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on Econometric Time Series |
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Issue of 2025–07–21
eighteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Antonis Demos (www.aueb.gr/users/demos) |
| Abstract: | Here we investigate the statistical properties of two autoregressive normal asymmetric SV models with possibly time varying risk premia. These, although they seem very similar, it turns out, that they possess quite different statistical properties. The derived properties can be employed to develop tests or to check for up to forth order stationarity, something important for the asymptotic properties of various estimators. |
| Date: | 2025–06–26 |
| URL: | https://d.repec.org/n?u=RePEc:aue:wpaper:2546 |
| By: | Karim Moussa (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | This paper introduces a novel approach to simulation smoothing for nonlinear and non-Gaussian state space models. It allows for computing smoothed estimates of the states and nonlinear functions of the states, as well as visualizing the joint smoothing distribution. The approach combines extremum estimation with simulated data from the model to estimate the conditional distributions in the backward smoothing decomposition. The method is generally applicable and can be paired with various estimators of conditional distributions. Several applications to nonlinear models are presented for illustration. An empirical application based on a stochastic volatility model with stable errors highlights the flexibility of the approach. |
| Date: | 2025–05–16 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250034 |
| By: | Silva Lopes, Artur |
| Abstract: | Several reasons explain the absence of a precise, complete and widely accepted definition of trend for economic time series, and the existence of two major disparate models is one of the most important. A recent operational proposal tried to overcome this difficulty resorting to a statistical test with good asymptotic properties against both those alternatives. However, this proposal may be criticized because it rests on a tool for inductive, not deductive, inference. Besides criticizing this recent definition, drawing heavily on previous ones, the paper provides a new proposal, more complete, containing several necessary but no sufficient condition(s). |
| Keywords: | trend; time series; macroeconomy; statistical testing |
| JEL: | B41 C12 C18 C22 |
| Date: | 2025–04–14 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:125073 |
| By: | Dou, Zhiwei; Ariens, Sigert; Ceulemans, Eva; Lafit, Ginette |
| Abstract: | The first order autoregressive [AR(1)] model is widely used to investigate psycholog- ical dynamics. This study focuses on the estimation and inference of the autoregressive (AR) effect in AR(1) models under a limited sample size—a common scenario in psy- chological research. State-of-the-art estimators of the autoregressive effect are known to be biased when sample sizes are small. We analytically demonstrate the causes and consequences of this small sample bias on the estimation of the AR effect, its variance, and the AR(1) model’s intercept, particularly when using OLS. In addition, we reviewed various bias correction methods proposed in the time series literature. A simulation study compares the OLS estimator with these correction methods in terms of estimation accuracy and inference. The main result indicates that the small sam- ple bias of the OLS estimator of the autoregressive effect is a consequence of limited information and correcting for this bias without more information always induces a bias-variance trade-off. Nevertheless, correction methods discussed in this research may offer improved statistical power under moderate sample sizes when the primary research goal is hypothesis testing. |
| Date: | 2025–06–17 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:esfpy_v1 |
| By: | Karim Moussa (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | In the analysis of multivariate stochastic volatility models, many estimation procedures begin by transforming the data, taking the logarithm of the squared returns to obtain a linear state space model. A well-known series representation links the correlations between elements of the observation error in the actual and linearized forms of the model. This note derives a closed-form expression for the series and discusses its statistical implications. Additionally, it offers a new interpretation of the correlations in the linearized model. |
| Date: | 2025–03–21 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250021 |
| By: | Yicong Lin (Vrije Universiteit Amsterdam and Tinbergen Institute); André Lucas (Vrije Universiteit Amsterdam and Tinbergen Institute); Shiqi Ye (AMSS Center for Forecasting Science) |
| Abstract: | We introduce a new time-varying parameter spatial matrix autoregressive model that integrates matrix-valued time series, heterogeneous spillover effects, outlier robustness, and time-varying parameters in one unified framework. The model allows for separate dynamic spatial spillover effects across both the row and column dimensions of the matrix-valued observations. Robustness is introduced through innovations that follow a (conditionally heteroskedastic) matrix Student's $t$ distribution. In addition, the proposed model nests many existing spatial autoregressive models, yet remains easy to estimate using standard maximum likelihood methods. We establish the stationarity and invertibility of the model and the consistency and asymptotic normality of the maximum likelihood estimator. Our simulations reveal that the latent time-varying two-way spatial spillover effects can be successfully recovered, even under severe model misspecification. The model's usefulness is illustrated both in-sample and out-of-sample using two different applications: one in international trade, and the other based on global stock market data. |
| Keywords: | matrix-valued time series; spatial autoregression; time-varying parame- ters; score-driven dynamics |
| JEL: | C31 C32 C58 |
| Date: | 2025–07–04 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250042 |
| By: | Xia Zou (Vrije Universiteit Amsterdam and Tinbergen Institute); Yicong Lin (Vrije Universiteit Amsterdam and Tinbergen Institute); André Lucas (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | Point forecasts of score-driven models have been shown to behave at par with those of state-space models under a variety of circumstances. We show, however, that density rather than point forecasts of plain-vanilla score-driven models substantially underperform their state-space counterparts in a factor model context. We uncover the origins of this phenomenon and show how a simple adjustment of the measurement density of the score-driven model can put score-driven and state-space models approximately back on an equal footing again. The score-driven models can subsequently easily be extended with non-Gaussian features to fit the data even better without complicating parameter estimation. We illustrate our findings using a factor model for the implied volatility surface of S&P500 index options data. |
| JEL: | C32 C38 |
| Date: | 2025–05–30 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250036 |
| By: | Marina Friedrich (Vrije Universiteit Amsterdam and Tinbergen Institute); Karim Moussa (Vrije Universiteit Amsterdam and Tinbergen Institute); Yuliya Shapovalova (Radboud University Nijmegen); David van der Straten (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | Understanding the developments of atmospheric ethane is essential for better identifying the anthropogenic sources of methane, a major greenhouse gas with high global warming potential. While previous studies have focused on analyzing past trends in ethane and modeling the inter-annual variability, this paper aims at forecasting the atmospheric ethane burden above the Jungfraujoch (Switzerland). Since measurements can only be taken under clear sky conditions, a substantial fraction of the data (around 76%) is missing. The presence of missing data together with a strong seasonal component complicates the analysis and limits the availability of appropriate forecasting methods. In this paper, we propose five distinct approaches which we compare to a simple benchmark – a deterministic trending seasonal model – which is one of the most commonly used models in the ethane literature. We find that a structural time series model performs best for one-day ahead forecasts, while damped exponential smoothing and Gaussian process regression provide the best results for longer horizons. Additionally, we observe that forecasts are mostly driven by the seasonal component. This emphasizes the importance of selecting methods capable of capturing the seasonal variation in ethane measurements. |
| Keywords: | climate econometrics, forecasting, time series analysis |
| JEL: | C32 C53 |
| Date: | 2025–04–11 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250025 |
| By: | Yicong Lin (Vrije Universiteit Amsterdam and Tinbergen Institute); André Lucas (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | We introduce a new class of location-scale models for dynamic functional data in arbitrary but fixed dimensions, where the location and scale functional parameters can evolve over time. A key feature of the parameter dynamics in these models is its observation-driven nature, where the one-step-ahead evolution is fully determined conditional on past observations, yet remains stochastic unconditionally. We estimate the model using a likelihood-based approach designed for sparsely observed data and establish the consistency and asymptotic normality of the underlying static parameters that govern the location-scale dynamics. The choice of objective function and the construction of the dynamics together shield the time-varying location and scale parameters from the potentially distorting effects of influential observations. Simulations reveal that our method can recover the unobserved location-scale dynamics from sparse data, even in the presence of model mis-specification and substantial outliers. We apply our framework to examine the intraday volatility dynamics of Pfizer stock returns during the COVID-19 pandemic, and PM2.5 concentrations measured by low-cost sensors across Europe. The proposed model exhibits robust performance in capturing dynamics for both datasets despite the presence of many large shocks. |
| Keywords: | time variation, location-scale, functional score-driven dynamics, sparse data, outlier robustness |
| JEL: | C22 C58 Q56 |
| Date: | 2025–04–17 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250027 |
| By: | Mr. Philip Barrett |
| Abstract: | I jointly estimate monthly series for GDP and eight subcomponents for the US since 1950. The series match 1) quarterly national accounts equivalents, 2) exact data on monthly consumption, and 3) past relationships with other monthly indicators. I estimate the Kalman filter parameters by GMM, allowing fast calculation of confidence intervals for monthly estimates including parameter uncertainty, and validate the confidence intervals. After 1970 standard errors are tight, less than 0.3pp of GDP, and point estimates informative, with standard deviations four times the standard error. I provide confidence intervals for recessions and show that output peaks line up well with the onset of NBER recessions, but troughs often predate NBER equivalents. |
| Keywords: | Kalman Filter; GDP; recession; GMM |
| Date: | 2025–07–04 |
| URL: | https://d.repec.org/n?u=RePEc:imf:imfwpa:2025/134 |
| By: | Laura Capera Romero (Vrije Universiteit Amsterdam and Tinbergen Institute); Anne Opschoor (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | This paper compares the statistical and economic performance of state-of-the-art highfrequency based multivariate volatility models with a simpler, widely used alternative - the Exponentially Weighted Moving Average (EWMA) filter. Using over two decades of 100 U.S. stock returns (2002–2023), we assess model performance through a Global Minimum Variance portfolio optimization exercise across various forecast horizons. We find that the EWMA model consistently outperforms more complex HF-based volatility models, delivering significant utility gains when including transaction costs, due in part to its lower turnover. Even in the absence of transaction costs, the EWMA filter cannot be beaten in most cases. Our results are robust to various dimensions, including no-short-selling constraints, varying portfolio sizes, and alternative parameter choices, highlighting the continued relevance of the EWMA model in high-frequency-based portfolio allocation. |
| Date: | 2025–06–26 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250041 |
| By: | Daan Schoemaker (Vrije Universiteit Amsterdam and Tinbergen Institute); André Lucas (Vrije Universiteit Amsterdam and Tinbergen Institute); Anne Opschoor (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | We investigate the conditional tail behaviour of asset price changes at high (10-second) frequencies using a new dynamic model for integer-valued tickdata. The model has fat tails, scale dynamics, and allows for possible over- or under-representation of zero price changes. The model can be easily estimated using standard maximum likelihood methods and accommodates both polynomially (fat) and geometrically declining tails. In an application to stock, cryptocurrency and foreign exchange markets during the COVID-19 crisis, we find that conditional fat-tailedness is empirically important for many assets, even at such high frequencies. The new model outperforms the thin-tailed (zero-initiated) dynamic benchmark Skellam model by a wide margin, both insample and out-of-sample. |
| Keywords: | high frequency tick data, polynomial tails, discrete data, Hurwitz zeta function, score-driven dynamics |
| JEL: | C22 C46 C58 |
| Date: | 2025–06–26 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250039 |
| By: | V. M. Belyaev |
| Abstract: | Here we demonstrate how we can use Small Volatility Approximation in calibration of Multi-Factor HJM model with deterministic correlations, factor volatilities and mean reversals. It is noticed that quality of this calibration is very good and it does not depend on number of factors. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.12584 |
| By: | Lee, Minho; Suh, Yon Soo |
| Abstract: | This paper presents a class of higher-order diagnostic classification models (HO–DCMs) capable of capturing complex, nonlinear hierarchical relationships among attributes. Building on and extending prior work, we adopt a nominal response model framework in item response theory and leverage standard maximum likelihood estimation (MLE). In parallel, we demonstrate that sequential HO–DCMs can likewise be implemented within an MLE framework. Furthermore, we introduce a novel chunk-based approach for representing attribute hierarchies, wherein attributes are organized into cognitively coherent subgraphs (chunks) nested within a continuous general ability continuum. The performance of the models is validated through simulation studies evaluating parameter recovery, classification accuracy, and null rejection rates of goodness-of-fit measures. An empirical demonstration showcases how the proposed framework can be applied in practice, highlighting its advantages in model flexibility, interpretability, and the additional diagnostic insights it affords. |
| Date: | 2025–06–17 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:aney6_v1 |
| By: | Frank Schorfheide; Zhiheng You |
| Abstract: | Econometricians invest substantial effort in constructing standard errors that yield valid inference under a hypothetical data-generating process. This paper asks a fundamental question: Are the uncertainty statements reported by applied researchers consistent with empirical frequencies? The short answer is no. Drawing on the forecasting literature, we predict estimates from “new” studies using estimates from corresponding baseline studies. By doing this across a large number of study groups and linking parameters through a hierarchical model, we compare stated probabilities to observed empirical frequencies. Alignment occurs only under limited external validity, namely, that the studies estimate different parameters. |
| JEL: | C11 C18 C21 |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:33962 |
| By: | Emmanouil SOFIANOS; Thierry BETTI; Emmanouil Theophilos PAPADIMITRIOU; Amélie BARBIER-GAUCHARD; Periklis GOGAS |
| Abstract: | Forecasting public debt is essential for effective policymaking and economic stability, yet traditional approaches face challenges due to data scarcity. While machine learning (ML) has demonstrated success in financial forecasting, its application to macroeconomic forecasting remains underexplored, hindered by short historical time series and low-frequency (e.g., quarterly/annual) data availability. This study proposes a novel hybrid framework integrating Dynamic Stochastic General Equilibrium (DSGE) modeling with ML techniques to address these limitations, focusing on the evolution of France’s public debt. We first generate a large synthetic macroeconomic dataset using an estimated DSGE model for France, which allows for efficient training of ML algorithms. These trained models are then applied to actual historical data for directional debt forecasting. The results show that the best machine learning model is an XGBoost achieving 90% accuracy. Our results highlight the viability of combining structural economic models with data-driven techniques to improve macroeconomic forecasting. |
| Keywords: | DSGE, Machine Learning, Public Debt, Forecasting, France. |
| JEL: | C53 E27 E37 H63 H68 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ulp:sbbeta:2025-18 |
| By: | Felipe Roldán-Ferrín; Julián A. Parra-Polania |
| Abstract: | This paper evaluates the predictive capacity of a machine learning model based on Random Forests (RF), combined with Google Trends (GT) data, for nowcasting monthly inflation in Colombia. The proposed RF-GT model is trained using historical inflation data, macroeconomic indicators, and internet search activity. After optimizing the model’s hyperparameters through time series cross-validation, we assess its out-of-sample performance over the period 2023–2024. The results are benchmarked against traditional approaches, including SARIMA, Ridge, and Lasso regressions, as well as professional forecasts from the Banco de la República’s monthly survey of financial analysts (MES). In terms of forecast accuracy, the RF-GT model consistently outperforms the statistical models and performs comparably to the analysts’ median forecast, while offering the additional advantage of producing predictions approximately one and a half weeks earlier. These findings highlight the practical value of integrating alternative data sources and machine learning techniques into the inflation monitoring toolkit of emerging economies. *****RESUMEN: Este artículo evalúa la capacidad predictiva de un modelo de aprendizaje automático basado en Random Forest (RF), combinado con datos de Google Trends (GT), para realizar nowcasting de la inflación mensual en Colombia. El modelo propuesto, denominado RF-GT, se entrena utilizando datos históricos de inflación, indicadores macroeconómicos y actividad de búsqueda en internet. Tras la optimización de los hiperparámetros mediante validación cruzada para series de tiempo, se evalúa su desempeño fuera de muestra durante el periodo 2023–2024. Los resultados se comparan con enfoques tradicionales, incluidos los modelos SARIMA, regresiones Ridge y Lasso, así como con los pronósticos profesionales de la Encuesta Mensual de Expectativas (EME) del Banco de la República. En términos de precisión predictiva, el modelo RF-GT supera de forma consistente a los modelos estadísticos y muestra un desempeño comparable al pronóstico mediano de los analistas, con la ventaja adicional de generar predicciones aproximadamente semana y media antes. Estos hallazgos destacan el valor práctico de integrar fuentes de datos alternativas y técnicas de aprendizaje automático en los sistemas de monitoreo de inflación de economías emergentes. |
| Keywords: | Inflation, Nowcasting, Forecasting, Random Forest, Google Trends, Machine Learning, Inflación, Pronóstico en Tiempo Real, Pronóstico, Bosques Aleatorios, Tendencias de Google, aprendizaje automático |
| JEL: | C14 C53 E17 E31 E37 |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:bdr:borrec:1318 |
| By: | Eric Engstrom |
| Abstract: | Amid ongoing trade policy shifts and geopolitical uncertainty, concerns about stagflation have reemerged as a key macroeconomic risk. This paper develops a probabilistic framework to estimate the likelihood of stagflation versus soft landing scenarios over a four-quarter horizon. Building on Bekaert, Engstrom, and Ermolov (2025), the model integrates survey forecasts, structural shock decomposition, and a non-Gaussian BEGE-GARCH approach to capture time-varying volatility and skewness. Results suggest that the probability of stagflation was elevated at around 30 percent in late 2022, while the chance of a soft landing was below 5 percent. As inflation moderated and growth remained strong through 2024, these probabilities reversed. However, by mid-2025, renewed tariff concerns drove stagflation risk back up and the probability of a soft landing lower. These shifts highlight the potential value of distributional forecasting for policymakers and market participants navigating uncertain macroeconomic conditions. |
| Keywords: | GARCH; Inflation; Recession; Soft landing; Stagflation; Time-varying uncertainty |
| JEL: | E31 E32 E37 E60 |
| Date: | 2025–07–07 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2025-47 |