A multivariate time series model for the analysis and prediction of carbon monoxide atmospheric concentrations

We use a Bayesian multivariate time series model for the analysis of the dynamics of carbon monoxide atmospheric concentrations. The data are observed at four sites. It is assumed that the logarithm of the observed process can be represented as the sum of unobservable components: a trend, a daily periodicity, a stationary autoregressive signal and an erratic term. Bayesian analysis is performed via Gibbs sampling. In particular, we consider the problem of joint temporal prediction when data are observed at a few sites and it is not possible to fit a complex space–time model. A retrospective analysis of the trend component is also given, which is important in that it explains the evolution of the variability in the observed process.     

仿射模型、广义仿射模型与上交所利率期限结构

本文以上交所利率期限结构从1996年6月至2003年2月的周样本数据作为分析对象,发现样本期内利率期限结构的平均形状是上斜的,而短期利率的基本趋势是下降的,说明长期债券具有较高的风险金。然后利用卡尔曼滤波法,实证分析了连续时间的两因子仿射、广义高斯仿射利率模型。结果表明模型下的利率期限结构与实际观测到的利率期限结构形状基本相同,说明模型能够反映利率期限结构的横截面特征。但两个模型对1,2,3,5,7年期利率的预测误差表现出一定序列相关性,说明模型还不能够很好地描述利率期限结构的时间序列特征。     

Prediction theory for autoregressivemoving average processes

This paper reviews statistical prediction theory for autoregressive-moving average processes wing techniques developed in control theory. It demonstrates explicitly the connectioluns between the statistical and control theory literatures. Both the forecasting problem and the Single extraction problem am considered, udng linear least squares methods. Whereas the classical Statistical theory developed by Wiener and Kolmogomv is restricted to stationary stochaotic processes, the recursive techniques known as the Kalman filter are shown to provide a satisfactory treatment of the difference-stationary care and other more general cases. Complete results for non-invertible moving averages are also obtained.     

Prediction and forecasting in linear models with measurement error

We consider measurement error models within the time series unobserved component framework. A variable of interest is observed with some measurement error and modelled as an unobserved component. The forecast and the prediction of this variable given the observed values is given by the Kalman filter and smoother along with their conditional variances. By expressing the forecasts and predictions as weighted averages of the observed values, we investigate the effect of estimation error in the measurement and observation noise variances. We also develop corrected standard errors for prediction and forecasting accounting for the fact that the measurement and observation error variances are estimated by the same sample that is used for forecasting and prediction purposes. We apply the theory to the Yellowstone grizzly bears and US index of production datasets.     

Bayesian Analysis of an Unobserved-Component Time Series Model of GDP With Markov-Switching and Time-Varying Growths

We propose an unobserved-component time series model of gross domestic product that includes Markov switching as an unobserved component. In addition to a trend component, the model has two time-varying drift components. One drift represents the expected rate of growth during recession; the other drift represents the expected rate during expansion. Estimates indicate a substantial decline in the latter annual rate for the United States from 6.4% in 1950 to 3.6% by 1990. We have employed weak priors based on prewar data. The estimation makes use of the Gibbs sampler and the Metropolis algorithm.     

An online estimation scheme for a Hull–White model with HMM-driven parameters

This paper considers the implementation of a mean-reverting interest rate model with Markov-modulated parameters. Hidden Markov model filtering techniques in Elliott (1994, Automatica, 30:1399–1408) and Elliott et al. (1995, Hidden Markov Models: Estimation and Control. Springer, New York) are employed to obtain optimal estimates of the model parameters via recursive filters of auxiliary quantities of the observation process. Algorithms are developed and implemented on a financial dataset of 30-day Canadian Treasury bill yields. We also provide standard errors for the model parameter estimates. Our analysis shows that within the dataset and period studied, a model with two regimes is sufficient to describe the interest rate dynamics on the basis of very small prediction errors and the Akaike information criterion.     

Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns

A stochastic volatility model may be estimated by a quasi-maximum likelihood procedure by transforming to a linear state-space form. The method is extended to handle correlation between the two disturbances in the model and applied to data on stock returns     

An alternative derivation of the Kalman filter using the quasi-likelihood method

The Kalman filter gives a recursive procedure for estimating state vectors. The recursive procedure is determined by a matrix, so-called gain matrix, where the gain matrix is varied based on the system to which the Kalman filter is applied. Traditionally the gain matrix is derived through the maximum likelihood approach when the probability structure of underlying system is known. As an alternative approach, the quasi-likelihood method is considered in this paper. This method is used to derive the gain matrix without the full knowledge of the probability structure of the underlying system. Two models are considered in this paper, the simple state space model and the model with correlated between measurement and transition equation disturbances. The purposes of this paper are (i) to show a simple way to derive the gain matrix; (ii) to give an alternative approach for obtaining optimal estimation of state vector when underlying system is relatively complex.     

Small domain estimation by empirical bayes and kalman filtering procedures - a case study

An application of empirical Bayes and Kalman filtering tecniques is reported, using live data from Indian Statistical Institute (ISI), Calcutta . to illustrate how initial small domain estimators may be vastly improved upon. A stratified two stage sampling procedure is adopted, allowing selection of first stage units with unequal probabilities but of second stage units with equal probabilities. Standard design-based estimators for domain totals are initialized based on domain specific survey data alone. Strength is then borrowed across domains and from past surveys. The resulting gains in efficacy are numlerically demonstrated, through replicated sampling from official records.     

货币政策对区域住房市场价格 的动态影响力研究 ———基于 Ｒ形聚类与状态空间模型的实证检验

运用R型系统聚类法将我国划分为高、中、低房价地区,通过建立状态空间模型和运用卡尔曼滤波解法,对比分析了历年货币政策变化对区域房价的动态影响。实证结果表明:贷款规模对房价的影响力较大且区域差别显著,而实际利率对房价的影响力较小,也有一定的区域差异。针对我国房地产市场局部过热且高房价有向全国扩散的态势,应该根据货币政策工具对区域房价影响的特点,从以往的以价格手段调控为主,转变为以数量手段调控为主、价格手段为辅,才能使房地产市场调控取得预期效果。