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on Econometric Time Series |
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Issue of 2026–01–12
eleven papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Aknouche, Abdelhakim; Bentarzi, Mohamed |
| Abstract: | Two estimation algorithms for Periodic Autoregressive Conditionally Heteroskedastic (PARCH ) models are developed in this work. The first is the two-stage weighted least squares (2S-WLS) algorithm, which adapts the ordinary least squares method for use in the periodic ARCH framework. The second, 2S-RLS, is an adaptation of the former for recursive online estimation contexts. Both algorithms produce consistent and asymptotically normally distributed estimators. Furthermore, the second method is particularly well-suited to capturing the dynamic characteristics of financial time series that are increasingly being observed at high frequencies. It also enables effective monitoring of positivity and periodic stationarity constraints. |
| Keywords: | Periodic ARCH, recursive online estimation, two-stage weighted least squares, two-stage recursive least squares, asymptotic normality. |
| JEL: | C10 C13 |
| Date: | 2025–12–20 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:127417 |
| By: | Elynn Chen; Yuefeng Han; Jiayu Li; Ke Xu |
| Abstract: | We introduce a Modewise Additive Factor Model (MAFM) for matrix-valued time series that captures row-specific and column-specific latent effects through an additive structure, offering greater flexibility than multiplicative frameworks such as Tucker and CP factor models. In MAFM, each observation decomposes into a row-factor component, a column-factor component, and noise, allowing distinct sources of variation along different modes to be modeled separately. We develop a computationally efficient two-stage estimation procedure: Modewise Inner-product Eigendecomposition (MINE) for initialization, followed by Complement-Projected Alternating Subspace Estimation (COMPAS) for iterative refinement. The key methodological innovation is that orthogonal complement projections completely eliminate cross-modal interference when estimating each loading space. We establish convergence rates for the estimated factor loading matrices under proper conditions. We further derive asymptotic distributions for the loading matrix estimators and develop consistent covariance estimators, yielding a data-driven inference framework that enables confidence interval construction and hypothesis testing. As a technical contribution of independent interest, we establish matrix Bernstein inequalities for quadratic forms of dependent matrix time series. Numerical experiments on synthetic and real data demonstrate the advantages of the proposed method over existing approaches. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.25025 |
| By: | Peng, Rundong; Mallory, Mindy; Ma, Meilin; Wang, H. Holly |
| Abstract: | Time series data have been extensively utilized in agricultural price analysis, with the Vector Auto-Regressive (VAR) and Vector Error Correction Model (VECM) being foundational tools. Over the past three decades, the availability of disaggregated agricultural commodity price data has increased, resulting in high-dimensional datasets. The efficacy of VECM and Johansen’s maximum likelihood test diminishes with increased dimensionality due to exponential growth in the required time series length, implying difficulty in extracting cointegrating relationships in high-dimensional data. This article addresses this challenge by employing time series clustering to reduce data dimensionality. Clusters are formed based on price similarity, dynamically adjusted for specified time period using hierarchical clustering with dynamic time warping. With clustered time series, we extract the mean price of each cluster and apply Johansen’s framework to estimate cointegration relationships. Applied to the Chinese hog market before and after the 2018 African Swine Fever outbreak, we show that the cointegrating relationship has changed suggesting less inter-provincial trade. The study identifies clusters based on price similarity and shows the advantages of this method compared to traditional geographical clustering. |
| Keywords: | Production Economics |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea25:360950 |
| By: | Håvard Hungnes (Statistics Norway) |
| Abstract: | This paper introduces two methodological improvements to the Hodrick– Prescott (HP) filter for decomposing GDP into trend and cycle components. First, we propose a robust univariate filter that accounts for extreme observations — such as the COVID–19 pandemic — by treating them as additive outliers. Second, we develop a multivariate HP filter that incorporates time–varying, import– adjusted budget shares of GDP sub–components. This adaptive weighting minimizes cyclical variance and yields a more stable trend estimate. Applying the framework to U.S. data, we find that private investment is the dominant source of cyclical fluctuations, while government expenditure exhibits a persistent counter–cyclical pattern. The proposed approach enhances real–time policy analysis by reducing endpoint bias and improving the identification of cyclical dynamics. |
| Keywords: | output gap; Hodrick–Prescott filter; robust filtering; multivariate decomposition; additive outliers; time–varying budget shares; business cycle analysis |
| JEL: | E32 C22 E37 C43 C51 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:ssb:dispap:1031 |
| By: | Simon Donker van Heel; Neil Shephard |
| Abstract: | We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper then focuses on working out the implications of this in the case of the canonical exponential family. The results are simple exact filters, predictors and smoothers with linear recursions. A theory for these models is developed and the models are illustrated on simulated and real data. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.16745 |
| By: | Lucas A. Souza |
| Abstract: | We study short-horizon forecasting in financial time series under strict causal constraints, treating the market as a non-stationary stochastic system in which any predictive observable must be computable online from information available up to the decision time. Rather than proposing a machine-learning predictor or a direct price-forecast model, we focus on \emph{constructing} an interpretable causal signal from heterogeneous micro-features that encode complementary aspects of the dynamics (momentum, volume pressure, trend acceleration, and volatility-normalized price location). The construction combines (i) causal centering, (ii) linear aggregation into a composite observable, (iii) causal stabilization via a one-dimensional Kalman filter, and (iv) an adaptive ``forward-like'' operator that mixes the composite signal with a smoothed causal derivative term. The resulting observable is mapped into a transparent decision functional and evaluated through realized cumulative returns and turnover. An application to high-frequency EURUSDT (1-minute) illustrates that causally constructed observables can exhibit substantial economic relevance in specific regimes, while degrading under subsequent regime shifts, highlighting both the potential and the limitations of causal signal design in non-stationary markets. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.24621 |
| By: | Dimitrios Bachtis; David S. Berman; Arabella Schelpe |
| Abstract: | We use a $\phi^{4}$ quantum field theory with inhomogeneous couplings and explicit symmetry-breaking to model an ensemble of financial time series from the S$\&$P 500 index. The continuum nature of the $\phi^4$ theory avoids the inaccuracies that occur in Ising-based models which require a discretization of the time series. We demonstrate this using the example of the 2008 global financial crisis. The $\phi^{4}$ quantum field theory is expressive enough to reproduce the higher-order statistics such as the market kurtosis, which can serve as an indicator of possible market shocks. Accurate reproduction of high kurtosis is absent in binarized models. Therefore Ising models, despite being widely employed in econophysics, are incapable of fully representing empirical financial data, a limitation not present in the generalization of the $\phi^{4}$ scalar field theory. We then investigate the scaling properties of the $\phi^{4}$ machine learning algorithm and extract exponents which govern the behavior of the learned couplings (or weights and biases in ML language) in relation to the number of stocks in the model. Finally, we use our model to forecast the price changes of the AAPL, MSFT, and NVDA stocks. We conclude by discussing how the $\phi^{4}$ scalar field theory could be used to build investment strategies and the possible intuitions that the QFT operations of dimensional compactification and renormalization can provide for financial modelling. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.17225 |
| By: | Matthieu Garcin; Louis Perot |
| Abstract: | Relative entropy, as a divergence metric between two distributions, can be used for offline change-point detection and extends classical methods that mainly rely on moment-based discrepancies. To build a statistical test suitable for this context, we study the distribution of empirical relative entropy and derive several types of approximations: concentration inequalities for finite samples, asymptotic distributions, and Berry-Esseen bounds in a pre-asymptotic regime. For the latter, we introduce a new approach to obtain Berry-Esseen inequalities for nonlinear functions of sum statistics under some convexity assumptions. Our theoretical contributions cover both one- and two-sample empirical relative entropies. We then detail a change-point detection procedure built on relative entropy and compare it, through extensive simulations, with classical methods based on moments or on information criteria. Finally, we illustrate its practical relevance on two real datasets involving temperature series and volatility of stock indices. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.16411 |
| By: | Christophe D. Hounwanou; Yae Ulrich Gaba; Pierre Ntakirutimana |
| Abstract: | Data scarcity and confidentiality in finance often impede model development and robust testing. This paper presents a unified multi-criteria evaluation framework for synthetic financial data and applies it to three representative generative paradigms: the statistical ARIMA-GARCH baseline, Variational Autoencoders (VAEs), and Time-series Generative Adversarial Networks (TimeGAN). Using historical S and P 500 daily data, we evaluate fidelity (Maximum Mean Discrepancy, MMD), temporal structure (autocorrelation and volatility clustering), and practical utility in downstream tasks, specifically mean-variance portfolio optimization and volatility forecasting. Empirical results indicate that ARIMA-GARCH captures linear trends and conditional volatility but fails to reproduce nonlinear dynamics; VAEs produce smooth trajectories that underestimate extreme events; and TimeGAN achieves the best trade-off between realism and temporal coherence (e.g., TimeGAN attained the lowest MMD: 1.84e-3, average over 5 seeds). Finally, we articulate practical guidelines for selecting generative models according to application needs and computational constraints. Our unified evaluation protocol and reproducible codebase aim to standardize benchmarking in synthetic financial data research. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.21791 |
| By: | Ian Dew-Becker; Stefano Giglio; Pooya Molavi |
| Abstract: | Financial markets (and more generally the real economy) display a wide range of important nonlinearities. This paper focuses on stock returns, which are skewed left – generating crashes – and whose volatility moves over time, is itself skewed, is strongly related to the level of prices, and displays long memory. This paper shows that such behavior is almost inevitable when prices are formed by investors acquiring information about the true, but latent, value of stocks. It studies a general model of filtering in which agents receive signals about the fundamental value of the stock market and dynamically update their beliefs (potentially with biases). When those beliefs are non-normal and investors believe crashes can happen, prices generically display the range of nonlinearities observed in the data. While the model does not explain where crashes come from, it shows that investors believing that prices can crash is sufficient to generate the rich higher-order dynamics observed empirically. In a simple calibration with iid shocks to fundamentals, the model fits well quantitatively, and regression-based tests support the model’s mechanism. |
| JEL: | G0 G1 G10 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:34584 |
| By: | Andrea Bastianin; Luca Rossini; Lorenzo Tonni |
| Abstract: | This paper develops a real-time forecasting framework for the monthly real prices of four key industrial metals -- aluminum, copper, nickel, and zinc -- whose demand is rising due to their widespread use in manufacturing and low-carbon technologies. To replicate the information set available to forecasters in real time, we construct a new dataset combining daily financial variables with first-release macroeconomic indicators and use nowcasting techniques to address publication lags. Within this real-time environment, we evaluate the predictive accuracy of a broad set of univariate, multivariate, and factor-augmented models, comparing their performance with two industry benchmarks: survey expectations and futures-spot spread models. Results show that although short-run metal price movements remain difficult to predict, medium-term horizons display substantial forecastability. Indicators of manufacturing activity tied to primary metals -- such as new orders and capacity utilization -- significantly improve forecasting accuracy for aluminum and copper, with more moderate gains for zinc and limited improvements for nickel. Futures and survey forecasts generally underperform the real-time econometric models. These findings highlight the value of incorporating timely macroeconomic information into forecasting frameworks for industrial metal markets. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.16521 |