Gold and Interest Rate relationship

I would like to analyze the daily price of Gold (GLD) with the relationship to the Daily Treasury Par Real Yield Curve Rates. The Yield Curve Rates has 5-year rate, 7-year rate, 10-year rate, 20-year rate, and 30-year rate. I use all these rates, with its previous from 1 to 4 days values as the features to predict the price of Gold in the next day. Data from 2010–02–22 was collected, and split into training (70%) and testing data (30%). Here is the code in Julia/MLJ I used for the training and testing. The full code can be found in the Julia notebook in my Git.

using MLJ
y, X = MLJ.unpack(full_df, ==(Symbol("target")), colname -> true)
train, test = partition(eachindex(y), 0.7)
using MLJLinearModels
reg = @load RidgeRegressor pkg = "MLJLinearModels"
model_reg = reg()
mach = machine(model_reg, X, y)
fit!(mach, rows=train)
yhat = predict(mach, X[test,:])

Ridge Regression Model is used for training and prediction. Here is the prediction value compared with the actual value.

Then I tried to use SHAP value to analysis the features importance.

using ShapML
function predict_function(model, data)
  data_pred = DataFrame(y_pred = predict(model, data))
  return data_pred
end
explain = copy(full_df[train, :]) 
# Remove the outcome column.
explain = select(explain, Not(Symbol("target"))) 
# An optional reference population to compute the baseline prediction. 
reference = copy(full_df)  
reference = select(reference, Not(Symbol("target")))
sample_size = 60  # Number of Monte Carlo samples.
data_shap = ShapML.shap(explain = explain,
                         reference = reference,
                         model = mach,
                         predict_function = predict_function,
                         sample_size = sample_size,
                         seed = 1
                         )
 
show(data_shap, allcols = true)

Then, plot the Mean Absolute Shapley Value with the Gadfly.jl

using Gadfly
data_plot = combine(DataFrames.groupby(data_shap, [:feature_name]),:shap_effect=>mean)
transform!(data_plot,:shap_effect_mean => x -> abs.(x))
data_plot = sort(data_plot, order(:shap_effect_mean_function, rev = true))
 
baseline = round(data_shap.intercept[1], digits = 1)
 
p = plot(data_plot, y = :feature_name, x = :shap_effect_mean_function, Coord.cartesian(yflip = true), Scale.y_discrete, Geom.bar(position = :dodge, orientation = :horizontal),Theme(bar_spacing = 1mm),Guide.xlabel("|Shapley effect| (baseline = $baseline)"), Guide.ylabel(nothing),Guide.title("Feature Importance - Mean Absolute Shapley Value"))
draw(PNG("features.png", 6inch, 6inch), p)

It can be seen that the 7-year yield rate is the most important features. Therefore, the Gold price is related to the 7-year yield rate. However, as the prediction is not fully matched with the actual value, there are other factors affecting the Gold price.