|
on Econometric Time Series |
| By: | Gabriel, Stefan (University of Vienna, Department of Finance, Vienna, Austria); Kunst, Robert M. (Institute for Advanced Studies and University of Vienna, Vienna, Austria) |
| Abstract: | We examine two major topics in the field of cryptocurrencies. On the one hand, we investigate possible long-run equilibrium relationships among ten major cryptocurrencies by applying two different cointegration tests. This analysis aims at constructing cointegrated portfolios that enable statistical arbitrage. Moreover, we find evidence for a connection between market volatility and the spread used for trading. The results of the trading strategies suggest that cointegrated portfolios based on the Johansen procedure generate the highest abnormal log-returns, both in-sample and out-of-sample. Five out of six trading strategies generate a positive overall profit and outperform a passive investment approach out-of-sample. The second part of the econometric analysis explores Granger causality between volatility and the spread. For this analysis, we implement two types of forecasting models for Bitcoin volatility: the GARCH (generalized autoregressive conditional heteroskedasticity) family using daily price data and the HAR (Heterogeneous AutoRegressive) model family based on 5-min high-frequency data. In both categories, we also consider potential jumps in the price series, as we found that price jumps play an important role in Bitcoin volatility forecasts. The findings indicate that the realized GARCH model is the only GARCH model that can compete against the HAR-RV (Heterogeneous Autoregressive Realized Volatility) model in out-of-sample forecasting. |
| Keywords: | cryptocurrencies, bitcoin volatility, realized variance, jump variation, cointegrated portfolios, statistical arbitrage |
| JEL: | C22 C52 C53 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihswps:52&r=ets |
| By: | Jonas E. Arias; Juan F. Rubio-Ramirez; Minchul Shin; Daniel F. Waggoner |
| Abstract: | We propose an approach for Bayesian inference in time-varying SVARs identified with sign restrictions. The linchpin of our approach is a class of rotation-invariant time-varying SVARs in which the prior and posterior densities of any sequence of structural parameters belonging to the class are invariant to orthogonal transformations of the sequence. Our methodology is new to the literature. In contrast to existing algorithms for inference based on sign restrictions, our algorithm is the first to draw from a uniform distribution over the sequences of orthogonal matrices given the reduced-form parameters. We illustrate our procedure for inference by analyzing the role played by monetary policy during the latest inflation surge |
| Keywords: | time-varying parameters; structural vector autoregressions; identification |
| JEL: | C11 C51 E52 E58 |
| Date: | 2024–02–27 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedpwp:97853&r=ets |
| By: | Steven Y. K. Wong; Jennifer S. K. Chan; Lamiae Azizi |
| Abstract: | Time-series with time-varying variance pose a unique challenge to uncertainty quantification (UQ) methods. Time-varying variance, such as volatility clustering as seen in financial time-series, can lead to large mismatch between predicted uncertainty and forecast error. Building on recent advances in neural network UQ literature, we extend and simplify Deep Evidential Regression and Deep Ensembles into a unified framework to deal with UQ under the presence of volatility clustering. We show that a Scale Mixture Distribution is a simpler alternative to the Normal-Inverse-Gamma prior that provides favorable complexity-accuracy trade-off. To illustrate the performance of our proposed approach, we apply it to two sets of financial time-series exhibiting volatility clustering: cryptocurrencies and U.S. equities. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.14476&r=ets |
| By: | Guglielmo Maria Caporale; Luis Alberiko Gil-Alana |
| Abstract: | This paper proposes a long-memory model including multiple cycles in addition to the long-run component. Specifically, instead of a single pole or singularity in the spectrum, it allows for multiple poles and thus different cycles with different degrees of persistence. It also incorporates non-linear deterministic structures in the form of Chebyshev polynomials in time. Simulations are carried out to analyse the finite sample properties of the proposed test, which is shown to perform well in the case of a relatively large sample with at least 1000 observations. The model is then applied to weekly data on the S&P500 from 1 January 1970 to 26 October 2023 as an illustration. The estimation results based on the first differenced logged values (i.e., the returns) point to the existence of three cyclical structures in the series with a length of approximately one month, one year and four years respectively, and to orders of integration in the range (0, 0.20), which implies stationary long memory in all cases. |
| Keywords: | fractional integration, multiple cycles, stock market indices, S&P500 |
| JEL: | C22 C15 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10947&r=ets |
| By: | Alexander Mayer; Dominik Wied; Victor Troster |
| Abstract: | We propose a new framework for assessing Granger causality in quantiles in unstable environments, for a fixed quantile or over a continuum of quantile levels. Our proposed test statistics are consistent against fixed alternatives, they have nontrivial power against local alternatives, and they are pivotal in certain important special cases. In addition, we show the validity of a bootstrap procedure when asymptotic distributions depend on nuisance parameters. Monte Carlo simulations reveal that the proposed test statistics have correct empirical size and high power, even in absence of structural breaks. Finally, two empirical applications in energy economics and macroeconomics highlight the applicability of our method as the new tests provide stronger evidence of Granger causality. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.09744&r=ets |
| By: | Zhang, Xinyu; Li, Dong; Tong, Howell |
| Abstract: | Most threshold models to-date contain a single threshold variable. However, in many empirical applications, models with multiple threshold variables may be needed and are the focus of this article. For the sake of readability, we start with the Two-Threshold-Variable Autoregressive (2-TAR) model and study its Least Squares Estimation (LSE). Among others, we show that the respective estimated thresholds are asymptotically independent. We propose a new method, namely the weighted Nadaraya-Watson method, to construct confidence intervals for the threshold parameters, that turns out to be, as far as we know, the only method to-date that enjoys good probability coverage, regardless of whether the threshold variables are endogenous or exogenous. Finally, we describe in some detail how our results can be extended to the K-Threshold-Variable Autoregressive (K-TAR) model, K > 2. We assess the finite-sample performance of the LSE by simulation and present two real examples to illustrate the efficacy of our modeling. |
| Keywords: | compound Poisson process; degeneracy of a spatial process; multiple threshold variables; TAR model; weighted Nadaraya-Watson method |
| JEL: | C1 |
| Date: | 2023–02–23 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:118377&r=ets |
| By: | Juan Carlos Escanciano; Ricardo Parra |
| Abstract: | Though out-of-sample forecast evaluation is systematically employed with modern machine learning methods and there exists a well-established classic inference theory for predictive ability, see, e.g., West (1996, Asymptotic Inference About Predictive Ability, \textit{Econometrica}, 64, 1067-1084), such theory is not directly applicable to modern machine learners such as the Lasso in the high dimensional setting. We investigate under which conditions such extensions are possible. Two key properties for standard out-of-sample asymptotic inference to be valid with machine learning are (i) a zero-mean condition for the score of the prediction loss function; and (ii) a fast rate of convergence for the machine learner. Monte Carlo simulations confirm our theoretical findings. For accurate finite sample inferences with machine learning, we recommend a small out-of-sample vs in-sample size ratio. We illustrate the wide applicability of our results with a new out-of-sample test for the Martingale Difference Hypothesis (MDH). We obtain the asymptotic null distribution of our test and use it to evaluate |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.12838&r=ets |