Dickey Fuller del paquete tseries

adf.test(diff(eth_close_ts,365))

## 
##  Augmented Dickey-Fuller Test
## 
## data:  diff(eth_close_ts, 365)
## Dickey-Fuller = -1.4958, Lag order = 10, p-value = 0.7917
## alternative hypothesis: stationary

Test Phillips-Perron

plot(ur.pp(diff(eth_close_ts,365),type="Z-tau",
     model="constant", lags="long"))

pp.test(diff(eth_close_ts,365))

## 
##  Phillips-Perron Unit Root Test
## 
## data:  diff(eth_close_ts, 365)
## Dickey-Fuller Z(alpha) = -5.0666, Truncation lag parameter = 7, p-value
## = 0.8271
## alternative hypothesis: stationary

ts_cor(diff(eth_close_ts,365), lag.max=40)

ts_cor(diff(eth_close_ts,30), lag.max=40)

ts_cor(diff(eth_close_ts,15), lag.max=40)

1. Transformación Logarítmica

eth_close_log <- log(eth_close_ts)

autoplot(eth_close_log) + ggtitle("Log-Transformed Ethereum Prices")

Arima LOG

model_log <- arima(eth_close_log, order=c(2,1,1))
summary(model_log)

## 
## Call:
## arima(x = eth_close_log, order = c(2, 1, 1))
## 
## Coefficients:
##          ar1     ar2      ma1
##       0.5601  0.0595  -0.5815
## s.e.  0.2430  0.0273   0.2427
## 
## sigma^2 estimated as 0.00203:  log likelihood = 2363.49,  aic = -4718.98
## 
## Training set error measures:
##                       ME       RMSE        MAE        MPE     MAPE      MASE
## Training set 0.001728614 0.04503583 0.03047377 0.02623036 0.441566 0.9983703
##                      ACF1
## Training set -0.002459091

BIC(model_log)

## [1] -4697.989

eth_close_diff_log <- diff(eth_close_log)

par(mfrow=c(3,1))
plot(eth_close_diff_log, main="Log-Transformed & Differenced Ethereum Prices")
acf(eth_close_diff_log, lag.max=40, main="ACF of Log-Transformed & Differenced Ethereum Prices")
pacf(eth_close_diff_log, lag.max=40, main="PACF of Log-Transformed & Differenced Ethereum Prices")

2. Transformación Box-Cox

lambda <- BoxCox.lambda(eth_close_ts)
eth_close_boxcox <- BoxCox(eth_close_ts, lambda)

autoplot(eth_close_boxcox) + ggtitle("Box-Cox Transformed Ethereum Prices")

ARIMA - Box-Cox

model_box <- arima(eth_close_boxcox, order=c(3,1,2))
summary(model_box)

## 
## Call:
## arima(x = eth_close_boxcox, order = c(3, 1, 2))
## 
## Coefficients:
##           ar1     ar2     ar3     ma1      ma2
##       -0.2109  0.6923  0.0458  0.1438  -0.5883
## s.e.   0.1504  0.1094  0.0354  0.1484   0.1106
## 
## sigma^2 estimated as 1.53e-08:  log likelihood = 10655.75,  aic = -21299.51
## 
## Training set error measures:
##                        ME         RMSE          MAE          MPE        MAPE
## Training set 4.984781e-06 0.0001264424 4.716271e-05 0.0005000895 0.004734736
##                  MASE        ACF1
## Training set 1.012657 -0.01616264

BIC(model_box)

## [1] -21268.02

Profundidad del modelo Logarítmico

et <- residuals(model_log)

par(mfrow=c(2,2))
plot(et, main="Residuales del modelo")
acf(et, main="ACF de Residuales")
pacf(et, main="PACF de Residuales")
qqnorm(et, main="QQ Plot de Residuales")
qqline(et)

Box.test(et,lag=7,type="Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  et
## X-squared = 13.67, df = 7, p-value = 0.05736

jarque.bera.test(et)

## 
##  Jarque Bera Test
## 
## data:  et
## X-squared = 4695.9, df = 2, p-value < 2.2e-16

#### Test de Aleatoriedad

#$H_0:$ Residuales exhiben un comport. de Aleatoriedad
#$H_a:$ Residuales no exhiben estructura (Tendencia, o cualquier otro comportamiento predecible)

runs.test(as.factor(sign(et)), alternative="two.sided")

## 
##  Runs Test
## 
## data:  as.factor(sign(et))
## Standard Normal = 1.0078, p-value = 0.3136
## alternative hypothesis: two.sided

Pronóstico Inicial

forecast_log <- forecast(model_log, h=10, fan = T)
plot(forecast(model_log,h=15, fan=T))
lines(fitted(model_log), col="red")

3.Modelado con Prophet - Sin LOG

eth_prophet <- data.frame(ds = eth_close_df$Date, y = eth_close_df$eth_close_zoo)

m <- prophet(eth_prophet)

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future <- make_future_dataframe(m, periods = 10)
forecast <- predict(m, future)
forecast_prophet <- predict(m, future)

plot(m, forecast)

prophet_plot_components(m, forecast)

4.Modelado con Prophet - Con LOG

eth_prophet_2 <- data.frame(ds = eth_close_df$Date, y = log(eth_close_df$eth_close_zoo))

m2 <- prophet(eth_prophet_2)

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future2 <- make_future_dataframe(m2, periods = 10)
forecast2 <- predict(m2, future2)
forecast_prophet_log <- predict(m2, future2)

plot(m2, forecast2)

prophet_plot_components(m2, forecast2)

5.Red Neuronal

Z <- as.ts(etherium$Close)
S <- (Z - min(Z)) / (max(Z) - min(Z))
plot(S)

tamano_total <- length(S)
tamano_train <- round(tamano_total * 0.75, digits = 0)

train <- 1:tamano_train
test <- (tamano_train+1):tamano_total

library(zoo)
slogN <- data.frame(y = S, 
                    lag.1 = stats::lag(S, -1), 
                    lag.2 = stats::lag(S, -2), 
                    lag.3 = stats::lag(S, -3), 
                    lag.4 = stats::lag(S, -4), 
                    lag.5 = stats::lag(S, -5), 
                    lag.6 = stats::lag(S, -6), 
                    lag.7 = stats::lag(S, -7), 
                    lag.8 = stats::lag(S, -8), 
                    lag.9 = stats::lag(S, -9), 
                    lag.10 = stats::lag(S, -10), 
                    lag.11 = stats::lag(S, -11), 
                    lag.12 = stats::lag(S, -12))

slogN <- na.omit(slogN)



inputs <- as.data.frame(slogN[,-1])
outputs <- slogN$y

library(RSNNS)

## 
## Attaching package: 'RSNNS'

## The following objects are masked from 'package:caret':
## 
##     confusionMatrix, train

# Definir rangos de hiperparámetros
sizes <- c(5, 10, 15)  # Número de neuronas en las capas
learning_rates <- c(0.1, 0.01)  # Tasas de aprendizaje

# Guardar el mejor modelo, su error y sus hiperparámetros
best_model <- NULL
best_error <- Inf
best_size <- NA
best_learning_rate <- NA

# Bucle sobre todas las combinaciones posibles de hiperparámetros
for (size in sizes) {
  for (lr in learning_rates) {
    # Entrenar el modelo
    fit <- elman(inputs[train,], outputs[train], size = c(size), learnFuncParams = c(lr), maxit = 200)
    
    # Evaluar el modelo
    predictions <- predict(fit, newdata = inputs[test,])
    error <- sum((predictions - outputs[test])^2)  # Puedes usar otra métrica de error
    
    # Actualizar el mejor modelo si es necesario
    if (error < best_error) {
      best_model <- fit
      best_error <- error
      best_size <- size
      best_learning_rate <- lr
    }
  }
}

# Mostrar los hiperparámetros del mejor modelo
cat("Mejor modelo con tamaño:", best_size, "y tasa de aprendizaje:", best_learning_rate, "con un error de:", best_error)

## Mejor modelo con tamaño: 5 y tasa de aprendizaje: 0.01 con un error de: 0.0003054597

plotIterativeError(fit, main = "Iterative Error for Elman ")

y <- as.vector(outputs[test])
plot(y, type = "l", ylim = range(c(y, predict(fit, newdata = inputs[test,]))))
lines(predict(fit, newdata = inputs[test,]), col = "red")

predictions <- predict(fit, newdata = inputs)
predictions_desnorm <- predictions * (max(Z) - min(Z)) + min(Z)

plot(Z, type = "l", col = "blue", lwd = 2, main = "Predicciones vs Datos Reales", xlab = "Tiempo", ylab = "Valor")
lines(predictions_desnorm, col = "red", lwd = 2)
legend("topright", legend = c("Real", "Predicción"), col = c("blue", "red"), lty = 1, cex = 0.8)

library(RSNNS)

slogN <- cbind(y = S, sapply(1:12, function(lag) stats::lag(S, -lag)))
slogN <- na.omit(slogN)

inputs <- slogN[,-1]
outputs <- slogN[,1]


predicciones <- numeric(15)
ultimos_datos <- as.matrix(tail(inputs, 12))

for(i in 1:15){
  pred <- predict(fit, newdata = t(ultimos_datos[1, ])) 
  predicciones[i] <- pred[1]
 
  ultimos_datos[1:(nrow(ultimos_datos) - 1), ] <- ultimos_datos[2:nrow(ultimos_datos), ]
 
  ultimos_datos[nrow(ultimos_datos), 1] <- pred[1]
}



# Desnormalizar las predicciones:
predicciones_desnorm <- predicciones * (max(Z) - min(Z)) + min(Z)


plot(Z, type = "l", col = "blue", lwd = 2, main = "Predicciones vs Datos Reales", xlab = "Tiempo", ylab = "Valor")
lines(c(rep(NA, length(Z)), predicciones_desnorm), col = "red", lwd = 2)
legend("topright", legend = c("Real", "Predicción"), col = c("blue", "red"), lty = 1, cex = 0.8)

library(RSNNS)

# Asegurarse de que 'inputs' sea una matriz con 12 columnas (una por cada lag)
inputs_matrix <- as.matrix(inputs)

# Entrenar la red de Jordan
fit_j <- jordan(inputs_matrix[train, ], outputs[train], size=6, learnFuncParams=c(0.1), maxit=300)

# Plot del error iterativo
plotIterativeError(fit_j, main = "Iterative Error for 6 Neuron Jordan Network")

# Comparar predicciones con valores reales
y_j <- as.vector(outputs[test])
plot(y_j, type = "l", ylim = range(c(y_j, predict(fit_j, newdata = inputs_matrix[test, ]))))
lines(predict(fit_j, newdata = inputs_matrix[test, ]), col = "red")

y_j <- as.vector(outputs[test])
plot(y_j, type = "l", ylim = range(c(y_j, predict(fit_j, newdata = inputs[test,]))))
lines(predict(fit_j, newdata = inputs[test,]), col = "red")

predictions <- predict(fit_j, newdata = inputs)
predictions_desnorm_jor <- predictions * (max(Z) - min(Z)) + min(Z)

plot(Z, type = "l", col = "blue", lwd = 2, main = "Predicciones vs Datos Reales", xlab = "Tiempo", ylab = "Valor")
lines(predictions_desnorm_jor, col = "red", lwd = 2)
legend("topright", legend = c("Real", "Predicción"), col = c("blue", "red"), lty = 1, cex = 0.8)

Ingreso de Datos reales:

etherium_real <- rio::import("https://github.com/EdwinHigueraA/bfi_s/raw/main/Etherium_real.csv")

cols_to_convert <- c("Open", "High", "Low", "Close")
for (col in cols_to_convert) {
  etherium_real[[col]] <- as.numeric(gsub(",", "", etherium_real[[col]]))
}

Comparación General de los modelos:

etherium_real$Date <- as.Date(etherium_real$Date, format="%m/%d/%Y")

ultimos_10_dias <- etherium_real$Close
fechas_correctas <- tail(etherium_real$Date, length(ultimos_10_dias))

forecast_prophet_log_values <- head(exp(forecast_prophet_log$yhat[(length(etherium$Close)+1):(length(etherium$Close)+10)]), length(ultimos_10_dias))
predicciones_desnorm_values <- head(predicciones_desnorm, length(ultimos_10_dias))
predictions_desnorm_values_jor <- tail(predictions_desnorm_jor,length(ultimos_10_dias))


fechas <- etherium_real$Date[1:length(ultimos_10_dias)]



tabla_predicciones <- data.frame(
  Fecha = fechas_correctas,
  Real = ultimos_10_dias,
  ProphetLog = forecast_prophet_log_values,
  RedNeuronal = predicciones_desnorm_values,
  RedNeuronal_Jordan = predictions_desnorm_values_jor
)

tabla_predicciones$Fecha <- fechas_correctas
print(tabla_predicciones, row.names = FALSE)

##       Fecha    Real ProphetLog RedNeuronal RedNeuronal_Jordan
##  2023-11-08 1888.25   1692.825    1749.890           1822.712
##  2023-11-09 2060.14   1684.167    1783.962           1827.257
##  2023-11-10 2094.24   1674.565    1813.334           1840.494
##  2023-11-11 2044.75   1666.843    1817.619           1881.253
##  2023-11-12 2060.08   1666.858    1832.389           1830.064
##  2023-11-13 2061.00   1659.992    1878.446           1855.733
##  2023-11-14 1981.95   1661.086    1798.769           1866.145
##  2023-11-15 2048.93   1660.127    1844.933           1897.740
##  2023-11-16 1956.32   1657.106    1851.229           1920.360
##  2023-11-17 1946.60   1653.903    1890.232           1921.662

grafico <- ggplot(tabla_predicciones, aes(x=Fecha)) + 
  geom_line(aes(y=Real, colour="Real")) + 
  geom_line(aes(y=ProphetLog, colour="Prophet Log")) + 
  geom_line(aes(y=RedNeuronal, colour="Red Neuronal Elman")) +
  geom_line(aes(y=RedNeuronal_Jordan, colour = "Red Neuronal Jordan"))+
  labs(title="Comparación de Predicciones vs Datos Reales", x="Fecha", y="Valor") +
  scale_color_manual(name="Leyenda", 
                     values=c("Real"="black", 
                              "Prophet Log"="blue", 
                              "Red Neuronal Elman"="purple", 
                              "Red Neuronal Jordan"="green")) +
  theme_minimal() +
  theme(legend.position="bottom")
grafico

# Funciones para calcular RMSE y MAE
rmse <- function(error) {
  sqrt(mean(error^2))
}

mae <- function(error) {
  mean(abs(error))
}

# Error para cada modelo
error_log <- tabla_predicciones$Real - tabla_predicciones$Log
error_prophet <- tabla_predicciones$Real - tabla_predicciones$Prophet
error_prophet_log <- tabla_predicciones$Real - tabla_predicciones$ProphetLog
error_red_neuronal <- tabla_predicciones$Real - tabla_predicciones$RedNeuronal
error_red_neuronal_jordan <- tabla_predicciones$Real - tabla_predicciones$RedNeuronal_Jordan

# RMSE
rmse_log <- rmse(error_log)
rmse_prophet <- rmse(error_prophet)
rmse_prophet_log <- rmse(error_prophet_log)
rmse_red_neuronal <- rmse(error_red_neuronal)
rmse_red_neuronal_jordan <- rmse(error_red_neuronal_jordan)

# MAE
mae_log <- mae(error_log)
mae_prophet <- mae(error_prophet)
mae_prophet_log <- mae(error_prophet_log)
mae_red_neuronal <- mae(error_red_neuronal)
mae_red_neuronal_jordan <- mae(error_red_neuronal_jordan)

# Creando un dataframe con los resultados
metricas <- data.frame(
  Modelo = c("Prophet", "Prophet Log", "Red Neuronal","Red Neuronal Jordan"),
  RMSE = c(rmse_prophet, rmse_prophet_log, rmse_red_neuronal,rmse_red_neuronal_jordan),
  MAE = c(mae_prophet, mae_prophet_log, mae_red_neuronal,mae_red_neuronal_jordan)
)

metricas

##                Modelo     RMSE      MAE
## 1             Prophet 352.5962 346.4788
## 2         Prophet Log 352.5962 346.4788
## 3        Red Neuronal 200.1187 188.1456
## 4 Red Neuronal Jordan 168.1885 147.8838

bitcoin <- rio::import("https://github.com/EdwinHigueraA/bfi_s/raw/main/BTC-USD.csv")
bitcoin <- na.omit(bitcoin)

cols_to_convert <- c("Open", "High", "Low", "Close")
for (col in cols_to_convert) {
  bitcoin[[col]] <- as.numeric(gsub(",", "", bitcoin[[col]]))
}

bitcoin_close_ts <- ts(bitcoin$Close, start = c(2020, 1), frequency = 365)

bitcoin_close_ts

## Time Series:
## Start = c(2020, 1) 
## End = c(2023, 312) 
## Frequency = 365 
##    [1]  7200.174  6985.470  7344.884  7410.657  7411.317  7769.219  8163.692
##    [8]  8079.863  7879.071  8166.554  8037.538  8192.494  8144.194  8827.765
##   [15]  8807.011  8723.786  8929.038  8942.809  8706.245  8657.643  8745.895
##   [22]  8680.876  8406.516  8445.435  8367.848  8596.830  8909.819  9358.590
##   [29]  9316.630  9508.993  9350.529  9392.875  9344.365  9293.521  9180.963
##   [36]  9613.424  9729.802  9795.943  9865.119 10116.674  9856.611 10208.236
##   [43] 10326.055 10214.380 10312.116  9889.425  9934.434  9690.143 10141.996
##   [50]  9633.387  9608.476  9686.441  9663.182  9924.516  9650.175  9341.705
##   [57]  8820.522  8784.494  8672.455  8599.509  8562.454  8869.670  8787.786
##   [64]  8755.246  9078.763  9122.546  8909.954  8108.116  7923.645  7909.729
##   [71]  7911.430  4970.788  5563.707  5200.366  5392.315  5014.480  5225.629
##   [78]  5238.438  6191.193  6198.778  6185.066  5830.255  6416.315  6734.804
##   [85]  6681.063  6716.440  6469.798  6242.194  5922.043  6429.842  6438.645
##   [92]  6606.776  6793.625  6733.387  6867.527  6791.129  7271.781  7176.415
##   [99]  7334.099  7302.089  6865.493  6859.083  6971.092  6845.038  6842.428
##  [106]  6642.110  7116.804  7096.185  7257.665  7189.425  6881.958  6880.323
##  [113]  7117.208  7429.725  7550.901  7569.936  7679.867  7795.601  7807.059
##  [120]  8801.038  8658.554  8864.767  8988.597  8897.469  8912.654  9003.070
##  [127]  9268.762  9951.519  9842.666  9593.896  8756.431  8601.796  8804.478
##  [134]  9269.987  9733.722  9328.197  9377.014  9670.739  9726.575  9729.038
##  [141]  9522.981  9081.762  9182.577  9209.287  8790.368  8906.935  8835.053
##  [148]  9181.018  9525.751  9439.124  9700.414  9461.059 10167.269  9529.804
##  [155]  9656.718  9800.637  9665.533  9653.680  9758.853  9771.489  9795.700
##  [162]  9870.095  9321.781  9480.844  9475.277  9386.788  9450.702  9538.024
##  [169]  9480.255  9411.841  9288.019  9332.341  9303.630  9648.718  9629.658
##  [176]  9313.610  9264.813  9162.918  9045.391  9143.582  9190.854  9137.993
##  [183]  9228.325  9123.410  9087.304  9132.488  9073.942  9375.475  9252.277
##  [190]  9428.333  9277.968  9278.808  9240.347  9276.500  9243.614  9243.214
##  [197]  9192.837  9132.228  9151.393  9159.040  9185.817  9164.231  9374.888
##  [204]  9525.363  9581.072  9536.893  9677.113  9905.167 10990.873 10912.823
##  [211] 11100.468 11111.214 11323.467 11759.593 11053.614 11246.349 11205.893
##  [218] 11747.022 11779.773 11601.473 11754.046 11675.739 11878.111 11410.525
##  [225] 11584.935 11784.138 11768.871 11865.698 11892.804 12254.402 11991.233
##  [232] 11758.283 11878.372 11592.489 11681.825 11664.848 11774.596 11366.135
##  [239] 11488.363 11323.397 11542.500 11506.865 11711.506 11680.820 11970.479
##  [246] 11414.034 10245.297 10511.813 10169.567 10280.352 10369.563 10131.517
##  [253] 10242.348 10363.139 10400.915 10442.171 10323.756 10680.838 10796.951
##  [260] 10974.905 10948.990 10944.586 11094.347 10938.271 10462.260 10538.460
##  [267] 10246.187 10760.066 10692.717 10750.724 10775.270 10709.652 10844.641
##  [274] 10784.491 10619.452 10575.975 10549.329 10669.583 10793.340 10604.406
##  [281] 10668.969 10915.686 11064.458 11296.361 11384.182 11555.363 11425.899
##  [288] 11429.507 11495.350 11322.123 11358.102 11483.359 11742.037 11916.335
##  [295] 12823.689 12965.892 12931.539 13108.062 13031.174 13075.248 13654.219
##  [302] 13271.285 13437.883 13546.522 13780.995 13737.109 13550.489 13950.301
##  [309] 14133.707 15579.849 15565.881 14833.754 15479.567 15332.315 15290.902
##  [316] 15701.340 16276.344 16317.809 16068.139 15955.588 16716.111 17645.406
##  [323] 17804.006 17817.090 18621.314 18642.232 18370.002 18364.121 19107.465
##  [330] 18732.121 17150.623 17108.402 17717.414 18177.484 19625.836 18802.998
##  [337] 19201.092 19445.398 18699.766 19154.230 19345.121 19191.631 18321.145
##  [344] 18553.916 18264.992 18058.904 18803.656 19142.383 19246.645 19417.076
##  [351] 21310.598 22805.162 23137.961 23869.832 23477.295 22803.082 23783.029
##  [358] 23241.346 23735.949 24664.791 26437.037 26272.295 27084.809 27362.438
##  [365] 28840.953 29001.721 29374.152 32127.268 32782.023 31971.914 33992.430
##  [372] 36824.363 39371.043 40797.609 40254.547 38356.441 35566.656 33922.961
##  [379] 37316.359 39187.328 36825.367 36178.141 35791.277 36630.074 36069.805
##  [386] 35547.750 30825.699 33005.762 32067.643 32289.379 32366.393 32569.850
##  [393] 30432.547 33466.098 34316.387 34269.523 33114.359 33537.176 35510.289
##  [400] 37472.090 36926.066 38144.309 39266.012 38903.441 46196.465 46481.105
##  [407] 44918.184 47909.332 47504.852 47105.516 48717.289 47945.059 49199.871
##  [414] 52149.008 51679.797 55888.133 56099.520 57539.945 54207.320 48824.426
##  [421] 49705.332 47093.852 46339.762 46188.453 45137.770 49631.242 48378.988
##  [428] 50538.242 48561.168 48927.305 48912.383 51206.691 52246.523 54824.117
##  [435] 56008.551 57805.121 57332.090 61243.086 59302.316 55907.199 56804.902
##  [442] 58870.895 57858.922 58346.652 58313.645 57523.422 54529.145 54738.945
##  [449] 52774.266 51704.160 55137.312 55973.512 55950.746 57750.199 58917.691
##  [456] 58918.832 59095.809 59384.312 57603.891 58758.555 59057.879 58192.359
##  [463] 56048.938 58323.953 58245.004 59793.234 60204.965 59893.453 63503.457
##  [470] 63109.695 63314.012 61572.789 60683.820 56216.184 55724.266 56473.031
##  [477] 53906.090 51762.273 51093.652 50050.867 49004.254 54021.754 55033.117
##  [484] 54824.703 53555.109 57750.176 57828.051 56631.078 57200.293 53333.539
##  [491] 57424.008 56396.516 57356.402 58803.777 58232.316 55859.797 56704.574
##  [498] 49150.535 49716.191 49880.535 46760.188 46456.059 43537.512 42909.402
##  [505] 37002.441 40782.738 37304.691 37536.633 34770.582 38705.980 38402.223
##  [512] 39294.199 38436.969 35697.605 34616.066 35678.129 37332.855 36684.926
##  [519] 37575.180 39208.766 36894.406 35551.957 35862.379 33560.707 33472.633
##  [526] 37345.121 36702.598 37334.398 35552.516 39097.859 40218.477 40406.270
##  [533] 38347.062 38053.504 35787.246 35615.871 35698.297 31676.693 32505.660
##  [540] 33723.027 34662.438 31637.779 32186.277 34649.645 34434.336 35867.777
##  [547] 35040.836 33572.117 33897.047 34668.547 35287.781 33746.004 34235.195
##  [554] 33855.328 32877.371 33798.012 33520.520 34240.188 33155.848 32702.025
##  [561] 32822.348 31780.730 31421.539 31533.068 31796.811 30817.832 29807.348
##  [568] 32110.693 32313.105 33581.551 34292.445 35350.188 37337.535 39406.941
##  [575] 39995.906 40008.422 42235.547 41626.195 39974.895 39201.945 38152.980
##  [582] 39747.504 40869.555 42816.500 44555.801 43798.117 46365.402 45585.031
##  [589] 45593.637 44428.289 47793.320 47096.945 47047.004 46004.484 44695.359
##  [596] 44801.188 46717.578 49339.176 48905.492 49321.652 49546.148 47706.117
##  [603] 48960.789 46942.219 49058.668 48902.402 48829.832 47054.984 47166.688
##  [610] 48847.027 49327.723 50025.375 49944.625 51753.410 52633.535 46811.129
##  [617] 46091.391 46391.422 44883.910 45201.457 46063.270 44963.074 47092.492
##  [624] 48176.348 47783.359 47267.520 48278.363 47260.219 42843.801 40693.676
##  [631] 43574.508 44895.098 42839.750 42716.594 43208.539 42235.730 41034.543
##  [638] 41564.363 43790.895 48116.941 47711.488 48199.953 49112.902 51514.812
##  [645] 55361.449 53805.984 53967.848 54968.223 54771.578 57484.789 56041.059
##  [652] 57401.098 57321.523 61593.949 60892.180 61553.617 62026.078 64261.992
##  [659] 65992.836 62210.172 60692.266 61393.617 60930.836 63039.824 60363.793
##  [666] 58482.387 60622.137 62227.965 61888.832 61318.957 61004.406 63226.402
##  [673] 62970.047 61452.230 61125.676 61527.480 63326.988 67566.828 66971.828
##  [680] 64995.230 64949.961 64155.941 64469.527 65466.840 63557.871 60161.246
##  [687] 60368.012 56942.137 58119.578 59697.195 58730.477 56289.289 57569.074
##  [694] 56280.426 57274.680 53569.766 54815.078 57248.457 57806.566 57005.426
##  [701] 57229.828 56477.816 53598.246 49200.703 49368.848 50582.625 50700.086
##  [708] 50504.797 47672.121 47243.305 49362.508 50098.336 46737.480 46612.633
##  [715] 48896.723 47665.426 46202.145 46848.777 46707.016 46880.277 48936.613
##  [722] 48628.512 50784.539 50822.195 50429.859 50809.516 50640.418 47588.855
##  [729] 46444.711 47178.125 46306.445 47686.812 47345.219 46458.117 45897.574
##  [736] 43569.004 43160.930 41557.902 41733.941 41911.602 41821.262 42735.855
##  [743] 43949.102 42591.570 43099.699 43177.398 43113.879 42250.551 42375.633
##  [750] 41744.328 40680.418 36457.316 35030.250 36276.805 36654.328 36954.004
##  [757] 36852.121 37138.234 37784.332 38138.180 37917.602 38483.125 38743.273
##  [764] 36952.984 37154.602 41500.875 41441.164 42412.434 43840.285 44118.445
##  [771] 44338.797 43565.113 42407.938 42244.469 42197.516 42586.918 44575.203
##  [778] 43961.859 40538.012 40030.977 40122.156 38431.379 37075.281 38286.027
##  [785] 37296.570 38332.609 39214.219 39105.148 37709.785 43193.234 44354.637
##  [792] 43924.117 42451.789 39137.605 39400.586 38419.984 38062.039 38737.270
##  [799] 41982.926 39437.461 38794.973 38904.012 37849.664 39666.754 39338.785
##  [806] 41143.930 40951.379 41801.156 42190.652 41247.824 41077.996 42358.809
##  [813] 42892.957 43960.934 44348.730 44500.828 46820.492 47128.004 47465.730
##  [820] 47062.664 45538.676 46281.645 45868.949 46453.566 46622.676 45555.992
##  [827] 43206.738 43503.848 42287.664 42782.137 42207.672 39521.902 40127.184
##  [834] 41166.730 39935.516 40553.465 40424.484 39716.953 40826.215 41502.750
##  [841] 41374.379 40527.363 39740.320 39486.730 39469.293 40458.309 38117.461
##  [848] 39241.121 39773.828 38609.824 37714.875 38469.094 38529.328 37750.453
##  [855] 39698.371 36575.141 36040.922 35501.953 34059.266 30296.953 31022.906
##  [862] 28936.355 29047.752 29283.104 30101.266 31305.113 29862.918 30425.857
##  [869] 28720.271 30314.334 29200.740 29432.227 30323.723 29098.910 29655.586
##  [876] 29562.361 29267.225 28627.574 28814.900 29445.957 31726.391 31792.311
##  [883] 29799.080 30467.488 29704.391 29832.914 29906.662 31370.672 31155.479
##  [890] 30214.355 30111.998 29083.805 28360.811 26762.648 22487.389 22206.793
##  [897] 22572.840 20381.650 20471.482 19017.643 20553.271 20599.537 20710.598
##  [904] 19987.029 21085.877 21231.656 21502.338 21027.295 20735.479 20280.635
##  [911] 20104.023 19784.727 19269.367 19242.256 19297.076 20231.262 20190.115
##  [918] 20548.246 21637.588 21731.117 21592.207 20860.449 19970.557 19323.914
##  [925] 20212.074 20569.920 20836.328 21190.316 20779.344 22485.689 23389.434
##  [932] 23231.732 23164.629 22714.979 22465.479 22609.164 21361.701 21239.754
##  [939] 22930.549 23843.887 23804.633 23656.207 23336.896 23314.199 22978.117
##  [946] 22846.508 22630.957 23289.314 22961.279 23175.891 23809.486 23164.318
##  [953] 23947.643 23957.529 24402.818 24424.068 24319.334 24136.973 23883.291
##  [960] 23335.998 23212.738 20877.553 21166.061 21534.121 21398.908 21528.088
##  [967] 21395.020 21600.904 20260.020 20041.738 19616.814 20297.994 19796.809
##  [974] 20049.764 20127.141 19969.771 19832.088 19986.713 19812.371 18837.668
##  [981] 19290.324 19329.834 21381.152 21680.539 21769.256 22370.449 20296.707
##  [988] 20241.090 19701.211 19772.584 20127.576 19419.506 19544.129 18890.789
##  [995] 18547.400 19413.551 19297.639 18937.012 18802.098 19222.672 19110.547
## [1002] 19426.721 19573.051 19431.789 19312.096 19044.107 19623.580 20336.844
## [1009] 20160.717 19955.443 19546.850 19416.568 19446.426 19141.484 19051.418
## [1016] 19157.445 19382.904 19185.656 19067.635 19268.094 19550.758 19334.416
## [1023] 19139.535 19053.740 19172.469 19208.189 19567.008 19345.572 20095.857
## [1030] 20770.441 20285.836 20595.352 20818.477 20635.604 20495.773 20485.273
## [1037] 20159.504 20209.988 21147.230 21282.691 20926.486 20602.816 18541.271
## [1044] 15880.780 17586.771 17034.293 16799.186 16353.365 16618.199 16884.613
## [1051] 16669.439 16687.518 16697.777 16711.547 16291.832 15787.284 16189.770
## [1058] 16610.707 16604.465 16521.842 16464.281 16444.627 16217.322 16444.982
## [1065] 17168.566 16967.133 17088.660 16908.236 17130.486 16974.826 17089.504
## [1072] 16848.127 17233.475 17133.152 17128.725 17104.193 17206.438 17781.318
## [1079] 17815.650 17364.865 16647.484 16795.092 16757.977 16439.680 16906.305
## [1086] 16817.535 16830.342 16796.953 16847.756 16841.986 16919.805 16717.174
## [1093] 16552.572 16642.342 16602.586 16547.496 16625.080 16688.471 16679.857
## [1100] 16863.238 16836.736 16951.969 16955.078 17091.145 17196.555 17446.293
## [1107] 17934.896 18869.588 19909.574 20976.299 20880.799 21169.633 21161.520
## [1114] 20688.781 21086.793 22676.553 22777.625 22720.416 22934.432 22636.469
## [1121] 23117.859 23032.777 23078.729 23031.090 23774.566 22840.139 23139.283
## [1128] 23723.770 23471.871 23449.322 23331.848 22955.666 22760.109 23264.291
## [1135] 22939.398 21819.039 21651.184 21870.875 21788.203 21808.102 22220.805
## [1142] 24307.842 23623.475 24565.602 24641.277 24327.643 24829.148 24436.354
## [1149] 24188.844 23947.492 23198.127 23175.375 23561.213 23522.871 23147.354
## [1156] 23646.551 23475.467 22362.680 22353.350 22435.514 22429.758 22219.770
## [1163] 21718.080 20363.021 20187.244 20632.410 22163.949 24197.533 24746.074
## [1170] 24375.961 25052.789 27423.930 26965.879 28038.676 27767.236 28175.816
## [1177] 27307.438 28333.973 27493.285 27494.707 27994.330 27139.889 27268.131
## [1184] 28348.441 28033.562 28478.484 28411.035 28199.309 27790.221 28168.090
## [1191] 28177.984 28044.141 27925.859 27947.795 28333.051 29652.980 30235.059
## [1198] 30139.053 30399.066 30485.699 30318.496 30315.355 29445.045 30397.553
## [1205] 28822.680 28245.988 27276.910 27817.500 27591.385 27525.340 28307.598
## [1212] 28422.701 29473.787 29340.262 29248.488 29268.807 28091.568 28680.537
## [1219] 29006.309 28847.711 29534.385 28904.623 28454.979 27694.273 27658.775
## [1226] 27621.756 27000.789 26804.990 26784.078 26930.639 27192.693 27036.650
## [1233] 27398.803 26832.209 26890.129 27129.586 26753.826 26851.277 27225.727
## [1240] 26334.818 26476.207 26719.291 26868.354 28085.646 27745.885 27702.350
## [1247] 27219.658 26819.973 27249.590 27075.129 27119.066 25760.098 27238.783
## [1254] 26345.998 26508.217 26480.375 25851.240 25940.168 25902.500 25918.729
## [1261] 25124.676 25576.395 26327.463 26510.676 26336.213 26851.029 28327.488
## [1268] 30027.297 29912.281 30695.469 30548.695 30480.262 30271.131 30688.164
## [1275] 30086.246 30445.352 30477.252 30590.078 30620.770 31156.439 30777.582
## [1282] 30514.166 29909.338 30342.266 30292.541 30171.234 30414.471 30620.951
## [1289] 30391.646 31476.049 30334.068 30295.807 30249.133 30145.889 29856.562
## [1296] 29913.924 29792.016 29908.744 29771.803 30084.539 29176.916 29227.391
## [1303] 29354.973 29210.689 29319.246 29356.918 29275.309 29230.111 29675.732
## [1310] 29151.959 29178.680 29074.092 29042.127 29041.855 29180.578 29765.492
## [1317] 29561.494 29429.592 29397.715 29415.965 29282.914 29408.443 29170.348
## [1324] 28701.779 26664.551 26049.557 26096.205 26189.584 26124.141 26031.656
## [1331] 26431.641 26162.373 26047.668 26008.463 26089.693 26106.150 27727.393
## [1338] 27297.266 25931.473 25800.725 25868.799 25969.566 25812.416 25779.982
## [1345] 25753.236 26240.195 25905.654 25895.678 25832.227 25162.654 25833.344
## [1352] 26228.324 26539.674 26608.693 26568.281 26534.188 26754.281 27211.117
## [1359] 27132.008 26567.633 26579.568 26579.391 26256.826 26298.480 26217.250
## [1366] 26352.717 27021.547 26911.721 26967.916 27983.750 27530.785 27429.979
## [1373] 27799.395 27415.912 27946.598 27968.840 27935.090 27583.678 27391.020
## [1380] 26873.320 26756.799 26862.375 26861.707 27159.652 28519.467 28415.748
## [1387] 28328.342 28719.807 29682.949 29918.412 29993.896 33086.234 33901.527
## [1394] 34502.820 34156.648 33909.801 34089.574 34538.480 34502.363 34667.781
## [1401] 35437.254 34938.242 34732.324 35082.195 35049.355 35037.371 35443.562

bit_close_zoo <- as.zoo(bitcoin_close_ts)
bit_close_df <- fortify.zoo((bit_close_zoo))
bit_close_df$Year <- floor(bit_close_df$Index)
bit_close_df$Days <-  round((bit_close_df$Index - bit_close_df$Year) * 365.25)


bit_close_df$Date <- as.Date(paste0(bit_close_df$Year, "-01-01")) + bit_close_df$Days
hchart(bit_close_df, "line", hcaes(x = Date, y = bit_close_zoo)) %>% 
  hc_add_theme(hc_theme_darkunica())

eth_chart <- hchart(eth_close_df, "line", hcaes(x = Date, y = eth_close_zoo), 
                    name = "Ethereum") %>%
  hc_add_theme(hc_theme_darkunica()) %>%
  hc_title(text = "Comparación Ethereum vs Bitcoin") %>%
  hc_xAxis(title = list(text = "Fecha")) %>%
  hc_yAxis(title = list(text = "Precio de cierre"))

# Luego, agregamos la serie de Bitcoin al gráfico de Ethereum
combined_chart <- eth_chart %>%
  hc_add_series(data = bit_close_df, type = "line", 
                hcaes(x = Date, y = bit_close_zoo), name = "Bitcoin")

# Mostrar el gráfico combinado
combined_chart

primer_valor_bit <- bit_close_df$`(bit_close_zoo)`[1]

# Normalizar las series de precios
eth_close_df$Close_norm <- eth_close_df$eth_close_zoo / eth_close_df$eth_close_zoo[1]
bit_close_df$Close_norm <- bit_close_df$`(bit_close_zoo)` / primer_valor_bit

# Crear gráfico combinado con series normalizadas
combined_chart_norm <- hchart(eth_close_df, "line", hcaes(x = Date, y = Close_norm), name = "Ethereum") %>%
  hc_add_theme(hc_theme_darkunica()) %>%
  hc_title(text = "Comparación de Tendencias Normalizadas: Ethereum vs Bitcoin") %>%
  hc_xAxis(title = list(text = "Fecha")) %>%
  hc_yAxis(title = list(text = "Cambio Relativo desde el Inicio")) %>%
  hc_add_series(data = bit_close_df, type = "line", hcaes(x = Date, y = Close_norm), name = "Bitcoin")

# Mostrar el gráfico
combined_chart_norm

primer_valor_bit <- bit_close_df$`(bit_close_zoo)`[1]

# Normalizar las series de precios
eth_close_df$Close_norm <- eth_close_df$eth_close_zoo / eth_close_df$eth_close_zoo[1]
bit_close_df$Close_norm <- bit_close_df$`(bit_close_zoo)` / primer_valor_bit
# Convertir las series normalizadas en una matriz con nombres de columnas
series_matrix <- cbind(eth = eth_close_df$Close_norm, btc = bit_close_df$Close_norm)

# Verifica que la matriz tiene los nombres de columnas correctos
colnames(series_matrix) <- c("eth", "btc")

# Utiliza la matriz para la prueba de cointegración
vecm <- ca.jo(series_matrix, ecdet = "const", type = "eigen", K = 18)

# Resumen de los resultados de la prueba de cointegración
summary(vecm)

## 
## ###################### 
## # Johansen-Procedure # 
## ###################### 
## 
## Test type: maximal eigenvalue statistic (lambda max) , without linear trend and constant in cointegration 
## 
## Eigenvalues (lambda):
## [1] 1.103235e-02 3.749186e-03 3.469447e-18
## 
## Values of teststatistic and critical values of test:
## 
##           test 10pct  5pct  1pct
## r <= 1 |  5.22  7.52  9.24 12.97
## r = 0  | 15.41 13.75 15.67 20.20
## 
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
## 
##            eth.l18   btc.l18  constant
## eth.l18   1.000000   1.00000  1.000000
## btc.l18  -3.837225  13.57153 -1.273475
## constant  1.749204 -73.77702 18.441222
## 
## Weights W:
## (This is the loading matrix)
## 
##            eth.l18       btc.l18     constant
## eth.d -0.018541122 -1.610937e-05 1.115584e-18
## btc.d -0.003090166 -1.958748e-04 8.367718e-20

# Determinar el número óptimo de retrasos
lag_selection <- VARselect(series_matrix, lag.max=20, type="both")
print(lag_selection)

## $selection
## AIC(n)  HQ(n)  SC(n) FPE(n) 
##     18      2      2     18 
## 
## $criteria
##                   1            2            3            4            5
## AIC(n) -5.065682834 -5.115188478 -5.113933300 -5.110561888 -5.112267668
## HQ(n)  -5.054390360 -5.098249768 -5.091348353 -5.082330704 -5.078390246
## SC(n)  -5.035488755 -5.069897360 -5.053545143 -5.035076691 -5.021685431
## FPE(n)  0.006309601  0.006004847  0.006012389  0.006032695  0.006022416
##                   6           7            8            9           10
## AIC(n) -5.119960198 -5.13087295 -5.129526139 -5.127456707 -5.133459822
## HQ(n)  -5.080436539 -5.08570306 -5.078710007 -5.070994338 -5.071351216
## SC(n)  -5.014280922 -5.01009663 -4.993652784 -4.976486313 -4.967392388
## FPE(n)  0.005976269  0.00591141  0.005919382  0.005931651  0.005896157
##                  11           12           13           14           15
## AIC(n) -5.129121024 -5.131743149 -5.130771479 -5.133274490 -5.128491719
## HQ(n)  -5.061366182 -5.058342069 -5.051724163 -5.048580936 -5.038151929
## SC(n)  -4.947956551 -4.935481636 -4.919412927 -4.906818898 -4.886939088
## FPE(n)  0.005921804  0.005906308  0.005912063  0.005897298  0.005925588
##                  16           17           18           19           20
## AIC(n) -5.135275947 -5.137447717 -5.143545723 -5.139053494 -5.140157410
## HQ(n)  -5.039289920 -5.035815453 -5.036267222 -5.026128756 -5.021586435
## SC(n)  -4.878626277 -4.865701008 -4.856701974 -4.837112705 -4.823119582
## FPE(n)  0.005885543  0.005872796  0.005837117  0.005863424  0.005856985

# Ajusta un modelo VECM a tus datos
# El argumento 'r' es el número de relaciones de cointegración, que parece ser 1 basado en tus resultados
# El argumento 'lag' debe ser seleccionado basado en criterios de información como AIC o BIC

vecm_model <- VECM(series_matrix, lag=18, r=1, include="const")

# Muestra el resumen del modelo
summary(vecm_model)

## #############
## ###Model VECM 
## #############
## Full sample size: 1407   End sample size: 1388
## Number of variables: 2   Number of estimated slope parameters 76
## AIC -7134.037    BIC -6730.895   SSR 595.3997
## Cointegrating vector (estimated by 2OLS):
##    eth       btc
## r1   1 -3.339873
## 
## 
##              ECT                Intercept          eth -1            
## Equation eth -0.0178(0.0048)*** 0.0046(0.0174)     -0.1741(0.0374)***
## Equation btc -0.0034(0.0012)**  0.0021(0.0043)     -0.0294(0.0092)** 
##              btc -1             eth -2              btc -2            
## Equation eth 1.0102(0.1530)***  0.0726(0.0375).     -0.2771(0.1559).  
## Equation btc 0.0592(0.0377)     -0.0021(0.0092)     0.0244(0.0384)    
##              eth -3              btc -3              eth -4            
## Equation eth 0.0310(0.0375)      -0.0324(0.1565)     0.0313(0.0374)    
## Equation btc -0.0004(0.0092)     0.0232(0.0385)      0.0150(0.0092)    
##              btc -4              eth -5             btc -5            
## Equation eth 0.0827(0.1564)      -0.1032(0.0374)**  0.1576(0.1565)    
## Equation btc -0.0279(0.0385)     -0.0171(0.0092).   0.0518(0.0385)    
##              eth -6             btc -6             eth -7            
## Equation eth 0.1307(0.0374)***  -0.2765(0.1562).   0.0389(0.0376)    
## Equation btc 0.0045(0.0092)     0.0102(0.0384)     0.0016(0.0093)    
##              btc -7              eth -8              btc -8             
## Equation eth -0.2065(0.1566)     -0.0151(0.0376)     -0.2256(0.1568)    
## Equation btc -0.0649(0.0386).    -0.0057(0.0093)     -0.0396(0.0386)    
##              eth -9              btc -9            eth -10           
## Equation eth -0.0409(0.0376)     0.4625(0.1568)**  0.0154(0.0376)    
## Equation btc -0.0181(0.0092).    0.1394(0.0386)*** 0.0065(0.0093)    
##              btc -10             eth -11            btc -11           
## Equation eth -0.0133(0.1573)     -0.1220(0.0376)**  0.3227(0.1571)*   
## Equation btc -0.0077(0.0387)     -0.0208(0.0093)*   0.0559(0.0387)    
##              eth -12            btc -12            eth -13            
## Equation eth 0.0840(0.0377)*    -0.4515(0.1572)**  0.0405(0.0376)     
## Equation btc 0.0090(0.0093)     -0.0751(0.0387).   -0.0058(0.0092)    
##              btc -13            eth -14             btc -14            
## Equation eth -0.3127(0.1572)*   -0.0032(0.0375)     -0.0997(0.1578)    
## Equation btc 0.0246(0.0387)     -0.0011(0.0092)     -0.0130(0.0388)    
##              eth -15             btc -15            eth -16            
## Equation eth -0.1082(0.0374)**   0.3682(0.1574)*    0.0071(0.0375)     
## Equation btc -0.0115(0.0092)     0.0134(0.0387)     -0.0016(0.0092)    
##              btc -16             eth -17            btc -17            
## Equation eth -0.3090(0.1582).    0.0225(0.0374)     0.2660(0.1582).    
## Equation btc -0.0167(0.0389)     0.0091(0.0092)     -0.0231(0.0389)    
##              eth -18             btc -18           
## Equation eth -0.0268(0.0367)     0.0394(0.1575)    
## Equation btc -0.0114(0.0090)     0.0324(0.0388)

# Pronosticar los próximos valores usando el modelo VECM
forecast <- predict(vecm_model, n.ahead = 10)

# La salida de 'forecast' incluirá los pronósticos para cada una de las variables en el modelo
# Puedes extraer los pronósticos para Ethereum y Bitcoin así:
eth_forecast <- forecast[, "eth", drop = FALSE]

# Revertir la normalización para Ethereum
eth_forecast_real <- eth_forecast * eth_close_df$eth_close_zoo[1]

tabla_predicciones <- data.frame(
  Fecha = fechas_correctas,
  Real = ultimos_10_dias,
  ProphetLog = forecast_prophet_log_values,
  RedNeuronal = predicciones_desnorm_values,
  RedNeuronal_Jordan = predictions_desnorm_values_jor,
  Ethereum_vec = eth_forecast_real
)

tabla_predicciones

##              Fecha    Real ProphetLog RedNeuronal RedNeuronal_Jordan      eth
## [1398,] 2023-11-08 1888.25   1692.825    1749.890           1822.712 1884.876
## [1399,] 2023-11-09 2060.14   1684.167    1783.962           1827.257 1905.037
## [1400,] 2023-11-10 2094.24   1674.565    1813.334           1840.494 1909.345
## [1401,] 2023-11-11 2044.75   1666.843    1817.619           1881.253 1920.794
## [1402,] 2023-11-12 2060.08   1666.858    1832.389           1830.064 1923.933
## [1403,] 2023-11-13 2061.00   1659.992    1878.446           1855.733 1929.599
## [1404,] 2023-11-14 1981.95   1661.086    1798.769           1866.145 1921.229
## [1405,] 2023-11-15 2048.93   1660.127    1844.933           1897.740 1933.981
## [1406,] 2023-11-16 1956.32   1657.106    1851.229           1920.360 1939.024
## [1407,] 2023-11-17 1946.60   1653.903    1890.232           1921.662 1941.101

grafico <- ggplot(tabla_predicciones, aes(x=Fecha)) + 
  geom_line(aes(y=Real, colour="Real")) + 
  geom_line(aes(y=ProphetLog, colour="Prophet Log")) + 
  geom_line(aes(y=RedNeuronal, colour="Red Neuronal Elman")) +
  geom_line(aes(y=RedNeuronal_Jordan, colour = "Red Neuronal Jordan"))+
  geom_line(aes(y=eth, colour = "Modelo Vec"))+
  labs(title="Comparación de Predicciones vs Datos Reales", x="Fecha", y="Valor") +
  scale_color_manual(name="Leyenda", 
                     values=c("Real"="black", 
                              "Prophet Log"="blue", 
                              "Red Neuronal Elman"="purple",
                              "Modelo Vec" = "red", 
                              "Red Neuronal Jordan"="green")) +
  theme_minimal() +
  theme(legend.position="bottom")
grafico

# Asumiendo que 'vec' es tu modelo VEC ajustado
var_model <- vec2var(vecm, r = 1)  # 'r' es el número de relaciones de cointegración
serial_test <- serial.test(var_model, lags.pt = 18, type = "PT.asymptotic")
print(serial_test$serial)

## 
##  Portmanteau Test (asymptotic)
## 
## data:  Residuals of VAR object var_model
## Chi-squared = 6.7057, df = 2, p-value = 0.03498

normality_test <- normality.test(var_model)
print(normality_test$jb.mul)

## $JB
## 
##  JB-Test (multivariate)
## 
## data:  Residuals of VAR object var_model
## Chi-squared = 10591, df = 4, p-value < 2.2e-16
## 
## 
## $Skewness
## 
##  Skewness only (multivariate)
## 
## data:  Residuals of VAR object var_model
## Chi-squared = 171.93, df = 2, p-value < 2.2e-16
## 
## 
## $Kurtosis
## 
##  Kurtosis only (multivariate)
## 
## data:  Residuals of VAR object var_model
## Chi-squared = 10419, df = 2, p-value < 2.2e-16

arch_test <- arch.test(var_model, lags.multi = 18)
print(arch_test$arch.mul)

## 
##  ARCH (multivariate)
## 
## data:  Residuals of VAR object var_model
## Chi-squared = 983.33, df = 162, p-value < 2.2e-16