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1 – 6 of 6Xiaohu Wang, Weilin Xiao and Jun Yu
This chapter derives asymptotic properties of the least squares (LS) estimator of the autoregressive (AR) parameter in local to unity processes with errors being fractional…
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This chapter derives asymptotic properties of the least squares (LS) estimator of the autoregressive (AR) parameter in local to unity processes with errors being fractional Gaussian noise (FGN) with the Hurst parameter
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Nikolay Gospodinov, Alex Maynard and Elena Pesavento
It is widely documented that while contemporaneous spot and forward financial prices trace each other extremely closely, their difference is often highly persistent and the…
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It is widely documented that while contemporaneous spot and forward financial prices trace each other extremely closely, their difference is often highly persistent and the conventional cointegration tests may suggest lack of cointegration. This chapter studies the possibility of having cointegrated errors that are characterized simultaneously by high persistence (near-unit root behavior) and very small (near zero) variance. The proposed dual parameterization induces the cointegration error process to be stochastically bounded which prevents the variables in the cointegrating system from drifting apart over a reasonably long horizon. More specifically, this chapter develops the appropriate asymptotic theory (rate of convergence and asymptotic distribution) for the estimators in unconditional and conditional vector error correction models (VECM) when the error correction term is parameterized as a dampened near-unit root process (local-to-unity process with local-to-zero variance). The important differences in the limiting behavior of the estimators and their implications for empirical analysis are discussed. Simulation results and an empirical analysis of the forward premium regressions are also provided.
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Kohtaro Hitomi, Keiji Nagai, Yoshihiko Nishiyama and Junfan Tao
In this study, the authors investigate methods of sequential analysis to test prospectively for the existence of a unit root against stationary or explosive states in a p-th order…
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In this study, the authors investigate methods of sequential analysis to test prospectively for the existence of a unit root against stationary or explosive states in a p-th order autoregressive (AR) process monitored over time. Our sequential sampling schemes use stopping times based on the observed Fisher information of a local-to-unity parameter. In contrast to the Dickey–Fuller (DF) test statistic, the sequential test statistic has asymptotic normality. The authors derive the joint limit of the test statistic and the stopping time, which can be characterized using a 3/2-dimensional Bessel process driven by a time-changed Brownian motion. The authors obtain their limiting joint Laplace transform and density function under the null and local alternatives. In addition, simulations are conducted to show that the theoretical results are valid.
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Martín Almuzara, Gabriele Fiorentini and Enrique Sentana
The authors analyze a model for N different measurements of a persistent latent time series when measurement errors are mean-reverting, which implies a common trend among…
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The authors analyze a model for N different measurements of a persistent latent time series when measurement errors are mean-reverting, which implies a common trend among measurements. The authors study the consequences of overdifferencing, finding potentially large biases in maximum likelihood estimators (MLE) of the dynamics parameters and reductions in the precision of smoothed estimates of the latent variable, especially for multiperiod objects such as quinquennial growth rates. The authors also develop an R2 measure of common trend observability that determines the severity of misspecification. Finally, the authors apply their framework to US quarterly data on GDE and GDI, obtaining an improved aggregate output measure.
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Kun Ho Kim, Hira L. Koul and Jiwoong Kim
This chapter proposes a test for a parametric specification of the autoregressive function of a given stationary autoregressive time series. This test is based on the integrated…
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This chapter proposes a test for a parametric specification of the autoregressive function of a given stationary autoregressive time series. This test is based on the integrated square difference between the empirical distribution function estimate and a convolution-type distribution function estimate of the stationary distribution function obtained from the autoregressive residuals. Some asymptotic properties of the proposed convolution-type distribution function estimate are studied when the model’s innovation density is unknown. These properties are in turn used to derive the asymptotic null distribution of the proposed test statistic. We also discuss some finite sample properties of the test statistic based on the block bootstrap methodology. A simulation study shows that the proposed test competes favorably with some existing tests in terms of the empirical level and power.
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