Temporal Structural Forecasting:
Evidence of Exploitable Temporal Structure in S&P 500 Equity Returns
Kevin B. Burk
TSF Inc.
ORCID: 0009-0005-5343-7913
February 2026
Abstract
This study tests whether temporal structure exists in equity price data and can be systematically exploited for position entry timing. Using a preregistered methodology, we generate specific limit order entry prices one week in advance for 346 S&P 500 constituents across all 11 GICS sectors. We test 1,386 parameter permutations over the 10-year period 2016–2025, encompassing 6 factor strategies, 7 forecast models, and 3 confidence thresholds.
Results demonstrate statistically significant directional accuracy across all permutations. Mean win rate across the full sample is 80.3% (median 80.9%), with sector means ranging from 73.4% (Consumer Staples) to 86.3% (Information Technology). The maximum p-value observed across all 1,386 tests is 1.91 × 10−16; the minimum is 2.69 × 10−184. No permutation fails to reject the null hypothesis of random directional accuracy at any conventional significance level.
Applied to sector-based position trading portfolios over the out-of-sample period 2021–2025, the methodology generates compound annual growth rates of 18–21% with win rates exceeding 88% and Sharpe ratios of 0.58–0.87. These results constitute evidence against the semi-strong form of the Efficient Market Hypothesis and demonstrate the existence of exploitable temporal patterns in equity returns.
Keywords: market timing, temporal structure, seasonality, entry signals, market efficiency
JEL Classification: G11, G12, G14, G17
1. Introduction
The question of whether systematic market timing is possible remains contested in financial economics. The Efficient Market Hypothesis (Fama, 1970) posits that asset prices fully reflect available information, implying that predictable patterns in returns should not persist once identified. Empirical evidence for calendar anomalies—including day-of-week effects (French, 1980; Gibbons & Hess, 1981), turn-of-month effects (Ariel, 1987), and holiday effects (Lakonishok & Smidt, 1988)—suggests temporal patterns exist, though their economic significance after transaction costs remains debated.
This study contributes to the literature by presenting evidence of exploitable temporal structure in S&P 500 equity returns using a methodology we term Temporal Structural Forecasting (TSF). Unlike traditional calendar anomaly research, which identifies aggregate patterns across securities, TSF generates security-specific entry signals at specific prices for specific dates, one week in advance. The methodology is fully deterministic, requires no optimization or model training, and produces replicable outputs from identical inputs.
Our primary contribution is demonstrating that temporal structure can be exploited with sufficient accuracy to generate economically significant returns in position trading applications. Across 1,386 parameter permutations tested on 346 S&P 500 constituents over 10 years, we observe mean directional accuracy of 80.3% with no permutation producing a p-value above 1.91 × 10−16. Applied to sector-based portfolios, the methodology generates 18–21% CAGR with win rates exceeding 88%.
1.1 Research Questions
This study addresses two primary research questions. First, does temporal structure exist in individual equity returns at a level that permits statistically reliable entry timing? Second, can this temporal structure be exploited to generate economically significant portfolio returns?
1.2 Contribution to Literature
This work extends the calendar anomaly literature in three ways. First, we demonstrate that temporal patterns exist at the individual security level with sufficient consistency to generate actionable entry signals. Second, we show that these patterns persist across all GICS sectors and multiple factor exposures, suggesting the effect is not concentrated in specific market segments. Third, we provide evidence of economic significance through portfolio-level returns that substantially exceed passive benchmarks and typical active management performance.
2. Methodology
2.1 Theoretical Framework
TSF is grounded in the Model of Temporal Inertia, which extends Newton's First Law to time series behavior. The model proposes that values in a time series follow their established trend until acted upon by an unbalancing force, and that these forces exhibit seasonal patterns that can be identified and forecast. The complete theoretical framework is detailed in Burk (2024); here we summarize the key methodological components.
2.2 Signal Generation
For each security and each future trading date, TSF generates a target entry price based on the convergence of multiple seasonal models operating at different cadences (annual, quarterly, monthly). Each seasonal model produces a forecast with an associated confidence interval derived from historical accuracy patterns. When confidence intervals exceed predefined thresholds (ci85, ci90, ci95), an entry signal is generated with a specific limit order price.
The signal generation process is fully deterministic: identical inputs produce identical outputs. No machine learning, neural networks, or parameter optimization is employed. All calculations use simple moving averages and seasonal relatives—mathematical operations that can be expressed in closed form and independently verified.
2.3 Trade Execution Protocol
Entry signals are generated one week (5 trading days) in advance. Each signal specifies a security, a date, and a limit order price. Positions are opened only when the market reaches the specified price on the specified date. If the limit order does not fill, no position is opened.
Exit protocol employs a 5% profit target with a 120-day maximum holding period. Positions that reach the profit target are closed immediately. Positions that do not reach the profit target within 120 days are closed at market price (forced exit). This protocol is applied uniformly across all securities and all tests.
2.4 Permutation Structure
To test robustness, we examine all combinations of three parameter dimensions:
Factor strategies (6): high_beta, high_momentum, high_volatility, low_beta, low_momentum, low_volatility. These determine which securities within each sector are eligible for signals based on trailing factor exposures.
Forecast models (7): all_forecasts, arima_a0, arima_a1, arima_a2, arima_a2w, arima_a3, arima_a3w. These represent different specifications of the base forecast model used to generate entry prices.
Confidence thresholds (3): ci85, ci90, ci95. These determine the minimum confidence level required to generate an entry signal.
This yields 6 × 7 × 3 = 126 permutations per sector, and 126 × 11 = 1,386 permutations across all GICS sectors.
3. Data
3.1 Sample Construction
The sample consists of all constituents of the S&P 500 index with continuous price data for the period January 1, 2016 through December 31, 2025. Securities with incomplete data due to listing, delisting, or corporate actions are excluded, yielding a final sample of 346 securities.
3.2 Sector Classification
Securities are assigned to GICS sectors based on classification as of December 31, 2025. The 11 sectors and their sample sizes are: Communication Services (n=26), Consumer Discretionary (n=53), Consumer Staples (n=38), Energy (n=23), Financials (n=65), Health Care (n=63), Industrials (n=74), Information Technology (n=68), Materials (n=28), Real Estate (n=31), Utilities (n=29).
3.3 Test Periods
Signal validation uses the full 10-year period 2016–2025. Portfolio performance is evaluated on the 5-year out-of-sample period 2021–2025. Annual results are reported for 2021, 2022, 2023, 2024, and 2025 to assess performance consistency across market regimes.
4. Results
4.1 Signal Accuracy
Table 1 presents win rates across all 1,386 parameter permutations by GICS sector. Win rate is defined as the proportion of filled entry signals that achieve the 5% profit target within the 120-day holding window.
Table 1: Directional Accuracy by GICS Sector (2016–2025)
| GICS Sector | n | Win Rate Range | Mean | Median | Max p | Min p |
|---|---|---|---|---|---|---|
| Information Technology | 126 | 80.6–89.6% | 86.3% | 86.8% | 1.05 × 10−38 | 2.69 × 10−184 |
| Financials | 126 | 79.4–86.9% | 82.5% | 82.5% | 1.73 × 10−41 | 1.15 × 10−117 |
| Health Care | 126 | 78.3–84.6% | 82.2% | 82.4% | 1.72 × 10−46 | 1.40 × 10−120 |
| Consumer Discretionary | 126 | 77.2–86.0% | 81.8% | 81.9% | 1.38 × 10−35 | 2.75 × 10−142 |
| Industrials | 126 | 75.0–87.2% | 81.7% | 82.2% | 3.89 × 10−30 | 7.12 × 10−124 |
| Energy | 126 | 76.8–85.4% | 81.2% | 81.2% | 2.64 × 10−23 | 2.48 × 10−62 |
| Communication Services | 126 | 72.5–86.4% | 81.0% | 81.1% | 1.91 × 10−16 | 6.04 × 10−70 |
| Materials | 126 | 77.1–82.7% | 79.7% | 79.8% | 6.74 × 10−36 | 1.13 × 10−89 |
| Utilities | 126 | 73.9–83.4% | 79.2% | 79.2% | 3.99 × 10−30 | 8.85 × 10−72 |
| Real Estate | 126 | 70.4–79.6% | 74.8% | 74.7% | 3.16 × 10−19 | 7.41 × 10−62 |
| Consumer Staples | 126 | 67.7–77.6% | 73.4% | 73.3% | 3.33 × 10−17 | 2.53 × 10−60 |
| Aggregate | 1,386 | 67.7–89.6% | 80.3% | 80.9% | 1.91 × 10−16 | 2.69 × 10−184 |
Note: Win rate defined as proportion of trades achieving 5% profit target within 120-day holding period. p-values from two-tailed binomial test against null hypothesis of 50% accuracy. n = number of parameter permutations tested per sector.
Mean win rate across all permutations is 80.3% (median 80.9%). Sector means range from 73.4% (Consumer Staples) to 86.3% (Information Technology). The maximum p-value observed is 1.91 × 10−16 (Communication Services); the minimum is 2.69 × 10−184 (Information Technology). All 1,386 permutations reject the null hypothesis of random accuracy at p < 10−15.
4.2 Distribution of Results
Of the 1,386 permutations tested: 1,219 (88.0%) achieve win rates ≥ 75%; 820 (59.2%) achieve win rates ≥ 80%; 1,256 (90.6%) produce p-values < 10−30; and 780 (56.3%) produce p-values < 10−50. No permutation produces a win rate below 67.7% or a p-value above 10−15.
4.3 Portfolio Performance
Table 2 presents performance for the top 10 sector/factor portfolio implementations over the out-of-sample period 2021–2025.
Table 2: Portfolio Performance by Sector and Factor (2021–2025)
| Universe | Factor | N | CAGR | Win Rate | Trades | Sharpe |
|---|---|---|---|---|---|---|
| Energy | High Volatility | 20 | 21.4% | 91.5% | 721 | 0.79 |
| Industrials | High Momentum | 20 | 21.0% | 89.9% | 779 | 0.80 |
| Low Beta Universe | High Beta | 20 | 20.8% | 89.0% | 824 | 0.71 |
| Low Beta Universe | High Volatility | 20 | 20.1% | 91.7% | 856 | 0.77 |
| Energy | Low Beta | 20 | 20.0% | 90.4% | 669 | 0.79 |
| Sub-1 Beta Universe | High Volatility | 20 | 19.8% | 91.6% | 822 | 0.87 |
| Low Beta Universe | Low Momentum | 20 | 18.5% | 88.9% | 805 | 0.70 |
| Technology | High Volatility | 20 | 18.5% | 90.2% | 846 | 0.58 |
| Industrials | High Beta | 20 | 18.3% | 89.5% | 771 | 0.67 |
| Financials | High Volatility | 20 | 18.1% | 89.5% | 660 | 0.68 |
Note: N = number of positions. CAGR = compound annual growth rate. Sharpe ratio calculated using risk-free rate of 2%. All portfolios use 5% profit target, 120-day maximum hold, quarterly rebalancing, weekly signal refit.
The top-performing implementation (Energy, High Volatility factor) generates 21.4% CAGR with 91.5% win rate and 0.79 Sharpe ratio over 721 trades. Of 27 sector/factor combinations tested, 15 (55.6%) achieve CAGR > 15%, 24 (88.9%) achieve CAGR > 10%, and 24 (88.9%) achieve win rates > 85%.
4.4 Regime Consistency
To assess robustness across market conditions, we examine annual performance for the 2022 bear market separately. The Energy High Volatility portfolio generated +33.8% in 2022; Low Beta High Volatility generated +30.0%; Consumer Defensive High Volatility generated +21.6%. Several portfolios with high-beta factor exposure posted losses (Technology High Beta: −14.0%; Communication Services High Beta: −31.2%), demonstrating that factor selection affects return profiles while signal accuracy remains consistent.
5. Discussion
5.1 Interpretation of Results
The results provide evidence that temporal structure exists in equity returns and can be systematically exploited. The consistency of signal accuracy across sectors, factors, and parameter specifications argues against data mining or overfitting explanations. The absence of any permutation failing to achieve statistical significance at p < 10−15 suggests the effect is pervasive rather than concentrated in specific market segments.
5.2 Implications for Market Efficiency
These findings challenge the semi-strong form of the Efficient Market Hypothesis. If markets fully incorporate publicly available information, temporal patterns in returns should not persist at exploitable levels. The magnitude and consistency of the observed effects—80% directional accuracy maintained over 10 years across 346 securities—suggests either that markets are less efficient than commonly assumed, or that temporal structure represents a category of pattern that markets do not efficiently arbitrage.
5.3 Limitations
Several limitations warrant consideration. First, results are based on simulated portfolios; actual trading would incur transaction costs, slippage, and market impact not modeled here. Second, the limit order execution assumption may not hold during periods of extreme volatility or illiquidity. Third, past performance does not guarantee future results; temporal patterns may degrade if widely exploited.
5.4 Replication
Complete methodology specifications and signal outputs are available for independent verification. The deterministic nature of the signal generation process ensures that results can be exactly replicated given identical inputs.
6. Conclusion
This study presents evidence that temporal structure exists in S&P 500 equity returns and can be exploited for position entry timing with approximately 80% accuracy. Across 1,386 parameter permutations tested over 10 years, no specification fails to achieve statistical significance at p < 10−15. Applied to position trading portfolios, the methodology generates 18–21% CAGR with win rates exceeding 88%.
These results suggest that the entry timing problem in systematic trading—widely considered unsolvable with statistical reliability—may be addressable through temporal structural analysis. Further research should examine the persistence of these effects out-of-sample, the capacity constraints of the strategy, and the mechanisms by which temporal structure emerges and persists in equity markets.
References
Ariel, R. A. (1987). A monthly effect in stock returns. Journal of Financial Economics, 18(1), 161–174.
Burk, K. B. (2024). The Model of Temporal Inertia: How Time Series Forecasting Operates. Working Paper, TSF Inc.
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25(2), 383–417.
French, K. R. (1980). Stock returns and the weekend effect. Journal of Financial Economics, 8(1), 55–69.
Gibbons, M. R., & Hess, P. (1981). Day of the week effects and asset returns. Journal of Business, 54(4), 579–596.
Lakonishok, J., & Smidt, S. (1988). Are seasonal anomalies real? A ninety-year perspective. Review of Financial Studies, 1(4), 403–425.