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on Econometric Time Series |
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Issue of 2025–08–25
fifteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Zhiren Ma; Qian Zhao; Riquan Zhang; Zhaoxing Gao |
| Abstract: | This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression linking future outcomes to these factors, estimated via iterative least squares. To handle weak factor structures, we introduce a supervised screening step to select informative rows and columns. Theoretical properties, including consistency and asymptotic normality, are established. Simulations and real data show that our method significantly improves forecast accuracy, with the screening procedure providing additional gains over standard benchmarks in out-of-sample mean squared forecast error. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.04259 |
| By: | Degui Li (Faculty of Business Administration, Asia-Pacific Academy of Economics and Management, and Department of Economics, University of Macau); Yayi Yan (School of Statistics and Data Science, Shanghai University of Finance and Economics); Qiwei Yao (Department of Statistics, London School of Economics) |
| Abstract: | In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully explore the intrinsic matrix structure in the data, allowing interaction between the row and column stochastic trends, and subsequently improving the estimation convergence. It also reduces the computation complexity in estimation. The main estimation methodology is built on the eigenanalysis of sample row and column covariance matrices when the nonstationary matrix factors are of full rank and the idiosyncratic components are temporally stationary, and is further extended to tackle a more flexible setting when the matrix factors are cointegrated and the idiosyncratic components may be nonstationary. Under some mild conditions which allow the existence of weak factors, we derive the convergence theory for the estimated factor loading matrices and nonstationary factor matrices. In particular, the developed methodology and theory are applicable to the general case of heterogeneous strengths over weak factors. An easy-to-implement ratio criterion is adopted to consistently estimate the size of latent factor matrix. Both simulation and empirical studies are conducted to examine the numerical performance of the developed model and methodology in finite samples. |
| Keywords: | common stochastic trends, eigenanalysis, matrix error-correction models, matrix factor models, ratio criterion |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202534 |
| By: | Degui Li; Yayi Yan; Qiwei Yao |
| Abstract: | In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully explore the intrinsic matrix structure in the data, allowing interaction between the row and column stochastic trends, and subsequently improving the estimation convergence. It also reduces the computation complexity in estimation. The main estimation methodology is built on the eigenanalysis of sample row and column covariance matrices when the nonstationary matrix factors are of full rank and the idiosyncratic components are temporally stationary, and is further extended to tackle a more flexible setting when the matrix factors are cointegrated and the idiosyncratic components may be nonstationary. Under some mild conditions which allow the existence of weak factors, we derive the convergence theory for the estimated factor loading matrices and nonstationary factor matrices. In particular, the developed methodology and theory are applicable to the general case of heterogeneous strengths over weak factors. An easy-to-implement ratio criterion is adopted to consistently estimate the size of latent factor matrix. Both simulation and empirical studies are conducted to examine the numerical performance of the developed model and methodology in finite samples. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.11358 |
| By: | Yambolov, Andrian |
| Abstract: | When economic analysis requires simultaneous inference across multiple variables and time horizons, this paper shows that conventional pointwise quantiles in Bayesian structural vector autoregressions significantly understate the uncertainty of impulse responses. The performance of recently proposed joint inference methods, which produce noticeably different error band estimates, is evaluated, and calibration routines are suggested to ensure that they achieve the intended nominal probability coverage. Two practical applications illustrate the implications of these findings: (i) within a structural vector autoregression, the fiscal multiplier exhibits error bands that are 51% to 91% wider than previous estimates, and (ii) a pseudo-out-of-sample projection exercise for inflation and gross domestic product shows that joint inference methods could effectively summarize uncertainty for forecasts as well. These results underscore the importance of using joint inference methods for more robust econometric analysis. JEL Classification: C22, C32, C52 |
| Keywords: | forecasts, impulse responses, joint inference, pointwise inference, vector autoregressions |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20253100 |
| By: | Haojie Liu; Zihan Lin |
| Abstract: | We introduce Galerkin-ARIMA, a novel time-series forecasting framework that integrates Galerkin projection techniques with the classical ARIMA model to capture potentially nonlinear dependencies in lagged observations. By replacing the fixed linear autoregressive component with a spline-based basis expansion, Galerkin-ARIMA flexibly approximates the underlying relationship among past values via ordinary least squares, while retaining the moving-average structure and Gaussian innovation assumptions of ARIMA. We derive closed-form solutions for both the AR and MA components using two-stage Galerkin projections, establish conditions for asymptotic unbiasedness and consistency, and analyze the bias-variance trade-off under basis-size growth. Complexity analysis reveals that, for moderate basis dimensions, our approach can substantially reduce computational cost compared to maximum-likelihood ARIMA estimation. Through extensive simulations on four synthetic processes-including noisy ARMA, seasonal, trend-AR, and nonlinear recursion series-we demonstrate that Galerkin-ARIMA matches or closely approximates ARIMA's forecasting accuracy while achieving orders-of-magnitude speedups in rolling forecasting tasks. These results suggest that Galerkin-ARIMA offers a powerful, efficient alternative for modeling complex time series dynamics in high-volume or real-time applications. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.07469 |
| By: | Peter C. B. Phillips (Yale University); Liang Jiang (Fudan University) |
| Abstract: | This paper is part of a joint study of parametric autoregression with cross section curve time series, focussing on unit root (UR) nonstationary curve data autoregression. The Hilbert space setting extends scalar UR and local UR models to accommodate high dimensional cross section dependent data under very general conditions. New limit theory is introduced that involves two parameter Gaussian processes that generalize the standard UR and local UR asymptotics. Bias expansions provide extensions of the well-known results in scalar autoregression and fixed effect dynamic panels to functional dynamic regressions. Semiparametric and ADF-type UR tests are developed with corresponding limit theory that enables time series inference with high dimensional curve cross section data, allowing also for functional fixed effects and deterministic trends. The asymptotics reveal the effects of general forms of cross section dependence in wide nonstationary panel data modeling and show dynamic panel regression limit theory as a special limiting case of curve time series asymptotics. Simulations provide evidence of the impact of curve cross section data on estimation and test performance and the adequacy of the asymptotics. An empirical illustration of the methodology is provided to assess the presence of time series nonstationarity in household Engel curves among ageing seniors in Singapore using the Singapore life panel dataset. |
| Date: | 2025–08–10 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2454 |
| By: | Oguzhan Akgun; Alain Pirotte; Giovanni Urga; Zhenlin Yang |
| Abstract: | This paper proposes a selective inference procedure for testing equal predictive ability in panel data settings with unknown heterogeneity. The framework allows predictive performance to vary across unobserved clusters and accounts for the data-driven selection of these clusters using the Panel Kmeans Algorithm. A post-selection Wald-type statistic is constructed, and valid $p$-values are derived under general forms of autocorrelation and cross-sectional dependence in forecast loss differentials. The method accommodates conditioning on covariates or common factors and permits both strong and weak dependence across units. Simulations demonstrate the finite-sample validity of the procedure and show that it has very high power. An empirical application to exchange rate forecasting using machine learning methods illustrates the practical relevance of accounting for unknown clusters in forecast evaluation. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.14621 |
| By: | Kenneth D. West; Kurt G. Lunsford |
| Abstract: | We study the use of a misspecified overdifferenced model to forecast the level of a stationary scalar time series. Let x(t) be the series, and let bias be the sample average of a series of forecast errors. Then, the bias of forecasts of x(t) generated by a misspecified overdifferenced ARMA model for Δx(t) will tend to be smaller in magnitude than the bias of forecasts of x(t) generated by a correctly specified model for x(t). Formally, let P be the number of forecasts. The bias from the model for Δx(t) has a variance that is O(1/P^2), while the variance of the bias from the model for x(t) generally is O(1/P). With a driftless random walk as our baseline overdifferenced model, we confirm this theoretical result with simulations and empirical work: random walk bias is generally one-tenth to one-half that of an appropriately specified model fit to levels. |
| JEL: | C22 C53 E37 E47 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:34112 |
| By: | Oday Masoudi; Farhad Shahbazi; Mohammad Sharifi |
| Abstract: | We employed Multifractal Detrended Fluctuation Analysis (MF-DFA) and Refined Composite Multiscale Sample Entropy (RCMSE) to investigate the complexity of Bitcoin, GBP/USD, gold, and natural gas price log-return time series. This study provides a comparative analysis of these markets and offers insights into their predictability and associated risks. Each tool presents a unique method to quantify time series complexity. The RCMSE and MF-DFA methods demonstrate a higher complexity for the Bitcoin time series than others. It is discussed that the increased complexity of Bitcoin may be attributable to the presence of higher nonlinear correlations within its log-return time series. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.23414 |
| By: | Dilip M. Nachane (Indira Gandhi Institute of Development Research) |
| Abstract: | The maximum entropy principle is characterized as assuming the least about the unknown parameters in a statistical model. In its applied manifestations, it uses all the available information and makes the fewest possible assumptions regarding the unavailable information. The application of this principle to parametric spectrum estimation leads to an autoregressive transfer function. By appeal to a well known theorem in stochastic processes, a rational transfer function leads to a factorizable spectrum. This result combined with a classical theorem of analysis (due to Szego") forms the basis for two important algorithms for estimating the autoregressive spectrum viz. the Levinson-Durbin and Burg algorithms. The latter leads to estimators which are asymptotically MLEs (maximum likelihood estimators). |
| Keywords: | Entropy, Jaynes' Principle, autoregressive spectrum, spectral factorization, Levinson, Durbin |
| JEL: | C22 C32 |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:ind:igiwpp:2025-020 |
| By: | Sourojyoti Barick |
| Abstract: | This paper provides insight into the estimation and asymptotic behavior of parameters in interest rate models, focusing primarily on the Cox-Ingersoll-Ross (CIR) process and its extension -- the more general Chan-Karolyi-Longstaff-Sanders (CKLS) framework ($\alpha\in[0.5, 1]$). The CIR process is widely used in modeling interest rates which possess the mean reverting feature. An Extension of CIR model, CKLS model serves as a foundational case for analyzing more complex dynamics. We employ Euler-Maruyama discretization to transform the continuous-time stochastic differential equations (SDEs) of these models into a discretized form that facilitates efficient simulation and estimation of parameters using linear regression techniques. We established the strong consistency and asymptotic normality of the estimators for the drift and volatility parameters, providing a theoretical underpinning for the parameter estimation process. Additionally, we explore the boundary behavior of these models, particularly in the context of unattainability at zero and infinity, by examining the scale and speed density functions associated with generalized SDEs involving polynomial drift and diffusion terms. Furthermore, we derive sufficient conditions for the existence of a stationary distribution within the CKLS framework and the corresponding stationary density function; and discuss its dependence on model parameters for $\alpha\in[0.5, 1]$. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.10041 |
| By: | Yu Shi; Zongliang Fu; Shuo Chen; Bohan Zhao; Wei Xu; Changshui Zhang; Jian Li |
| Abstract: | The success of large-scale pre-training paradigm, exemplified by Large Language Models (LLMs), has inspired the development of Time Series Foundation Models (TSFMs). However, their application to financial candlestick (K-line) data remains limited, often underperforming non-pre-trained architectures. Moreover, existing TSFMs often overlook crucial downstream tasks such as volatility prediction and synthetic data generation. To address these limitations, we propose Kronos, a unified, scalable pre-training framework tailored to financial K-line modeling. Kronos introduces a specialized tokenizer that discretizes continuous market information into token sequences, preserving both price dynamics and trade activity patterns. We pre-train Kronos using an autoregressive objective on a massive, multi-market corpus of over 12 billion K-line records from 45 global exchanges, enabling it to learn nuanced temporal and cross-asset representations. Kronos excels in a zero-shot setting across a diverse set of financial tasks. On benchmark datasets, Kronos boosts price series forecasting RankIC by 93% over the leading TSFM and 87% over the best non-pre-trained baseline. It also achieves a 9% lower MAE in volatility forecasting and a 22% improvement in generative fidelity for synthetic K-line sequences. These results establish Kronos as a robust, versatile foundation model for end-to-end financial time series analysis. Our pre-trained model is publicly available at https://github.com/shiyu-coder/Kronos. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.02739 |
| By: | Yihao Ang; Qiang Wang; Qiang Huang; Yifan Bao; Xinyu Xi; Anthony K. H. Tung; Chen Jin; Zhiyong Huang |
| Abstract: | Synthetic time series are essential tools for data augmentation, stress testing, and algorithmic prototyping in quantitative finance. However, in cryptocurrency markets, characterized by 24/7 trading, extreme volatility, and rapid regime shifts, existing Time Series Generation (TSG) methods and benchmarks often fall short, jeopardizing practical utility. Most prior work (1) targets non-financial or traditional financial domains, (2) focuses narrowly on classification and forecasting while neglecting crypto-specific complexities, and (3) lacks critical financial evaluations, particularly for trading applications. To address these gaps, we introduce \textsf{CTBench}, the first comprehensive TSG benchmark tailored for the cryptocurrency domain. \textsf{CTBench} curates an open-source dataset from 452 tokens and evaluates TSG models across 13 metrics spanning 5 key dimensions: forecasting accuracy, rank fidelity, trading performance, risk assessment, and computational efficiency. A key innovation is a dual-task evaluation framework: (1) the \emph{Predictive Utility} task measures how well synthetic data preserves temporal and cross-sectional patterns for forecasting, while (2) the \emph{Statistical Arbitrage} task assesses whether reconstructed series support mean-reverting signals for trading. We benchmark eight representative models from five methodological families over four distinct market regimes, uncovering trade-offs between statistical fidelity and real-world profitability. Notably, \textsf{CTBench} offers model ranking analysis and actionable guidance for selecting and deploying TSG models in crypto analytics and strategy development. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.02758 |
| By: | Tauheed, Tahira; Tauseef, Tahira |
| Abstract: | This study addresses the challenge of estimating the NAIRU in developing countries, focusing on Pakistan from 1972 to 2022. Due to data constraints in such contexts, it introduces robust methodologies, including Hodrick-Prescott and Kalman filters within a univariate framework, to derive NAIRU estimates and their precision. The NAIRU estimates average around five percent, fluctuating over time, indicating a time-varying NAIRU in Pakistan. An analysis of unemployment decomposition reveals that cyclical and non-structural factors are more influential than structural ones in the labor market, emphasizing the need for counter-cyclical policies alongside necessary structural reforms. The unemployment gap and inflation analysis provide mixed evidence on NAIRU's theoretical foundation, recommending simultaneous supply shocks' control and demand management in inflation-targeting. The study indicates Kalman filter estimates the NAIRU more effectively than the HP filter, though both lack precision. Therefore, future research in developing countries with limited data should focus on developing structural approaches suitable for lower degrees of freedom alongside univariate methods. |
| Keywords: | NAIRU, NAIRU’s Precision, Univariate Approach, Kalman Filter, State Space Model, HP Filter |
| JEL: | C13 C14 E24 E27 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:323970 |
| By: | Sophia Rabe-Hesketh (University of California, Berkeley); Feng Ji (University of California, Berkeley); JoonHo Lee (University of Alabama) |
| Abstract: | Giordano and Broderick (2024) introduced infinitesimal jackknife (IJ) standard errors for Bayesian estimators (posterior means). Just like resampling standard errors, IJ standard errors are robust to model misspecification and can be adapted to account for clustering. Importantly, IJ standard errors do not require resampling but can be obtained from a single MCMC run. Standard Bayesian quantile regression, as implemented in bayes: qreg bayes: qreg bayes: qreg bayes: qreg, is generally misspecified. This is because the motivation for the asymmetric Laplace (AL) likelihood is merely that its maximum coincides with the classical quantile regression estimator of Koenker and Bassett (1978). There is no reason to believe that the AL distribution is a plausible data-generating mechanism. For example, the shape of the distribution depends on the quantile you are interested in. While point estimation is consistent, credible intervals often have poor frequentist coverage. We therefore propose using IJ standard errors for Bayesian quantile regression and show, via simulations, that they have good frequentist properties, both for independent and clustered data. If made available as an option in bayes: bayes: bayes: bayes: and bayesmh bayesmh bayesmh bayesmh, IJ standard errors may soon become as popular for Bayesian inference as the vce(robust) vce(robust) vce(robust) vce(robust) option for frequentist inference. |
| Date: | 2025–08–08 |
| URL: | https://d.repec.org/n?u=RePEc:boc:usug25:08 |