Modelling Strategies for Repeated Multiple Response Data

This article discusses modelling strategies for repeated measurements of multiple response variables. Such data arise in the context of categorical variables where one can select more than one of the categories as the response. We consider each of the multiple responses as a binary outcome and use a marginal (or population‐averaged) modelling approach to analyse its means. Generalized estimating equations are used to account for different correlation structures, both over time and between items. We also discuss an alternative approach using a generalized linear mixed model with conditional interpretations. We illustrate the methods using data from a panel study in Australia called the Household, Income, and Labour Dynamics Survey.     

Time Series Modelling of Daily Tax Revenues

We provide a detailed discussion of time series modelling of daily data in general and daily tax revenues in particular. The main feature of the daily tax revenue series is the pattern within calendar months. Standard time series methods for seasonal adjustment and forecasting cannot be used since the number of banking days per calendar month varies and because there are two levels of seasonality: between months and within months. We propose a daily time series model based on unobserved components that allows for the classic decomposition into trend, seasonal plus irregular, but it also includes components for intra-monthly, trading-day and length-of-month effects. Such components typically rely on stochastic cubic spline, polynomial and dummy variable functions. State space techniques are used for the recursive computation of the likelihood and forecasts functions with special allowance for irregular spacing. The model is operational for daily forecasting at the Dutch Ministry of Finance. We present the model specification and discuss estimation and forecasting results up to December 1999. A comparative forecast evaluation is also presented.     

Nonlinear Time Series Modelling: An Introduction

Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear model are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of model. Finally forecasting and impulse response analysis is developed.     

Geometrical Interpretation of the Mean and the Constant in a Box-Jenkins Time Series Model

Certain manuals and computer programs mistakenly identify the mean with the constant in Box-Jenkins time series models. In this paper, it will be shown that (a) the mean and the constant have different values in autoregressive models, and (b) they have an algebraic and graphical relationship.     

A General Approach to Testing Volatility Models in Time Series

Volatility models have been playing important roles in economics and finance. Using a generalized spectral second order derivative approach, we propose a new class of generally applicable omnibus tests for the adequacy of linear and nonlinear volatility models. Our tests have a convenient asymptotic null N(0,1) distribution, and can detect a wide range of misspecifications for volatility dynamics, including both neglected linear and nonlinear volatility dynamics. Distinct from the existing diagnostic tests for volatility models, our tests are robust to time-varying higher order moments of unknown form (e.g., time-varying skewness and kurtosis). They check a large number of lags and are therefore expected to be powerful against neglected volatility dynamics that occurs at higher order lags or display long memory properties. Despite using a large number of lags, our tests do not suffer much from the loss of a large number of degrees of freedom, because our approach naturally discounts higher order lags, which is consistent with the stylized fact that economic or financial markets are affected more by the recent past events than by the remote past events. No specific estimation method is required, and parameter estimation uncertainty has no impact on the convenient limit N(0,1) distribution of the test statistics. Moreover, there is no need to formulate an alternative volatility model, and only estimated standardized residuals are needed to implement our tests. We do not have to calculate tedious and model-specific score functions or derivatives of volatility models with respect to estimated parameters, which are required in some existing popular diagnostic tests for volatility models. We examine the finite sample performance of the proposed tests. It is documented that the new tests are rather powerful in detecting neglected nonlinear volatility dynamics which the existing tests can easily miss. They are useful diagnostic tools for practitioners when modelling volatility dynamics.     

基于动态贝叶斯网络的通货膨胀风险预测研究

利用动态朴素贝叶斯分类器对我国的通货膨胀风险进行了预测,并在此基础上计算了不同风险因素对通货膨胀风险等级的影响程度,结果表明,动态朴素贝叶斯分类器方法能够较好地预测和分析通货膨胀风险。利用我国实际经济数据进行模拟预测,结果显示在88.24%的可信度下,我国2012年第二季度的通货膨胀风险等级为2级,通货膨胀率预测值约为3.8%。通过分别使用包含和不包含企业家信心指数的动态朴素贝叶斯分类器进行预测,结果发现考虑了企业家信心指数的分类器大约能将预测准确率提高5%,这说明对通货膨胀风险等级预测有必要考虑经济主体的预期因素。通过计算6个指标对通货膨胀风险等级的影响程度,发现货币供应和产出缺口仍是解释我国通货膨胀风险的两个主要因素。     

Approximate Bayesian Computation for a Class of Time Series Models

In the following article, we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which we mean that one cannot evaluate the likelihood even up to a non‐negative unbiased estimate. This paper reviews and develops a class of approximation procedures based upon the idea of ABC, but specifically maintains the probabilistic structure of the original statistical model. This latter idea is useful, in that one can adopt or adapt established computational methods for statistical inference. Several existing results in the literature are surveyed, and novel developments with regards to computation are given.     

Bootstrapping Financial Time Series

It is well known that time series of returns are characterized by volatility clustering and excess kurtosis. Therefore, when modelling the dynamic behavior of returns, inference and prediction methods, based on independent and/or Gaussian observations may be inadequate. As bootstrap methods are not, in general, based on any particular assumption on the distribution of the data, they are well suited for the analysis of returns. This paper reviews the application of bootstrap procedures for inference and prediction of financial time series. In relation to inference, bootstrap techniques have been applied to obtain the sample distribution of statistics for testing, for example, autoregressive dynamics in the conditional mean and variance, unit roots in the mean, fractional integration in volatility and the predictive ability of technical trading rules. On the other hand, bootstrap procedures have been used to estimate the distribution of returns which is of interest, for example, for Value at Risk (VaR) models or for prediction purposes. Although the application of bootstrap techniques to the empirical analysis of financial time series is very broad, there are few analytical results on the statistical properties of these techniques when applied to heteroscedastic time series. Furthermore, there are quite a few papers where the bootstrap procedures used are not adequate.     

Modern Strategies for Time Series Regression

This paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been proposed recently in the machine learning literature. The approaches are compared and contrasted, and it will be seen that there are advantages and disadvantages to most currently available approaches. There is ample room for methodological developments in this area. The work is motivated by an application involving the prediction of water levels as a function of rainfall and other climate variables in an aquifer in eastern Australia.     

Short Time Series Analysis: C Statistic vs Edgington Model

Young's C statistic (1941) makes it possible to compare the randomization of a set of sequentially organized data and constitutes an alternative of appropriate analysis in short time series designs. On the other hand, models based on the randomization of stimuli are also very important within the behavioral content applied. For this reason, a comparison is established between the C statistic and the Edgington model. The data analyzed in the comparative study have been obtained from graphs in studies published in behavioral journals. According to the results obtained, it is concluded that the Edgington model in experimental designs AB involves many measurements while the C statistic requires fewer observations to reach the conventional significance level.     

BAYESIAN INFERENCE METHODS FOR UNIVARIATE AND MULTIVARIATE GARCH MODELS: A SURVEY

This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non‐parametric approaches for GARCH models that avoid imposing arbitrary parametric distributional assumptions. These novel approaches implicitly assume infinite mixture of Gaussian distributions on the standardized returns which have been shown to be more flexible and describe better the uncertainty about future volatilities. Finally, the survey presents an illustration using real data to show the flexibility and usefulness of the non‐parametric approach.     

Input–Output Based Measures of Underlying Domestic Inflation: Empirical Evidence from Denmark 1903–2002

The paper presents input–output based time-series data for the underlying domestic inflation in Denmark 1903–2002 and analyses the inflationary development during the last century. More conceptual issues in relation to the interpretation and use of input–output based domestic inflation measures are also discussed. The purpose of such inflation measures is to track the development in the domestic market-determined inflation, which is closely related to the price of gross value added in the domestic market-based private business sector. A price index for value added often displays a different short-term development than the headline CPI. Such differences can be useful in an assessment of the current inflationary environment and in relation to an interpretation of the historical inflation development.     

Calvo vs. Rotemberg in a trend inflation world: An empirical investigation

This paper estimates and compares New-Keynesian DSGE monetary models of the business cycle derived under two different pricing schemes—Calvo (1983) and Rotemberg (1982)—under a positive trend inflation rate. Our empirical findings (i) support trend inflation as an empirically relevant feature of the U.S. great moderation; (ii) provide evidence in favor of the statistical superiority of the Calvo setting; (iii) point to a substantially lower degree of price indexation under Calvo. We show that the superiority of the Calvo model is due to the restrictions imposed by such a pricing scheme on the aggregate demand equation.     

Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency

This paper analyzes the productivity of farms across 370 municipalities in the Center-West region of Brazil. A stochastic frontier model with a latent spatial structure is proposed to account for possible unknown geographical variation of the outputs. The paper compares versions of the model that include the latent spatial effect in the mean of output or as a variable that conditions the distribution of inefficiency, include or not observed municipal variables, and specify independent normal or conditional autoregressive priors for the spatial effects. The Bayesian paradigm is used to estimate the proposed models. As the resultant posterior distributions do not have a closed form, stochastic simulation techniques are used to obtain samples from them. Two model comparison criteria provide support for including the latent spatial effects, even after considering covariates at the municipal level. Models that ignore the latent spatial effects produce significantly different rankings of inefficiencies across agents.

Modelling optimal strategies for the allocation of wealth in multicurrency investments

This paper analyzes rates of return on financial assets denominated in five major currencies and provides a framework for the determination of optimal strategies for the allocation of wealth in multicurrency investments. Three models are estimated: a univariate autoregressive conditional heteroskedasticity (ARCH) model, an extended ARCH model using the random coefficient (RC) procedure, and a pure RC model. A comparison of the forecasts of these models with those generated by a random walk model demonstrates that forecasts based on the RC/extended ARCH procedure are superior to those based on the random walk model and those based on direct ARCH estimation. These results could be useful for both international investors for the allocation of their wealth among fixed-income investment securities and central banks for the management of their external reserve assets.     

预期、混合菲利普斯曲线与中国通货膨胀动态特征

将货币因素与输入性因素（如汇率、国际石油价格等）引入新凯恩斯混合菲利普斯曲线框架构建高阶滞后的混合菲利普斯曲线模型,并利用1995年第1季度至2013年第2季度的数据进行实证分析,结果显示：总需求变化对我国通货膨胀率的影响很小,而货币因素与输入性因素（如汇率以及国际大宗商品价格变化）成为影响我国通货膨胀率的重要因素;我国通货膨胀主要受到前瞻性预期的影响,而通胀惯性对通货膨胀水平的影响不大;相对而言,货币因素对我国通货膨胀具有最重要的影响。     

连续时间系统线性特性的判别方法研究

本文用两种方法对含初始状态的连续时间系统的线性性进行判别。第一种方法直接由定义判别,在数学上更为严谨;第二种由线性系统的延伸特点进行判别,其物理意义更加明确。     

Bayesian semiparametric stochastic volatility modeling

This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. A Markov chain Monte Carlo sampling approach to estimation is presented with theoretical and computational issues for simulation from the posterior predictive distributions. An empirical example compares the new model to standard parametric stochastic volatility models.     

A Comparative Simulation Study of Wavelet Shrinkage Estimators for Poisson Counts

Using computer simulations, the finite sample performance of a number of classical and Bayesian wavelet shrinkage estimators for Poisson counts is examined. For the purpose of comparison, a variety of intensity functions, background intensity levels, sample sizes, primary resolution levels, wavelet filters and performance criteria are employed. A demonstration is given of the use of some of the estimators to analyse a data set arising in high-energy astrophysics. Following the philosophy of reproducible research, the M atlab programs and real-life data example used in this study are made freely available.     

Modelling the inflation process in transition economies: Empirical comparison of Poland, Hungary and Czech Republic

This paper starts from the observation that inflation in transition economies appears to be persistently high and volatile and attempts to provide some empirical characterisation of the inflation process in three such transition economies: Poland, Hungary and Czech Republic. We first consider the role of monetary growth as a major causal factor for inflation in these economies, and argue that the evidence provides rather weak support for the causal relationship. We then propose a transition economy cost-plus model and estimate this using the equilibrium-correction modelling (ECM) strategy augmented by introduction of a number of transitory factors and changes in the internal structure of the real economy which we believe may have had a significant impact on inflation in these economies. We show that this approach enables us to account for long-run inflation in these economies from the early 1980s to the present despite the turbulence of the latter part of the sample period. Our results support wage and exchange rate based inflation policies.