|
on Econometric Time Series |
| By: | Rohit Deo (New York University); Clifford Hurvich (New York University); Philippe Soulier (University of Paris X); Yi Wang (New York University) |
| Abstract: | We establish sufficient conditions on durations that are stationary with finite variance and memory parameter $d \in [0,1/2)$ to ensure that the corresponding counting process $N(t)$ satisfies $\textmd{Var} \, N(t) \sim C t^{2d+1}$ ($C>0$) as $t \rightarrow \infty$, with the same memory parameter $d \in [0,1/2)$ that was assumed for the durations. Thus, these conditions ensure that the memory in durations propagates to the same memory parameter in counts and therefore in realized volatility. We then show that any Autoregressive Conditional Duration ACD(1,1) model with a sufficient number of finite moments yields short memory in counts, while any Long Memory Stochastic Duration model with $d>0$ and all finite moments yields long memory in counts, with the same $d$. Finally, we present a result implying that the only way for a series of counts aggregated over a long time period to have nontrivial autocorrelation is for the short-term counts to have long memory. In other words, aggregation ultimately destroys all autocorrelation in counts, if and only if the counts have short memory. |
| Keywords: | Long Memory Stochastic Duration, Autoregressive Conditional Duration, Rosenthal-type Inequality. |
| JEL: | C1 C2 C3 C4 C5 C8 |
| Date: | 2005–11–08 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpem:0511010&r=ets |
| By: | CHARFEDDINE Lanouar (University of Paris II, Centre de recherche ERMES, doctorant associés à L'ENS Cahcan) |
| Abstract: | In recent years two classes of switching models have been proposed, the Markov switching models, Hamilton (1989) and the Threshold Auto- Regressive Models (TAR), Lim and Tong (1980). These two models have the advantage of being able to modelize and capture asymmetry, sudden changes and irreversibility time observed in many economic and financial time series. Despite these similarities and common points, these models have been envolved, in the literature, largely independently. In this paper, using the $SupLR$ test, we study the possibility of discrimination between these two models. This approach is motivated by the fact that the majority of authors, in applications, use switching models without any statistical justification. We show that when the null hypothesis is rejected it appears that different switching models are significant. Then, using simulation experiments we show that it is very difficult to differenciate between MSAR and SETAR models specially with large samples. The power of the $SupLR$ test seems to be sensitive to the mean, the noise variance and the delay parameter which appear in each model. Finally, we apply this methodology to the US GNP growth rate and the US/UK exchange rate. |
| Keywords: | Switching Models, SETAR processes SupLR test, Empirical power, exchange rates |
| JEL: | C12 C15 F31 |
| Date: | 2005–11–04 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpif:0511002&r=ets |