
on Econometric Time Series 
By:  Grant Hillier (CeMMAP and University of Southampton); Federico Martellosio (University of Surrey) 
Abstract:  The (quasi) maximum likelihood estimator (QMLE) for the autoregressive parameter in a spatial autoregressive model cannot in general be written explicitly in terms of the data. The only known properties of the estimator have hitherto been its firstorder asymptotic properties (Lee, 2004, Econometrica), derived under specific assumptions on the evolution of the spatial weights matrix involved. In this paper we show that the exact cumulative distribution function of the estimator can, under mild assumptions, be written in terms of that of a particular quadratic form. A number of immediate consequences of this result are discussed, and some examples are analyzed in detail. The examples are of interest in their own right, but also serve to illustrate some unexpected features of the distribution of the MLE. In particular, we show that the distribution of the MLE may not be supported on the entire parameter space, and may be nonanalytic at some points in its support. 
JEL:  C12 C21 
Date:  2016–05 
URL:  http://d.repec.org/n?u=RePEc:sur:surrec:0716&r=ets 
By:  Herbst, Edward; Schorfheide, Frank 
Abstract:  The accuracy of particle filters for nonlinear statespace models crucially depends on the proposal distribution that mutates time t1 particle values into time t values. In the widelyused bootstrap particle filter this distribution is generated by the statetransition equation. While straightforward to implement, the practical performance is often poor. We develop a selftuning particle filter in which the proposal distribution is constructed adaptively through a sequence of Monte Carlo steps. Intuitively, we start from a measurement error distribution with an inflated variance, and then gradually reduce the variance to its nominal level in a sequence of steps that we call tempering. We show that the filter generates an unbiased and consistent approximation of the likelihood function. Holding the run time fixed, our filter is substantially more accurate in two DSGE model applications than the bootstrap particle filter. 
Keywords:  Bayesian Analysis ; DSGE Models ; Monte Carlo Methods ; Nonlinear Filtering 
JEL:  C11 C15 E10 
Date:  2016–08–25 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgfe:201672&r=ets 
By:  Manabu Asai (Soka University, Japan); ChiaLin Chang (National Chung Hsing University, Taiwan); Michael McAleer (National Tsing Hua University, Taiwan; Erasmus School of Economics, Erasmus University Rotterdam; Complutense University of Madrid, Spain; Yokohama National University, Japan) 
Abstract:  The paper develops a novel realized matrixexponential stochastic volatility model of multivariate returns and realized covariances that incorporates asymmetry and long memory (hereafter the RMESVALM model). The matrix exponential transformation guarantees the positivedefiniteness of the dynamic covariance matrix. The contribution of the paper ties in with Robert Basmann’s seminal work in terms of the estimation of highly nonlinear model specifications (“Causality tests and observationally equivalent representations of econometric models”, Journal of Econometrics , 1988, 39(12), 69–104), especially for developing tests for leverage and spillover effects in the covariance dynamics. Efficient importance sampling is used to maximize the likelihood function of RMESVALM, and the finite sample properties of the quasimaximum likelihood estimator of the parameters are analysed. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The forecasting performance of the new model is compared with a novel dynamic realized matrixexponential conditional covariance model. The volatility and covolatility spillovers are examined via the news impact curves and the impulse response functions from returns to volatility and covolatility. 
Keywords:  Matrixexponential transformation; Realized stochastic covariances; Realized conditional covariances; Asymmetry; Long memory; Spillovers; Dynamic covariance matrix; Finite sample properties; Forecasting performance 
JEL:  C22 C32 C58 G32 
Date:  2016–09–12 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:20160076&r=ets 
By:  W. Robert Reed (University of Canterbury); Aaron Smith 
Abstract:  We show that cointegration among times series paradoxically makes it more likely that a unit test will reject the unit root null hypothesis on the individual series. If one time series is cointegrated with another, then it can be written as the sum of two processes, one with a unit root and one stationary. It follows that the series cannot be represented as a finiteorder autoregressive process. Unit root tests use an autoregressive model to account for autocorrelation, so they perform poorly in this setting, even if standard methods are used to choose the number of lags. This finding implies that univariate unit root tests are of questionable use in cointegration analysis. 
Keywords:  Unit root testing, cointegration, Augmented DickeyFuller test, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Modified Akaike Information Criterion (MAIC) 
JEL:  C32 C22 C18 
Date:  2016–09–06 
URL:  http://d.repec.org/n?u=RePEc:cbt:econwp:16/19&r=ets 
By:  Francis X. Diebold; Frank Schorfheide; Minchul Shin 
Abstract:  Recent work has analyzed the forecasting performance of standard dynamic stochastic general equilibrium (DSGE) models, but little attention has been given to DSGE models that incorporate nonlinearities in exogenous driving processes. Against that background, we explore whether incorporating stochastic volatility improves DSGE forecasts (point, interval, and density). We examine realtime forecast accuracy for key macroeconomic variables including output growth, inflation, and the policy rate. We find that incorporating stochastic volatility in DSGE models of macroeconomic fundamentals markedly improves their density forecasts, just as incorporating stochastic volatility in models of financial asset returns improves their density forecasts. 
JEL:  E17 
Date:  2016–09 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:22615&r=ets 