|
on Econometric Time Series |
| By: | Chiu, Ching-Wai (Jeremy) (Bank of England); hayes, simon (Bank of England); kapetanios, george (Kings College); Theodoridis, Konstantinos (Cardiff University) |
| Abstract: | Forecasts play a critical role at inflation-targeting central banks, such as the Bank of England. Breaks in the forecast performance of a model can potentially incur important policy costs. Commonly used statistical procedures, however, implicitly put a lot of weight on type I errors (or false positives), which result in a relatively low power of tests to identify forecast breakdowns in small samples. We develop a procedure which aims at capturing the policy cost of missing a break. We use data-based rules to find the test size that optimally trades off the costs associated with false positives with those that can result from a break going undetected for too long. In so doing, we also explicitly study forecast errors as a multivariate system. The covariance between forecast errors for different series, though often overlooked in the forecasting literature, not only enables us to consider testing in a multivariate setting but also increases the test power. As a result, we can tailor the choice of the critical values for each series not only to the in-sample properties of each series but also to how the series for forecast errors covary. |
| Keywords: | Forecast breaks; statistical decision making; central banking |
| JEL: | C53 E47 E58 |
| Date: | 2018–04–13 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0721&r=ets |
| By: | Alessandro Casini (Boston University); Pierre Perron (Boston University) |
| Abstract: | Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2017a) for inference in structural change models, we propose a Laplace-based (quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. The procedure relies on a Laplace-type estimator defined by an integration-based rather than an optimization-based method. A transformation of the least-integration-based rather than an optimization-based method. A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is defined as the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more precise-lower mean absolute error (MAE) and lower root-mean squared error (RMSE)-than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure proposed is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large. |
| Keywords: | Asymptotic distribution, bias, break date, change-point, Generalized Laplace, infill asymptotics, semimartingale |
| JEL: | C12 C13 C22 |
| Date: | 2017–12 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2018-011&r=ets |
| By: | Alessandro Casini (Boston University); Pierre Perron (Boston University) |
| Abstract: | Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998). The GL estimator is defined by an integration rather than optimization-based method and relies on the least-squares criterion function. It is interpreted as a classical (non-Bayesian) estimator and the inference methods proposed retain a frequentist interpretation. Since inference about the change-point dates is a nonstandard statistical problem, the origional insight of Laplace to interpret a certain transformation of a least-squares criterion function as a statistical believe over the parameter space provides a better approximation about the uncertainty in the data about the change-points relative to existing methods. Simulations show that the GL estimator is in general more precise than the OLS estimator. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution; namely, the classical shrinkage asymptotic distribution of Bai an Perron (1998), or a Bayes-type asymptotic distribution. |
| Keywords: | Asymptotic distribution, break date, change-point, Generalized Laplace, Highest Density Region, Quasi-Bayes |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2018-012&r=ets |
| By: | Gianluca Cubadda (DEF and CEIS, University of Rome "Tor Vergata"); Alain Hecq (Maastricht University); Sean Telg (Maastricht University) |
| Abstract: | This paper introduces the notion of common noncausal features and proposes tools to detect them in multivariate time series models. We argue that the existence of co-movements might not be detected using the conventional stationary vector autoregressive (VAR) model as the common dynamics are present in the noncausal (i.e. forward-looking) component of the series. In particular, we show that the presence of a reduced rank structure allows to identify purely causal and noncausal VAR processes of order two and higher even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can still be applied, where both lags and leads are used as instruments to determine whether the common features are present in either the backward-or forward-looking dynamics of the series. The proposed definitions of co-movements also valid for the mixed causal-noncausal VAR, with the exception that an approximate non-Gaussian maximum likelihood estimator is necessary for these cases. This means however that one loses the benefits of the simple tools proposed in this paper. An empirical analysis on European Brent and U.S. West Texas Intermediate oil prices illustrates the main findings. Whereas we fail to find any short run co-movements in a conventional causal VAR, they are detected in the growth rates of the series when considering a purely noncausal VAR. |
| Keywords: | causal and noncausal process, common features, vector autoregressive models, oil prices |
| JEL: | C12 C32 E32 |
| Date: | 2018–04–23 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:430&r=ets |