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.     

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.     

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.     

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.     

Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk

According to the classic no arbitrage theory of asset pricing, in a frictionless market a No Free Lunch dynamic price process associated with any essentially bounded asset is a martingale under an equivalent probability measure. However, real financial markets are not frictionless. We introduce an axiomatic approach of Time Consistent Pricing Procedure (TCPP), in a model free setting, to assign to every financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity) of the ask (resp. bid) price. We prove that the No Free Lunch condition for a TCPP is equivalent to the existence of an equivalent probability measure R that transforms a process between the bid price process and the ask price process of every financial instrument into a martingale. Furthermore we prove that the ask (resp. bid) price process associated with every financial instrument is then a R super-martingale (resp. R sub-martingale) which has a càdlàg version.     

Linear transformations of vector ARMA processes

Linear transformations of stochastic processes are used in many ways in economic analyses, for example when linear aggregates or subprocesses are considered. It is demonstrated that a linear transformation of a vector ARMA process is again an ARMA process and conditions for stationarity are given. Three different predictors for a linearly transformed process are compared. Forecasting the original process and transforming the predictions is superior to forecasting the transformed process directly and to transforming univariate predictions of the components of the original process. Conditions for equality of the three different forecasts are provided.     

基于时间序列模型在物流需求预测中的应用

本文采用时间序列模型进行物流需求预测，用实例从数据平稳性的判断，平稳化、标准化，建模，经模型的识别、定价、参数估计和检验，到预测及误差和置信区间的计算，详细地说明了时间序列模型在物流需求预测中是如何应用的。结果表明该ARMA模型能够较好地拟合并可获得较高的中短期预测精度。     

Thresholds,news impact surfaces and dynamic asymmetric multivariate GARCH

Dynamic Asymmetric Multivariate GARCH (DAMGARCH) is a new model that extends the Vector ARMA‐GARCH (VARMA‐GARCH) model of Ling and Mc Aleer (2003) by introducing multiple thresholds and time‐dependent structure in the asymmetry of the conditional variances. Analytical expressions for the news impact surface implied by the new model are also presented. DAMGARCH models the shocks affecting the conditional variances on the basis of an underlying multivariate distribution. It is possible to model explicitly asset‐specific shocks and common innovations by partitioning the multivariate density support. This article presents the model structure, describes the implementation issues, and provides the conditions for the existence of a unique stationary solution, and for consistency and asymptotic normality of the quasi‐maximum likelihood estimators. The article also presents an empirical example to highlight the usefulness of the new model.     

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.     

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.     

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.     

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.     

Discrete time Wishart term structure models

This paper reveals that the class of Affine Term Structure Models (ATSMs) introduced by Duffie and Kan (1996) is larger than previously considered in the literature. In the framework of risk factors following a Wishart autoregressive process, we define the Wishart Term Structure Model (WTSM) as an extension of a subclass of Quadratic Term Structure Models (QTSMs), derive simple parameter restrictions that ensure positive bond yields at all maturities, and observe that the usual constraint on affine processes requiring that the volatility matrix be diagonal up to a path independent linear invertible transformation can be considerably relaxed.     

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.     

Decision-making in organizations: when to delegate and whom to delegate

A production process involves a principal and two privately informed agents. Production requires coordinated decision making. It might be carried in a centralized organization or through delegated contracting in a hierarchical structure. We compare the performance of different organizational structures when renegotiation of initial contracts is possible. We show that delegated contracting always dominates centralization if the downstream contract between the agents is observable. Contracting (resp. control) should be delegated to the agent with the least (resp. most) important information. If downstream contracts are not observable, we obtain a tradeoff between centralization and delegation.     

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).     

Modelling Group Heterogeneity for Small Area Estimation Using M‐Quantiles

Small area estimation typically requires model‐based methods that depend on isolating the contribution to overall population heterogeneity associated with group (i.e. small area) membership. One way of doing this is via random effects models with latent group effects. Alternatively, one can use an M‐quantile ensemble model that assigns indices to sampled individuals characterising their contribution to overall sample heterogeneity. These indices are then aggregated to form group effects. The aim of this article is to contrast these two approaches to characterising group effects and to illustrate them in the context of small area estimation. In doing so, we consider a range of different data types, including continuous data, count data and binary response data.     

Estimating the codifference function of linear time series models with infinite variance

We consider the codifference and the normalized codifference function as dependence measures for stationary processes. Based on the empirical characteristic function, we propose estimators of the codifference and the normalized codifference function. We show consistency of the proposed estimators, where the underlying model is the ARMA with symmetric α-stable innovations, 0 < α ≤ 2. In addition, we derive their limiting distribution. We present a simulation study showing the dependence of the estimator on certain design parameters. Finally, we provide an empirical example using some stocks from Indonesia Stock Exchange.     

z-Transform and identification of linear econometric models with autocorrelated errors

The paper consists of two main parts. In the first part we derive the solution of systems of linear stochastic difference equations by means of thez-transform. In the second part thisz-transform is used to treat the problem of identification of linear econometric systems (the term econometric is used to stress the special aspects of the identification problem dealt with in econometrics). It is shown, that under suitable restrictions observationally equivalent structures are related by unimodular matrices. Using this result, we state (rank-) conditions which ensure, that the unimodular matrices are constant, such that the classical econometric identification theorems can be applied. These conditions are given for stationary errors in the general case as well as in the MA, AR and ARMA case.     

Opmerkingen en berekeningen betreffende "Poisson-proces met interrupties" van J. C. A. Zaat

Summary
In an earlier paper by J.C. A. ZAAT an interrupted Poisson process was studied. Here we clarify some of the results there obtained. The process is obtained from a stationary Poisson process on the real axis by covering the axis with a sequence of adjoining intervals which have alternatively length a and b, the first left-hand endpoint of an a-interval to the right of 0 being chosen in a stochastic point with If has a rectangular distribution on [0, a + b] the interrupted Poisson process is stationary, but the distribution of the length of an interval between two successive points in the interrupted process is now different for different intervals. For each distribution ofy over [0, a + b] the distribution of the length of the interval between the nth and the (n + I)st point to the right ofO in the interrupted Poisson process tends to the distribution function G(y) as n tends to infinity. Somehow ZAAT based his calculations exclusively on this stationary distribution.