Time Series Machine Learning: S&P 500

It does not seem to be a safe entry point for the S&P 500 market ahead of the FED rate cuts.

Source code:

library(tidyverse)
library(tidymodels)
library(timetk)
library(tidyquant)
library(modeltime)
library(ggthemes)


#FED Interest Rates
df_fedfunds <- 
  read_csv("https://raw.githubusercontent.com/mesdi/investingcom/main/fedfunds.csv") %>% 
  janitor::clean_names() %>% 
  select(date = release_date, fedfunds = actual) %>% 
  #Converts string to date object
  mutate(date = case_when(
    !is.na(parse_date(date, format = "%b %d, %Y")) ~ parse_date(date, format = "%b %d, %Y"),
    !is.na(parse_date(date, format = "%d-%b-%y")) ~ parse_date(date, format = "%d-%b-%y")
  )) %>% 
  mutate(date = floor_date(date, "month") %m+% months(1),
         fedfunds = str_remove(fedfunds, "%") %>% as.numeric()) %>% 
  #makes regular time series by filling the time gaps
  pad_by_time(date, .by = "month") %>% 
  fill(fedfunds, .direction = "down") %>% 
  #removes duplicated points
  distinct(date, .keep_all = TRUE) %>% 
  drop_na()


#S&P 500 (^GSPC)
df_sp500 <- 
  tq_get("^GSPC", to = "2024-09-01") %>% 
  tq_transmute(select = close,
               mutate_fun = to.monthly,
               col_rename = "sp500") %>% 
  mutate(date = as.Date(date)) %>% 
  drop_na()

#Merging all the datasets
df_merged <- 
  df_sp500 %>% 
  left_join(df_fedfunds) %>% 
  drop_na()


#Splitting
split <- 
  df_merged %>% 
  time_series_split(assess = "1 year", 
                    cumulative = TRUE)

df_train <- training(split)
df_test <- testing(split)

#Time series cross validation for tuning
df_folds <- time_series_cv(df_train,
                           initial = 80, 
                           assess = 12)


#Preprocessing for Boosting ARIMA
rec_arima_boost <- 
  recipe(nvidia ~ ., data = df_train) %>% 
  step_date(date, features = c("year", "month")) %>% 
  step_dummy(date_month, one_hot = TRUE) %>% 
  step_normalize(all_numeric_predictors())



#Boosted ARIMA Regression Models
#(https://business-science.github.io/modeltime/reference/arima_boost.html)
mod_arima_boost <- 
  arima_boost(
    min_n = tune(),
    learn_rate = tune(),
    trees = tune()
  ) %>%
  set_engine(engine = "auto_arima_xgboost")


#Workflow set
wflow_arima_boost <- 
  workflow_set(
    preproc = list(rec = rec_arima_boost),
    models = list(mod = mod_arima_boost)
  ) 


#Tuning and evaluating the model on all the samples
grid_ctrl <-
  control_grid(
    save_pred = TRUE,
    parallel_over = "everything",
    save_workflow = TRUE
  )

grid_results <-
  wflow_arima_boost %>%
  workflow_map(
    seed = 98765,
    resamples = df_folds,
    grid = 10,
    control = grid_ctrl
  )


#Accuracy of the grid results
grid_results %>% 
  rank_results(select_best = TRUE, 
               rank_metric = "rsq") %>%
  select(Models = wflow_id, .metric, mean)


#Finalizing the model with the best parameters
best_param <- 
  grid_results %>%
  extract_workflow_set_result("rec_mod") %>% 
  select_best(metric = "rsq")


wflw_fit <- 
  grid_results %>% 
  extract_workflow("rec_mod") %>% 
  finalize_workflow(best_param) %>% 
  fit(df_train)


#Calibrate the model to the testing set
calibration_boost <- 
  wflw_fit %>%
  modeltime_calibrate(new_data = df_test)

#Accuracy of the finalized model
calibration_boost %>%
  modeltime_accuracy(metric_set = metric_set(rmse,rsq)) %>% 
  select(.model_desc)


#Predictive intervals
calibration_boost %>%
  modeltime_forecast(actual_data = df_merged %>% 
                       filter(date >= last(date) - months(12)),
                     new_data = df_test) %>%
  plot_modeltime_forecast(.interactive = FALSE,
                          .legend_show = FALSE,
                          .line_size = 1.5,
                          .color_lab = "",
                          .title = "Predictive Intervals for S&P 500 ") +
  labs(subtitle = "Monthly Index<br><span style = 'color:red;'>Point Forecast Line</span>") + 
  scale_x_date(breaks = c(make_date(2023,8,1), 
                          make_date(2024,1,1),
                          make_date(2024,8,1)),
               labels = scales::label_date(format = "%Y %b"),
               expand = expansion(mult = c(.1, .1))) +
  theme_wsj(base_family = "Bricolage Grotesque",
            color = "blue",
            base_size = 12) +
  theme(legend.position = "none",
        plot.background = element_rect(fill = "khaki", color = "khaki"),
        plot.title = element_text(size = 24),
        axis.text = element_text(size = 16),
        plot.subtitle = ggtext::element_markdown(size = 20, face = "bold"))