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on Econometric Time Series |
| By: | Cavaliere, Giuseppe; De Angelis, Luca; Rahbek, Anders; Taylor, A M Robert |
| Abstract: | We investigate the asymptotic and finite sample properties of a number of methods for estimating the cointegration rank in integrated vector autoregressive systems of unknown autoregressive order driven by heteroskedastic shocks. We allow for both conditional and unconditional heteroskedasticity of a very general form. We establish the conditions required on the penalty functions such that standard information criterion-based methods, such as the Bayesian information criterion [BIC], when employed either sequentially or jointly, can be used to consistently estimate both the cointegration rank and the autoregressive lag order. In doing so we also correct errors which appear in the proofs provided for the consistency of information-based estimators in the homoskedastic case by Aznar and Salvador (2002). We also extend the corpus of available large sample theory for the conventional sequential approach of Johansen (1995) and the associated wild bootstrap implementation thereof of Cavaliere, Rahbek and Taylor (2014) to the case where the lag order is unknown. In particular, we show that these methods remain valid under heteroskedasticity and an unknown lag length provided the lag length is first chosen by a consistent method, again such as the BIC. The relative finite sample properties of the different methods discussed are investigated in a Monte Carlo simulation study. The two best performing methods in this study are a wild bootstrap implementation of the Johansen (1995) procedure implemented with BIC selection of the lag length and joint IC approach (cf. Phillips, 1996) which uses the BIC to jointly select the lag order and the cointegration rank. |
| Keywords: | Cointegration rank; Information criteria; Wild bootstrap; Trace statistic; Lag length; Heteroskedasticity |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:17454&r=ets |
| By: | Amir-Ahmadi, Pooyan (Gothe University Frankfurt); Matthes, Christian (Federal Reserve Bank of Richmond); Wang, Mu-Chun (University of Hamburg) |
| Abstract: | Bayesian inference is common in models with many parameters, such as large VAR models, models with time-varying parameters, or large DSGE models. A common practice is to focus on prior distributions that themselves depend on relatively few hyperparameters. The choice of these hyperparameters is crucial because their influence is often sizeable for standard sample sizes. In this paper we treat the hyperparameters as part of a hierarchical model and propose a fast, tractable, easy-to-implement, and fully Bayesian approach to estimate those hyperparameters jointly with all other parameters in the model. In terms of applications, we show via Monte Carlo simulations that in time series models with time-varying parameters and stochastic volatility, our approach can drastically improve on using fixed hyperparameters previously proposed in the literature. |
| Date: | 2016–08–23 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedrwp:16-09&r=ets |
| By: | Manabu Asai (Soka University, Japan); Michael McAleer (National Tsing Hua University Taiwan; Erasmus School of Economics Erasmus University Rotterdam, The Netherlands; Yokohama National University, Japan) |
| Abstract: | The paper derives a Multivariate Asymmetric Long Memory conditional volatility model with Exogenous Variables (X), or the MALMX model, with dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. The underlying vector random coefficient autoregressive process, which has well established regularity conditions and associated asymptotic properties, is discussed, and a simple explanation is given as to why only the diagonal BEKK model, and not the Hadamard, triangular or full BEKK models, has regularity conditions and asymptotic properties. Various special cases, including the diagonal BEKK model of Baba et al. (1985) and Engle and Kroner (1995), VARMA-GARCH model of Ling and McAleer (2003), and VARMA-AGARCH model of McAleer et al. (2009), are discussed. There does not seem to have been a derivation of a univariate conditional volatility model with exogenous variables (X) that has dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. Therefore, the derivation of a multivariate conditional volatility model with exogenous variables (X) that has regularity conditions and asymptotic theory would seem to be a significant extension of the existing literature. |
| Keywords: | Multivariate conditional volatility; Vector random coefficient autoregressive process; Asymmetry; Long memory; Exogenous variables; Dynamic conditional correlations; Regularity conditions; Asymptotic properties |
| JEL: | C22 C52 C58 G32 |
| Date: | 2016–08–29 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20160065&r=ets |