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on Econometric Time Series |
| By: | Pesaran, M.H.; Smit, L.V.; Yamagata, T. |
| Abstract: | This paper extends the cross sectionally augmented panel unit root test proposed by Pesaran (2007) to the case of a multifactor error structure. The basic idea is to exploit information regarding the unobserved factors that are shared by other time series in addition to the variable under consideration. Importantly, our test procedure only requires specification of the maximum number of factors, in contrast to other panel unit root tests based on principal components that require in addition the estimation of the number of factors as well as the factors themselves. Small sample properties of the proposed test are investigated by Monte Carlo experiments, which suggest that it controls well for size in almost all cases, especially in the presence of serial correlation in the error term, contrary to alternative test statistics. Empirical applications to Fisher's inflation parity and real equity prices across different markets illustrate how the proposed test works in practice. |
| Keywords: | Panel unit root tests, Cross Section Dependence, Multi-factor Residual Structure, Fisher In.ation Parity, Real Equity Prices. |
| JEL: | C12 C15 C22 C23 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0775&r=ets |
| By: | Dees, S.; Pesaran, M.H.; Smith, L.V.; Smith, R.P. |
| Abstract: | New Keynesian Phillips Curves (NKPC) have been extensively used in the analysis of monetary policy, but yet there are a number of issues of concern about how they are estimated and then related to the underlying macroeconomic theory. The first is whether such equations are identified. To check identification requires specifying the process for the forcing variables (typically the output gap) and solving the model for inflation in terms of the observables. In practice, the equation is estimated by GMM, relying on statistical criteria to choose instruments. This may result in failure of identification or weak instruments. Secondly, the NKPC is usually derived as a part of a DSGE model, solved by log-linearising around a steady state and the variables are then measured in terms of deviations from the steady state. In practice the steady states, e.g. for output, are usually estimated by some statistical procedure such as the Hodrick-Prescott (HP) filter that might not be appropriate. Thirdly, there are arguments that other variables, e.g. interest rates, foreign inflation and foreign output gaps should enter the Phillips curve. This paper examines these three issues and argues that all three benefit from a global perspective. The global perspective provides additional instruments to alleviate the weak instrument problem, yields a theoretically consistent measure of the steady state and provides a natural route for foreign inflation or output gap to enter the NKPC. |
| Keywords: | Global VAR (GVAR), identification, New Keynesian Phillips Curve, Trend-Cycle decomposition. |
| JEL: | C32 E17 F37 F42 |
| Date: | 2008–01 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0803&r=ets |
| By: | Harvey, A. |
| Abstract: | The relationship between in.ation and the output gap can be modeled simply and effectively by including an unobserved random walk component in the model. The dynamic properties match the stylized facts and the random walk component satisfies the properties normally required for core in.ation. The model may be generalized to as to include a term for the expectation of next period's output, but it is shown that this is difficult to distinguish from the original specification. The model is fited as a single equation and as part of a bivariate model that includes an equation for GDP. Fitting the bivariate model highlights some new aspects of unobserved components modeling. Single equation and bivariate models tell a similar story: an output gap two per cent above trend is associated with an annual inflation rate that is one percent above core inflation. |
| Keywords: | Cycle; hybrid new Keynesian Phillips curve; inflation gap; Kalman filter, output gap. |
| Date: | 2008–01 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0805&r=ets |
| By: | Pesaran, M.H.; Schuermann, T.; Smit, L.V. |
| Abstract: | This paper considers the problem of forecasting real and financial macroeconomic variables across a large number of countries in the global economy. To this end a global vector autoregressive (GVAR) model previously estimated over the 1979Q1-2003Q4 period by Dees, de Mauro, Pesaran, and Smith (2007), is used to generate out-of-sample one quarter and four quarters ahead forecasts of real output, inflation, real equity prices, exchange rates and interest rates over the period 2004Q1-2005Q4. Forecasts are obtained for 134 variables from 26 regions made up of 33 countries covering about 90% of world output. The forecasts are compared to typical benchmarks: univariate autoregressive and random walk models. Building on the forecast combination literature, the effects of model and estimation uncertainty on forecast outcomes are examined by pooling forecasts obtained from different GVAR models estimated over alternative sample periods. Given the size of the modeling problem, and the heterogeneity of economies considered — industrialised, emerging, and less developed countries — as well as the very real likelihood of possibly multiple structural breaks, averaging forecasts across both models and windows makes a significant difference. Indeed the double-averaged GVAR forecasts performed better than the benchmark competitors, especially for output, inflation and real equity prices. |
| Keywords: | Forecasting using GVAR, structural breaks and forecasting, average forecasts across models and windows, financial and macroeconomic forecasts. |
| JEL: | C32 C51 C53 |
| Date: | 2008–01 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:0807&r=ets |
| By: | Donald W.K. Andrews (Cowles Foundation, Yale University); Patrik Guggenberger (Dept. of Economics, UCLA) |
| Abstract: | This paper considers a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter and the distribution of the time series of innovations. In particular, we consider the full range of cases in which the autoregressive parameter rho_n satisfies (i) n(1 - rho_n) -> infinity and (ii) n(1 - rho_n) -> h_1 < infinity as n -> infinity, where n is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics. |
| Keywords: | Asymptotic distribution, Autoregression, Conditional heteroskedasticity, Generalized least squares, Least squares |
| JEL: | C22 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1665&r=ets |
| By: | Markku Lanne; Pentti Saikkonen |
| Abstract: | This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. We argue that noncausal autoregressive models are especially well suited for modeling expectations. Unlike conventional causal autoregressive models, they explicitly show how the considered economic variable is affected by expectations and how expectations are formed. Noncausal autoregressive models can also be used to examine the related issue of backward-looking or forward-looking dynamics of an economic variable. We show in the paper how the parameters of a noncausal autoregressive model can be estimated by the method of maximum likelihood and how related test procedures can be obtained. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a detailed discussion on their specification is provided. Motivated by economic applications we explicitly use a forward-looking autoregressive polynomial in the formulation of the model. This is di¤erent from the practice used in previous statistics literature on noncausal autoregressions and, in addition to its economic motivation, it is also convenient from a statistical point of view. In particular, it facilitates obtaining likelihood based diagnostic tests for the specified orders of the backward-looking and forward-looking autoregressive polynomials. Such test procedures are not only useful in the specification of the model but also in testing economically interesting hypotheses such as whether the considered variable only exhibits forward-looking behavior. As an empirical application, we consider modeling the U.S. in.ation dynamics which, according to our results, is purely forward-looking. |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2008/20&r=ets |
| By: | Marc Hallin; Roman Liska |
| Abstract: | Macroeconometric data often come under the form of large panels of time series, themselves decomposing into smaller but still quite large subpanels or blocks. We show how the dynamic factor analysis method proposed in Forni et al (2000), combined with the identification method of Hallin and Liska (2007), allows for identifying and estimating joint and block-specific common factors. This leads to a more sophisticated analysis of the structures of dynamic interrelations within and between the blocks in such datasets, along with an informative decomposition of explained variances. The method is illustrated with an analysis of the Industrial Production Index data for France, Germany, and Italy. |
| Keywords: | Panel data; Time series; High dimensional data; Dynamic factor model; Business cycle; Block specific factors; Dynamic principal components; Information criterion. |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2008/22&r=ets |
| By: | Matei Demetrescu; Helmut Luetkepohl; Pentti Saikkonen |
| Abstract: | When applying Johansen's procedure for determining the cointegrating rank to systems of variables with linear deterministic trends, there are two possible tests to choose from. One test allows for a trend in the cointegration relations and the other one restricts the trend to be orthogonal to the cointegration relations. The first test is known to have reduced power relative to the second one if there is in fact no trend in the cointegration relations, whereas the second one is based on a misspecified model if the linear trend is not orthogonal to the cointegration relations. Hence, the treatment of the linear trend term is crucial for the outcome of the rank determination procedure. We compare two alternative testing strategies which are applicable if there is uncertainty regarding the proper trend specification. In the first one a specific cointegrating rank is rejected if one of the two tests rejects and in the second one the trend term is decided upon by a pretest. The first strategy is shown to be preferable in applied work. |
| Keywords: | Cointegration analysis, likelihood ratio test, vector autoregressive model, vector error correction model |
| JEL: | C32 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2008/24&r=ets |
| By: | Mika Meitz; Pentti Saikkonen |
| Abstract: | This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a functional coefficient autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. Strong consistency and asymptotic normality of the global Gaussian quasi maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors. |
| Keywords: | AR-GARCH, asymptotic normality, consistency, nonlinear time series, quasi maximum likelihood estimation |
| JEL: | C13 C22 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2008/25&r=ets |
| By: | Bent Nielsen (Department of Economics, University of Oxford); Heino Bohn Nielsen (Department of Economics, University of Copenhagen) |
| Abstract: | Estimated characteristic roots in stationary autoregressions are shown to give rather noisy information about their population equivalents. This is remarkable given the central role of the characteristic roots in the theory of autoregressive processes. In the asymptotic analysis the problems appear when multiple roots are present as this imply a non-differentiability so the δ-method does not apply, convergence rates are slow, and the asymptotic distribution is non-normal. In finite samples this has a considerable influence on the finite sample distribution unless the roots are far apart. With increasing order of the autoregressions it becomes increasingly difficult to place the roots far apart giving a very noisy signal from the characteristic roots. |
| Keywords: | autoregression; characteristic root |
| JEL: | C22 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:0813&r=ets |
| By: | Brendan K. Beare (Nuffield College, Oxford University) |
| Abstract: | It is known that unit root test statistics may not have the usual asymptotic properties when the variance of innovations is unstable. In particular, persistent changes in volatility can cause the size of unit root tests to differ from the nominal level. In this paper we propose a class of modified unit root test statistics that are robust to the presence of unstable volatility. The modification is achieved by purging heteroskedasticity from the data using a kernel estimate of volatility prior to the application of standard tests. In the absence of deterministic trend components, this approach delivers test statistics that achieve standard asymptotics under the null hypothesis of a unit root. When the data are homoskedastic, the local power of unit root tests is unchanged by our modification. We use Monte Carlo simulations to compare the finite sample performance of our modified tests with that of existing methods of correcting for unstable volatility. |
| Keywords: | unit root, heteroskedasticity, nonstationary volatility. |
| JEL: | C14 C22 |
| Date: | 2008–05–05 |
| URL: | http://d.repec.org/n?u=RePEc:nuf:econwp:0806&r=ets |
| By: | Mika Meitz; Pentti Saikkonen |
| Abstract: | This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a functional coefficient autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH (1,1)) model. Strong consistency and asymptotic normality of the global Gaussian quasi maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors. |
| Keywords: | AR-GARCH, Asymptotic Normality, Consistency, Nonlinear Time Series, Quasi Maximum Likelihood |
| JEL: | C13 C22 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:396&r=ets |
| By: | Framroze Moller, Niels |
| Abstract: | Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity in the economic model implies the econometric concept of strong exogeneity for â. The economic equilibrium corresponds to the so-called long-run value (Johansen 2005), the comparative statics are captured by the long-run impact matrix, C; and the exogenous variables are the common trends. Also, the adjustment parameters of the CVAR are shown to be interpretable in terms of expectations formation, market clearing, nominal rigidities, etc. The general-partial equilibrium distinction is also discussed. |
| Keywords: | Cointegrated VAR, unit root approximation, economic theory models, expectations, general equilibrium, DSGE models |
| JEL: | C32 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ifwedp:7283&r=ets |
| By: | Mendes, Rui Vilela; Oliveira, Maria J. |
| Abstract: | Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes and a new option pricing formula are also obtained. |
| Keywords: | Fractional noise, induced volatility, statistics of returns, option pricing |
| JEL: | C51 G12 G14 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ifwedp:7284&r=ets |
| By: | Bernardi, Mauro; Della Corte, Giuseppe; Proietti, Tommaso |
| Abstract: | The series on average hours worked in the manufacturing sector is a key leading indicator of the U.S. business cycle. The paper deals with robust estimation of the cyclical component for the seasonally adjusted time series. This is achieved by an unobserved components model featuring an irregular component that is represented by a Gaussian mixture with two components. The mixture aims at capturing the kurtosis which characterizes the data. After presenting a Gibbs sampling scheme, we illustrate that the Gaussian mixture model provides a satisfactory representation of the data, allowing for the robust estimation of the cyclical component of per capita hours worked. Another important piece of evidence is that the outlying observations are not scattered randomly throughout the sample, but have a distinctive seasonal pattern. Therefore, seasonal adjustment plays a role. We ¯nally show that, if a °exible seasonal model is adopted for the unadjusted series, the level of outlier contamination is drastically reduced. |
| Keywords: | Gaussian Mixtures; Robust signal extraction; State Space Models; Bayesian model selection; Seasonality |
| JEL: | E32 C52 C22 C11 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8880&r=ets |