mirror of
https://github.com/ArthurDanjou/ArtStudies.git
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155 lines
3.0 KiB
Plaintext
155 lines
3.0 KiB
Plaintext
# Exercise 1 :
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```{r}
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set.seed(123)
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n <- 100
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t <- 1:n
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eps <- rnorm(n, mean = 0, sd = 1)
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X <- eps
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Y <- 3 * t + 2 + 15 * eps
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Z <- 3 * t + 2 + 15 * eps + 55 * sin(t * pi / 6)
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par(mfrow = c(3, 1))
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plot(ts(X), main = "Série X_t : Bruit blanc", ylab = "X_t", col = "blue")
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plot(ts(Y), main = "Série Y_t : Tendance + bruit", ylab = "Y_t", col = "red")
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plot(
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ts(Z),
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main = "Série Z_t : Tendance + saisonnalité + bruit",
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ylab = "Z_t",
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col = "darkgreen"
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)
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```
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```{r}
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library(forecast)
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alpha_vals <- c(0.1, 0.3, 0.5, 0.7, 0.9)
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mse_simple <- function(series) {
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mse <- c()
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for (a in alpha_vals) {
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fit <- ses(series, alpha = a, initial = "simple", h = 1)
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fitted_vals <- fitted(fit)
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mse <- c(mse, mean((series - fitted_vals)^2, na.rm = TRUE))
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}
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data.frame(alpha = alpha_vals, MSE = mse)
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}
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mse_simple(X)
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mse_simple(Y)
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mse_simple(Z)
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```
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```{r}
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holt_mse <- function(series) {
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beta_vals <- seq(0.1, 0.9, 0.2)
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alpha_vals <- seq(0.1, 0.9, 0.2)
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res <- expand.grid(alpha = alpha_vals, beta = beta_vals)
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res$MSE <- NA_real_
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for (i in seq_len(nrow(res))) {
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fit <- tryCatch(
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suppressWarnings(forecast::holt(
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series,
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alpha = res$alpha[i],
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beta = res$beta[i],
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h = 1
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)),
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error = function(e) NULL
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)
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if (!is.null(fit)) {
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fitted_vals <- stats::fitted(fit)
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res$MSE[i] <- mean((series - fitted_vals)^2, na.rm = TRUE)
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} else {
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res$MSE[i] <- NA_real_
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}
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}
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res[order(res$MSE, na.last = TRUE), , drop = FALSE][1:5, ]
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}
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holt_mse(X)
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holt_mse(Y)
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holt_mse(Z)
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```
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```{r}
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fit_X <- ses(X)
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fit_Y <- ses(Y)
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fit_Z <- ses(Z)
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accuracy(fit_X)
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accuracy(fit_Y)
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accuracy(fit_Z)
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```
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```{r}
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fit_X_holt <- holt(X)
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fit_Y_holt <- holt(Y)
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fit_Z_holt <- holt(Z)
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accuracy(fit_X_holt)
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accuracy(fit_Y_holt)
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accuracy(fit_Z_holt)
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```
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# Exercise 2
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```{r}
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library(tseries)
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library(forecast)
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data("AirPassengers")
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log_air <- log(AirPassengers)
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n <- length(log_air)
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n_test <- 12
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train <- window(log_air, end = c(1959, 12))
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test <- window(log_air, start = c(1960, 1))
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plot(log_air, main = "Série AirPassengers (Log)")
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lines(train, col = "blue")
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lines(test, col = "red")
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legend("topleft", legend = c("Train", "Test"), col = c("blue", "red"), lty = 1)
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```
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```{r}
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library(forecast)
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fit_simple <- ses(train, h = n_test)
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fit_holt <- holt(train, h = n_test)
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plot(log_air)
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lines(fit_simple$mean, col = "green", lwd = 2)
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lines(fit_holt$mean, col = "orange", lwd = 2)
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legend(
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"topleft",
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legend = c("Série", "Simple", "Holt"),
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col = c("black", "green", "orange"),
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lty = 1
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)
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accuracy(fit_simple, test)
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accuracy(fit_holt, test)
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```
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```{r}
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fit_hw_add <- hw(train, h = n_test, seasonal = "additive")
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fit_hw_mult <- hw(train, h = n_test, seasonal = "multiplicative")
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plot(log_air)
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lines(fit_hw_add$mean, col = "purple", lwd = 2)
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lines(fit_hw_mult$mean, col = "darkgreen", lwd = 2)
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legend("topleft", legend = c("Série", "HW Additif", "HW Multiplicatif"), col = c("black", "purple", "darkgreen"), lty = 1)
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accuracy(fit_hw_add, test)
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accuracy(fit_hw_mult, test)
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```
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