Working on RL project

M2/Time Series/TD4.qmd

@@ -0,0 +1,154 @@
+# Exercise 1 : 
+
+```{r}
+set.seed(123)
+
+n <- 100
+t <- 1:n
+eps <- rnorm(n, mean = 0, sd = 1)
+
+X <- eps
+Y <- 3 * t + 2 + 15 * eps
+Z <- 3 * t + 2 + 15 * eps + 55 * sin(t * pi / 6)
+
+par(mfrow = c(3, 1))
+
+plot(ts(X), main = "Série X_t : Bruit blanc", ylab = "X_t", col = "blue")
+plot(ts(Y), main = "Série Y_t : Tendance + bruit", ylab = "Y_t", col = "red")
+plot(
+  ts(Z),
+  main = "Série Z_t : Tendance + saisonnalité + bruit",
+  ylab = "Z_t",
+  col = "darkgreen"
+)
+```
+
+```{r}
+library(forecast)
+
+alpha_vals <- c(0.1, 0.3, 0.5, 0.7, 0.9)
+
+mse_simple <- function(series) {
+  mse <- c()
+
+  for (a in alpha_vals) {
+    fit <- ses(series, alpha = a, initial = "simple", h = 1)
+
+    fitted_vals <- fitted(fit)
+    mse <- c(mse, mean((series - fitted_vals)^2, na.rm = TRUE))
+  }
+
+  data.frame(alpha = alpha_vals, MSE = mse)
+}
+
+mse_simple(X)
+mse_simple(Y)
+mse_simple(Z)
+```
+
+```{r}
+holt_mse <- function(series) {
+  beta_vals <- seq(0.1, 0.9, 0.2)
+  alpha_vals <- seq(0.1, 0.9, 0.2)
+
+  res <- expand.grid(alpha = alpha_vals, beta = beta_vals)
+  res$MSE <- NA_real_
+
+  for (i in seq_len(nrow(res))) {
+    fit <- tryCatch(
+      suppressWarnings(forecast::holt(
+        series,
+        alpha = res$alpha[i],
+        beta = res$beta[i],
+        h = 1
+      )),
+      error = function(e) NULL
+    )
+
+    if (!is.null(fit)) {
+      fitted_vals <- stats::fitted(fit)
+      res$MSE[i] <- mean((series - fitted_vals)^2, na.rm = TRUE)
+    } else {
+      res$MSE[i] <- NA_real_
+    }
+  }
+
+  res[order(res$MSE, na.last = TRUE), , drop = FALSE][1:5, ]
+}
+
+holt_mse(X)
+holt_mse(Y)
+holt_mse(Z)
+```
+
+```{r}
+fit_X <- ses(X)
+fit_Y <- ses(Y)
+fit_Z <- ses(Z)
+
+accuracy(fit_X)
+accuracy(fit_Y)
+accuracy(fit_Z)
+```
+
+```{r}
+fit_X_holt <- holt(X)
+fit_Y_holt <- holt(Y)
+fit_Z_holt <- holt(Z)
+
+accuracy(fit_X_holt)
+accuracy(fit_Y_holt)
+accuracy(fit_Z_holt)
+```
+
+# Exercise 2
+
+```{r}
+library(tseries)
+library(forecast)
+data("AirPassengers")
+log_air <- log(AirPassengers)
+
+n <- length(log_air)
+n_test <- 12
+train <- window(log_air, end = c(1959, 12))
+test <- window(log_air, start = c(1960, 1))
+
+plot(log_air, main = "Série AirPassengers (Log)")
+lines(train, col = "blue")
+lines(test, col = "red")
+legend("topleft", legend = c("Train", "Test"), col = c("blue", "red"), lty = 1)
+```
+
+```{r}
+library(forecast)
+
+fit_simple <- ses(train, h = n_test)
+fit_holt <- holt(train, h = n_test)
+
+plot(log_air)
+lines(fit_simple$mean, col = "green", lwd = 2)
+lines(fit_holt$mean, col = "orange", lwd = 2)
+legend(
+  "topleft",
+  legend = c("Série", "Simple", "Holt"),
+  col = c("black", "green", "orange"),
+  lty = 1
+)
+
+accuracy(fit_simple, test)
+accuracy(fit_holt, test)
+```
+
+```{r}
+fit_hw_add <- hw(train, h = n_test, seasonal = "additive")
+fit_hw_mult <- hw(train, h = n_test, seasonal = "multiplicative")
+
+plot(log_air)
+lines(fit_hw_add$mean, col = "purple", lwd = 2)
+lines(fit_hw_mult$mean, col = "darkgreen", lwd = 2)
+legend("topleft", legend = c("Série", "HW Additif", "HW Multiplicatif"), col = c("black", "purple", "darkgreen"), lty = 1)
+
+accuracy(fit_hw_add, test)
+accuracy(fit_hw_mult, test)
+```

pyproject.toml

@@ -5,51 +5,27 @@ description = "A curated collection of mathematics and data science projects dev
 readme = "README.md"
 requires-python = ">= 3.12,<3.14"
 dependencies = [
-    "accelerate>=1.12.0",
     "ale-py>=0.11.2",
     "catboost>=1.2.10",
-    "datasets>=4.6.1",
-    "faiss-cpu>=1.13.2",
-    "folium>=0.20.0",
-    "geopandas>=1.1.2",
-    "google-api-python-client>=2.191.0",
-    "google-auth-oauthlib>=1.3.0",
-    "google-generativeai>=0.8.6",
-    "gymnasium[toy-text]>=1.2.3",
-    "imblearn>=0.0",
     "ipykernel>=7.2.0",
     "ipywidgets>=8.1.8",
     "langchain>=1.2.10",
-    "langchain-community>=0.4.1",
     "langchain-core>=1.2.17",
     "langchain-huggingface>=1.2.1",
     "langchain-mistralai>=1.1.1",
-    "langchain-ollama>=1.0.1",
-    "langchain-openai>=1.1.10",
-    "langchain-text-splitters>=1.1.1",
-    "mapclassify>=2.10.0",
     "matplotlib>=3.10.8",
-    "nbformat>=5.10.4",
     "numpy>=2.4.2",
     "opencv-python>=4.13.0.92",
-    "openpyxl>=3.1.5",
     "pandas>=3.0.1",
     "pandas-stubs>=3.0.0.260204",
     "pettingzoo[atari]>=1.24.3",
     "plotly>=6.6.0",
-    "polars>=1.38.1",
-    "pypdf>=6.7.5",
-    "rasterio>=1.5.0",
-    "requests>=2.32.5",
     "scikit-learn>=1.8.0",
     "scipy>=1.17.1",
     "seaborn>=0.13.2",
-    "sentence-transformers>=5.2.3",
     # "sequenzo>=0.1.20",
     "shap>=0.50.0",
     "spacy>=3.8.11",
-    "statsmodels>=0.14.6",
-    "supersuit>=3.10.0",
     "tensorflow>=2.20.0",
     "tf-keras>=2.20.1",
     "tiktoken>=0.12.0",
@@ -57,9 +33,7 @@ dependencies = [
     "torch>=2.10.0",
     "umap-learn>=0.5.11",
     "uv>=0.10.7",
-    "wbdata>=1.1.0",
     "xgboost>=3.2.0",
-    "yfinance>=1.2.0",
 ]
 
 [dependency-groups]