How SalaryTea Used ARIMA to Forecast AAA Bond Yields with Exogenous Data
AAA Corporate Bond Yield Forecast using an ARIMA model with exogenous variables, where the blue line represents the actual yields, and the red dashed line represents the forecasted yields.
Introduction
SalaryTea’s mission is to bring sophisticated financial tools, typically used by large corporations, to small businesses at a fraction of the cost. By leveraging simple AI algorithms like ARIMA and incorporating key exogenous data such as the Federal Funds Rate and 10-Year Treasury Yield, SalaryTea aimed to project AAA corporate bond yields and create reliable financial forecasts. This approach empowers everyday business owners with the same powerful insights that Wall Street analysts use, but at little to no cost, making high-quality forecasting more accessible.
ARIMA and Its Application in Financial Forecasting
The ARIMA model is a widely-used statistical technique for time series analysis. It can capture underlying trends in data using:
AutoRegression (AR): Utilizing past data to predict future values.
Integrated (I): Differencing data to ensure it is stationary.
Moving Average (MA): Using past forecast errors for adjustments.
ARIMA can also be enhanced by incorporating exogenous variables (ARIMAX), which provide external context to the data being analyzed. In SalaryTea's application, the Federal Funds Rate and 10-Year Treasury Yield were used as exogenous inputs to forecast AAA corporate bond yields.
The Formula Behind ARIMA
The ARIMA model, denoted as ARIMA(p, d, q), is characterized by three key components:
p: The number of lag observations included in the model (autoregressive term).
d: The number of times the raw observations are differenced to make the data stationary (integrated term).
q: The size of the moving average window (moving average term).
The general ARIMA formula can be written as:
The equation for a time series model with exogenous variables (ARIMAX) is an extension of the standard ARIMA model:
ARIMA Formula: yt = c + ∑i=1p ϕiyt−i + ∑i=1q θiϵt−i + ∑k=1r βkXt−k + ϵt
Where:
Xt−kX_{t-k}Xt−k are the exogenous variables (in this case, the Federal Funds Rate and 10-Year Treasury Yield).
βk\beta_kβk are the coefficients associated with these exogenous variables.
Exogenous Data Sources
SalaryTea pulled data from publicly available resources to inform its forecasts:
AAA Corporate Bond Yields (Moody’s Seasoned Aaa Corporate Bond Yield) from FRED, Federal Reserve Bank of St. Louis: https://fred.stlouisfed.org/series/AAA (“Moody’s Seasoned Aaa Corporate Bond Yield”).
Federal Funds Rate from FRED, Federal Reserve Bank of St. Louis: https://fred.stlouisfed.org/series/FEDFUNDS (“Federal Funds Effective Rate”).
10-Year Treasury Yield from FRED, Federal Reserve Bank of St. Louis: https://fred.stlouisfed.org/series/DGS10 (“10-Year Treasury Constant Maturity Rate”).
Forecast Results and Performance
The ARIMA model, enhanced by exogenous variables, produced a forecast of 4.92% for the AAA corporate bond yield in December 2024. This projection stands in contrast to external forecasts, such as those from the Financial Forecast Center, which estimate the yield to be around 4.34% by the same period (Financial Forecast Center, “Forecast of Aaa Corporate Bond Yields”). The Wall Street Journal (WSJ) also provides more conservative estimates, taking into account expert opinions and broader market trends that factor in inflation and interest rate expectations. This 0.58 percentage point difference between SalaryTea’s forecast and these external sources highlights the variation between SalaryTea’s model and other industry projections.
Key error metrics for the ARIMA model were as follows:
Mean Absolute Error (MAE): 0.13
Mean Squared Error (MSE): 0.03
Root Mean Squared Error (RMSE): 0.16
Although these results indicate that the ARIMA model performed well, the discrepancy between SalaryTea’s forecast and external predictions raised questions about the underlying causes of the deviation.
AAA Corporate Bond Yield Forecast for the remainder of 2024, with historical yields (blue line) from 2020 to 2024 and forecasted yields (red line) extending into the future.
Key Observations:
Historical Trend (2020-2023):
From 2020 to early 2023, AAA bond yields have shown significant growth, rising from around 2.0% to over 5.0%. This indicates a period of increased corporate bond yields, likely driven by macroeconomic factors such as rising interest rates or inflation concerns.
There are some fluctuations in the historical trend, reflecting bond market volatility.
Forecast (Late 2023 - 2024):
The forecast from late 2023 to the end of 2024 shows a flattening trend, with bond yields stabilizing around the 5.0% mark.
The model predicts a slight decrease but mostly a leveling off, suggesting that bond yields may not experience the same rapid increase seen in previous years.
This forecast aligns with the assumption that interest rates are likely to stabilize or decrease, reflecting expectations of potential economic normalization after significant increases in rates to combat inflation.
Analysis:
Stabilization Phase: The ARIMA forecast anticipates a plateau in bond yields, which aligns with broader economic forecasts suggesting a more stable interest rate environment in the near future.
Macroeconomic Implications: A flat bond yield curve might indicate that inflation is expected to be under control and that central banks (such as the Fed) may not raise rates further, which could help bond yields stabilize.
Analyzing the Size of the Deviation
The 0.58 percentage point difference between SalaryTea's ARIMA forecast and external predictions stems from several factors:
Dependence on Historical Data:
ARIMA models, by nature, heavily rely on past trends and patterns. While effective in many cases, this reliance may not always capture potential shifts in market conditions or policy changes, leading to slight overestimations or underestimations in projections.
Differing Assumptions:
Advanced financial institutions, such as the Financial Forecast Center and WSJ, may incorporate a broader range of economic assumptions, including expected changes in Federal Reserve policy or shifts in global economic conditions. SalaryTea's ARIMA model, while incorporating exogenous variables, may not have accounted for certain nuanced factors influencing bond yields.
Sensitivity to Exogenous Variables:
The ARIMA model’s emphasis on the Federal Funds Rate and 10-Year Treasury Yield may have led to a higher projection. As interest rates fluctuate, these exogenous variables can have a profound impact on bond yields, potentially causing SalaryTea's forecast to deviate from the consensus.
Key Points to Consider:
Size of the Deviation (0.58 percentage points):
For bond yields, a deviation of 0.58 percentage points is significant, especially for decisions involving bond pricing, portfolio allocation, or interest rate-sensitive strategies. Small changes in bond yields can cause large fluctuations in bond prices and investment performance. While deviations between 0.05%-0.1% are typically acceptable for precision financial forecasting, the 0.58% difference between SalaryTea’s ARIMA forecast and external forecasts represents a relatively large gap.
Nature of the Forecasts:
ARIMA Model: ARIMA’s reliance on historical data and exogenous variables like the Federal Funds Rate or 10-Year Treasury Yield might explain the higher yield forecast. These exogenous variables could weigh more heavily on the model’s outcome compared to external forecasts, which may rely on broader market sentiment and qualitative factors.
External Forecasts (e.g., Financial Forecast Center and WSJ): Advanced institutions, including WSJ, use broader macroeconomic data, future Federal Reserve actions, inflation expectations, and geopolitical risks that might not be fully captured by the ARIMA model. These factors contribute to the lower projected yield of 4.34%.
Possible Reasons for the Difference:
Exogenous Variables: SalaryTea’s ARIMA model may have placed greater weight on rising interest rates or inflation, resulting in a higher forecast.
ARIMA Parameters: Specific parameter choices, such as autoregressive terms, moving average terms, or differencing orders, might also have contributed to the forecast deviation. Fine-tuning these settings could bring the forecast closer to consensus estimates.
Implications for Small Businesses and Individual Investors
One of the core goals of SalaryTea’s approach was to show that high-quality financial forecasting is within reach, even without the use of complex models. By relying on simple AI algorithms, smaller businesses and individual investors can benefit from robust financial projections that provide actionable insights without requiring large teams of analysts or costly infrastructure.
The 0.58 percentage point deviation highlights the limitations of simpler models but also underscores their potential. In many cases, smaller deviations like this may be acceptable for broader financial planning, especially for those not engaged in high-frequency trading or institutional portfolio management. SalaryTea’s work emphasizes that accurate, data-driven forecasts can be achieved with accessible tools, democratizing financial analysis for a wider audience.
Conclusion
SalaryTea successfully demonstrated how simple AI algorithms like ARIMA, when combined with exogenous data, can produce reliable financial forecasts. Although the 0.58 percentage point deviation from external forecasts highlights some limitations, the overall accuracy and interpretability of the ARIMA model make it a viable tool for smaller businesses and individual investors.
By integrating publicly available data from the Federal Funds Rate, 10-Year Treasury Yield, and AAA corporate bond yields, SalaryTea showcased the potential of basic AI techniques for financial forecasting. While more advanced models may offer greater precision, SalaryTea's approach proves that robust financial insights are not limited to large institutions and can be accessible to anyone with the right tools and data.
Looking ahead, further refinements to the model—such as incorporating additional exogenous variables or exploring more advanced algorithms—could help reduce forecast error and improve the competitiveness of SalaryTea's projections in the financial forecasting landscape.
Works Cited
“Federal Funds Effective Rate.” FRED, Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/series/FEDFUNDS.
“Moody’s Seasoned Aaa Corporate Bond Yield.” FRED, Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/series/AAA.
“10-Year Treasury Constant Maturity Rate.” FRED, Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/series/DGS10.
“Forecast of Aaa Corporate Bond Yields.” Financial Forecast Center, https://www.forecasts.org/aaabonds.htm.
Strauss, Lawrence. "With Interest Rates Falling, Which Bonds Should You Buy?" The Wall Street Journal, 3 Oct. 2024, https://www.wsj.com/finance/investing/investing-bonds-interest-rates-falling-375caffe.
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