时间序列分析在经济预测中的应用

社会消费品零售总额是一项重要、敏感的政府统计。定期发布的消费品零售统计资料,常常引起国内外的强烈关注,间或还会引发一些疑义和争议。文章拟通过运用EXCEL及SAS软件建立季节分解模型和季节哑变量、ARIMA模型,对我国的社会消费零售总额的情况进行预测分析,从初步确定几个不同的模型中,把拟合效果最好的模型保留,并对模型的实用性进行了探讨。     

Sampling the Future: A Bayesian Approach to Forecasting From Univariate Time Series Models

The Box–Jenkins methodology for modeling and forecasting from univariate time series models has long been considered a standard to which other forecasting techniques have been compared. To a Bayesian statistician, however, the method lacks an important facet—a provision for modeling uncertainty about parameter estimates. We present a technique called sampling the future for including this feature in both the estimation and forecasting stages. Although it is relatively easy to use Bayesian methods to estimate the parameters in an autoregressive integrated moving average (ARIMA) model, there are severe difficulties in producing forecasts from such a model. The multiperiod predictive density does not have a convenient closed form, so approximations are needed. In this article, exact Bayesian forecasting is approximated by simulating the joint predictive distribution. First, parameter sets are randomly generated from the joint posterior distribution. These are then used to simulate future paths of the time series. This bundle of many possible realizations is used to project the future in several ways. Highest probability forecast regions are formed and portrayed with computer graphics. The predictive density's shape is explored. Finally, we discuss a method that allows the analyst to subjectively modify the posterior distribution on the parameters and produce alternate forecasts.     

Forecasting Performance of Information Criteria with Many Macro Series

Stock & Watson (1999) consider the relative quality of different univariate forecasting techniques. This paper extends their study on forecasting practice, comparing the forecasting performance of two popular model selection procedures, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). This paper considers several topics: how AIC and BIC choose lags in autoregressive models on actual series, how models so selected forecast relative to an AR(4) model, the effect of using a maximum lag on model selection, and the forecasting performance of combining AR(4), AIC, and BIC models with an equal weight.     

Some Properties and Generalizations of Non-negative Bayesian Time Series Models

We study the most basic Bayesian forecasting model for exponential family time series, the power steady model (PSM) of Smith, in terms of observable properties of one-step forecast distributions and sample paths. The PSM implies a constraint between location and spread of the forecast distribution. Including a scale parameter in the models does not always give an exact solution free of this problem, but it does suggest how to define related models free of the constraint. We define such a class of models which contains the PSM. We concentrate on the case where observations are non-negative. Probability theory and simulation show that under very mild conditions almost all sample paths of these models converge to some constant, making them unsuitable for modelling in many situations. The results apply more generally to non-negative models defined in terms of exponentially weighted moving averages. We use these and related results to motivate, define and apply very simple models based on directly specifying the forecast distributions.     

Forecasting With Nonspurious Factors in U.S. Macroeconomic Time Series

This study examines the practical implications of the fact that structural changes in factor loadings can produce spurious factors (or irrelevant factors) in forecasting exercises. These spurious factors can induce an overfitting problem in factor-augmented forecasting models. To address this concern, we propose a method to estimate nonspurious factors by identifying the set of response variables that have no structural changes in their factor loadings. Our theoretical results show that the obtained set may include a fraction of unstable response variables. However, the fraction is so small that the original factors are able to be identified and estimated consistently. Moreover, using this approach, we find that a significant portion of 132 U.S. macroeconomic time series have structural changes in their factor loadings. Although traditional principal components provide eight or more factors, there are significantly fewer nonspurious factors. The forecasts using the nonspurious factors can significantly improve out-of-sample performance.     

An Application of Nonlinear Time Series Forecasting

By means of a real application, it is seen how ARIMA forecasts can be improved when nonlinearities are present. The autocorrelation function (ACF) of the squared residuals provides a convenient tool to check the linearity assumption. Once nonlinearity has been detected, parsimonious bilinear processes seem rather adequate to model it. The detection of nonlinearity and the forecast improvement appear to be rather robust with respect to changes in the linear and bilinear specification. Finally, what bilinear models seem to capture are periods of atypical behavior or sequences of outliers.     

Cross-entropy method for estimation of posterior expectation in Bayesian VAR models

In this article, an importance sampling (IS) method for the posterior expectation of a non linear function in a Bayesian vector autoregressive (VAR) model is developed. Most Bayesian inference problems involve the evaluation of the expectation of a function of interest, usually a non linear function of the model parameters, under the posterior distribution. Non linear functions in Bayesian VAR setting are difficult to estimate and usually require numerical methods for their evaluation. A weighted IS estimator is used for the evaluation of the posterior expectation. With the cross-entropy (CE) approach, the IS density is chosen from a specified family of densities such that the CE distance or the Kullback–Leibler divergence between the optimal IS density and the importance density is minimal. The performance of the proposed algorithm is assessed in an iterated multistep forecasting of US macroeconomic time series.     

An Application of Vector Time Series Techniques to Macroeconomic Forecasting

A wide variety of time series techniques are now used for generating forecasts of economic variables, with each technique attempting to summarize and exploit whatever regularities exist in a given data set. It appears that many researchers arbitrarily choose one of these techniques. The purpose of this article is to provide an example for which the choice of time series technique appears important; merely choosing arbitrarily among available techniques may lead to suboptimal results.