Nested Forecasting: Analyzing the Relationship Between the Dollar and Stock Market Trends

The prevailing opinion is that because countries are exporting more goods to the US than it exports to them, resulting in a trade deficit. In return for their exports, these countries receive US dollars, which they often use to purchase US government bonds and stocks. Over time, this process contributes to the strengthening of the dollar.

However, the below chart indicates a negative correlation between the stock market and the dollar index over recent periods.

Source code:

library(tidyverse)
library(tidymodels)
library(timetk)
library(modeltime)
library(tidyquant)
library(splines)
library(ggh4x)

#US Dollar Index (DX-Y.NYB)
df_dollar_index <-
  tq_get("DX-Y.NYB", to = "2025-07-01") %>%
  tq_transmute(select = close,
               mutate_fun = to.monthly,
               col_rename = "value") %>%
  mutate(date = as.Date(date),
         id = "Dollar Index")

#S&P 500
df_sp500 <-
  tq_get("^GSPC", to = "2025-07-01") %>%
  tq_transmute(select = close,
               mutate_fun = to.monthly,
               col_rename = "value") %>%
  mutate(date = as.Date(date),
         id = "S&P 500")

#Panel Data
df_panel <-
  df_dollar_index %>%
  bind_rows(df_sp500) %>%
  mutate(id = as_factor(id))


df_panel %>%
  group_by(id) %>%
  plot_time_series(
    date, value, .interactive = F, .facet_ncol = 1
  ) +
  scale_y_continuous(labels = scales::label_currency())

#Nested data
nested_data_tbl <-
  df_panel %>%

  # 1. Extending: We'll predict 52 weeks into the future.
  extend_timeseries(
    .id_var        = id,
    .date_var      = date,
    .length_future = 12
  ) %>%

  # 2. Nesting: We'll group by id, and create a future dataset
  #    that forecasts 52 weeks of extended data and
  #    an actual dataset that contains 104 weeks (2-years of data)
  nest_timeseries(
    .id_var        = id,
    .length_future = 12,
    .length_actual = 12*2
  ) %>%

  # 3. Splitting: We'll take the actual data and create splits
  #    for accuracy and confidence interval estimation of 52 weeks (test)
  #    and the rest is training data
  split_nested_timeseries(
    .length_test = 12
  )


#Nested Modeltime Workflow
#Create Tidymodels Workflows

#Prophet
rec_prophet <-
  recipe(value ~ date, extract_nested_train_split(nested_data_tbl))

wflw_prophet <-
  workflow() %>%
  add_model(
    prophet_reg("regression") %>%
      set_engine("prophet")
  ) %>%
  add_recipe(rec_prophet)


#Linear Regression
rec_glmnet <-
  recipe(value ~ date, data = extract_nested_train_split(nested_data_tbl)) %>%
  step_mutate(date_num = as.numeric(date)) %>%
  step_date(date, features = "month") %>%
  step_ns(date_num) %>%
  step_rm(date) %>%
  step_dummy(all_nominal_predictors(), one_hot = TRUE) %>%
  step_normalize(all_numeric_predictors())

wflw_glmnet <-
  workflow() %>%
  add_model(linear_reg(penalty = 0.2) %>%
              set_engine("glmnet")) %>%
  add_recipe(rec_glmnet)

#XGBoost
rec_xgb <-
  recipe(value ~ date, extract_nested_train_split(nested_data_tbl)) %>%
  step_timeseries_signature(date) %>%
  step_rm(date) %>%
  step_zv(all_predictors()) %>%
  step_dummy(all_nominal_predictors(), one_hot = TRUE)

wflw_xgb <-
  workflow() %>%
  add_model(boost_tree("regression") %>% set_engine("xgboost")) %>%
  add_recipe(rec_xgb)

#Nested Modeltime Tables
nested_modeltime_tbl <-
  modeltime_nested_fit(
  # Nested data
  nested_data = nested_data_tbl,

  # Add workflows
  wflw_prophet,
  wflw_glmnet,
  wflw_xgb
)

#Extract Nested Test Accuracy
best_nested_modeltime_tbl <-
  nested_modeltime_tbl %>%
  modeltime_nested_select_best(
    metric                = "mape",
    minimize              = TRUE,
    filter_test_forecasts = TRUE
  )

#Extract Nested Best Model Report
best_nested_modeltime_tbl %>%
  extract_nested_best_model_report()

#Extract Nested Test Accuracy
nested_modeltime_tbl %>%
  extract_nested_test_accuracy() %>%
  table_modeltime_accuracy()


#Extract Nested Best Test Forecasts
best_nested_modeltime_tbl %>%
  extract_nested_test_forecast() %>%
  group_by(id) %>%
  plot_modeltime_forecast(
    .facet_ncol  = 1,
    .interactive = FALSE,
    .line_size = 1
  ) +
  labs(title = "Nested Forecasting",
       subtitle = "<span style = 'color:dimgrey;'>Predictive Intervals</span> of <span style = 'color:red;'>XGBoost</span> and <span style = 'color:darkgreen;'>Prophet</span> Models",
       y = "", x = "") +
  facet_wrap(~ id,
             ncol = 1,
             scales = "free_y") +
  facetted_pos_scales(
    y = list(
      id == "Dollar Index" ~ scale_y_continuous(labels = scales::number_format()),
      id == "S&P 500" ~ scale_y_continuous(labels = scales::label_currency())
    )
  ) +
  scale_x_date(labels = scales::label_date("%b'%Y")) +
  theme_tq(base_family = "Roboto Slab", base_size = 16) +
  theme(plot.subtitle = ggtext::element_markdown(face = "bold"),
        plot.title = element_text(face = "bold"),
        strip.text = element_text(face = "bold"),
        axis.text.x = element_text(angle = 60, hjust = 1, vjust = 1),
        legend.position = "none")

Continue reading: Nested Forecasting: Analyzing the Relationship Between the Dollar and Stock Market Trends

Long-Term Implications and Future Developments

The existing opinion is that as countries export more goods to the US than what it exports to them, leading to a trade deficit that gradually strengthens the dollar. These countries use the US dollars earned from their exports to invest in US government bonds and stocks. However, recent data presents a contradictory picture, suggesting a negative correlation between the stock market and the dollar index over selected periods.

Fiscal Position and Stock Market Trends

The findings stir interesting questions about our understanding of the US’s fiscal position and the stock market trends, posing an opportunity for economists and data scientists to re-evaluate long-standing beliefs and theories.

Economic Policy

Economic policy development may also be influenced by these findings. If this negative correlation strengthens or becomes consistent over time, policymakers need to devise new strategies that ensure the strength of the dollar is not compromised while simultaneously maintaining stock market stability.

Actionable Advice

Opportunity for Economists

Economists need to reassess the potentially changing relationship between the US dollar’s strength and its impact on the stock market. In-depth research should be conducted using deeper data sets and analytical models to validate these initial findings. Future developments in the area should closely monitor, as this could be an essential piece of the puzzle understanding global economic dynamics.

Suggested Policy Actions

Policy makers should consider this revelation as crucial information in shaping the future economic policy of the country. If the pattern proves to be a consistent one, strategies that balance the strength of the dollar and the vitality of the stock market should be developed. Otherwise, it could lead to a situation where attempts to strengthen the dollar leads to a weakened stock market, and vice versa.

Investment Considerations

Investors and financial analysts should also scrutinize these trends while formulating investment strategies and trading decisions closely. Rigorous data tracking and interpretation can potentially prevent substantial monetary losses and leverage market conditions for maximum profitability.

Development of Advanced Predictive Models

Data scientists and statisticians should continue utilizing the latest techniques and models to maintain accurate predictions about these trends, as done here with the nested forecasting model. The employed model has the potential to test multiple theories at once, making it an excellent tool for exploring these complex relationships.

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