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on Econometric Time Series |
| By: | Alban Moura |
| Abstract: | Hamilton (2018) argues that one should never use the Hodrick-Prescott (HP) filter, given its drawbacks and the existence of a better alternative. This comment shows that the main drawback Hamilton finds in the HP filter, the presence of filter-induced dynamics in the estimate of the cyclical component, is also a key feature of the alternative filter proposed by Hamilton. As with the HP filter, the Hamilton filter applied to a random walk extracts a cyclical component that is highly predictable, that can predict other variables, and whose properties reflect as much the filter as the underlying data-generating process. In addition, the Hamilton trend lags the data by construction and there is some arbitrariness in the choice of a key parameter defining the filter. Therefore, a more balanced assessment is that the HP and Hamilton filters provide different ways to look at the data, with neither being clearly superior from a practical perspective. |
| Keywords: | HP filter; Hamilton filter; business cycles; detrending; filtering. |
| JEL: | B41 C22 E32 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:bcl:bclwop:bclwp162&r= |
| By: | Prüser, Jan; Blagov, Boris |
| Abstract: | We propose a prior for VAR models that exploits the panel structure of macroeconomic time series while also providing shrinkage towards zero to address overfitting concerns. The prior is flexible as it detects shared dynamics of individual variables across endogenously determined groups of countries. We demonstrate the usefulness of our approach via a Monte Carlo study and use our model to capture the hidden homo- and heterogeneities of the euro area member states. Combining pairwise pooling with zero shrinkage delivers sharper parameter inference that improves point and density forecasts over only zero shrinkage or only pooling specifications, and helps with structural analysis by lowering the estimation uncertainty. |
| Keywords: | BVAR,shrinkage,forecasting,structural analysis |
| JEL: | C11 C32 C53 E37 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:rwirep:960&r= |
| By: | Sebastian Letmathe (Paderborn University) |
| Abstract: | This paper focuses on data-driven selection of the smoothing parameter in P-splines for time series with short-range dependence. Well-known asymptotic results of Psplines are first adapted to the current context. A fully automatic iterative plug-in (IPI) algorithm for P-splines is investigated in a comprehensive simulation study. Practical relevance of the IPI is shown by application to economic time series. Moreover, it is illustrated that the IPI can be used for automatic selection of the smoothing parameter of the Hodrick-Prescott filter. Furthermore, a P-spline Log-ACD model is proposed and applied to average daily trade duration data. Smoothing parameter selection is carried via the proposed IPI-algorithm, which performs very well in this context too. |
| Keywords: | P-Splines for time series, selection of the smoothing parameter, iterative plug-in, Hodrick-Prescott filter |
| JEL: | C14 C51 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:152&r= |
| By: | Lena Sasal; Tanujit Chakraborty; Abdenour Hadid |
| Abstract: | Deep learning utilizing transformers has recently achieved a lot of success in many vital areas such as natural language processing, computer vision, anomaly detection, and recommendation systems, among many others. Among several merits of transformers, the ability to capture long-range temporal dependencies and interactions is desirable for time series forecasting, leading to its progress in various time series applications. In this paper, we build a transformer model for non-stationary time series. The problem is challenging yet crucially important. We present a novel framework for univariate time series representation learning based on the wavelet-based transformer encoder architecture and call it W-Transformer. The proposed W-Transformers utilize a maximal overlap discrete wavelet transformation (MODWT) to the time series data and build local transformers on the decomposed datasets to vividly capture the nonstationarity and long-range nonlinear dependencies in the time series. Evaluating our framework on several publicly available benchmark time series datasets from various domains and with diverse characteristics, we demonstrate that it performs, on average, significantly better than the baseline forecasters for short-term and long-term forecasting, even for datasets that consist of only a few hundred training samples. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.03945&r= |
| By: | Jinyuan Chang; Qing Jiang; Xiaofeng Shao |
| Abstract: | In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at different lags. To conduct the inference, we approximate the null distribution of our test statistic by Gaussian approximation and provide a simulation-based approach to generate critical values. The asymptotic behavior of the test statistic under the alternative is also studied. Our approach is nonparametric as the null hypothesis only assumes the time series concerned is martingale difference without specifying any parametric forms of its conditional moments. As an advantage of Gaussian approximation, our test is robust to the cross-series dependence of unknown magnitude. To the best of our knowledge, this is the first valid test for the martingale difference hypothesis that not only allows for large dimension but also captures nonlinear serial dependence. The practical usefulness of our test is illustrated via simulation and a real data analysis. The test is implemented in a user-friendly R-function. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.04770&r= |
| By: | Matteo Iacopini; Aubrey Poon; Luca Rossini; Dan Zhu |
| Abstract: | Timely characterizations of risks in economic and financial systems play an essential role in both economic policy and private sector decisions. However, the informational content of low-frequency variables and the results from conditional mean models provide only limited evidence to investigate this problem. We propose a novel mixed-frequency quantile vector autoregression (MF-QVAR) model to address this issue. Inspired by the univariate Bayesian quantile regression literature, the multivariate asymmetric Laplace distribution is exploited under the Bayesian framework to form the likelihood. A data augmentation approach coupled with a precision sampler efficiently estimates the missing low-frequency variables at higher frequencies under the state-space representation. The proposed methods allow us to nowcast conditional quantiles for multiple variables of interest and to derive quantile-related risk measures at high frequency, thus enabling timely policy interventions. The main application of the model is to nowcast conditional quantiles of the US GDP, which is strictly related to the quantification of Value-at-Risk and the Expected Shortfall. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.01910&r= |