Rational Expectations and Macroeconomic Forecasts

The article presents extensive results from testing for bias and serially correlated errors in a collection of time series of quarterly multiperiod forecasts for six variables including real GNP growth, inflation, and unemployment. The analysis covers responses by 79 frequent participants in economic outlook surveys conducted regularly since 1968. It shows much greater incidence of apparently systematic errors for inflation than for the other variables. Also, the tests are more favorable to composite group forecasts than to most of the individual forecast sets.     

Estimation of Current-Quarter Gross National Product by Pooling Preliminary Labor-Market Data

Two methods of using labor-market data as indicators of contemporaneous gross national product (GNP) are developed. The establishment survey data are used by inverting a partial-adjustment equation for hours. A second GNP forecast can be extracted from the household survey by using Okun's law. Using preliminary rather than final data adds about .2 to .4 percentage point to the expected value of the root mean squared errors and changes the weights that the pooling procedure assigns to the two forecasts. The use of preliminary rather than final data results in a procedure that assigns more importance to the Okun's-law forecast.     

Ain't Behavin': Forecast Errors and Measurement Errors in Early GNP Estimates

Revisions of the early GNP estimates may contain elements of measurement errors as well as forecast errors. These types of error behave differently but need to satisfy a common set of criteria for well-behavedness. This article tests these criteria for U.S. GNP revisions. The tests are similar to tests of rationality and are based on the generalized method of moments estimator. The flash, 15-day, and 45-day estimates are found to be ill behaved, but the 75-day estimate satisfies the criteria for well-behavedness.     

Predictive Accuracy Gain From Disaggregate Sampling in ARIMA Models

We compare the forecast accuracy of autoregressive integrated moving average (ARIMA) models based on data observed with high and low frequency, respectively. We discuss how, for instance, a quarterly model can be used to predict one quarter ahead even if only annual data are available, and we compare the variance of the prediction error in this case with the variance if quarterly observations were indeed available. Results on the expected information gain are presented for a number of ARIMA models including models that describe the seasonally adjusted gross national product (GNP) series in the Netherlands. Disaggregation from annual to quarterly GNP data has reduced the variance of short-run forecast errors considerably, but further disaggregation from quarterly to monthly data is found to hardly improve the accuracy of monthly forecasts.     

对未来15年经济增长率的分析和预测

The paper makes a forecast and analysis of economic growth rate in the next 15 years, both quantitatively and qualitatively, by using the Harrod-Doma Economic growth model and economic cycle model. The results show that the goal of quadrupling GNP per capita by the end of 2000 proposed in the fifth plenary session of the 14th central committee of the CPC can be realized two years ahead of schedule, the goal that the 2010 GNP should double the 2000 GNP may be attained a year in advance.     

Univariate ARIMA Forecasts of Defined Variables

Many important variables in business and economics are neither measured nor measurable but are simply defined in terms of other measured variables. For instance, the real interest rate is defined as the difference between the nominal interest rate and the inflation rate. There are two ways to forecast a defined variable: one can directly forecast the variable itself, or one can derive the forecast of the defined variable indirectly from the forecasts of the constituent variables. Using Box-Jenkins univariate time series analysis for four defined variables—real interest rate, money multiplier, real GNP, and money velocity—the forecasting accuracy of the two methods is compared. The results show that indirect forecasts tend to outperform direct methods for these defined variables.     

Prbposterior expected loss as a scoring rule for prior distributions

A scoring rule for evaluating the usefulness of an assessed prior distribution should reflect the purpose for which the distribution is to be used. In this paper we suppose that sample data is to become available and that the posterior distribution will be used to estimate some quantity under a quadratic loss function. The utility of a prior distribution is consequently determined by its preposterior expected quadratic loss. It is shown that this loss function has properties desirable in a scoring rule and formulae are derived for calculating the scores it gives in some common problems. Many scoring rules give a very poor score to any improper prior distribution but, in contrast, the scoring rule proposed here provides a meaningful measure for comparing the usefulness of assessed prior distributions and non-informative (improper) prior distributions. Results for making this comparison in various situations are also given.     

Optimal Forecasts from Markov Switching Models

We derive forecasts for Markov switching models that are optimal in the mean square forecast error (MSFE) sense by means of weighting observations. We provide analytic expressions of the weights conditional on the Markov states and conditional on state probabilities. This allows us to study the effect of uncertainty around states on forecasts. It emerges that, even in large samples, forecasting performance increases substantially when the construction of optimal weights takes uncertainty around states into account. Performance of the optimal weights is shown through simulations and an application to U.S. GNP, where using optimal weights leads to significant reductions in MSFE. Supplementary materials for this article are available online.     

Some aspects of probability forecasting

The problems of assessing, comparing and combining probability forecasts for a binary events sequence are considered. A Gaussian threshold model (analytically of closed form) is introduced which allows generation of different probability forecast sequences valid for the same events. Chi - squared type test statistics, and also a marginal-conditional method are proposed for the assessment problem, and an asymptotic normality result is given. A graphical method is developed for the comparison problem, based upon decomposing arbitrary proper scoring rules into certain elementary scoring functions. The special role of the logarithmic scoring rule is examined in the context of Neyman - Pearson theory.     

Measurement Problems of Inflation Disaggregation

Why do the three quarterly GNP inflation measures differ so much when they are constructed from the same underlying price data? Algebraically and in tables using data of the second quarter of 1984, it is shown that these differences occur because of quarterly shifts in the composition of the nation's product. Disaggregation of the inflation contributions of the GNP components also makes it clear why, for quarterly analyses, the GNP chain price index is superior to both the implicit GNP deflator and the fixed-weight GNP price index. In particular, the implicit GNP deflator can give severely distorted inflation signals.     

Minimum Scoring Rule Inference

Proper scoring rules are devices for encouraging honest assessment of probability distributions. Just like log‐likelihood, which is a special case, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory of such equations can be applied to understand the properties of the associated estimator. In this paper, we discuss some novel applications of scoring rules to parametric inference. In particular, we focus on scoring rule test statistics, and we propose suitable adjustments to allow reference to the usual asymptotic chi‐squared distribution. We further explore robustness and interval estimation properties, by both theory and simulations.     

k-sample rank tests using pair-specific scoring functions

In this paper we consider generalizations of the distribution-free one-way ANOVA test procedures studied by Puri (1965), such generalizations allowing for possibly different scoring functions for different pairs of samples. The asymptotic distributions of the test statistics are derived and formulas for the asymptotic relative efficiencies of these tests with respect to a parametric competitor are obtained. Applications of these procedures to settings of ordered and umbrella alternatives are presented and potential advantages of this pair-specific scoring scheme are discussed.     

Power of the Neyman Smooth Test for Evaluating Multivariate Forecast Densities

We compare and investigate Neyman's smooth test, its components, and the Kolmogorov-Smirnov (KS) goodness-of-fit test for testing the uniformity of multivariate forecast densities. Simulations indicate that the KS test lacks power when the forecast distributions are misspecified, especially for correlated sequences of random variables. Neyman's smooth test and its components work well in samples of size typically available, although there sometimes are size distortions. The components provide directed diagnosis regarding the kind of departure from the null. For illustration, the tests are applied to forecast densities obtained from a bivariate threshold model fitted to high-frequency financial data.     

Distribution-free partially sequential piacment procedures

The concept of a partially sequential hypothesis test was introduced by Wolfe (1977a), an{associated procedures were developed for both parametric and nonparametric assumptions. In this paper we consider distribution-free extensions of those indicator tests, based on the placements of the sequentially obtained observations among the previously collected fixed size sample. Exact and asymptotic, as the fixed sample size in¬creases to infinity, properties of these sequential placements procedures are obtained, including statements about the power and expected number of sequentially obtained observations. The results of a Monte Carlo study are used to differentiate be¬tween various placement scoring schemes.     

Sequential estimation of the variance of an unknown distribution

Sequential fixed-width and risk-efficient estimation of the variance of an unspecified distribution is considered. The second-order asymptotic properties of the sequential rules are studied. Extensive simulation studies are carried out in order to study the small sample behavior of the sequential rules for some frequently used distributions.     

Evaluation of realized volatility predictions from models with leptokurtically and asymmetrically distributed forecast errors

Accurate volatility forecasting is a key determinant for portfolio management, risk management and economic policy. The paper provides evidence that the sum of squared standardized forecast errors is a reliable measure for model evaluation when the predicted variable is the intra-day realized volatility. The forecasting evaluation is valid for standardized forecast errors with leptokurtic distribution as well as with leptokurtic and asymmetric distributions. Additionally, the widely applied forecasting evaluation function, the predicted mean-squared error, fails to select the adequate model in the case of models with residuals that are leptokurtically and asymmetrically distributed. Hence, the realized volatility forecasting evaluation should be based on the standardized forecast errors instead of their unstandardized version.     

Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.     

Optimal design of variable acceptance sampling plans for mixture distribution

ABSTRACT

The paper investigates the design of single and sequential variable acceptance sampling plans for a mixture distribution. Mixture distributions are seen in many practical problems such as life testing experiments of electronic components and clinical trials. The sampling plans for this kind of situations are not well addressed in the literature. We first propose a single sampling plan for a distribution which is a mixture of two exponential distributions. An optimization problem which minimizes the total cost of testing at given producer's and consumer's risks is solved to obtain the plan parameters. Two different sequential sampling plans are also defined and plan parameters are obtained by solving corresponding optimization problems. Finally, a case study, a simulation study and a sensitivity analysis are presented to illustrate our sampling plans.     

基于重复购买理论的一种新的客户选择方法

在今天越来越激烈的市场竞争之中,越来越多的公司已经从产品驱动的市场竞争策略转向客户驱动的市场竞争策略。并且随着计算机技术及数据挖掘方法的飞速发展,直接市场营销越来越受到重视。如何选择目标客户邮寄货单的问题也就越来越引起市场直销者的兴趣。计分模型及增益表选择方法和单群预测及选择方法是目前普遍采用的两种客户选择方法。在平稳市场的假设下,客户的购买模式服从著名的重复购买理论。基于这个理论,本文提出了一种新的客户选择方法,即两群预测及选择方法。应用实际的客户数据比较这三种不同的方法,结果表明新方法表现最好。