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on Econometric Time Series |
| By: | Silvia Goncalves; Ana María Herrera; Lutz Kilian; Elena Pesavento |
| Abstract: | Do state-dependent local projections asymptotically recover the population responses of macroeconomic aggregates to structural shocks? The answer to this question depends on how the state of the economy is determined and on the magnitude of the shocks. When the state is exogenous, the local projection estimator recovers the population response regardless of the shock size. When the state depends on macroeconomic shocks, as is common in empirical work, local projections only recover the conditional response to an infinitesimal shock, but not the responses to larger shocks of interest in many applications. Simulations suggest that fiscal multipliers may be off by as much as 40 percent. |
| Keywords: | local projections; business cycle; state-dependence; impulse response; multiplier; nonlinear structural model; potential outcomes model |
| JEL: | C22 C32 H20 C51 E32 E52 E60 E62 |
| Date: | 2023–04–19 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddwp:96045&r=ets |
| By: | Christis Katsouris |
| Abstract: | In this paper, we study the estimation of the threshold predictive regression model with hybrid stochastic local unit root predictors. We demonstrate the estimation procedure and derive the asymptotic distribution of the least square estimator and the IV based estimator proposed by \cite{magdalinos2009limit}, under the null hypothesis of a diminishing threshold effect. Simulation experiments focus on the finite sample performance of our proposed estimators and the corresponding predictability tests as in \cite{gonzalo2012regime}, under the presence of threshold effects with stochastic local unit roots. An empirical application to stock return equity indices, illustrate the usefulness of our framework in uncovering regimes of predictability during certain periods. In particular, we focus on an aspect not previously examined in the predictability literature, that is, the effect of economic policy uncertainty. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.00860&r=ets |
| By: | Luis J. Álvarez (Banco de España); Florens Odendahl (Banco de España) |
| Abstract: | We propose a method to adjust for data outliers in Bayesian Vector Autoregressions (BVARs), which allows for different outlier magnitudes across variables and rescales the reduced form error terms. We use the method to document several facts about the effect of outliers on estimation and out-of-sample forecasting results using euro area macroeconomic data. First, the COVID-19 pandemic led to large swings in macroeconomic data that distort the BVAR estimation results. Second, these swings can be addressed by rescaling the shocks’ variance. Third, taking into account outliers before 2020 leads to mild improvements in the point forecasts of BVARs for some variables and horizons. However, the density forecast performance considerably deteriorates. Therefore, we recommend taking into account outliers only on pre-specified dates around the onset of the COVID-19 pandemic. |
| Keywords: | COVID-19 pandemic, outliers, Bayesian VARs, forecasting, euro area |
| JEL: | C11 C32 C51 E37 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:bde:wpaper:2239&r=ets |
| By: | Paulo M.M. Rodrigues; João Nicolau; Marian Z. Stoykov |
| Abstract: | This paper provides novel theoretical results for the estimation of the conditional tail index of Pareto and Pareto-type distributions in a time series context. We show that both the estimators and relevant test statistics are normally distributed in the limit, when independent and identically distributed or dependent data are considered. Simulation results provide support for the theoretical findings and highlight the good finite sample properties of the approach in a time series context. The proposed methodology is then used to analyze stock returns’ tail risk dynamics. Two empirical applications are provided. The first consists in testing whether the time-varying tail exponents across firms follow Kelly and Jiang’s (2014) assumption of common firm level tail dynamics. The results obtained from our sample seem not to favour this hypothesis. The second application, consists of the evaluation of the impact of two market risk indicators, VIX and Expected Shortfall (ES) and two firm specific covariates, capitalization and market-to-book on stocks tail risk dynamics. Although all variables seem important drivers of firms’ tail risk dynamics, it is found that overall ES and firms’ capitalization seem to have overall wider impact. |
| JEL: | C22 C58 G12 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w202306&r=ets |
| By: | Baye Matar Kandji (CREST, ENSAE, Institut Polytechnique de Paris) |
| Abstract: | We extend the result of Kesten (Proc. Am. Math. Soc., 49:205- 211, 1975) on the growth rate of random walks with stationary increments to superadditive processes. We show that superadditive processes which remain positive after a certain time diverge at least linearly to infinity. Our proof relies on new techniques based on concepts from ergodic theory. Different versions of this result are also given, generalizing Lemma 3.4 of Bougerol and Picard (Ann. Probab., 20:1714-1730, 1992) on the contraction property of products of random matrices. We use our results to provide necessary and sufficient conditions for the stability of a class of Stochastic Recurrent Equations (SRE) with positive coefficients in the space of continuous functions with compact support, including continuous functional GARCH models. |
| Keywords: | Ergodic theorem Contraction property, functional Garch, Lyapunov exponent, Stochastic Recurrence Equation, Strict stationarity, Subadditive sequence. |
| Date: | 2023–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2023-07&r=ets |
| By: | Mohamed Hamdouche (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité); Pierre Henry-Labordere (Qube RT); Huyên Pham (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité) |
| Abstract: | We propose a novel generative model for time series based on Schrödinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We can estimate the drift function from data samples either by kernel regression methods or with LSTM neural networks, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with a toy autoregressive model, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal and temporal dependencies metrics. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets. Finally, we illustrate the SB approach for generating sequence of images. |
| Keywords: | generative models, time series, Schrödinger bridge, kernel estimation, deep hedging |
| Date: | 2023–04–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-04063041&r=ets |
| By: | Carsten H. Chong; Viktor Todorov |
| Abstract: | We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the conditional characteristic function of the price increment until the options' expiration and we use these estimates to recover spot volatility. Our volatility of volatility estimator is then formed from the sample variance and first-order autocovariance of the spot volatility increments, with the latter correcting for the bias in the former due to option observation errors. The leverage effect estimator is the sample covariance between price increments and the estimated volatility increments. The rate of convergence of the estimators depends on the diffusive innovations in the latent volatility process as well as on the observation error in the options with strikes in the vicinity of the current spot price. Feasible inference is developed in a way that does not require prior knowledge of the source of estimation error that is asymptotically dominating. |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.04137&r=ets |
| By: | Cheng Zhang; Nilam Nur Amir Sjarif; Roslina Binti Ibrahim |
| Abstract: | Forecasting financial time series has long been a challenging problem that has attracted attention from both researchers and practitioners. Statistical and machine learning techniques have both been explored to develop effective forecasting models in the past few decades. With recent developments in deep learning models, financial time series forecasting models have advanced significantly, and these developments are often difficult to keep up with. Hence, we have conducted this literature review to provide a comprehensive assessment of recent research from 2020 to 2022 on deep learning models used to predict prices based on financial time series. Our review presents different data sources and neural network structures, as well as their implementation details. Our goals are to ensure that interested researchers remain up-to-date on recent developments in the field and facilitate the selection of baselines based on models used in prior studies. Additionally, we provide suggestions for future research based on the content in this review. |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2305.04811&r=ets |
| By: | Lutz Kilian; Michael D. Plante; Alexander W. Richter |
| Abstract: | This paper clarifies the conditions under which the state-of-the-art approach to identifying TFP news shocks in Kurmann and Sims (2021, KS) identifies not only news shocks but also surprise shocks. We examine the ability of the KS procedure to recover responses to these shocks from data generated by a conventional New Keynesian DSGE model. Our analysis shows that the KS response estimator tends to be strongly biased even in the absence of measurement error. This bias worsens in realistically small samples, and the estimator becomes highly variable. Incorporating a direct measure of TFP news into the model and adapting the identification strategy accordingly removes this asymptotic bias and greatly reduces the RMSE when TFP news are correctly measured. However, the high variability of this alternative estimator in small samples suggests caution in interpreting empirical estimates. We examine to what extent empirical estimates of the responses to news and surprise shocks from a range of VAR models based on alternative measures of TFP news are economically plausible. |
| Keywords: | Structural VAR; total factor productivity (TFP); productivity shock; news; expectation |
| JEL: | C32 C51 C61 E32 |
| Date: | 2023–04–20 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddwp:96048&r=ets |