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on Econometric Time Series |
| By: | Mike G. Tsionas (Lancaster University) |
| Abstract: | In this paper we exploit properties of the likelihood function of the stochastic volatility model to show that it can be approximated accurately and efficiently using a response surface methodology. The approximation is across the plausible range of parameter values and all possible data and is found to be highly accurate. The methods extend easily to multivariate models and are applied to artificial data as well as ten exchange rates and all stocks of FTSE100 using daily data. Formal comparisons with multivariate GARCH models are undertaken using a special prior for the GARCH parameters. The comparisons are based on marginal likelihood and the Bayes factors. |
| Keywords: | Stochastic volatility; response surface; likelihood; Monte Carlo. |
| JEL: | C13 C15 |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:bog:wpaper:294&r=ets |
| By: | Nikolas Michael; Mihai Cucuringu; Sam Howison |
| Abstract: | We introduce OFTER, a time series forecasting pipeline tailored for mid-sized multivariate time series. OFTER utilizes the non-parametric models of k-nearest neighbors and Generalized Regression Neural Networks, integrated with a dimensionality reduction component. To circumvent the curse of dimensionality, we employ a weighted norm based on a modified version of the maximal correlation coefficient. The pipeline we introduce is specifically designed for online tasks, has an interpretable output, and is able to outperform several state-of-the art baselines. The computational efficacy of the algorithm, its online nature, and its ability to operate in low signal-to-noise regimes, render OFTER an ideal approach for financial multivariate time series problems, such as daily equity forecasting. Our work demonstrates that while deep learning models hold significant promise for time series forecasting, traditional methods carefully integrating mainstream tools remain very competitive alternatives with the added benefits of scalability and interpretability. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.03877&r=ets |
| By: | Rafael Alves; Diego S. de Brito; Marcelo C. Medeiros; Ruy M. Ribeiro |
| Abstract: | We propose a model to forecast large realized covariance matrices of returns, applying it to the constituents of the S\&P 500 daily. To address the curse of dimensionality, we decompose the return covariance matrix using standard firm-level factors (e.g., size, value, and profitability) and use sectoral restrictions in the residual covariance matrix. This restricted model is then estimated using vector heterogeneous autoregressive (VHAR) models with the least absolute shrinkage and selection operator (LASSO). Our methodology improves forecasting precision relative to standard benchmarks and leads to better estimates of minimum variance portfolios. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.16151&r=ets |
| By: | Demian Pouzo (University of California); Zacharias Psaradakis (University of London); Martin Sola (Universidad Torcuato di Tella) |
| Abstract: | We consider hidden Markov models with a discrete-valued regime sequence whose transition probabilities are covariate-dependent. We show that consistent estimation of the parameters of the conditional distribution of the observable variables is possible via quasi-maximum-likelihood based on a (misspecified) mixture model without Markov dependence. Some related numerical results are also discussed. |
| Keywords: | Consistency; covariate-dependent transition probabilities; hidden Markov model; mixture model; quasi-maximum-likelihood; misspecified model |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:234&r=ets |
| By: | Daan Opschoor (Erasmus University Rotterdam); Dick van Dijk (Erasmus University Rotterdam) |
| Abstract: | This paper addresses the poor performance of the Expectation-Maximization (EM) algorithm in the estimation of low-noise dynamic factor models, commonly used in macroeconomic forecasting and nowcasting. We show analytically and in Monte Carlo simulations how the EM algorithm stagnates in a low-noise environment, leading to inaccurate estimates of factor loadings and latent factors. An adaptive version of EM considerably speeds up convergence, producing substantial improvements in estimation accuracy. Modestly increasing the noise level also accelerates convergence. A nowcasting exercise of euro area GDP growth shows gains up to 34% by using adaptive EM relative to the usual EM. |
| Keywords: | Dynamic factor models, EM algorithm, artificial noise, convergence speed, nowcasting |
| JEL: | C32 C51 C53 E37 |
| Date: | 2023–04–05 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20230018&r=ets |
| By: | Francisco Blasques (Vrije Universiteit Amsterdam); Siem Jan Koopman (Vrije Universiteit Amsterdam); Karim Moussa (Vrije Universiteit Amsterdam) |
| Abstract: | This paper introduces a novel simulation-based filtering method for general state space models. It allows for the computation of time-varying conditional means, quantiles, and modes, but also for the prediction of latent variables in general. The method relies on generating artificial samples of data from the joint distribution implied by the model and on estimating the conditional quantities of interest via extremum estimation. We call this procedure Extremum Monte Carlo and define a corresponding class of filters for signal extraction. The method can be applied to any model from which data can be simulated and is not liable to the curse of dimensionality. Furthermore, the use of extremum estimation allows for a wide range of conditioning sets, including data with missing entries and unequal spacing. The filtering method also places the computational burden predominantly in the off-line phase, which makes it particularly suitable for real-time applications. We present illustrations for some challenging problems characterized by nonlinearity, high-dimensionality, and intractable density functions. |
| Keywords: | Nonlinear non-Gaussian state space models, Least squares Monte Carlo, Real-time filtering, Intractable densities, Curse of dimensionality |
| Date: | 2023–03–24 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20230016&r=ets |
| By: | William H. Press |
| Abstract: | Given two time series, A and B, sampled asynchronously at different times {t_A_i} and {t_B_j}, termed "ticks", how can one best estimate the correlation coefficient \rho between changes in A and B? We derive a natural, minimum-variance estimator that does not use any interpolation or binning, then derive from it a fast (linear time) estimator that is demonstrably nearly as good. This "fast tickwise estimator" is compared in simulation to the usual method of interpolating changes to a regular grid. Even when the grid spacing is optimized for the particular parameters (not often possible in practice), the fast tickwise estimator has generally smaller estimation errors, often by a large factor. These results are directly applicable to tick-by-tick price data of financial assets. |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2303.16153&r=ets |
| By: | Javier G. Gómez-Pineda; Julián Roa-Rozo |
| Abstract: | The business cycle is the cycle in the output gap and also in a stationary measure of trend output. Both the output gap and trend output are driven by joint trend-cycle shocks. The model is a univariate trend-cycle decomposition with hysteresis in trend output that enables the estimation of the output gap and trend output in 81 economies in quarterly frequency, since 1995Q1; and 184 economies in yearly frequency, in several cases since 1950, and in a few cases since 1820. Volatility and dispersion, as well as the frequency of large joint trend-cycle shocks, were low during the Gilded Age period; high during the interwar period, even more so in advanced (AD) economies compared to emerging market and developing economies (EMDE); and low in AD economies and high in EMDE economies in the post WWII period. In contrast with other existing estimates of trend output, those from the trend-cycle decomposition with hysteresis do not evolve smoothly, do not result in an artificial boom before recessions and are less sensitive to new data. **** RESUMEN: El ciclo económico es el ciclo en la brecha del producto y también en una medida estacionaria del producto tendencial. Tanto la brecha del producto como el producto tendencial son impulsados por choques conjuntos al ciclo y la tendencia. El modelo es una descomposición ciclo tendencia univariada con histéresis en el producto tendencia que permite la estimación de la brecha del producto y el producto tendencial en 81 economías en frecuencia trimestral desde 1995Q1 y en 184 economías en frecuencia anual desde 1975. La volatilidad, dispersión y frecuencia de choques conjuntos grandes fueron bajos durante el período de la Época Dorada; altos durante el período entre guerras, aún más en economías avanzadas (AD) en comparación con las emergentes y en desarrollo (EMDE); y bajo en las economías AD y alto en las economías EMDE en la segunda postguerra. En contraste con otros estimativos existentes del producto tendencial, los de la descomposición tendencia-ciclo con histéresis no evolucionan de forma suave, no resultan en un boom artificial antes de las recesiones y son menos sensibles a los datos nuevos. |
| Keywords: | Hysteresis, Business cycles, Business Fluctuations, Univariate model, Trend-cycle decomposition, Trend output, Output gap, Potential output, Histéresis, Ciclo de los negocios, Fluctuaciones económicas, Modelo univariado, Descomposición tendencia ciclo, Producto tendencial, Brecha del producto, Producto potencial |
| JEL: | E32 E50 O47 E58 E37 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:bdr:borrec:1230&r=ets |
| By: | Jir\^o Akahori; Nien-Lin Liu; Maria Elvira Mancino; Tommaso Mariotti; Yukie Yasuda |
| Abstract: | In this paper we propose an estimator of spot covariance matrix which ensure symmetric positive semi-definite estimations. The proposed estimator relies on a suitable modification of the Fourier covariance estimator in Malliavin and Mancino (2009) and it is consistent for suitable choices of the weighting kernel. The accuracy and the ability of the estimator to produce positive semi-definite covariance matrices is evaluated with an extensive numerical study, in comparison with the competitors present in the literature. The results of the simulation study are confirmed under many scenarios, that consider the dimensionality of the problem, the asynchronicity of data and the presence of several specification of market microstructure noise. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2304.04372&r=ets |