Time-Series Analysis

Stock Market Charts You Never Saw ArXiv ID: ssrn-3050736 “View on arXiv” Authors: Unknown Abstract Investors have seen countless charts of US stock market performance which start in 1926 and end near the present. But US trading long predates 1926, and the for Keywords: Historical Data, Stock Market, Equity Markets, Time Series Analysis Complexity vs Empirical Score Math Complexity: 2.5/10 Empirical Rigor: 3.0/10 Quadrant: Philosophers Why: The paper focuses on historical analysis and visual critique of existing charts, with minimal advanced mathematics beyond basic returns calculations, and lacks rigorous backtesting or new quantitative implementation. flowchart TD A["Research Goal:<br>Extend stock market analysis<br>pre-1926 using historical data"] --> B{"Methodology"}; B --> C["Data Collection:<br>Pre-1926 US equity data"]; B --> D["Analysis:<br>Time series & statistical<br>backtesting"]; C --> E["Computational Process:<br>Performance simulation<br>& volatility modeling"]; D --> E; E --> F["Key Findings/Outcomes:<br>Validated long-term trends,<br>revealed pre-1926 market cycles"];

Improving S&P 500 Volatility Forecasting through Regime-Switching Methods ArXiv ID: 2510.03236 “View on arXiv” Authors: Ava C. Blake, Nivika A. Gandhi, Anurag R. Jakkula Abstract Accurate prediction of financial market volatility is critical for risk management, derivatives pricing, and investment strategy. In this study, we propose a multitude of regime-switching methods to improve the prediction of S&P 500 volatility by capturing structural changes in the market across time. We use eleven years of SPX data, from May 1st, 2014 to May 27th, 2025, to compute daily realized volatility (RV) from 5-minute intraday log returns, adjusted for irregular trading days. To enhance forecast accuracy, we engineered features to capture both historical dynamics and forward-looking market sentiment across regimes. The regime-switching methods include a soft Markov switching algorithm to estimate soft-regime probabilities, a distributional spectral clustering method that uses XGBoost to assign clusters at prediction time, and a coefficient-based soft regime algorithm that extracts HAR coefficients from time segments segmented through the Mood test and clusters through Bayesian GMM for soft regime weights, using XGBoost to predict regime probabilities. Models were evaluated across three time periods–before, during, and after the COVID-19 pandemic. The coefficient-based clustering algorithm outperformed all other models, including the baseline autoregressive model, during all time periods. Additionally, each model was evaluated on its recursive forecasting performance for 5- and 10-day horizons during each time period. The findings of this study demonstrate the value of regime-aware modeling frameworks and soft clustering approaches in improving volatility forecasting, especially during periods of heightened uncertainty and structural change. ...

Predictive Performance of LSTM Networks on Sectoral Stocks in an Emerging Market: A Case Study of the Pakistan Stock Exchange ArXiv ID: 2509.14401 “View on arXiv” Authors: Ahad Yaqoob, Syed M. Abdullah Abstract The application of deep learning models for stock price forecasting in emerging markets remains underexplored despite their potential to capture complex temporal dependencies. This study develops and evaluates a Long Short-Term Memory (LSTM) network model for predicting the closing prices of ten major stocks across diverse sectors of the Pakistan Stock Exchange (PSX). Utilizing historical OHLCV data and an extensive set of engineered technical indicators, we trained and validated the model on a multi-year dataset. Our results demonstrate strong predictive performance ($R^2 > 0.87$) for stocks in stable, high-liquidity sectors such as power generation, cement, and fertilizers. Conversely, stocks characterized by high volatility, low liquidity, or sensitivity to external shocks (e.g., global oil prices) presented significant forecasting challenges. The study provides a replicable framework for LSTM-based forecasting in data-scarce emerging markets and discusses implications for investors and future research. ...

Multi Scale Analysis of Nifty 50 Return Characteristics Valuation Dynamics and Market Complexity 1990 to 2024 ArXiv ID: 2509.00697 “View on arXiv” Authors: Chandradew Sharma Abstract This study presents a unified, distribution-aware, and complexity-informed framework for understanding equity return dynamics in the Indian market, using 34 years (1990 to 2024) of Nifty 50 index data. Addressing a key gap in the literature, we demonstrate that the price to earnings ratio, as a valuation metric, may probabilistically map return distributions across investment horizons spanning from days to decades. Return profiles exhibit strong asymmetry. One-year returns show a 74 percent probability of gain, with a modal return of 10.67 percent and a reward-to-risk ratio exceeding 5. Over long horizons, modal CAGRs surpass 13 percent, while worst-case returns remain negative for up to ten years, defining a historical trapping period. This horizon shortens to six years in the post-1999 period, reflecting growing market resilience. Conditional analysis of the P/E ratio reveals regime-dependent outcomes. Low valuations (P/E less than 13) historically show zero probability of loss across all horizons, while high valuations (P/E greater than 27) correspond to unstable returns and extended breakeven periods. To uncover deeper structure, we apply tools from complexity science. Entropy, Hurst exponents, and Lyapunov indicators reveal weak persistence, long memory, and low-dimensional chaos. Information-theoretic metrics, including mutual information and transfer entropy, confirm a directional and predictive influence of valuation on future returns. These findings offer actionable insights for asset allocation, downside risk management, and long-term investment strategy in emerging markets. Our framework bridges valuation, conditional distributions, and nonlinear dynamics in a rigorous and practically relevant manner. ...

Directional Price Forecasting in the Continuous Intraday Market under Consideration of Neighboring Products and Limit Order Books ArXiv ID: 2509.04452 “View on arXiv” Authors: Timothée Hornek, Sergio Potenciano Menci, Ivan Pavić Abstract The increasing penetration of variable renewable energy and flexible demand technologies, such as electric vehicles and heat pumps, introduces significant uncertainty in power systems, resulting in greater imbalance; defined as the deviation between scheduled and actual supply or demand. Short-term power markets, such as the European continuous intraday market, play a critical role in mitigating these imbalances by enabling traders to adjust forecasts close to real time. Due to the high volatility of the continuous intraday market, traders increasingly rely on electricity price forecasting to guide trading decisions and mitigate price risk. However most electricity price forecasting approaches in the literature simplify the forecasting task. They focus on single benchmark prices, neglecting intra-product price dynamics and price signals from the limit order book. They also underuse high-frequency and cross-product price data. In turn, we propose a novel directional electricity price forecasting method for hourly products in the European continuous intraday market. Our method incorporates short-term features from both hourly and quarter-hourly products and is evaluated using German European Power Exchange data from 2024-2025. The results indicate that features derived from the limit order book are the most influential exogenous variables. In addition, features from neighboring products; especially those with delivery start times that overlap with the trading period of the target product; improve forecast accuracy. Finally, our evaluation of the value captured by our electricity price forecasting suggests that the proposed electricity price forecasting method has the potential to generate profit when applied in trading strategies. ...

Slomads Rising: Stay Length Shifts in Digital Nomad Travel, United States 2019-2024 ArXiv ID: 2507.21298 “View on arXiv” Authors: Harrison Katz, Erica Savage Abstract Using all U.S. Airbnb reservations created in 2019-2024 (booking-count weighted), we quantify pandemic-era shifts in nights per booking (NPB) and the mechanism behind them. The mean rose from 3.68 pre-COVID to 4.36 during restrictions and stabilized near 4.07 post-2021 (about 10% above 2019); the booking-weighted median moved from 2 to 3 nights. A two-parameter log-normal fits best by wide AIC/BIC margins, indicating heavy tails. A negative-binomial model with month effects implies post-vaccine bookings are 6.5% shorter than restriction-era bookings, while pre-COVID bookings are 16% shorter. In a two-part model at 28 nights, the booking share of month-plus stays rose from 1.43% (pre) to 2.72% (restriction) and settled at 2.04% (post); conditional means among long stays were about 55-60 nights. Thus the higher average reflects more long stays rather than longer long stays. A SARIMA(0,1,1)(0,1,1)12 with pandemic-phase dummies improves fit (LR=8.39, df=2, p=0.015), consistent with a structural level shift. ...

Advancing Exchange Rate Forecasting: Leveraging Machine Learning and AI for Enhanced Accuracy in Global Financial Markets ArXiv ID: 2506.09851 “View on arXiv” Authors: Md. Yeasin Rahat, Rajan Das Gupta, Nur Raisa Rahman, Sudipto Roy Pritom, Samiur Rahman Shakir, Md Imrul Hasan Showmick, Md. Jakir Hossen Abstract The prediction of foreign exchange rates, such as the US Dollar (USD) to Bangladeshi Taka (BDT), plays a pivotal role in global financial markets, influencing trade, investments, and economic stability. This study leverages historical USD/BDT exchange rate data from 2018 to 2023, sourced from Yahoo Finance, to develop advanced machine learning models for accurate forecasting. A Long Short-Term Memory (LSTM) neural network is employed, achieving an exceptional accuracy of 99.449%, a Root Mean Square Error (RMSE) of 0.9858, and a test loss of 0.8523, significantly outperforming traditional methods like ARIMA (RMSE 1.342). Additionally, a Gradient Boosting Classifier (GBC) is applied for directional prediction, with backtesting on a $10,000 initial capital revealing a 40.82% profitable trade rate, though resulting in a net loss of $20,653.25 over 49 trades. The study analyzes historical trends, showing a decline in BDT/USD rates from 0.012 to 0.009, and incorporates normalized daily returns to capture volatility. These findings highlight the potential of deep learning in forex forecasting, offering traders and policymakers robust tools to mitigate risks. Future work could integrate sentiment analysis and real-time economic indicators to further enhance model adaptability in volatile markets. ...

Forecasting Nigerian Equity Stock Returns Using Long Short-Term Memory Technique ArXiv ID: 2507.01964 “View on arXiv” Authors: Adebola K. Ojo, Ifechukwude Jude Okafor Abstract Investors and stock market analysts face major challenges in predicting stock returns and making wise investment decisions. The predictability of equity stock returns can boost investor confidence, but it remains a difficult task. To address this issue, a study was conducted using a Long Short-term Memory (LSTM) model to predict future stock market movements. The study used a historical dataset from the Nigerian Stock Exchange (NSE), which was cleaned and normalized to design the LSTM model. The model was evaluated using performance metrics and compared with other deep learning models like Artificial and Convolutional Neural Networks (CNN). The experimental results showed that the LSTM model can predict future stock market prices and returns with over 90% accuracy when trained with a reliable dataset. The study concludes that LSTM models can be useful in predicting financial time-series-related problems if well-trained. Future studies should explore combining LSTM models with other deep learning techniques like CNN to create hybrid models that mitigate the risks associated with relying on a single model for future equity stock predictions. ...

Impact of the COVID-19 pandemic on the financial market efficiency of price returns, absolute returns, and volatility increment: Evidence from stock and cryptocurrency markets ArXiv ID: 2504.18960 “View on arXiv” Authors: Tetsuya Takaishi Abstract This study examines the impact of the coronavirus disease 2019 (COVID-19) pandemic on market efficiency by analyzing three time series – price returns, absolute returns, and volatility increments – in stock (Deutscher Aktienindex, Nikkei 225, Shanghai Stock Exchange (SSE), and Volatility Index) and cryptocurrency (Bitcoin and Ethereum) markets. The effect is found to vary by asset class and market. In the stock market, while the pandemic did not influence the Hurst exponent of volatility increments, it affected that of returns and absolute returns (except in the SSE, where returns remained unaffected). In the cryptocurrency market, the pandemic did not alter the Hurst exponent for any time series but influenced the strength of multifractality in returns and absolute returns. Some Hurst exponent time series exhibited a gradual decline over time, complicating the assessment of pandemic-related effects. Consequently, segmented analyses by pandemic periods may erroneously suggest an impact, warranting caution in period-based studies. ...

Market-Based Portfolio Variance ArXiv ID: 2504.07929 “View on arXiv” Authors: Unknown Abstract The variance measures the portfolio risks the investors are taking. The investor, who holds his portfolio and doesn’t trade his shares, at the current time can use the time series of the market trades that were made during the averaging interval with the securities of his portfolio and assess the current return, variance, and hence the current risks of his portfolio. We show how the time series of trades with the securities of the portfolio determine the time series of trades with the portfolio as a single market security. The time series of trades with the portfolio determine its return and variance in the same form as the time series of trades with securities determine their returns and variances. The description of any portfolio and any single market security is equal. The time series of the portfolio trades define the decomposition of the portfolio variance by its securities, which is a quadratic form in the variables of relative amounts invested into securities. Its coefficients themselves are quadratic forms in the variables of relative numbers of shares of its securities. If one assumes that the volumes of all consecutive deals with each security are constant, the decomposition of the portfolio variance coincides with Markowitz’s (1952) variance, which ignores the effects of random trade volumes. The use of the variance that accounts for the randomness of trade volumes could help majors like BlackRock, JP Morgan, and the U.S. Fed to adjust their models, like Aladdin and Azimov, to the reality of random markets. ...