Forecasting the UK economy with a medium-scale Bayesian VAR

We estimate a Bayesian VAR (BVAR) for the UK economy and assess its performance in forecasting GDP growth and CPI inflation in real time relative to forecasts from COMPASS, the Bank of England’s DSGE model, and other benchmarks. We find that the BVAR outperformed COMPASS when forecasting both GDP and its expenditure components. In contrast, their performances when forecasting CPI were similar. We also find that the BVAR density forecasts outperformed those of COMPASS, despite under-predicting inflation at most forecast horizons. Both models over-predicted GDP growth at all forecast horizons, but the issue was less pronounced in the BVAR. The BVAR’s point and density forecast performances are also comparable to those of a Bank of England in-house statistical suite for both GDP and CPI inflation, as well as to the official Inflation Report projections. Our results are broadly consistent with the findings of similar studies for other advanced economies.     

A Bayesian analysis of a variance decomposition for stock returns

We apply Bayesian methods to study a common vector autoregression (VAR)-based approach for decomposing the variance of excess stock returns into components reflecting news about future excess stock returns, future real interest rates, and future dividends. We develop a new prior elicitation strategy, which involves expressing beliefs about the components of the variance decomposition. Previous Bayesian work elicited priors from the difficult-to-interpret parameters of the VAR. With a commonly used data set, we find that the posterior standard deviations for the variance decomposition based on these previously used priors, including “non-informative” limiting cases, are much larger than classical standard errors based on asymptotic approximations. Therefore, the non-informative researcher remains relatively uninformed about the variance decomposition after observing the data. We show the large posterior standard deviations arise because the “non-informative” prior is implicitly very informative in a highly undesirable way. However, reasonably informative priors using our elicitation method allow for much more precise inference about components of the variance decomposition.     

The Structural Relation Between Mortgage and Market Interest Rates

This paper analyzes the dynamic relationship between primary and secondary mortgage markets and the short-term and long-term market interest rates. Using a series of monthly data on fixed rate mortgage rates and GNMA rates, we explore the dependence and speed of adjustment in these primary and secondary mortgage rates to each other as well as to the long and short-term government rates. The results indicate that residential mortgage rates in general, appear to follow the long-term rate and are not very sensitive to movements in the short-term interest rate.     

Analysis of cointegrated VARMA processes

VARMA (vector autoregressive moving average) processes are proposed for modelling cointegrated variables. For this purpose the echelon form is combined with the error correction form. Procedures for estimating the Kronecker indices which characterize the echelon form and for specifying the cointegration rank are discussed. The asymptotic distribution of the coefficient estimators is given. An example based o n US macroeconomic data illustrates the procedure and demonstrates its feasibility in practice.     

中国股市波动与经济波动的传递性研究

基于1994~2004年度的月份数据,对股市波动与经济波动的关系进行研究。我们采用Schwert(1989)的12阶自回归模型对各经济变量序列的波动性进行估计,并进一步通过Granger因果检验和冲击反应函数考察各波动序列之间的内在关系。检验结果表明:在Granger因果检定中,股市波动并未受到总体经济波动的影响,说明股市在一定程度上反映了当前的经济信息;股市波动与经济波动的冲击反应函数则显示,股市波动与经济波动之间的影响大体在6~8个月以内传递完毕。     

Minnesota-type adaptive hierarchical priors for large Bayesian VARs

Large Bayesian VARs with stochastic volatility are increasingly used in empirical macroeconomics. The key to making these highly parameterized VARs useful is the use of shrinkage priors. We develop a family of priors that captures the best features of two prominent classes of shrinkage priors: adaptive hierarchical priors and Minnesota priors. Like adaptive hierarchical priors, these new priors ensure that only ‘small’ coefficients are strongly shrunk to zero, while ‘large’ coefficients remain intact. At the same time, these new priors can also incorporate many useful features of the Minnesota priors such as cross-variable shrinkage and shrinking coefficients on higher lags more aggressively. We introduce a fast posterior sampler to estimate BVARs with this family of priors—for a BVAR with 25 variables and 4 lags, obtaining 10,000 posterior draws takes about 3 min on a standard desktop computer. In a forecasting exercise, we show that these new priors outperform both adaptive hierarchical priors and Minnesota priors.     

The Austrian current account deficit: Driven by twin deficits or by intertemporal expenditure allocation?

The evidence presented in the paper rejects the twin deficit hypothesis for the Austrian current account balance during the last two decades. The results are based on an estimate of a vector error correction model including quarterly data for the current account balance and potentially relevant variables driving its dynamics. We compute the variance decomposition of the current account's forecast error and its generalized impulse responses to shocks in the innovations of the system. The results in favor of intertemporal expenditure reallocation cannot be reproduced within a second analysis including the current account and a measure of net output, however. The estimated implicit current account balance, interpreted as the discounted expected change in future net output, does not follow the actual behaviour of the current account. First version received: June 1999/Final version received: March 2001     

协整向量误设对相关检验的影响

常用于检验既定协整关系的统计量有tDF和tECM两种，但由于真实数据生成过程未知，估计模型中可能存在一定程度的协整向量误设，从而使统计量的分布特征受到影响。本文首先探讨tDF检验的隐含系数约束α=γ，即短期弹性等于先验长期弹性；其次分析零假设下两种统计量的分布特征，以及先验设定γ对信号噪声比q进而对tECM分布特征的影响；最后在局部备择假设下，给出两种统计量的渐近分布，并表明向量误设会降低协整检验的势，其程度与设定误差d正相关。     

Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models

This paper provides closed-form formulae for computing the asymptotic covariance matrices of the estimated autocovariance and autocorrelation functions of stable VAR models by means of the delta method. These covariance matrices can be used to construct asymptotic confidence bands for the estimated autocovariance and autocorrelation functions to assess the underlying estimation uncertainty. The usefulness of the formulae for empirical work is illustrated by an application to inflation and output gap data for the U.S. economy indicating the existence of a significant short-run Phillips-curve tradeoff.First version received: November 2002/Final version received: September 2003     

A critical overview of privacy-preserving approaches for collaborative forecasting

Cooperation between different data owners may lead to an improvement in forecast quality—for instance, by benefiting from spatiotemporal dependencies in geographically distributed time series. Due to business competitive factors and personal data protection concerns, however, said data owners might be unwilling to share their data. Interest in collaborative privacy-preserving forecasting is thus increasing. This paper analyzes the state-of-the-art and unveils several shortcomings of existing methods in guaranteeing data privacy when employing vector autoregressive models. The methods are divided into three groups: data transformation, secure multi-party computations, and decomposition methods. The analysis shows that state-of-the-art techniques have limitations in preserving data privacy, such as (i) the necessary trade-off between privacy and forecasting accuracy, empirically evaluated through simulations and real-world experiments based on solar data; and (ii) iterative model fitting processes, which reveal data after a number of iterations.