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on Econometric Time Series |
| By: | Stefano Iacus (Department of Economics, Business and Statistics, University of Milan, IT); Alessandro De Gregorio (Department of Statistics, University of Padova) |
| Abstract: | The telegraph process $X(t)$, $t>0$, (Goldstein, 1951) and the geometric telegraph process $S(t) = s_0 \exp\{(\mu -\frac12\sigma^2)t + \sigma X(t)\}$ with $\mu$ a known constant and $\sigma>0$ a parameter are supposed to be observed at $n+1$ equidistant time points $t_i=i\Delta_n,i=0,1,\ldots, n$. For both models $\lambda$, the underlying rate of the Poisson process, is a parameter to be estimated. In the geometric case, also $\sigma>0$ has to be estimated. We propose different estimators of the parameters and we investigate their performance under the high frequency asymptotics, i.e. $\Delta_n \to 0$, $n\Delta = T<\infty$ as $n \to \infty$, with $T>0$ fixed. The process $X(t)$ in non markovian, non stationary and not ergodic thus we use approximation arguments to derive estimators. Given the complexity of the equations involved only estimators on the first model can be studied analytically. Therefore, we run an extensive Monte Carlo analysis to study the performance of the proposed estimators also for small sample size $n$. |
| Keywords: | telegraph process, discretely observed process, inference for stochastic processes, |
| Date: | 2006–07–25 |
| URL: | http://d.repec.org/n?u=RePEc:bep:unimip:1033&r=ets |
| By: | M. Hashem Pesaran; Allan Timmermann |
| Abstract: | The contingency table literature on tests for dependence among discrete multi-category variables is extensive. Existing tests assume, however, that draws are independent, and there are no tests that account for serial dependencies?a problem that is particularly important in economics and finance. This paper proposes a new test of independence based on the maximum canonical correlation between pairs of discrete variables. We also propose a trace canonical correlation test using dynamically augmented reduced rank regressions or an iterated weighting method in order to account for serial dependence. Such tests are useful, for example, when testing for predictability of one sequence of discrete random variables by means of another sequence of discrete random variables as in tests of market timing skills or business cycle analysis. The proposed tests allow for an arbitrary number of categories, are robust in the presence of serial dependencies and are simple to implement using multivariate regression methods. Monte Carlo experiments show that the proposed tests have good finite sample properties. An empirical application to survey data on forecasts of GDP growth demonstrates the importance of correcting for serial dependencies in predictability tests. |
| Keywords: | contingency tables, canonical correlations, serial dependence, tests of predictability |
| JEL: | C12 C22 C42 C52 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_1770&r=ets |
| By: | BARRIENTOS-MARÍN, Jorge |
| Abstract: | This work presents a tool for the additivity test. The additive model is widely used for parametric and semiparametric modeling of economic data. The additivity hypothesis is of interest because it is easy to interpret and produces reasonably fast convergence rates for non-parametric estimators. Another advantage of additive models is that they allow attacking the problem of the curse of dimensionality that arises in non- parametric estimation. Hypothesis testing is based in the well-known bootstrap residual process. In nonparametric testing literature, the dominant idea is that bandwidth utilized to produce bootstrap sample should be bigger that bandwidth for estimating model under null hypothesis. However, there is no hint so far about how to choose such bandwidth in practice. We will discuss a first step to find some rule of thumb to choose bandwidth in that context. Our suggestions are accompanied by simulation studies. |
| Date: | 2005–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:col:001065:002618&r=ets |