelo4$coef!=0)])))

##          ar1         sma1         xreg 
## 7.194207e-10 0.000000e+00 3.154170e-01

et <- residuals(modelo4)
Box.test(et,lag=12,type="Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  et
## X-squared = 15.916, df = 12, p-value = 0.1951

tsdiag(modelo4, gof.lag=20)

jarque.bera.test(et) # Los residuos no son normales

## 
##  Jarque Bera Test
## 
## data:  et
## X-squared = 107.18, df = 2, p-value < 2.2e-16

plotresiduos(et, rec1)

Pronostico

newxreg1=soi[442:453]
newxreg1

##  [1]  0.1260000  0.3330000  0.5190000  0.3990000  0.5190000  0.4320000
##  [7]  0.3550000 -0.1260000 -0.5080001 -0.3880000  0.3880000  0.0710000

pred <- predict(modelo2, n.ahead=12, newxreg =newxreg1)
pred

## $pred
##           Jan      Feb      Mar      Apr      May      Jun      Jul      Aug
## 1986                                                                        
## 1987 96.44286 95.05236 92.64900 89.07007 84.73919 78.23811 70.97533 68.62346
##           Sep      Oct      Nov      Dec
## 1986          86.28009 91.94758 96.73341
## 1987 76.19914                           
## 
## $se
##            Jan       Feb       Mar       Apr       May       Jun       Jul
## 1986                                                                      
## 1987 23.235697 26.517904 29.444075 32.106664 34.565292 36.860434 39.020852
##            Aug       Sep       Oct       Nov       Dec
## 1986                      9.135761 14.887921 19.443804
## 1987 41.067784 43.017425

pred2 <- predict(modelo4, n.ahead=6, newxreg =newxreg1)  # modelo 4 soi hace seis periodos
pred2

## $pred
##           Jan      Feb      Mar      Apr      May      Jun      Jul      Aug
## 1986                                                                        
## 1987 96.44286 95.05236 92.64900 86.41641 91.67435 96.12205 95.97437 94.97437
##           Sep      Oct      Nov      Dec
## 1986          86.28009 91.94758 96.73341
## 1987 92.43410                           
## 
## $se
##            Jan       Feb       Mar Apr May Jun Jul Aug Sep       Oct       Nov
## 1986                                                        9.135761 14.887921
## 1987 23.235697 26.517904 29.444075                                            
##            Dec
## 1986 19.443804
## 1987

#comparacion


length(soi)

## [1] 453

z2<-ts(rec, start = c(1950,1), frequency = 12)

plot(forecast(modelo2, xreg =newxreg1 ))
lines(z2, col="blue")

plot(forecast(modelo4, xreg =newxreg1 ))
lines(z2, col="blue")

b=as.vector(pred$pred)
b

##  [1] 86.28009 91.94758 96.73341 96.44286 95.05236 92.64900 89.07007 84.73919
##  [9] 78.23811 70.97533 68.62346 76.19914

reales=rec[442:453]

pron=as.vector(pred2$pred)

sqrt((sum((reales- pron)^2))/length(reales))

## [1] 39.07078

ajustado=as.vector(modelo4$fitted)
reales1=rec[1:441]
sqrt((sum((reales1- ajustado)^2))/length(reales1))

## [1] 8.846518

ajustado2=as.vector(modelo2$fitted)
reales1=rec[1:441]
sqrt((sum((reales1- ajustado2)^2))/length(reales1))

## [1] 8.846518

sqrt((sum((reales- b)^2))/length(reales))

## [1] 26.94002

SARIMAX

Wilson Sandoval

2022-08-03

SARIMAX

FUNCIONES DE AYUDA

Función \(1\)

función \(2\)

Función \(3\)

Función \(4\)

Función \(5\)

Funcion \(6\)

FASE 1: IDENTIFICACION

Modelo 1

Modelo 2

modelo 3: Soi rezagado

modelo 4: SOi rezagado hace 6 periodos

Pronostico