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on Econometric Time Series |
| By: | Jonas Krampe; Luca Margaritella |
| Abstract: | We reconcile the two worlds of dense and sparse modeling by exploiting the positive aspects of both. We employ a dynamic factor model and assume the idiosyncratic term follows a sparse vector autoregressive model (VAR) which allows for cross-sectional and time dependence. The estimation is articulated in two steps: first, the factors and their loadings are estimated via principal component analysis and second, the sparse VAR is estimated by regularized regression on the estimated idiosyncratic components. We prove consistency of the proposed estimation approach as the time and cross-sectional dimension diverge. In the second step, the estimation error of the first step needs to be accounted for. Here, we do not follow the naive approach of simply plugging in the standard rates derived for the factor estimation. Instead, we derive a more refined expression of the error. This enables us to derive tighter rates. We discuss the implications to forecasting and semi-parametric estimation of the inverse of the spectral density matrix and we complement our procedure with a joint information criteria for the VAR lag-length and the number of factors. The finite sample performance is illustrated by means of an extensive simulation exercise. Empirically, we assess the performance of the proposed method for macroeconomic forecasting using the FRED-MD dataset. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.07149&r= |
| By: | Kumar Yashaswi |
| Abstract: | The use of Bayesian filtering has been widely used in mathematical finance, primarily in Stochastic Volatility models. They help in estimating unobserved latent variables from observed market data. This field saw huge developments in recent years, because of the increased computational power and increased research in the model parameter estimation and implied volatility theory. In this paper, we design a novel method to estimate underlying states (volatility and risk) from option prices using Bayesian filtering theory and Posterior Cramer-Rao Lower Bound (PCRLB), further using it for option price prediction. Several Bayesian filters like Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF) are used for latent state estimation of Black-Scholes model under a GARCH model dynamics. We employ an Average and Best case switching strategy for adaptive state estimation of a non-linear, discrete-time state space model (SSM) like Black-Scholes, using PCRLB based performance measure to judge the best filter at each time step [1]. Since estimating closed-form solution of PCRLB is non-trivial, we employ a particle filter based approximation of PCRLB based on [2]. We test our proposed framework on option data from S$\&$P 500, estimating the underlying state from the real option price, and using it to estimate theoretical price of the option and forecasting future prices. Our proposed method performs much better than the individual applied filter used for estimating the underlying state and substantially improve forecasting capabilities. |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2112.03193&r= |
| By: | Pan, Jingwei |
| Abstract: | The dissertation consists of three studies concerning the research fields of evaluating volatility and correlation forecasts as well as modeling of tail dependence. Based on theoretical discussions and empirical studies the methods for modeling the time-varying volatilities and dependence for the financial market data are evaluated. The first study evaluates the volatility forecasts with the basic generalized conditional autoregressive heteroskedasticity (GARCH) model and its asymmetric extensions. The concepts of loss function and model confidence set (MCS) are introduced. The realized volatility is used as benchmark. The main results of Brownlees et al. (2011) can be confirmed and extended. In particular, the one-step forecasts achieve significantly lower average losses than the multi-step forecasts in times of crises. The difference between the one-step and the multi-step forecasts in pre-crisis times is relatively small. The evaluation results demonstrate the strong forecasting performance of the asymmetric model variants. The second study evaluates the multivariate correlation forecasts. The Baba-Engle-Kraft-Kroner (BEKK) model of Engle and Kroner (1995) is compared with the dynamic conditional correlation (DCC) model of Engle (2002). Using a two-stage estimation method, the DCC model is well suited for large correlation matrices. In contrast, the more flexible BEKK model suffers from the curse of dimensionality. The evaluation is based on the class of asymmetric loss functions proposed by Komunjer and Owyang (2012). The results show that the BEKK model cannot better predict the correlations than the simpler DCC model in the trivariate system. Therefore, the application of the DCC model appears to be superior. The third study leads to a flexible approach which separates the univariate marginal distributions from the joint distribution. The different copula functions are presented and the corresponding tail dependence is calculated. The empirical analysis compares different copula functions with a non-parametric approach and three time-dependent approaches. The results show noticeable reactions of tail dependence to the major financial market events. In addition, the lower tail dependence dominates over time. This can be interpreted in a way that joint losses occur more frequently than joint gains. |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:dar:wpaper:129944&r= |
| By: | Damir Filipović (Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute); Amir Khalilzadeh (Ecole Polytechnique Fédérale de Lausanne) |
| Abstract: | We use machine learning methods to predict stock return volatility. Our out-of-sample prediction of realised volatility for a large cross-section of US stocks over the sample period from 1992 to 2016 is on average 44.1% against the actual realised volatility of 43.8% with an R2 being as high as double the ones reported in the literature. We further show that machine learning methods can capture the stylized facts about volatility without relying on any assumption about the distribution of stock returns. Finally, we show that our long short-term memory model outperforms other models by properly carrying information from the past predictor values. |
| Keywords: | Volatility Prediction, Volatility Clustering, LSTM, Neural Networks, Regression Trees. |
| JEL: | C51 C52 C53 C58 G17 |
| Date: | 2021–12 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2195&r= |