1,720,988 research outputs found
Mildly explosive autoregression under weak and strong dependence
No full textA limit theory is developed for mildly explosive autoregression under both weakly and strongly dependent innovation errors. The asymptotic behaviour of the sample moments is affected by the memory of the innovation process both in the form of the limiting distribution and, in the case of long range dependence, in the rate of convergence. However, this effect is not present in least squares regression theory as it is cancelled out by the interaction between the sample moments. As a result, the Cauchy regression theory of Phillips and Magdalinos (2007a) is invariant to the dependence structure of the innovation sequence
On the inconsistency of the unrestricted estimator of the information matrix near a unit root
No full textThe unrestricted estimator of the information matrix is shown to be inconsistent for an autoregressive process with a root lying in a neighbourhood of unity with radial length proportional or smaller than n−1, i.e. a root that takes the form ρ= 1 +c/nα,α≥ 1. In this case the information evaluated at graphic converges to a non‐degenerate random variable and contributes to the asymptotic distribution of a Wald test for the null hypothesis of a random walk versus a stable AR(1) alternative. With this newly derived asymptotic distribution, the above Wald test is found to improve its performance. A non‐local criterion of asymptotic relative efficiency based on Bahadur slopes has been employed for the first time to the problem of unit root testing. The Wald test derived in the paper is found to be as efficient as the Dickey Fuller t ratio test and to outperform the non‐studentised Dickey Fuller test and a Lagrange Multiplier test
Least squares and IVX limit theory in systems of predictive regressions with GARCH innovations
No full textThe paper examines the effect of conditional heteroskedasticity on least squares inference in stochastic regression models of unknown integration order and proposes an inference procedure that is robust to models within the (near) I(0)-(near) I(1) range with GARCH innovations. We show that a regressor signal of exact order Op (mκn) for arbitrary κn → ∞ is sufficient to eliminate stationary GARCH effects from the limit distributions of least squares based estimators and self-normalized test statistics. The above order dominates the Op (n) signal of stationary regressors but may be dominated by the Op (n2) signal of I(1) regressors, thereby showing that least squares invariance to GARCH effects is not an exclusively I(1) phenomenon but extends to processes with persistence degree arbitrarily close to stationarity. The theory validates standard inference for self normalized test statistics based on the ordinary least squares estimator when κn → ∞ and κn/n → 0 and the IVX estimator (Phillips and Magdalinos (2009a), Econometric Inference in the Vicinity of Unity. Working paper, Singapore Management University; Kostakis, Magdalinos, and Stamatogiannis, 2015a, Review of Financial Studies 28(5), 1506-1553.) when κn → ∞ and the innovation sequence of the system is a covariance stationary vec-GARCH process. An adjusted version of the IVX-Wald test is shown to also accommodate GARCH effects in purely stationary regressors, thereby extending the procedure's validity over the entire (near) I(0)-(near) I(1) range of regressors under conditional heteroskedasticity in the innovations. It is hoped that the wide range of applicability of this adjusted IVX-Wald test, established in Theorem 4.4, presents an advantage for the procedure's suitability as a tool for applied research.</p
Problems and solutions: The characteristic function of a family of truncated normal distributions
No full textMildly explosive autoregression under stationary conditional heteroskedasticity
No full textA limit theory is developed for mildly explosive autoregressions under stationary (weakly or strongly dependent) conditionally heteroskedastic errors. The conditional variance process is allowed to be stationary, integrable and mixingale, thus encompassing general classes of GARCH type or stochastic volatility models. No mixing conditions nor moments of higher order than 2 are assumed for the innovation process. As in Magdalinos (2012), we find that the asymptotic behaviour of the sample moments is affected by the memory of the innovation process both in the form of the limiting distribution and, in the case of long range dependence, the rate of convergence, while conditional heteroskedasticity affects only the asymptotic variance. These effects are cancelled out in least squares regression theory and thereby the Cauchy limit theory of Phillips and Magdalinos (2007a) remains invariant to a wide class of stationary conditionally heteroskedastic innovations processes
Bayesian learning under non-stationary dependence
No full textWe study limit beliefs in a learning-by-experimentation environment where: (a) givenan opportunity for experimentation, an agent decides to experiment if past experimen-tation is below a history-dependent threshold; (b) an experimentation opportunity ariseswith a conditional probability that is non-decreasing in the extent of past experimenta-tion; (c) the degree of monotonicity in (b) is governed by a parameter which is unknownto a Bayesian agent making inferences based on observed history. Since experimentationopportunities are dependent and heterogeneously distributed random variables with sam-ple moments that do not necessarily concentrate around their population counterparts,the usual techniques for establishing asymptotic learning based on laws of large numberscannot be used. We overcome this difficulty by establishing a novela.s.positive asymp-totic lower bound for the sample mean of experimentation opportunities. We can thusestablish that asymptotic learning of the true value of the initially unknown parameteroccurs, with convergence of posterior beliefs taking place at an exponential rate
- …
