Forecasting Contemporaneously Aggregated Vector ARMA Processes

Given a multiple time series that is generated by a multivariate ARMA process and assuming the objective is to forecast a weighted sum of the individual variables, then under a mean squared error measure of forecasting precision, it is preferable to forecast the disaggregated multiple time series and aggregate the forecasts, rather than forecast the aggregated series directly, if the involved processes are known. This result fails to hold if the processes used for forecasting are estimated from a given set of time series data. The implications of these results for empirical research are investigated using different sets of economic data.     

Real-Time Forecasts of the Real Price of Oil

We construct a monthly real-time dataset consisting of vintages for 1991.1–2010.12 that is suitable for generating forecasts of the real price of oil from a variety of models. We document that revisions of the data typically represent news, and we introduce backcasting and nowcasting techniques to fill gaps in the real-time data. We show that real-time forecasts of the real price of oil can be more accurate than the no-change forecast at horizons up to 1 year. In some cases, real-time mean squared prediction error (MSPE) reductions may be as high as 25% 1 month ahead and 24% 3 months ahead. This result is in striking contrast to related results in the literature for asset prices. In particular, recursive vector autoregressive (VAR) forecasts based on global oil market variables tend to have lower MSPE at short horizons than forecasts based on oil futures prices, forecasts based on autoregressive (AR) and autoregressive moving average (ARMA) models, and the no-change forecast. In addition, these VAR models have consistently higher directional accuracy.     

Correcting Estimation Bias in Dynamic Term Structure Models

The affine dynamic term structure model (DTSM) is the canonical empirical finance representation of the yield curve. However, the possibility that DTSM estimates may be distorted by small-sample bias has been largely ignored. We show that conventional estimates of DTSM coefficients are indeed severely biased, and this bias results in misleading estimates of expected future short-term interest rates and of long-maturity term premia. We provide a variety of bias-corrected estimates of affine DTSMs, for both maximally flexible and overidentified specifications. Our estimates imply interest rate expectations and term premia that are more plausible from a macrofinance perspective. This article has supplementary material online.     

Simulating Properties of the Likelihood Ratio Test for a Unit Root in an Explosive Second-Order Autoregression

This paper provides a means of accurately simulating explosive autoregressive processes and uses this method to analyze the distribution of the likelihood ratio test statistic for an explosive second-order autoregressive process of a unit root. While the standard Dickey–Fuller distribution is known to apply in this case, simulations of statistics in the explosive region are beset by the magnitude of the numbers involved, which cause numerical inaccuracies. This has previously constituted a bar on supporting asymptotic results by means of simulation, and analyzing the finite sample properties of tests in the explosive region.     

Testing for intercept‐scale switch in linear autoregression

Autoregressive models with switching regime are a frequently used class of nonlinear time series models, which are popular in finance, engineering, and other fields. We consider linear switching autoregressions in which the intercept and variance possibly switch simultaneously, while the autoregressive parameters are structural and hence the same in all states, and we propose quasi‐likelihood‐based tests for a regime switch in this class of models. Our motivation is from financial time series, where one expects states with high volatility and low mean together with states with low volatility and higher mean. We investigate the performance of our tests in a simulation study, and give an application to a series of IBM monthly stock returns. The Canadian Journal of Statistics 40: 427–446; 2012 © 2012 Statistical Society of Canada     

山东省农业经济增长影响因素动态分析

运用1980~2009年山东省农业经济的相关数据,通过建立山东省第一产业GDP,第一产业就业人数,农作物播种总面积以及财政支农支出四变量的无约束向量自回归模型（VAR）以及向量误差修正模型（VEC）,对影响农业经济增长的因素进行了动态分析,进而探讨了山东省农业经济增长的长期趋势。结果表明,第一产业就业人数以及财政支农支出对山东省农业经济的增长有重要的影响,在此结论的基础上,提出相应的政策建议。     

Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach

We propose data generating structures which can be represented as a mixture of autoregressive-autoregressive conditionally heteroscedastic models. The switching between the states is governed by a hidden Markov chain. We investigate semi-parametric estimators for estimating the functions based on the quasi-maximum likelihood approach and provide sufficient conditions for geometric ergodicity of the process. We also present an expectation–maximization algorithm for calculating the estimates numerically.     

The Co-Integrated Vector Autoregression with Errors–in–Variables

The co-integrated vector autoregression is extended to allow variables to be observed with classical measurement errors (ME). For estimation, the model is parametrized as a time invariant state-space form, and an accelerated expectation-maximization algorithm is derived. A simulation study shows that (i) the finite-sample properties of the maximum likelihood (ML) estimates and reduced rank test statistics are excellent (ii) neglected measurement errors will generally distort unit root inference due to a moving average component in the residuals, and (iii) the moving average component may–in principle–be approximated by a long autoregression, but a pure autoregression cannot identify the autoregressive structure of the latent process, and the adjustment coefficients are estimated with a substantial asymptotic bias. An application to the zero-coupon yield-curve is given.     

Recursive online EM estimation of mixture autoregressions

This paper develops a recursive expectation–maximization (REM) algorithm for estimating a mixture autoregression (MAR) with an independent and identically distributed regime transition process. The proposed method, which is useful for long time series as well as for data available in real time, follows a recursive predictor error-type scheme. Based on a slightly modified system to the expectation–maximization (EM) equations for an MAR model, the REM algorithm consists of two steps at each iteration: the expectation step, in which the current unobserved regime transition is estimated from new data using previous recursive estimates, and the minimization step, in which the MAR parameter estimates are recursively updated following a minimization direction. Details of implementation of the REM algorithm are given and its finite-sample performance is shown via simulation experiments. In particular, the EM and REM provide roughly similar estimates, especially for moderate and long time series.     

Specification Test for Spatial Autoregressive Models

This article considers a simple test for the correct specification of linear spatial autoregressive models, assuming that the choice of the weight matrix W_n is true. We derive the limiting distributions of the test under the null hypothesis of correct specification and a sequence of local alternatives. We show that the test is free of nuisance parameters asymptotically under the null and prove the consistency of our test. To improve the finite sample performance of our test, we also propose a residual-based wild bootstrap and justify its asymptotic validity. We conduct a small set of Monte Carlo simulations to investigate the finite sample properties of our tests. Finally, we apply the test to two empirical datasets: the vote cast and the economic growth rate. We reject the linear spatial autoregressive model in the vote cast example but fail to reject it in the economic growth rate example. Supplementary materials for this article are available online.