1,720,970 research outputs found
Overlapping sub-sampling and invariance to initial conditions
No full textThis paper studies the use of the overlapping blocking scheme in unit root autoregression. When the underlying process is that of a random walk, the blocks’ initial conditions are not fixed, but are equal to the sum of all the previous observations’ error terms. When non- overlapping subsamples are used, as first shown by Chambers and Kyriacou (2010), these initial conditions do not disappear asymptotically. In this paper we show that a simple way of overcoming this issue is to use overlapping blocks. By doing so, the effect of these initial conditions vanishes asymptotically. An application of these findings to jackknife estimators indicates that an estimator based on moving-blocks is able to provide obvious reductions to the mean square erro
Jackknife estimation with a unit root
No full textWe study jackknife estimators in a first-order autoregression with a unit root. Non-overlapping sub-sample estimators have different limit distributions, so the jackknife does not fully eliminate first-order bias. We therefore derive explicit limit distributions of the numerator and denominator to calculate the expectations that determine optimal jackknife weights. Simulations show that the resulting jackknife estimator produces substantial reductions in bias and RMS
Jackknife bias reduction in autoregressive models with a unit root
Full text linkThis paper is concerned with the application of jackknife methods as a means of bias reduction in the estimation of autoregressive models with a unit root. It is shown that the usual jackknife estimator based on non-overlapping sub-samples does not remove fully the first-order bias as intended, but that an ‘optimal’ jackknife estimator can be defined that is capable of removing this bias. The results are based on a demonstration that the sub-sample estimators converge to different limiting distributions, and the joint moment generating function of the numerator and denominator of these distributions (which are functionals of a Wiener process over a sub-interval of [0,1]) is derived and utilised to extract the optimal weights. Simulations demonstrate the ability of the jackknife estimator to produce substantial bias reductions in the parameter of interest. It is also shown that incorporating an intercept in the regressions allows the standard jackknife estimator to be used and it is able also to produce substantial bias reduction despite the fact that the distributions of the full-sample and sub-sample estimators have greater bias in this case. Of interest, too, is the fact that the jackknife estimators can also reduce the overall root mean squared error compared to the ordinary least squares estimator, this requiring a larger (though still small) number of sub-samples compared to the value that produces maximum bias reduction (which is typically equal to two)
Jackknife bias reduction in the presence of a unit root
No full textThis paper analyses the properties of jackknife estimators of the first-order autoregressive coefficient when the time series of interest contains a unit root. It is shown that, when the sub-samples do not overlap, the sub-sample estimators have different limiting distributions from the full-sample estimator and, hence, the jackknife estimator in its usual form does not eliminate fully the first-order bias as intended. The joint moment generating function of the numerator and denominator of these limiting distributions is derived and used to calculate the expectations that determine the optimal jackknife weights. Two methods of avoiding this procedure are proposed and investigated, one based on inclusion of an intercept in the regressions, the other based on adjusting the observations in the sub-samples. Extensions to more general augmented Dickey-Fuller (ADF) regressions are also considered. In addition to the theoretical results extensive simulations reveal the impressive bias reductions that can be obtained with these computationally simple jackknife estimators and they also highlight the importance of correct lag-length selection in ADF regressions
Jackknife bias reduction in the presence of a near-unit root
No full textThis paper considers the specification and performance of jackknife estimators of the autoregressive coefficient in a model with a near-unit root. The limit distributions of sub-sample estimators that are used in the construction of the jackknife estimator are derived and the joint moment generating function (MGF) of two components of these distributions is obtained and its properties are explored. The MGF can be used to derive the weights for an optimal jackknife estimator that removes fully the first-order finite sample bias from the estimator. The resulting jackknife estimator is shown to perform well in finite samples and, with a suitable choice of the number of sub-samples, is shown to reduce the overall finite sample root mean squared error as well as bias. However, the optimal jackknife weights rely on knowledge of the near-unit root parameter, which is typically unknown in practice, and so an alternative, feasible, jackknife estimator is proposed which achieves the intended bias reduction but does not rely on knowledge of this parameter. This feasible jackknife estimator is also capable of substantial bias and root mean squared error reductions in finite samples across a range of values of the near-unit root parameter and across different sample sizes
Uncovering the distribution of option implied risk aversion
No full textThis paper explores the dynamics of risk aversion of a representative agent with an iso-elastic utility function. In contrast to most of the existing literature, we estimate the coefficient of relative risk aversion from option prices. To do this, we transform the risk-neutral density function obtained from a cross-section of option prices to an objective distribution function that reflects individuals’ risk aversion through a CRRA utility function. The dynamics of the relative risk-aversion coefficient are obtained by repeating the same estimation procedure over rolling windows. This procedure uncovers strong variation in risk aversion over time. We also propose a simulation procedure to construct confidence intervals for the risk-aversion coefficient in each period. We assess the robustness of these confidence intervals under different assumptions on the data generating process of stock prices. The results imply a strong influence of volatility on the variation of risk aversion. In an empirical application, we compare the forecasting performance of our approach based on our risk-aversion estimates against the method proposed in [1]. Overall, we find that our simulation based approach obtains better forecasting results than bootstrap methods
Optimal portfolio allocation using option implied information
No full textThis paper explores option-implied information measures for optimal portfolio allocation. We introduce two state variables constructed from option prices. The first state variable is the risk-premium on the risky asset and the second variable is the market price of risk. We also explore a lognormal distribution, a mixture of lognormal distributions, and a binomial tree for constructing the implied risk-neutral density function. Using a combination of statistical and economic measures applied to a portfolio given by the 1-month US Treasury bill and the S&P 500 Index we show the good performance of option-implied information measures for optimal portfolio allocation.</p
Indirect inference in spatial autoregression
No full textOrdinary least squares (OLS) is well-known to produce an inconsistent estimator of the spatial parameter in pure spatial autoregression (SAR). This paper explores the potential of indirect inference to correct the inconsistency of OLS. Under broad conditions, it is shown that indirect inference (II) based on OLS produces consistent and asymptotically normal estimates in pure SAR regression. The II estimator is robust to departures from normal disturbances and is computationally straightforward compared with pseudo Gaussian maximum likelihood (PML). Monte Carlo experiments based on various specifications of the weighting matrix confirm that the indirect inference estimator displays little bias even in very small samples and gives overall performance that is comparable to the Gaussian PML
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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