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on Econometric Time Series |
| By: | Loïc Cantin (CREST, 5 Avenue Henri Le Chatelier, 91120 Palaiseau, France); Christian Francq (CREST, 5 Avenue Henri Le Chatelier, 91120 Palaiseau, France); Jean-Michel Zakoïan (CREST, 5 Avenue Henri Le Chatelier, 91120 Palaiseau, France) |
| Abstract: | We propose a two-step semi-parametric estimation approach for dynamic Conditional VaR (CoVaR), from which other important systemic risk measures such as the Delta-CoVaR can be derived. The CoVaR allows to define reserves for a given financial entity, in order to limit exceeding losses when a system is in distress. We assume that all financial returns in the system follow semi-parametric GARCH-type models. Our estimation method relies on the fact that the dynamic CoVaR is the product of the volatility of the financial entity’s return and a conditional quantile term involving the innovations of the different returns. We show that the latter quantity can be easily estimated from residuals of the GARCH-type models estimated by Quasi-Maximum Likelihood (QML). The study of the asymptotic behaviour of the corresponding estimator and the derivation of asymptotic confidence intervals for the dymanic CoVaR are the main purposes of the paper. Our theoretical results are illustrated via Monte-Carlo experiments and real financial time series. |
| Keywords: | conditional CoVaR and Delta-CoVaR, empirical distribution of bivariate residuals, model-free estimation risk, multivariate risks. |
| Date: | 2022–01–24 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2022-11&r= |
| By: | Wichert, Oliver (Tilburg University, School of Economics and Management) |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiutis:f926ab90-382b-4aa5-9532-86f937dc5fa1&r= |
| By: | Silvia Goncalves; Ana María Herrera; Lutz Kilian; Elena Pesavento |
| Abstract: | Many empirical studies estimate impulse response functions that depend on the state of the economy. Most of these studies rely on a variant of the local projection (LP) approach to estimate the state-dependent impulse response functions. Despite its widespread application, the asymptotic validity of the LP approach to estimating state-dependent impulse responses has not been established to date. We formally derive this result for a structural state-dependent vector autoregressive process. The model only requires the structural shock of interest to be identified. A sufficient condition for the consistency of the state-dependent LP estimator of the response function is that the first- and second-order conditional moments of the structural shocks are independent of current and future states, given the information available at the time the shock is realized. This rules out models in which the state of the economy is a function of current or future realizations of the outcome variable of interest, as is often the case in applied work. Even when the state is a function of past values of this variable only, consistency may hold only at short horizons. |
| Keywords: | local projection; state-dependent impulse responses; threshold; identification; nonlinear VAR |
| JEL: | C22 C32 C51 |
| Date: | 2022–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddwp:94175&r= |
| By: | Reisenhofer, Rafael; Bayer, Xandro; Hautsch, Nikolaus |
| Abstract: | Despite the impressive success of deep neural networks in many application areas, neural network models have so far not been widely adopted in the context of volatility forecasting. In this work, we aim to bridge the conceptual gap between established time series approaches, such as the Heterogeneous Autoregressive (HAR) model (Corsi, 2009), and state-of-the-art deep neural network models. The newly introduced HARNet is based on a hierarchy of dilated convolutional layers, which facilitates an exponential growth of the receptive field of the model in the number of model parameters. HARNets allow for an explicit initialization scheme such that before optimization, a HARNet yields identical predictions as the respective baseline HAR model. Particularly when considering the QLIKE error as a loss function, we find that this approach significantly stabilizes the optimization of HARNets. We evaluate the performance of HARNets with respect to three different stock market indexes. Based on this evaluation, we formulate clear guidelines for the optimization of HARNets and show that HARNets can substantially improve upon the forecasting accuracy of their respective HAR baseline models. In a qualitative analysis of the filter weights learnt by a HARNet, we report clear patterns regarding the predictive power of past information. Among information from the previous week, yesterday and the day before, yesterday's volatility makes by far the most contribution to today's realized volatility forecast. Moroever, within the previous month, the importance of single weeks diminishes almost linearly when moving further into the past. |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cfswop:680&r= |
| By: | Urga, Giovanni; Wang, Fa |
| Abstract: | This paper proposes maximum (quasi)likelihood estimation for high dimensional factor models with regime switching in the loadings. The model parameters are estimated jointly by EM algorithm, which in the current context only requires iteratively calculating regime probabilities and principal components of the weighted sample covariance matrix. When regime dynamics are taken into account, smoothed regime probabilities are calculated using a recursive algorithm. Consistency, convergence rates and limit distributions of the estimated loadings and the estimated factors are established under weak cross-sectional and temporal dependence as well as heteroscedasticity. It is worth noting that due to high dimension, regime switching can be identified consistently right after the switching point with only one observation. Simulation results show good performance of the proposed method. An application to the FRED-MD dataset demonstrates the potential of the proposed method for quick detection of business cycle turning points. |
| Keywords: | Factor model, Regime switching, Maximum likelihood, High dimension, EM algorithm, Turning points |
| JEL: | C13 C38 C55 |
| Date: | 2022–05–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:113172&r= |
| By: | Meenagh, David (Cardiff Business School); Minford, Patrick (Cardiff Business School); Xu, Yongdeng (Cardiff Business School) |
| Abstract: | Maximum Likelihood (ML) shows both lower power and higher bias in small sample Monte Carlo experiments than Indirect Inference (II) and IIís higher power comes from its use of the model-restricted distribution of the auxiliary model coefficients (Le et al. 2016). We show here that IIís higher power causes it to have lower bias, because false parameter values are rejected more frequently under II; this greater rejection frequency is partly offset by a lower tendency for ML to choose unrejected false parameters as estimates, due again to its lower power allowing greater competition from rival unrejected parameter sets. |
| Keywords: | Bias, Indirect Inference, Maximum Likelihood |
| JEL: | C12 C32 C52 |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:cdf:wpaper:2022/10&r= |
| By: | Agrippino, Silvia Miranda (Bank of England); Ricco, Giovanni (University of Warwick) |
| Abstract: | IV methods have become the leading approach to identify the effects of macroeconomic shocks. Conditions for identification generally involve all the shocks in the VAR even when only a subset of them is of interest. This paper provides more general conditions that only involve the shocks of interest and the properties of the instrument of choice. We introduce a heuristic and a formal test to guide the specification of the empirical models, and provide formulas for the bias when the conditions are violated. We apply our results to the study of the transmission of conventional and unconventional monetary policy shocks. |
| Keywords: | Identification with external instruments; structural VAR; invertibility; monetary policy shocks |
| JEL: | C32 C36 E30 E52 |
| Date: | 2022–04–14 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0973&r= |