Time-Series Analysis of 20+ Year Treasury Bond ETF

Abstract

This paper analyzes the behavior of daily returns of the iShares 20+ Year Treasury Bond ETF (TLT), focusing on the impact of macroeconomic and financial market variables, including market volatility index, S&P500 returns, changes in Fed rates, Treasury bond market yield, and inflation. Models utilized daily data from January 2004 to July 2024, the analysis incorporates advanced time-series models to capture the dynamics of returns in TLT. An ARIMAX model with state-dependent dynamics using a Threshold Autoregressive (TAR) framework reveals the significant role of Federal Funds Rate changes in regime-dependent effects on returns. Additionally, a GARCH-ARIMAX model was employed to address volatility clustering and persistence, highlighting the impact of recent shocks and long-term volatility persistence. Both models demonstrate the critical influence of market volatility and equity returns on the daily performance of TLT. The findings provide a comprehensive understanding of the drivers of long-term Treasury bond returns and underscore the importance of accounting for regime changes and time-varying volatility in modeling.

Data

• Asset: TLT daily returns (R_TLT)
• Sample: Jan 5, 2004 – Jul 1, 2024 (5,156 trading-day observations)
• Sources: Yahoo Finance (prices/returns) + FRED (macro/market series aligned to daily frequency)
• Core drivers: VIX, S&P 500 returns (R_GSPC), inflation (INFL), 20-year Treasury yield (DGS20), changes in Fed funds rate (dFEDRATE)
• Regime definition: Monetary-policy state based on dFEDRATE (rate-cut regimes vs stable/increasing-rate regimes)

Methods

• Baseline benchmark: ARIMA(2,0,2) selected by AIC
  AIC: 13,765.91
  Ex-post RMSFE: 1.0598
• Preferred mean-dynamics extension (regime switching): ARIMAX(2,0,2) + TAR
  Regimes defined by dFEDRATE and implemented using regime-specific lag interactions (TLT lag effects vary by policy state)
  AIC: 13,148.81
  Ex-post RMSFE: 0.9097872
• Volatility modeling (best overall in the writeup): GARCH(1,2) variance layered on an ARIMA(1,0,3)
  Captures volatility clustering and persistent variance dynamics
  ARCH effects: ARCH LM χ² = 725.141 (p = 0.0000)
  AIC: 12,191.62
  Ex-post RMSFE: 0.90935889

Key Results

What the models agree on:

• Flight-to-safety is the dominant daily mechanism. Across specifications, VIX is positively associated with TLT returns and S&P 500 returns are negatively associated, consistent with risk-off periods supporting long-duration Treasuries.
• Monetary policy regimes materially change return dynamics. The ARIMAX+TAR results show that the impact of lagged TLT returns differs between rate-cut and stable/increasing-rate regimes (dFEDRATE-based state interactions).
• Volatility clustering is large and persistent. Strong ARCH effects and GARCH dynamics indicate that volatility shocks propagate forward, making constant-variance models inadequate for this series.
• Regime + volatility structure improves forecast performance vs baseline. Relative to the ARIMA benchmark (RMSFE 1.0598), both the TAR and GARCH specifications reduce forecast error to approximately 0.91, with the GARCH-ARIMAX model also delivering the strongest overall fit (lowest AIC).

Conclusion

Across 2004–2024, TLT's daily returns are best explained by risk-off conditions (higher VIX and weaker equities) and monetary-policy regime shifts captured by changes in the Fed funds rate. Incorporating regime dependence and time-varying volatility improves fit and reduces forecast error relative to a baseline ARIMA model, and the GARCH-ARIMAX specification provides the most realistic description of volatility behavior in TLT returns.

Key Model Outputs