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on Econometric Time Series |
| By: | Zexuan Yin; Paolo Barucca |
| Abstract: | We propose Neural GARCH, a class of methods to model conditional heteroskedasticity in financial time series. Neural GARCH is a neural network adaptation of the GARCH 1,1 model in the univariate case, and the diagonal BEKK 1,1 model in the multivariate case. We allow the coefficients of a GARCH model to be time varying in order to reflect the constantly changing dynamics of financial markets. The time varying coefficients are parameterised by a recurrent neural network that is trained with stochastic gradient variational Bayes. We propose two variants of our model, one with normal innovations and the other with Students t innovations. We test our models on a wide range of univariate and multivariate financial time series, and we find that the Neural Students t model consistently outperforms the others. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.11285&r= |
| By: | Verena Monschang; Bernd Wilfling |
| Abstract: | We investigate mean-squared-forecast-error (MSE) accuracy improvements for linear-convex combination forecasts, whose components are pretreated by a procedure called 'Vector Autoregressive Forecast Error Modeling' (VAFEM). Assuming that the fore-cast-error series of the individual forecasts are governed by a stable VAR process under classic conditions, we obtain the following results: (i) VAFEM treatment bias-corrects all individual and linear-convex combination forecasts. (ii) Any VAFEM-treated combination has smaller theoretical MSE than its untreated analogue, if the VAR parameters are known. (iii) In empirical applications, VAFEM gains depend on (1) in-sample sizes, (2) out-of-sample forecast horizons, (3) the biasedness of the untreated forecast combination. We demonstrate the VAFEM capacity for realized-volatility forecasting, using S&P 500 data. |
| Keywords: | Combination forecasts, mean-squared-error loss, VAR forecast-error molding, multivariate least squares estimation |
| JEL: | C10 C32 C51 C53 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:cqe:wpaper:9722&r= |
| By: | Zongwu Cai (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA); Xiyuan Liu (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA) |
| Abstract: | In this article, we propose a vector autoregressive model for conditional quantiles with functional coefficients to construct a novel class of nonparametric dynamic network systems, of which the interdependences among tail risks such as Value-at-Risk are allowed to vary smoothly with a variable of general economy. Methodologically, we develop an easy-to-implement two-stage procedure to estimate functionals in the dynamic network system by the local linear smoothing technique. We establish the consistency and the asymptotic normality of the proposed estimator under strongly mixing time series settings. The simulation studies are conducted to show that our new methods work fairly well. The potential of the proposed estimation procedures is demonstrated by an empirical study of constructing and estimating a new type of nonparametric dynamic financial network. |
| Keywords: | Conditional quantile models; Dynamic financial network; Functional coefficient models; Nonparametric estimation; VAR modeling. |
| JEL: | C14 C58 C45 G32 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:202209&r= |
| By: | Thanasis Stengos (Department of Economics and Finance, University of Guelph, Guelph ON Canada); Theodore Panagiotidis (University of Macedonia); Georgios Papapanagiotou (University of Macedonia) |
| Abstract: | We perform a large-scale analysis to evaluate the performance of traditional and Markov-switching GARCH models for the volatility of 292 cryptocurrencies. For each cryptocurrency, we estimate a total of 27 alternative GARCH specifications. We consider models that allow up to three different regimes. First, the models are compared in terms of goodness-of-fit using the Deviance Information Criterion and the Bayesian Predictive Information Criterion. Next, we evaluate the ability of the models in forecasting one-day ahead conditional volatility and Value-at-Risk. The results indicate that for a wide range of cryptocurrencies, time-varying models outperform traditional ones. |
| Keywords: | Bitcoin, Cryptocurrency, Volatility, GARCH, Markov-switching, Information criteria |
| JEL: | C12 C13 C15 C22 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:gue:guelph:2022-02&r= |
| By: | Xu, Yongdeng (Cardiff Business School) |
| Abstract: | This paper proposes an Exponential HEAVY (EHEAVY) model. The model specifies the dynamics of returns and realized measures of volatility in an exponential form, which guarantees the positivity of volatility without restrictions on parameters and naturally allows the asymmetric effects. It provides a more flexible modelling of the volatility than the HEAVY models. A joint quasi-maximum likelihood estimation and closed form multi-step ahead forecasting is derived. The model is applied to 31 assets extracted from the Oxford-Man Institute's realized library. The empirical results show that the dynamic of return volatility is driven by the realized measure, while the asymmetric effect is captured by the return shock (not by the realized return shock). Hence, both return and realized measure are included in the return volatility equation. Out-of-sample forecast and portfolio exercise further shows the superior forecasting performance of the EHEAVY model, in both statistical and economic sense. |
| Keywords: | HEAVY model, High-frequency data, Asymmetric effects, Realized variance, Portfolio |
| JEL: | C32 C53 G11 G17 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:cdf:wpaper:2022/5&r= |
| By: | Baye Matar Kandji (1CREST, ENSAE, Institut Polytechnique de Paris) |
| Abstract: | The paper investigates the existence of a strictly stationary solution to an Iterated Function System (IFS) driven by a stationary and ergodic sequence. When the driving sequence is not independent, the strictly stationary solution may admit no moment but we show an exponen- tial control of the trajectories. We exploit these results to prove, under mild conditions, the consistency of the quasi-maximum likelihood es- timator of GARCH models with non independent innovations. |
| Keywords: | Stochastic Recurrence Equation, Semi-strong GARCH, Quasi Maximum Likelihood, inference without moments |
| Date: | 2022–01–26 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2022-03&r= |
| By: | Tae-Hwy Lee (Department of Economics, University of California Riverside); Shahnaz Parsaeian (University of Kansas); Aman Ullah (University of California Riverside) |
| Abstract: | This paper develops an optimal combined estimator to forecast out-of-sample under structural breaks. When it comes to forecasting, using only the post-break observations after the most recent break point may not be optimal. In this paper we propose a new estimation method that exploits the pre-break information. In particular, we show how to combine the estimator using the full-sample (i.e., both the pre-break and post-break data) and the estimator using only the post-break sample. The full-sample estimator is inconsistent when there is a break while it is efficient. The post-break estimator is consistent but inefficient. Hence, depending on the severity of the breaks, the full-sample estimator and the post-break estimator can be combined to balance the consistency and efficiency. We derive the Stein-like combined estimator of the full-sample and the post-break estimators, to balance the bias-variance trade-off. The combination weight depends on the break severity, which we measure by the Wu-Hausman statistic. We examine the properties of the proposed method, analytically in theory, numerically in simulation, and also empirically in forecasting real output growth across nine industrial economies. |
| Keywords: | Forecasting, Structural breaks, Stein-like combined estimator, Output growth |
| JEL: | C13 C32 C53 |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:202208&r= |