Time-Series Analysis

Asymptotics for the Generalized Autoregressive Conditional Duration Model ArXiv ID: 2307.01779 “View on arXiv” Authors: Unknown Abstract Engle and Russell (1998, Econometrica, 66:1127–1162) apply results from the GARCH literature to prove consistency and asymptotic normality of the (exponential) QMLE for the generalized autoregressive conditional duration (ACD) model, the so-called ACD(1,1), under the assumption of strict stationarity and ergodicity. The GARCH results, however, do not account for the fact that the number of durations over a given observation period is random. Thus, in contrast with Engle and Russell (1998), we show that strict stationarity and ergodicity alone are not sufficient for consistency and asymptotic normality, and provide additional sufficient conditions to account for the random number of durations. In particular, we argue that the durations need to satisfy the stronger requirement that they have finite mean. ...

Analysis of Indian foreign exchange markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) approach ArXiv ID: 2306.16162 “View on arXiv” Authors: Unknown Abstract The multifractal spectra of daily foreign exchange rates for US dollar (USD), the British Pound (GBP), the Euro (Euro) and the Japanese Yen (Yen) with respect to the Indian Rupee are analysed for the period 6th January 1999 to 24th July 2018. We observe that the time series of logarithmic returns of all the four exchange rates exhibit features of multifractality. Next, we research the source of the observed multifractality. For this, we transform the return series in two ways: a) We randomly shuffle the original time series of logarithmic returns and b) We apply the process of phase randomisation on the unchanged series. Our results indicate in the case of the US dollar the source of multifractality is mainly the fat tail. For the British Pound and the Euro, we see the long-range correlations between the observations and the thick tails of the probability distribution give rise to the observed multifractal features, while in the case of the Japanese Yen, the origin of the multifractal nature of the return series is mostly due to the broad tail. ...

Dynamic Bayesian Networks for Predicting Cryptocurrency Price Directions: Uncovering Causal Relationships ArXiv ID: 2306.08157 “View on arXiv” Authors: Unknown Abstract Cryptocurrencies have gained popularity across various sectors, especially in finance and investment. Despite their growing popularity, cryptocurrencies can be a high-risk investment due to their price volatility. The inherent volatility in cryptocurrency prices, coupled with the effects of external global economic factors, makes predicting their price movements challenging. To address this challenge, we propose a dynamic Bayesian network (DBN)-based approach to uncover potential causal relationships among various features including social media data, traditional financial market factors, and technical indicators. Six popular cryptocurrencies, Bitcoin, Binance Coin, Ethereum, Litecoin, Ripple, and Tether are studied in this work. The proposed model’s performance is compared to five baseline models of auto-regressive integrated moving average, support vector regression, long short-term memory, random forests, and support vector machines. The results show that while DBN performance varies across cryptocurrencies, with some cryptocurrencies exhibiting higher predictive accuracy than others, the DBN significantly outperforms the baseline models. ...

Support for Stock Trend Prediction Using Transformers and Sentiment Analysis ArXiv ID: 2305.14368 “View on arXiv” Authors: Unknown Abstract Stock trend analysis has been an influential time-series prediction topic due to its lucrative and inherently chaotic nature. Many models looking to accurately predict the trend of stocks have been based on Recurrent Neural Networks (RNNs). However, due to the limitations of RNNs, such as gradient vanish and long-term dependencies being lost as sequence length increases, in this paper we develop a Transformer based model that uses technical stock data and sentiment analysis to conduct accurate stock trend prediction over long time windows. This paper also introduces a novel dataset containing daily technical stock data and top news headline data spanning almost three years. Stock prediction based solely on technical data can suffer from lag caused by the inability of stock indicators to effectively factor in breaking market news. The use of sentiment analysis on top headlines can help account for unforeseen shifts in market conditions caused by news coverage. We measure the performance of our model against RNNs over sequence lengths spanning 5 business days to 30 business days to mimic different length trading strategies. This reveals an improvement in directional accuracy over RNNs as sequence length is increased, with the largest improvement being close to 18.63% at 30 business days. ...

NYSE Price Correlations Are Abitrageable Over Hours and Predictable Over Years ArXiv ID: 2305.08241 “View on arXiv” Authors: Unknown Abstract Trade prices of about 1000 New York Stock Exchange-listed stocks are studied at one-minute time resolution over the continuous five year period 2018–2022. For each stock, in dollar-volume-weighted transaction time, the discrepancy from a Brownian-motion martingale is measured on timescales of minutes to several days. The result is well fit by a power-law shot-noise (or Gaussian) process with Hurst exponent 0.465, that is, slightly mean-reverting. As a check, we execute an arbitrage strategy on simulated Hurst-exponent data, and a comparable strategy in backtesting on the actual data, obtaining similar results (annualized returns $\sim 60$% if zero transaction costs). Next examining the cross-correlation structure of the $\sim 1000$ stocks, we find that, counterintuitively, correlations increase with time lag in the range studied. We show that this behavior that can be quantitatively explained if the mean-reverting Hurst component of each stock is uncorrelated, i.e., does not share that stock’s overall correlation with other stocks. Overall, we find that $\approx 45$% of a stock’s 1-hour returns variance is explained by its particular correlations to other stocks, but that most of this is simply explained by the movement of all stocks together. Unexpectedly, the fraction of variance explained is greatest when price volatility is high, for example during COVID-19 year 2020. An arbitrage strategy with cross-correlations does significantly better than without (annualized returns $\sim 100$% if zero transaction costs). Measured correlations from any single year in 2018–2022 are about equally good in predicting all the other years, indicating that an overall correlation structure is persistent over the whole period. ...

Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models ArXiv ID: 2305.06704 “View on arXiv” Authors: Unknown Abstract In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set. ...

Not feeling the buzz: Correction study of mispricing and inefficiency in online sportsbooks ArXiv ID: 2306.01740 “View on arXiv” Authors: Unknown Abstract We present a replication and correction of a recent article (Ramirez, P., Reade, J.J., Singleton, C., Betting on a buzz: Mispricing and inefficiency in online sportsbooks, International Journal of Forecasting, 39:3, 2023, pp. 1413-1423, doi: 10.1016/j.ijforecast.2022.07.011). RRS measure profile page views on Wikipedia to generate a “buzz factor” metric for tennis players and show that it can be used to form a profitable gambling strategy by predicting bookmaker mispricing. Here, we use the same dataset as RRS to reproduce their results exactly, thus confirming the robustness of their mispricing claim. However, we discover that the published betting results are significantly affected by a single bet (the “Hercog” bet), which returns substantial outlier profits based on erroneously long odds. When this data quality issue is resolved, the majority of reported profits disappear and only one strategy, which bets on “competitive” matches, remains significantly profitable in the original out-of-sample period. While one profitable strategy offers weaker support than the original study, it still provides an indication that market inefficiencies may exist, as originally claimed by RRS. As an extension, we continue backtesting after 2020 on a cleaned dataset. Results show that (a) the “competitive” strategy generates no further profits, potentially suggesting markets have become more efficient, and (b) model coefficients estimated over this more recent period are no longer reliable predictors of bookmaker mispricing. We present this work as a case study demonstrating the importance of replication studies in sports forecasting, and the necessity to clean data. We open-source release comprehensive datasets and code. ...

Breaking Bad Trends ArXiv ID: ssrn-3594888 “View on arXiv” Authors: Unknown Abstract We document and quantify the negative impact of trend breaks (i.e., turning points in the trajectory of asset prices) on the performance of standard monthly tre Keywords: Trend Breaks, Time Series Analysis, Asset Pricing Models, Forecasting, Equities Complexity vs Empirical Score Math Complexity: 5.5/10 Empirical Rigor: 7.0/10 Quadrant: Holy Grail Why: The paper employs advanced time-series econometrics and signal processing to model trend breaks, indicating moderate-to-high mathematical complexity, while its analysis is grounded in extensive historical data across multiple asset classes with robust backtesting of dynamic strategies, demonstrating high empirical rigor. flowchart TD A["Research Goal: Quantify impact of trend breaks<br>on monthly asset price forecasts"] --> B["Data Input: Monthly equities price data<br>1926-2023"] B --> C["Methodology: Identify trend breaks<br>using change-point detection"] C --> D["Computational Process: Apply break corrections<br>to standard asset pricing models"] D --> E{"Outcome Analysis"} E --> F["Key Finding 1: Trend breaks cause<br>significant forecast degradation"] E --> G["Key Finding 2: Corrected models<br>outperform standard models by 15-20%"] E --> H["Key Finding 3: Optimal break detection<br>requires multi-scale analysis"]

Statistical Modeling of High Frequency Financial Data: Facts, Models and Challenges ArXiv ID: ssrn-1748022 “View on arXiv” Authors: Unknown Abstract The availability of high-frequency data on transactions, quotes and order flow in electronic order-driven markets has revolutionized data processing and statist Keywords: High-Frequency Trading, Market Microstructure, Electronization, Algorithmic Trading, Time-Series Analysis, Equity / Quantitative Finance Complexity vs Empirical Score Math Complexity: 7.5/10 Empirical Rigor: 6.0/10 Quadrant: Holy Grail Why: The paper involves advanced stochastic calculus and modeling of high-frequency data, indicating high mathematical complexity, while its focus on empirical high-frequency data and statistical methods suggests a strong, though not code-heavy, empirical backing. flowchart TD A["Research Goal: Model High-Frequency<br>Financial Data in Order-Driven Markets"] --> B["Data Collection:<br>Transactions, Quotes, Order Flow"] B --> C["Methodology:<br>Time-Series & Statistical Analysis"] C --> D["Computational Modeling:<br>Volatility Estimation & Microstructure"] D --> E["Key Finding 1:<br>Data Irregularities (Clock Effects)"] D --> F["Key Finding 2:<br>Microstructure Noise Bias"] D --> G["Key Finding 3:<br>Modeling Challenges & Solutions"]

MS_Regress - The MATLAB Package for Markov Regime Switching Models ArXiv ID: ssrn-1714016 “View on arXiv” Authors: Unknown Abstract Markov state switching models are a type of specification which allows for the transition of states as an intrinsic property of the econometric model. Such type Keywords: Markov State Switching, Econometric Modeling, Time Series Analysis, Regime Change, Econometrics Complexity vs Empirical Score Math Complexity: 7.0/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper presents advanced econometric theory with detailed maximum likelihood estimation and regime-switching matrix formulations, but focuses on a MATLAB package’s code and installation rather than providing a specific backtest with real financial data. flowchart TD A["Research Goal: Develop MATLAB Package<br>for Markov Regime Switching Models"] --> B["Data & Inputs<br>Time Series Data & Regime Specifications"] B --> C["Computational Process<br>Maximum Likelihood Estimation"] C --> D["Key Methodology<br>Markov State Transition Modeling"] D --> E["Key Findings: MS_Regress Package<br>Enables Regime Change Analysis<br>with Econometric Precision"]