Modelling short- and long-term effects in the aggregate demand for soft drinks

A dynamic regression model for non-durable commodity demand is specified based on the additive unobserved components seasonal model with causal variables. The seasonal component which includes retailer stock effects is modelled as a seasonal ARMA process with fixed temperature effects. The non-seasonal component incorporates both short-run consumer responses and long-run adaptation to steady-state growth paths. Aggregation effects on per capita demand caused by the increase of new consumers as real income grows are investigated and the resulting growth trends accounted for. It is shown that neglecting these trends in the long-run adaptation process is likely to produce biased predictions and misleading estimates of crucial response parameters.     

The structure of ARMA solutions to a general linear model with rational expectations

A parameterc characterization is provided for the complete class of stationary and non-stationary ARMA solutions, generated by the fundamental exogenous innovation, to a general linear univariate model with rational expectations. The dimension of the solution space of ARMA parameters is given and shown to be generically equal to the maximum period forward over which expectations are formed. The validity of deleting common factors in non-stationary ARMA processes is discussed, and specific solution choices often recommended are shown to be ‘common factor’ solutions.     

The invertibility of sampled and aggregated ARMA models

Summary Necessary and sufficient conditions for a sampled (resp. aggregated) stationary ARMA process to be invertible are derived. It is shown that a sampled (resp. aggregated) invertible stationary ARMA process is always invertible.     

Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models

The limit distribution of the quasi-maximum likelihood estimator (QMLE) for parameters in the ARMA-GARCH model remains an open problem when the process has infinite 4th moment. We propose a self-weighted QMLE and show that it is consistent and asymptotically normal under only a fractional moment condition. Based on this estimator, the asymptotic normality of the local QMLE is established for the ARMA model with GARCH (finite variance) and IGARCH errors. Using the self-weighted and the local QMLEs, we construct Wald statistics for testing linear restrictions on the parameters, and their limiting distributions are given. In addition, we show that the tail index of the IGARCH process is always 2, which is independently of interest.     

Nonparametric transfer function models

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between ‘input’ and ‘output’ time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example.     

UNCERTAINTY AND DENSITY FORECASTS OF ARMA MODELS: COMPARISON OF ASYMPTOTIC,BAYESIAN, AND BOOTSTRAP PROCEDURES

The objective of this paper is to analyze the effects of uncertainty on density forecasts of stationary linear univariate ARMA models. We consider three specific sources of uncertainty: parameter estimation, error distribution, and lag order. Depending on the estimation sample size and the forecast horizon, each of these sources may have different effects. We consider asymptotic, Bayesian, and bootstrap procedures proposed to deal with uncertainty and compare their finite sample properties. The results are illustrated constructing fan charts for UK inflation.     

Bayesian time series analysis of periodic behaviour and spectral structure

Analysis, model selection and forecasting in univariate time series models can be routinely carried out for models in which the model order is relatively small. Under an ARMA assumption, classical estimation, model selection and forecasting can be routinely implemented with the Box–Jenkins time domain representation. However, this approach becomes at best prohibitive and at worst impossible when the model order is high. In particular, the standard assumption of stationarity imposes constraints on the parameter space that are increasingly complex. One solution within the pure AR domain is the latent root factorization in which the characteristic polynomial of the AR model is factorized in the complex domain, and where inference questions of interest and their solution are expressed in terms of the implied (reciprocal) complex roots; by allowing for unit roots, this factorization can identify any sustained periodic components. In this paper, as an alternative to identifying periodic behaviour, we concentrate on frequency domain inference and parameterize the spectrum in terms of the reciprocal roots, and, in addition, incorporate Gegenbauer components. We discuss a Bayesian solution to the various inference problems associated with model selection involving a Markov chain Monte Carlo (MCMC) analysis. One key development presented is a new approach to forecasting that utilizes a Metropolis step to obtain predictions in the time domain even though inference is being carried out in the frequency domain. This approach provides a more complete Bayesian solution to forecasting for ARMA models than the traditional approach that truncates the infinite AR representation, and extends naturally to Gegenbauer ARMA and fractionally differenced models.     

Gains in efficiency from joint estimation of systems of autoregressive-moving average processes

The paper examines gains in efficiency from joint estimation of systems of ARMA processes where cross-correlation is due to contemporaneous correlation among disturbances. The asymptotic variance of joint estimates is derived and it involves only variances and covariances among purely AR processes corresponding to the AR and MA parts of the constituent processes. Small sample gains are evaluated by Monte Carlo methods. Application of joint estimation to two short-term interest rates is shown to result in more accurate post-sample predictions relative to both univariate models and the FMP econometric model.     

How to implement the bootstrap in static or stable dynamic regression models: test statistic versus confidence region approach

By combining two alternative formulations of a test statistic with two alternative resampling schemes we obtain four different bootstrap tests. In the context of static linear regression models two of these are shown to have serious size and power problems, whereas the remaining two are adequate and in fact equivalent. The equivalence between the two valid implementations is shown to break down in dynamic regression models. Then, the procedure based on the test statistic approach performs best, at least in the AR(1)-model. Similar finite-sample phenomena are illustrated in the ARMA(1,1)-model through a small-scale Monte Carlo study and an empirical example.     

Retransformation bias: A look at the box-cox transformation to linear balanced mixed ANOVA models

Summary After a Box-Cox transformation to data following a linear balanced mixed ANOVA model, final results may be presented after retransformation to the original scale of measurement. Consequently, estimation of means which may be unbiased in the transformed scale will not be so after retransformation. In this article, the bias introduced together with the corresponding variance is assessed. It is found that whereas bias may not be a serious problem, the variances are inflated for positive transformation parameter the closer it is to zero.     

Fully Bayesian analysis of ARMA time series models

Statistical analysis of autoregressive-moving average (ARMA) models is an important non-standard problem. No classical approach is widely accepted; legitimacy for most classical approaches is based solely on asymptotic grounds, while small sample sizes are common. The only obstacle to the Bayesian approach are designing a structure through which prior information can be incorporated and designing a practical computational method. The objective of this work is to overcome these two obstacles. In addition to the standard results, the Bayesian approach gives a different method of determining the order of the ARMA model, that is (p, q).     

Mixed‐frequency models with moving‐average components

Temporal aggregation in general introduces a moving‐average (MA) component in the aggregated model. A similar feature emerges when not all but only a few variables are aggregated, which generates a mixed‐frequency (MF) model. The MA component is generally neglected, likely to preserve the possibility of ordinary least squares estimation, but the consequences have never been properly studied in the MF context. In this paper we show, analytically, in Monte Carlo simulations and in a forecasting application on US macroeconomic variables, the relevance of considering the MA component in MF mixed‐data sampling (MIDAS) and unrestricted MIDAS models (MIDAS–autoregressive moving average (ARMA) and UMIDAS‐ARMA). Specifically, the simulation results indicate that the short‐term forecasting performance of MIDAS‐ARMA and UMIDAS‐ARMA are better than that of, respectively, MIDAS and UMIDAS. The empirical applications on nowcasting US gross domestic product (GDP) growth, investment growth, and GDP deflator inflation confirm this ranking. Moreover, in both simulation and empirical results, MIDAS‐ARMA is better than UMIDAS‐ARMA.     

Stochastic volatility models with ARMA innovations: An application to G7 inflation forecasts

We introduce a new class of stochastic volatility models with autoregressive moving average (ARMA) innovations. The conditional mean process has a flexible form that can accommodate both a state space representation and a conventional dynamic regression. The ARMA component introduces serial dependence, which results in standard Kalman filter techniques not being directly applicable. To overcome this hurdle, we develop an efficient posterior simulator that builds on recently developed precision-based algorithms. We assess the usefulness of these new models in an inflation forecasting exercise across all G7 economies. We find that the new models generally provide competitive point and density forecasts compared to standard benchmarks, and are especially useful for Canada, France, Italy, and the U.S.     

Analysing inflation by the fractionally integrated ARFIMA–GARCH model

This paper considers the application of long-memory processes to describing inflation for ten countries. We implement a new procedure to obtain approximate maximum likelihood estimates of an ARFIMA—GARCH process; which is fractionally integrated I(d) with a superimposed stationary ARMA component in its conditional mean. Additionally, this long memory process is allowed to have GARCH type conditional heteroscedasticity. On analysing monthly post-World War II CPI inflation for ten different countries, we find strong evidence of long memory with mean reverting behaviour for all countries except Japan, which appears stationary. For three high inflation economies there is evidence that the mean and volatility of inflation interact in a way that is consistent with the Friedman hypothesis.     

我国证券市场股价运动非线性特征检验

文章首先运用ARMA模型对市场收益率序列和波动率序列去掉序列的线性相关,然后运用BDS检验法对我国证券市场的收益率序列和波动率序列是否具有非线性结构进行实证研究。检验结果发现:我国证券市场股价运动具有明显的非线性特征,拒绝了有效市场理论的基本假设。     

The gender diversity–performance relationship in services and manufacturing organizations

Empirical findings on the link between gender diversity and performance have been inconsistent. This paper presents three competing predictions of the organizational gender diversity–performance relationship: a positive linear prediction derived from the resource-based view of the firm, a negative linear prediction derived from self-categorization and social identity theories, and an inverted U-shaped curvilinear prediction derived from the integration of the resource-based view of the firm with self-categorization and social identity theories. This paper also proposes a moderating effect of industry type (services vs. manufacturing) on the gender diversity–performance relationship. The predictions were tested in publicly listed Australian organizations using archival quantitative data with a longitudinal research design. The results show partial support for the positive linear and inverted U-shaped curvilinear predictions as well as for the proposed moderating effect of industry type. The curvilinear relationship indicates that different proportions of organizational gender diversity have different effects on organizational performance, which may be attributed to different dynamics as suggested by the resource-based view and self-categorization and social identity theories. The results help reconcile the inconsistent findings of past research that focused on the linear gender diversity–performance relationship. The findings also show that industry context can strengthen or weaken the effects of organizational gender diversity on performance.     

Inference in dynamic models containing ‘surprise’ variables

Some new results on calculating moving average representation (MAR) coefficients and their limiting distribution from estimated vector ARMA processes are presented. The technique is applied to the problem of estimating the coefficients of unanticipated or ‘surprise’ variables in a single equation for a multi-period expectations horizon. The method naturally conditions the expectations on all past values of the process and avoids the necessity of using two-step regression procedures and adjusting the resulting standard errors.     

Estimation and forecasting in vector autoregressive moving average models for rich datasets

We address the issue of modelling and forecasting macroeconomic variables using rich datasets by adopting the class of Vector Autoregressive Moving Average (VARMA) models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares (IOLS) estimator. We establish the consistency and asymptotic distribution of the estimator for weak and strong VARMA(p,q) models. Monte Carlo results show that IOLS is consistent and feasible for large systems, outperforming the MLE and other linear regression based efficient estimators under alternative scenarios. Our empirical application shows that VARMA models are feasible alternatives when forecasting with many predictors. We show that VARMA models outperform the AR(1), ARMA(1,1), Bayesian VAR, and factor models, considering different model dimensions.     

Inference on transformed stationary time series

The paper is about an approach for parametric inference on instantaneously transformed stationary processes. The paper discusses the asymptotics of the Whittle estimator of the parameters involved and also provides the explicit expression of the asymptotic covariance matrix which does not necessarily require the innovation Gaussianity assumption. As a specific instantaneous transformation, the paper introduces a new version of the Box–Cox transformation and investigates in detail the vector ARMA processes implemented by that transformation, proposing a computation-intensive procedure for parametric estimation and testing. As a computationally feasible test not relying upon the knowledge of the explicit analytic form of the asymptotic covariance matrix or on the information equality, the paper proposes a Monte Carlo Wald test, providing illustrative simulation and real-data examples.     

Frequency Domain Tests for Residual Serial Correlation in Cointegration Regressions

This paper introduces tests for residual serial correlation in cointegrating regressions. The tests are devised in the frequency domain by using the spectral measure estimates. The asymptotic distributions of the tests are derived and test consistency is established. The asymptotic distributions are obtained by using the assumptions and methods that are different from those used in Grenander and Rosenblatt (1957) and Durlauf (1991). Small-scale simulation results are reported to illustrate the finite sample performance of the tests under various distributional assumptions on the data generating process. The distributions considered are normal and t-distributions. The tests are shown to have stable size at sample sizes as large as 50 or 100. Additionally, it is shown that the tests are reasonably powerful against the ARMA residuals. An empirical application of the tests to investigate the ‘weak-form’ efficiency in the foreign exchange market is also reported.