A New Model of Trend Inflation

This article introduces a new model of trend inflation. In contrast to many earlier approaches, which allow for trend inflation to evolve according to a random walk, ours is a bounded model which ensures that trend inflation is constrained to lie in an interval. The bounds of this interval can either be fixed or estimated from the data. Our model also allows for a time-varying degree of persistence in the transitory component of inflation. In an empirical exercise with CPI inflation, we find the model to work well, yielding more sensible measures of trend inflation and forecasting better than popular alternatives such as the unobserved components stochastic volatility model. This article has supplementary materials online.     

Derivation of the theoretical autocovariance and autocorrelation function of autoregessive moving average processes

Closed form expressions for the theoretical autocovariance and autocorrelation function of mixed autoregressive moving average processes are presented. The results provide insight into the construction of autocovariances and autocorrelatians and are useful in theoretical analysis, model identification as well as in implementing maximum likelihood estimation algorithms.     

Identification of composite (∑+II) arma models by relatively simpler models

In the real world situations, many time series are aggregates of two or more time series. An aggregation may take place due to an addition or the product or both of two or more time series. We are often interested in the study of the properties of aggregates which are, in turn, dependent on the properties of the constituent series. Motivated by this problem, the authors study in this paper the properties of models generated by the operator (Σ+II) on autoregressive-moving-average (ARMA) processes of orders (p_i,q_i), i = l→n . A few practical examples where such models have been used are given in the introduction and an illustrative numerical example is discussed at the end of the paper.     

A note on connectedness in fixed effects manova and gmanova models withmissing cells

Murray and Smith (1985) and Hocking (1985) give a generalized definition and test of connectedness in the case of missing cells using the univariate cell-means model with linear restrictions on the cell-means. The test of connectedness is here extended to multivariate fixed effects models, including the usual MANOVA model with linear restrictions, the MANOVA model with double linear restrictions, and the GMANOVA model.     

On the power of the durbin-watson test under high autocorrelation

In the linear regression model without an intercept, it is known that the limiting power of the Durbin-Watson test (as correlation among errors increases) equals either one or zero, depending on the underlying regressor matrix. This paper considers the limiting power in the model with an intercept, and proves that it will never equal one or zero.     

Unbiased estimation of a nonlinear function a normal mean with application to measurement err oorf models

Let W be a normal random variable with mean μand known variance σ². Conditions on the function f(·) are given under which there exists an unbiased estimator, f(W), of f(μ) for all real μ. In particular it is shown that f(·) must be an entire function over the complex plane. Infinite series solutions for F(·) are obtained which are shown to be valid under growth conditions of the derivatives, f^k( ·), of f(·). Approximate solutions are given for the cases in which no exact solution exists. The theory is applied to nonlinear measurement-error models as a means of finding unbiased score functions when measurement error is normally distributed. Relative efficiencies comparing the proposed method to the use of conditional scores (Stefanski and Carroll, 1987) are given for the Poisson regression model with canonical link.     

Testing a main effect in a three factor mixed model

In the present paper, the author has considered and compared the power of three test procedures, based on two preliminary tests of significance (PTS), for testing a main effect in a three factor factorial experiment. Davenport and Webster (1973) type test statistics are used in the final test. Recommendation for a suitable size of PTS has been made so that the power of a test procedure is adequately high.     

Estimation of parameters and reliability from generalized life models

Simultaneous estimation of parameters with p (≥ 2) components, where each component has a generalized life distribution, is considered under a sum of squared error loss function. Improved estimators are obtained which dominate the maximum likelihood and the niinimum mean square estimators. Robustness of the improved estimators is shown even when the component distributions are dependent. The result is extended to the estimation of the system reliability when the components are connected in series. Several numerical studies are performed to demonstrate the risk improvement and the Pitman closeness of the new estimators.     

Testing for lack of fit in linear multiresponse models based on exact or near replicates

Three procedures for testing the adequacy of a proposed linear multiresponse regression model against unspecified general alternatives are considered. The model has an error structure with a matrix normal distribution which allows the vector of responses for a particular run to have an unknown covariance matrix while the responses for different runs are uncorrelated. Furthermore, each response variable may be modeled by a separate design matrix. Multivariate statistics corresponding to the classical univariate lack of fit and pure error sums of squares are defined and used to determine the multivariate lack of fit tests. A simulation study was performed to compare the power functions of the test procedures in the case of replication. Generalizations of the tests for the case in which there are no independent replicates on all responses are also presented.