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## Autoregressive Parameter (autoregressive + parameter)
## Selected Abstracts## A patent analysis of global food and beverage firms: The persistence of innovation AGRIBUSINESS : AN INTERNATIONAL JOURNAL, Issue 3 2002Oscar AlfrancaWe explore whether current innovation has an enduring effect on future innovative activity in large, global food and beverage (F&B) companies. We analyze a sample of 16,698 patents granted in the United States over the period 1977 to 1994 to 103 F&B firms selected from the world's largest F&B multinationals. We test whether patent time series are trend stationary or difference stationary in order to detect how large the autoregressive parameter is and how enduring the impact of past innovation in these companies is. We conclude that the patent series are not consistent with the random walk model. The null hypothesis of a unit root can be rejected at the 5% level when a constant and a time trend are considered. Both utility and design patent series are stationary around a constant and a time trend. Moreover, there is a permanent component in the patent time series. Thus, global F&B firms show a stable pattern of technological accumulation in which "success breeds success." "Old" innovators are the ones to foster both important changes and new ways of packaging products among F&B multinationals. The effect of past innovation is almost permanent. By contrast, other potential stimuli to technological change have only transitory effects on innovation. Patterns of technological accumulation vary in specific F&B industries. Past experience in design is important in highly processed foods and beverages, but not in agribusinesses and basic foodstuffs. Patterns of technological accumulation are similar in both smaller multinationals/newcomers and large, established multinationals. [EconLit citations : O330, F230, L660] © 2002 Wiley Periodicals, Inc. [source] ## Local to unity, long-horizon forecasting thresholds for model selection in the AR(1) JOURNAL OF FORECASTING, Issue 7 2004John L. TurnerAbstract This article introduces a novel framework for analysing long-horizon forecasting of the near non-stationary AR(1) model. Using the local to unity specification of the autoregressive parameter, I derive the asymptotic distributions of long-horizon forecast errors both for the unrestricted AR(1), estimated using an ordinary least squares (OLS) regression, and for the random walk (RW). I then identify functions, relating local to unity ,drift' to forecast horizon, such that OLS and RW forecasts share the same expected square error. OLS forecasts are preferred on one side of these ,forecasting thresholds', while RW forecasts are preferred on the other. In addition to explaining the relative performance of forecasts from these two models, these thresholds prove useful in developing model selection criteria that help a forecaster reduce error. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Explosive Random-Coefficient AR(1) Processes and Related Asymptotics for Least-Squares Estimation JOURNAL OF TIME SERIES ANALYSIS, Issue 6 2005S. Y. HwangAbstract., Large sample properties of the least-squares and weighted least-squares estimates of the autoregressive parameter of the explosive random-coefficient AR(1) process are discussed. It is shown that, contrary to the standard AR(1) case, the least-squares estimator is inconsistent whereas the weighted least-squares estimator is consistent and asymptotically normal even when the error process is not necessarily Gaussian. Conditional asymptotics on the event that a certain limiting random variable is non-zero is also discussed. [source] ## Maximum Likelihood Estimation for a First-Order Bifurcating Autoregressive Process with Exponential Errors JOURNAL OF TIME SERIES ANALYSIS, Issue 6 2005J. ZhouAbstract., Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter. [source] ## Lower confidence limits for process capability indices Cp and Cpk when data are autocorrelated QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 6 2009Cynthia R. LovelaceAbstract Many organizations use a single estimate of Cp and/or Cpk for process benchmarking, without considering the sampling variability of the estimators and how that impacts the probability of meeting minimum index requirements. Lower confidence limits have previously been determined for the Cp and Cpk indices under the standard assumption of independent data, which are based on the sampling distributions of the index estimators. In this paper, lower 100(1-,)% confidence limits for Cp and Cpk were developed for autocorrelated processes. Simulation was used to generate the empirical sampling distribution of each estimator for various combinations of sample size (n), autoregressive parameter (,), true index value (Cp or Cpk), and confidence level. In addition, the minimum values of the estimators required in order to meet quality requirements with 100(1-,)% certainty were also determined from these empirical sampling distributions. These tables may be used by practitioners to set minimum capability requirements for index estimators, rather than true values, for the autocorrelated case. The implications of these results for practitioners will be discussed. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Bayesian analysis of switching ARCH models JOURNAL OF TIME SERIES ANALYSIS, Issue 4 2002SYLVIA KAUFMANNWe consider a time series model with autoregressive conditional heteroscedasticity that is subject to changes in regime. The regimes evolve according to a multistate latent Markov switching process with unknown transition probabilities, and it is the constant in the variance process of the innovations that is subject to regime shifts. The joint estimation of the latent process and all model parameters is performed within a Bayesian framework using the method of Markov chain Monte Carlo (MCMC) simulation. We perform model selection with respect to the number of states and the number of autoregressive parameters in the variance process using Bayes factors and model likelihoods. To this aim, the model likelihood is estimated by the method of bridge sampling. The usefulness of the sampler is demonstrated by applying it to the data set previously used by Hamilton and Susmel (1994) who investigated models with switching autoregressive conditional heteroscedasticity using maximum likelihood methods. The paper concludes with some issues related to maximum likelihood methods, to classical model selection, and to potential straightforward extensions of the model presented here. [source] |