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on Econometric Time Series |
| By: | Søren Johansen (Department of Economics, University of Copenhagen and CREATES, University of Aarhus) |
| Abstract: | There are simple well-known conditions for the validity of regression and correlation as statistical tools. We analyse by examples the effect of nonstationarity on inference using these methods and compare them to model based inference. Finally we analyse some data on annual mean temperature and sea level, by applying the cointegrated vector autoregressive model, which explicitly takes into account the nonstationarity of the variables. |
| Keywords: | Regression correlation cointegration, model based inference, likelihood inference, annual mean temperature, sea level |
| JEL: | C32 |
| Date: | 2010–10–15 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-69&r=ets |
| By: | Søren Johansen (University of Copenhagen and CREATES); Morten Ørregaard Nielsen (Queen?s University and CREATES) |
| Abstract: | We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x_{t}=Delta^{-d}u_{t}, where d in (-1/2,1/2) is the fractional integration parameter and u_{t} is weakly dependent. The classical condition is existence of q>max(2,(d+1/2)^{-1}) moments of the innovation sequence. When d is close to -1/2 this moment condition is very strong. Our main result is to show that under some relatively weak conditions on u_{t}, the existence of q=max(2,(d+1/2)^{-1}) is in fact necessary for the FCLT for fractionally integrated processes and that q>max(2,(d+1/2)^{-1}) moments are necessary and sufficient for more general fractional processes. Davidson and de Jong (2000) presented a fractional FCLT where only q>2 finite moments are assumed, which is remarkable because it is the only FCLT where the moment condition has been weakened relative to the earlier condition. As a corollary to our main theorem we show that their moment condition is not sufficient. |
| Keywords: | Fractional integration, functional central limit theorem, long memory, moment condition, necessary condition. |
| JEL: | C22 |
| Date: | 2010–10–21 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-70&r=ets |
| By: | Jia Chen (School of Economics, University of Adelaide); Jiti Gao (School of Economics, University of Adelaide); Degui Li (School of Economics, University of Adelaide) |
| Abstract: | In this paper, we consider a semiparametric time series regression model and establish a set of identication conditions such that the model under discussion is both identiable and estimable. We then discuss how to estimate a sequence of local alternative functions nonparametrically when the null hypothesis does not hold. An asymptotic theory is established in each case. An empirical application is also included. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2010-27&r=ets |
| By: | Jiti Gao (School of Economics, University of Adelaide); Peter C. B. Phillips |
| Abstract: | A system of vector semiparametric nonlinear time series models is studied with possible dependence structures and nonstationarities in the parametric and nonparametric components. The parametric regressors may be endogenous while the nonparametric regressors are strictly exogenous. The parametric regressors may be stationary or nonstationary and the nonparametric regressors are nonstationary time series. Semiparametric least squares (SLS) estimation is considered and its asymptotic properties are derived. Due to endogeneity in the parametric regressors, SLS is not consistent for the parametric component and a semiparametric instrumental variable least squares (SIVLS) method is proposed instead. Under certain regularity conditions, the SIVLS estimator of the parametric component is shown to be consistent with a limiting normal distribution. Interestingly, the rate of convergence in the parametric component depends on the properties of the regressors. It has been shown that the conventional rate is still achievable even when nonstationarity is involved in both the regressors. |
| Keywords: | Dynamic simultaneous equation, endogeneity, exogeneity, non-stationarity, partially linear model, vector semiparametric regression |
| JEL: | C23 C25 |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2010-26&r=ets |
| By: | Song Xi Chen (Guanghua School of Management, Peking University); Jiti Gao (School of Economics, University of Adelaide) |
| Abstract: | This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the variance components of the goodness{of{t. To reduce the dependence of the test on a single pair of smoothing bandwidths, we construct an adaptive test by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. The test procedure is based on a bootstrap calibration to the distribution of the empirical likelihood test statistic. We demonstrate that the empirical likelihood test is able to distinguish local alternatives which are different from the null hypothesis at an optimal rate. |
| Keywords: | Bootstrap, empirical likelihood, goodness{of{t test, kernel estimation, least squares empirical likelihood, rate-optimal test |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:adl:wpaper:2010-28&r=ets |
| By: | Monojit Chatterji; Homagni Choudhury |
| Abstract: | This study addresses the issue of the presence of a unit root on the growth rate estimation by the least-squares approach. We argue that when the log of a variable contains a unit root, i.e., it is not stationary then the growth rate estimate from the log-linear trend model is not a valid representation of the actual growth of the series. In fact, under such a situation, we show that the growth of the series is the cumulative impact of a stochastic process. As such the growth estimate from such a model is just a spurious representation of the actual growth of the series, which we refer to as a “pseudo growth rate”. Hence such an estimate should be interpreted with caution. On the other hand, we highlight that the statistical representation of a series as containing a unit root is not easy to separate from an alternative description which represents the series as fundamentally deterministic (no unit root) but containing a structural break. In search of a way around this, our study presents a survey of both the theoretical and empirical literature on unit root tests that takes into account possible structural breaks. We show that when a series is trendstationary with breaks, it is possible to use the log-linear trend model to obtain well defined estimates of growth rates for sub-periods which are valid representations of the actual growth of the series. Finally, to highlight the above issues, we carry out an empirical application whereby we estimate meaningful growth rates of real wages per worker for 51 industries from the organised manufacturing sector in India for the period 1973-2003, which are not only unbiased but also asymptotically efficient. We use these growth rate estimates to highlight the evolving inter-industry wage structure in India. |
| Keywords: | Growth Rate, CAGR, AAGR, Unit Root, Trend Stationary, Structural Breaks, Real Wages, Inter-Industry Wage Structure |
| JEL: | C12 C13 C22 J31 |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:dun:dpaper:245&r=ets |
| By: | MArcelo Cunha Medeiros (Department of Economics, PUC-Rio); Eduardo Mendes (DEPARTMENT OF STATISTICS, NORTHWESTERN UNIVERSITY,); Les Oxley (DEPARTMENT OF ECONOMICS, CANTERBURY UNIVERSITY,) |
| Abstract: | We show that the asymptotic distribution of the ordinary least squares estimator in a cointegration regression may be bimodal. A simple case arises when the intercept is erroneously omitted from the estimated model or in nonlinear-in-variables models with endogenous regressors. In the latter case, a solution is to use an instrumental variable estimator. The core results in this paper also generalises to more complicated nonlinear models involving integrated time series. |
| Keywords: | Cointegration, nonlinearity, bimodality, misspecification, instrumental variables, asymptotic theory. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:rio:texdis:577&r=ets |
| By: | Matthew Lorig |
| Abstract: | We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility surfaces induced by these time-changes are examined as a function of the model parameters. Three key features of our framework are that we are able to incorporate jumps into the price process of the underlying asset, allow for the leverage effect, and accommodate multiple factors of volatility, which operate on different time-scales. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1010.5203&r=ets |