|
on Econometric Time Series |
| By: | Christopher F Baum (Boston College; DIW Berlin); Mark E Schaffer (Heriot-Watt University) |
| Abstract: | Testing for the presence of autocorrelation in a time series is a common task for researchers working with time series data. The standard Q test statistic, introduced by Box and Pierce (1970) and refined by Ljung and Box (1978), is applicable to univariate time series and to testing for residual autocorrelation under the assumption of strict exogeneity.   Breusch (1978) and Godfrey (1978) in effect extended the L-B-P approach to testing for autocorrelations in residuals in models with weakly exogenous regressors. However, each of these readily-available tests have important limitations. We use the results of Cumby and Huizinga (1992) to extend the implementation of the Q test statistic of L-B-P-B-G to cover a much wider ranges of hypotheses and settings: (a) tests for the presence of autocorrelation of order p through q, where under the null hypothesis there may be autocorrelation of order p-1 or less; (b) tests following estimation in which regressors are endogenous and estimation is by IV or GMM methods; and (c) tests following estimation using panel data. We show that the Cumby-Huizinga test, although developed for the large-T setting, formally identical to the test developed by Arellano and Bond (1991) for AR(2) in a large-N panel setting. |
| Date: | 2013–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:boc:usug13:13&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Sainan Jin (Singapore Management University) |
| Abstract: | We propose new tests of the martingale hypothesis based on generalized versions of the Kolmogorov-Smirnov and Cramer-von Mises tests. The tests are distribution free and allow for a weak drift in the null model. The methods do not require either smoothing parameters or bootstrap resampling for their implementation and so are well suited to practical work. The paper develops limit theory for the tests under the null and shows that the tests are consistent against a wide class of nonlinear, non-martingale processes. Simulations show that the tests have good finite sample properties in comparison with other tests particularly under conditional heteroskedasticity and mildly explosive alternatives. An empirical application to major exchange rate data finds strong evidence in favor of the martingale hypothesis, confirming much earlier research. |
| Keywords: | Brownian functional, Martingale hypothesis, Kolmogorov-Smirnov test, Cramer-von Mises test, Explosive process, Exchange rates |
| JEL: | C12 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1912&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Shu-Ping Shi (Australian National University); Jun Yu (Singapore Management University) |
| Abstract: | This paper provides the limit theory of real time dating algorithms for bubble detection that were suggested in Phillips, Wu and Yu (2011, PWY) and Phillips, Shi and Yu (2013b, PSY). Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data evolves as a stochastic trend, thereby capturing normal market behavior as well as exuberance and collapse. Both the PWY and PSY estimates rely on recursive right tailed unit root tests (each with a different recursive algorithm) that may be used in real time to locate the origination and collapse dates of bubbles. Under certain explicit conditions, the moving window detector of PSY is shown to be a consistent dating algorithm even in the presence of multiple bubbles. The other algorithms are consistent detectors for bubbles early in the sample and, under stronger conditions, for subsequent bubbles in some cases. These asymptotic results and accompanying simulations guide the practical implementation of the procedures. They indicate that the PSY moving window detector is more reliable than the PWY strategy, sequential application of the PWY procedure and the CUSUM procedure. |
| Keywords: | Bubble duration, Consistency, Dating algorithm, Limit theory, Multiple bubbles, Real time detector |
| JEL: | C15 C22 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1915&r=ets |
| By: | GUO-FITOUSSI, Liang |
| Abstract: | Abstract In this paper, we compare the properties of the main criteria proposed for selecting the number of factors in dynamic factor model in a small sample. Both static and dynamic factor numbers' selection rules are studied. Simulations show that the GR ratio proposed by Ahn and Horenstein (2013) and the criterion proposed by Onatski (2010) outperform the others. Furthermore, the two criteria can select accurately the number of static factors in a dynamic factors design. Also, the criteria proposed by Hallin and Liska (2007) and Breitung and Pigorsch (2009) correctly select the number of dynamic factors in most cases. However, empirical application show most criteria select only one factor in presence of one strong factor. |
| Keywords: | dynamic factor model, factor numbers, small sample |
| JEL: | C13 C52 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:50005&r=ets |
| By: | Adam Clements (QUT); Yin Liao (QUT) |
| Abstract: | Understanding the dynamics of volatility and correlation is a crucially important issue. The literature has developed rapidly in recent years with more sophisticated estimates of volatility, and its associated jump and diffusion components. Previous work has found that jumps at an index level are not related to future volatility. Here we examine the links between co-jumps within a group of large stocks, the volatility of, and correlation between their returns. It is found that the occurrence of common, or co-jumps between the stocks are unrelated to the level of volatility or correlation. On the other hand, both volatility and correlation are lower subsequent to a co-jump. This indicates that co-jumps are a transient event but in contrast to earlier research have a greater impact that jumps at an index level. |
| Keywords: | Realized volatility, correlation, jumps, co-jumps, point process |
| JEL: | C22 G00 |
| Date: | 2013–02–24 |
| URL: | http://d.repec.org/n?u=RePEc:qut:auncer:2013_3&r=ets |
| By: | Richard A. Ashley; Kwok Ping Tsang |
| Abstract: | Credible Granger-causality analysis appears to require post-sample inference, as it is well-known that in-sample fit can be a poor guide to actual forecasting effectiveness. But post-sample model testing requires an often-consequential a priori partitioning of the data into an 'in-sample' period - purportedly utilized only for model specifi- cation/estimation - and a 'post-sample' period, purportedly utilized (only at the end of the analysis) for model validation/testing purposes. This partitioning is usually infeasible, however, with samples of modest length – e.g., T less than 100 - as is common in both quarterly data sets and/or in monthly data sets where institutional arrange- ments vary over time, simply because there is in such cases insufficient data available to credibly accomplish both purposes separately. A cross-sample validation (CSV) testing procedure is proposed below which substantially ameliorates this predicament - preserving most of the power of in-sample testing (by utilizing all of the sample data in the test), while also retaining most of the credibility of post-sample testing (by al- ways basing model forecasts on data not utilized in estimating that particular model's coefficients). Simulations show that the price paid, in terms of power relative to the in-sample Granger-causality F test, is manageable. An illustrative application is given, to a re-analysis of the Engel and West (2005) study of the causal relationship between macroeconomic fundamentals and the exchange rate. |
| Keywords: | Time Series, Granger-causality, causality, post-sample testing, exchange rates. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:vpi:wpaper:e07-40&r=ets |