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on Econometric Time Series |
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Issue of 2026–07–13
eleven papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Rouven Beiner; Bernd Süssmuth |
| Abstract: | Density expansions such as the Gram-Charlier (GC) expansion allow for the modeling of time-varying higher moments. However, they can suffer from spurious multimodality, negative densities, and asymptotically light tails if truncated. This paper introduces monotonic polynomial generalized autoregressive conditional heteroskedasticity (GARCH) models. They generate conditional skewness and kurtosis via a monotonic polynomial transformation of innovations. By construction, this approach guarantees a valid, unimodal probability density without requiring truncation. It naturally accommodates heavy Weibull-type tails. We provide a theoretical framework proving strict stationarity and ergodicity. In empirical applications to financial returns, the proposed estimator outperforms both GC-based and score-driven benchmarks in out-of-sample density forecasting. It demonstrates superior structural stability and robustness against overfitting. |
| Keywords: | GARCH, observation-driven models, conditional higher moments, density forecasting, monotonic polynomials |
| JEL: | C22 C53 C58 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12734 |
| By: | Blazsek, Szabolcs; Dupree, Raven Amina; Escribano, Álvaro |
| Abstract: | Understanding the persistence of climate shocks and the timing of major climate-state transitions is central to both climate science and climate economics. In this paper, we develop an observable-switching fractionally integrated score-driven model with conditional heteroscedasticity, denoted OS-t-FI[d(st)]-QARBeta-t-EGARCH, that jointly models long-memory dynamics, regime changes, and time-varying volatility. The framework combines score-driven filters with regime-dependent degrees of fractional integration and heavy-tailed conditional distributions, providing a robust and information-theoretically efficient approach for analyzing climate time series. We apply the model to the CENOGRID benthic foraminiferal δ13C and δ18O records covering the last 67.1 million years at 5-kyr resolution. Milankovitch orbital variables (i.e., eccentricity, obliquity, and precession) are incorporated as exogenous controls to account for low-frequency astronomical forcing. Model-comparison results show that the proposed regime-switching fractionally integrated specification outperforms benchmark score-driven and non-switching models according to likelihood-based criteria. The estimated fractional-integration parameters vary across climate regimes, with both regimes exhibiting persistent long-memory dynamics and one regime approaching unit-root behavior. The results provide evidence that Cenozoic climate evolution is characterized by changes in the strength of persistence. The regime dynamics broadly support previously identified climate-state boundaries near 56, 47, 39.7, 34, 13.9, 10, and 3.3 million years ago (Ma), while also suggesting potential additional subdivisions near 58 and 17 Ma. Our findings imply a hierarchical structure of climate evolution in which major climate states contain internally distinct dynamical subperiods. These results matter for long-horizon climate-risk modeling used in energy economics because they indicate that climate persistence and uncertainty vary systematically across climate states. |
| Keywords: | Long memory processes; Fractional degree of integration; Dynamic Conditional Score (DCS); Generalized Autoregressive Score (GAS); Score-driven regime-switching models; 67.1 million-year climate data |
| JEL: | C22 C51 C52 Q54 |
| Date: | 2026–06–24 |
| URL: | https://d.repec.org/n?u=RePEc:cte:werepe:50313 |
| By: | Barrio Castro, Tomás del; Escribano, Álvaro; Özer, Yeliz; Sibbertsen, Philipp |
| Abstract: | Long paleoclimate time series combine strong persistence, multiple orbital-scale periodicities, and structural changes across climate states. These features complicate the statistical analysis of deep-time proxy records, since common spectral peaks do not necessarily imply stable relationships between variables. We analyze Cenozoic climate variability using the Cenozoic Global Reference benthic isotope record over the last 67.1 million years. The cleaned and interpolated δ18O and δ13C series are studied in a regime-based setting, with segments defined by major Cenozoic climate-state transitions to investigate if a stable coupling occurs between the isotope proxies and Earth’s astronomical variables. The analysis combines long-memory estimation, sequential frequency identification, frequency-adapted unit-root and stationarity testing at zero and harmonic frequencies, and cyclical fractional cointegration. This allows us to distinguish zero-frequency persistence from persistent cyclical behaviour and to test whether shared cyclical frequencies correspond to stable frequency-specific relationships between the proxies and orbital reference variables. The results show that the proxy series are not well described by a simple stationary versus unitroot dichotomy. Instead, they exhibit persistent long-memory dynamics with pronounced cyclical structure. Shared spectral peaks occur across several climate-state segments, yet only selected frequencies support stable fractional cointegration. Thus, isotope proxies and orbital reference variables may overlap spectrally without necessarily forming a stable longmemory relationship. A key finding is that the additional split at the Eocene–Oligocene transition reveals a change in the frequency-specific relationship between δ18O and δ13C. Before the transition, stable fractional cointegration is associated with an orbital-scale band, whereas after the transition it shifts toward multi-million-year variability. This points to a substantial reorganisation of the frequency-specific coupling between the oxygen- and carbon-isotope records after the transition. |
| Keywords: | CENOGRID; Cyclical fractional cointegration; Deep-time paleoclimate |
| JEL: | C32 Q54 C22 |
| Date: | 2026–06–22 |
| URL: | https://d.repec.org/n?u=RePEc:cte:werepe:50302 |
| By: | Anlong Qin; Zhongjun Qu |
| Abstract: | We show analytically and via simulation that cross-sectional aggregation can substantially attenuate regime-switching signals in time-series data, making regime switches harder to detect. Building on this, we develop regime-switching models and an estimation algorithm which allow for autoregressive dynamics and grouped heterogeneity. We apply the approach to a U.S. macroeconomic dataset of 94 series, covering components of real gross domestic product, industrial production, capacity utilization, employment, and hours worked. The estimates give sharper business cycle classifications than those typically found in the literature. Monte Carlo simulations show that the computation is practical for datasets with a few hundred time series. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.08398 |
| By: | Karanasos, Menelaos (Brunel University of London, UK); Xu, Yongdeng (Cardiff University, UK); Yfanti, Stavroula (Queen Mary University of London, UK); Zopounidis, Constantin (Technical University of Crete, Greece) |
| Abstract: | We derive an admissible parameter space for vector Multiplicative Error Models (vMEMs), explicitly formulating it in terms of the model’s matrix parameters through a set of matrix inequalities. Another key contribution is the adoption of constrained maximum likelihood estimation for the multivariate process, which ensures compliance with these matrix inequalities and addresses the limitations of unconstrained approaches used in previous studies. To demonstrate the effectiveness of the proposed method, we apply it to four empirical cases in financial volatility modeling, emphasizing its practical relevance. |
| Keywords: | Admissible Parameter Space; Constrained Maximum Likelihood Estimation; Matrix Inequalities; MEM; Multivariate Volatility Modeling; Second Moment Structure |
| JEL: | C32 C53 C58 G15 |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:cdf:wpaper:2026/3 |
| By: | Miquel Noguer I Alonso; Rodolfo Pereira Franklin |
| Abstract: | Financial return forecasting is a difficult test case for time-series foundation models (TSFMs) due to low signal-to-noise ratios, structural breaks, heavy tails, and weak persistence. This paper benchmarks pretrained TSFMs against train-from-scratch neural baselines in a deliberately conservative financial setting. We evaluate TimeGPT/TimeGPT-LH, TimesFM-2.5, Moirai-2.0, Chronos, and Chronos-2 against NBEATS, NHITS, PatchTST, iTransformer, and KAN on five liquid U.S. equities (AAPL, AMZN, GOOG, JPM, META) using linear and log returns. Models are compared under an equalized context budget, a rolling-origin protocol, and against random-walk benchmarks. We provide a theoretical framing of pretraining as an inductive prior, linking PAC-Bayes transfer intuition, information-theoretic predictability limits, and attention geometry. This clarifies why strong model rankings need not imply economically meaningful predictability in noisy markets. Pragmatically, pretrained TSFMs dominate the ranking distribution, accounting for 8 of 10 task-level wins. Moirai-2.0 and TimesFM-2.5 achieve the strongest average ranks, leading tasks for AAPL, JPM, GOOG, and AMZN, while Chronos wins the remaining AMZN task. However, the iTransformer baseline wins both META tasks, showing local supervised learning can still outperform generic pretraining for specific assets. Crucially, gains over the random-walk benchmark are small and sparse. A one-sided Diebold-Mariano test rejects equal or inferior predictive accuracy only for Chronos on AMZN and Moirai-2.0 on GOOG. We conclude that TSFMs serve as useful practical priors that reduce model-development costs in low-data financial forecasting, but are not universal engines for statistically reliable alpha generation in realistic empirical deployment. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.27100 |
| By: | Li Chen (Paderborn University); Yuanhua Feng (Paderborn University) |
| Abstract: | Motivated by more and more semi- or nonparametric models applied in time series forecasting and their demonstrated superior performance in many empirical researches, this paper explores the adoption and integration of a semiparametric ARMA model in an enterprise system landscape. We begin by reviewing basic construction of the semiparametric ARMA model, the iterative plug-in algorithm for estimating the trend component of trend stationary times series, forecast techniques and quality measurements, which were well researched and published with the R package smoots. Subsequently, we showcase a novel approach to adopt the semiparametric ARMA model in a forecast application based on SAP Analytics Cloud (SAC), which leverages the platform’s strengths in system integrity, state-of-the-art user interface (UI) design as well as seamless connection to a R engine with smoots package embedded. The forecast application addresses key challenges in terms of cost efficiency, user experience, and the requirement for in-house statistical or machine learning expertise while adopting such statistical algorithms in enterprise context. Finally, we empirically evaluate the forecast quality of the integrated semiparametric ARMA model using real-world data, demonstrating promising results overall. |
| Keywords: | Time series forecasting, semiparametric algorithm, forecasting accuracy, smoots package, SAP Analytics Cloud, enterprise adoption |
| JEL: | C |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:dispap:179 |
| By: | Minford, Patrick (Cardiff University, UK and CEPR); Meenagh, David (Cardiff Business School) |
| Abstract: | Fat tails can in principle undermine the power of the standard indirect inference test. We examine this issue with Monte Carlo experiments, first for a New Keynesian model solved by the nonlinear algorithm method of Fair and Taylor. Here we find that the standard test has its usual high power, even in a model exhibiting potentially fat tails due to misspecification. If the model is solved by Dynare, then fat tails have only a minor effect on the power of the standard test so that the problem can be ignored except for very extreme fatness. It is therefore unlikely to occur; if it does, it can be solved either by eliminating outlier shocks, or by switching to the Fair-Taylor solution method. Second, we examine the case of the highly nonlinear CGE trade model where we find the fat tails problem is acute and pervasive, as shocks interact with the model nonlinearity to create high volatility. Here eliminating outliers restores the test power. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:cdf:wpaper:2026/7 |
| By: | Kasper Sunn Blumensaat |
| Abstract: | We generalize the convergence results of an explosive autoregression, pioneered in Anderson (1959), in three ways: First, we demonstrate that the centered least-squares estimator converges geometrically to a ratio of limits, even in settings where the innovations are correlated and not centered around zero. Secondly, we demonstrate that the requirement of independent innovations in Anderson (1959), Theorem 2.3, can be relaxed to $\alpha$-mixing. Third, we provide an autocorrelation-robust feasible test statistic for the explosive parameter under Gaussian ARMA innovations. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.09531 |
| By: | Abdulrahman Alswaidan; Cade Jin; Jeffrey D. Varner |
| Abstract: | Synthetic generators of daily equity returns let practitioners stress test, backtest, and design scenarios that a single realized market history cannot supply, but only if the generator reproduces the stylized facts of real returns: heavy tails, negligible linear autocorrelation, and slow decay of the absolute-return autocorrelation. Hidden Markov models with few Gaussian states were long thought unable to reproduce that slow decay, and the standard fix was to abandon them for more complex hidden semi-Markov models. We revisit this issue with a continuous hidden Markov model whose regime chain governs the autocorrelation while per-regime densities govern the marginal, separating the temporal and distributional sides of the original failure. A unified expectation-maximization framework fits Gaussian, Student-t, Laplace, and generalized-error emissions under shared forward-backward recursions and quantile-based initialization, and a spectral identity bounds the number of decay modes by the rank of the centred transition matrix. Across SPY walk-forward folds, a sector-balanced 30-ticker panel, a CRSP cross-decade transfer, and a six-asset basket, that bound was not binding once a few states were used: heavy-tailed marginals, not additional decay modes, closed most of the fit gap, recovering volatility clustering above the i.i.d. baseline and narrowing the kurtosis gap without a tuning hyperparameter. The original failure is therefore distributional, not temporal. On daily US equities, a simple, interpretable Markov model suffices, and unlike a bootstrap or semi-Markov fit that wins only on a single-window fit, the fitted model also yields a regime-conditional Value-at-Risk that passes a joint conditional-coverage test and a copula that reproduces cross-asset correlations: one interpretable generator serving both path simulation and downstream risk and portfolio tasks. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.23492 |
| By: | Venkitasubramanian, Kailas (University of North Carolina at Charlotte) |
| Abstract: | Quantile regression describes how covariates shift the conditional quantiles of an outcome, not merely its mean, and is indispensable when effects are heterogeneous across the response distribution. When data are clustered or longitudinal, a mixed-effects formulation is needed. I present bqmm, an R package for Bayesian multilevel quantile regression built on the asymmetric Laplace working likelihood and Stan. The package offers an lme4-style formula interface with nested and crossed random effects, optional LKJ-correlated random effects, estimation of one or several quantiles in a single call, post-hoc non-crossing rearrangement, and a transparent menu of fixed-effect interval methods — the naive posterior, the Yang–Wang–He (2016) sandwich correction, and the infinitesimal jackknife — because the asymmetric Laplace likelihood is misspecified and naive credible intervals can be invalid. The paper describes the model and software design, illustrates usage on longitudinal growth data, summarises a validation study (parameter recovery, simulation-based calibration, and a coverage study), and compares bqmm with related software. |
| Date: | 2026–06–16 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:7d5xb_v1 |