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on Econometric Time Series |
| By: | Jihyun Park; Andrey Sarantsev |
| Abstract: | We model time series of VIX (monthly average) and monthly stock index returns. We use log-Heston model: logarithm of VIX is modeled as an autoregression of order 1. Our main insight is that normalizing monthly stock index returns (dividing them by VIX) makes them much closer to independent identically distributed Gaussian. The resulting model is mean-reverting, and the innovations are non-Gaussian. The combined stochastic volatility model fits well, and captures Pareto-like tails of real-world stock market returns. This works for small and large stock indices, for both price and total returns. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.22471 |
| By: | Haowen Bao; Yongmiao Hong; Yuying Sun; Shouyang Wang |
| Abstract: | By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance estimation, which covers point-based estimators are special cases. We establish the consistency and oracle properties of the proposed penalized estimator, regardless of whether the number of predictors is diverging with the sample size. Monte Carlo simulations demonstrate the favorable finite sample properties of the proposed estimation. Empirical applications to interval-valued crude oil price forecasting and sparse index-tracking portfolio construction illustrate the robustness and effectiveness of our method against competing approaches, including random forest and multilayer perceptron for interval-valued data. Our findings highlight the potential of machine learning techniques in interval-valued time series analysis, offering new insights for financial forecasting and portfolio management. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09452 |
| By: | Jihyun Park; Andrey Sarantsev |
| Abstract: | Classic stochastic volatility models assume volatility is unobservable. We use the VIX for consider it observable, and use the Volatility Index: S\&P 500 VIX. This index was designed to measure volatility of S&P 500. We apply it to a different segment: Corporate bond markets. We fit time series models for spreads between corporate and 10-year Treasury bonds. Next, we divide residuals by VIX. Our main idea is such division makes residuals closer to the ideal case of a Gaussian white noise. This is remarkable, since these residuals and VIX come from separate market segments. We conclude with the analysis of long-term behavior of these models. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.22498 |
| By: | Philipp Gersing |
| Abstract: | We provide estimation and inference for the Generalised Dynamic Factor Model (GDFM) under the assumption that the dynamic common component can be expressed in terms of a finite number of lags of contemporaneously pervasive factors. The proposed estimator is simply an OLS regression of the observed variables on factors extracted via static principal components and therefore avoids frequency domain techniques entirely. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.20885 |
| By: | Daniele Ballinari; Alexander Wehrli |
| Abstract: | We introduce a double/debiased machine learning (DML) estimator for the impulse response function (IRF) in settings where a time series of interest is subjected to multiple discrete treatments, assigned over time, which can have a causal effect on future outcomes. The proposed estimator can rely on fully nonparametric relations between treatment and outcome variables, opening up the possibility to use flexible machine learning approaches to estimate IRFs. To this end, we extend the theory of DML from an i.i.d. to a time series setting and show that the proposed DML estimator for the IRF is consistent and asymptotically normally distributed at the parametric rate, allowing for semiparametric inference for dynamic effects in a time series setting. The properties of the estimator are validated numerically in finite samples by applying it to learn the IRF in the presence of serial dependence in both the confounder and observation innovation processes. We also illustrate the methodology empirically by applying it to the estimation of the effects of macroeconomic shocks. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.10009 |
| By: | Michal Koles\'ar; Mikkel Plagborg-M{\o}ller |
| Abstract: | Applied macroeconomists frequently use impulse response estimators motivated by linear models. We study whether the estimands of such procedures have a causal interpretation when the true data generating process is in fact nonlinear. We show that vector autoregressions and linear local projections onto observed shocks or proxies identify weighted averages of causal effects regardless of the extent of nonlinearities. By contrast, identification approaches that exploit heteroskedasticity or non-Gaussianity of latent shocks are highly sensitive to departures from linearity. Our analysis is based on new results on the identification of marginal treatment effects through weighted regressions, which may also be of interest to researchers outside macroeconomics. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.10415 |
| By: | Richard K. Crump; Nikolay Gospodinov; Ignacio Lopez Gaffney |
| Abstract: | We introduce a new regression diagnostic, tailored to time-series and panel-data regressions, which characterizes the sensitivity of the OLS estimate to distinct time-series variation at different frequencies. The diagnostic is built on the novel result that the eigenvectors of a random walk asymptotically orthogonalize a wide variety of time-series processes. Our diagnostic is based on leave-one-out OLS estimation on transformed variables using these eigenvectors. We illustrate how our diagnostic allows applied researchers to scrutinize regression results and probe for underlying fragility of the sample OLS estimate. We demonstrate the utility of our approach using a variety of empirical applications. |
| Keywords: | leave-one-out frequency approach; regression diagnostic; relative contributions of different frequencies; high time-series persistence and spurious regressions; trigonometric basis functions; orthogonalization |
| JEL: | C12 C13 C22 C23 |
| Date: | 2024–10–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:99063 |
| By: | Philipp Gersing |
| Abstract: | We consider the generalised dynamic factor model (GDFM) and assume that the dynamic common component is purely non-deterministic. We show that then the common shocks (and therefore the dynamic common component) can always be represented in terms of current and past observed variables. Hence, we further generalise existing results on the so called One-Sidedness problem of the GDFM. We may conclude that the existence of a one-sided representation that is causally subordinated to the observed variables is in the very nature of the GDFM and the lack of one-sidedness is an artefact of the chosen representation. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.18159 |