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on Econometric Time Series |
| By: | James A. Duffy; Sophocles Mavroeidis |
| Abstract: | While it is widely recognised that linear (structural) VARs may omit important features of economic time series, the use of nonlinear SVARs has to date been almost entirely confined to the modelling of stationary time series, because of a lack of understanding as to how common stochastic trends may be accommodated within nonlinear VAR models. This has unfortunately circumscribed the range of series to which such models can be applied -- and/or required that these series be first transformed to stationarity, a potential source of misspecification -- and prevented the use of long-run identifying restrictions in these models. To address these problems, we develop a flexible class of additively time-separable nonlinear SVARs, which subsume models with threshold-type endogenous regime switching, both of the piecewise linear and smooth transition varieties. We extend the Granger-Johansen representation theorem to this class of models, obtaining conditions that specialise exactly to the usual ones when the model is linear. We further show that, as a corollary, these models are capable of supporting the same kinds of long-run identifying restrictions as are available in linear cointegrated SVARs. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.05349&r=ets |
| By: | Matteo Mogliani; Anna Simoni |
| Abstract: | We propose a Machine Learning approach for optimal macroeconomic forecasting in a high-dimensional setting with covariates presenting a known group structure. Our model encompasses forecasting settings with many series, mixed frequencies, and unknown nonlinearities. We introduce in time-series econometrics the concept of bi-level sparsity, i.e. sparsity holds at both the group level and within groups, and we assume the true model satisfies this assumption. We propose a prior that induces bi-level sparsity, and the corresponding posterior distribution is demonstrated to contract at the minimax-optimal rate, recover the model parameters, and have a support that includes the support of the model asymptotically. Our theory allows for correlation between groups, while predictors in the same group can be characterized by strong covariation as well as common characteristics and patterns. Finite sample performance is illustrated through comprehensive Monte Carlo experiments and a real-data nowcasting exercise of the US GDP growth rate. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.02671&r=ets |
| By: | Artem Kraevskiy; Artem Prokhorov; Evgeniy Sokolovskiy |
| Abstract: | We develop and apply a new online early warning system (EWS) for what is known in machine learning as concept drift, in economics as a regime shift and in statistics as a change point. The system goes beyond linearity assumed in many conventional methods, and is robust to heavy tails and tail-dependence in the data, making it particularly suitable for emerging markets. The key component is an effective change-point detection mechanism for conditional entropy of the data, rather than for a particular indicator of interest. Combined with recent advances in machine learning methods for high-dimensional random forests, the mechanism is capable of finding significant shifts in information transfer between interdependent time series when traditional methods fail. We explore when this happens using simulations and we provide illustrations by applying the method to Uzbekistan's commodity and equity markets as well as to Russia's equity market in 2021-2023. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.03319&r=ets |
| By: | Eric Luxenberg; Stephen Boyd |
| Abstract: | An exponentially weighted moving model (EWMM) for a vector time series fits a new data model each time period, based on an exponentially fading loss function on past observed data. The well known and widely used exponentially weighted moving average (EWMA) is a special case that estimates the mean using a square loss function. For quadratic loss functions EWMMs can be fit using a simple recursion that updates the parameters of a quadratic function. For other loss functions, the entire past history must be stored, and the fitting problem grows in size as time increases. We propose a general method for computing an approximation of EWMM, which requires storing only a window of a fixed number of past samples, and uses an additional quadratic term to approximate the loss associated with the data before the window. This approximate EWMM relies on convex optimization, and solves problems that do not grow with time. We compare the estimates produced by our approximation with the estimates from the exact EWMM method. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.08136&r=ets |
| By: | Bai, Jushan; Wang, Peng |
| Abstract: | We propose a framework for causal inference using factor models. We base our identification strategy on the assumption that policy interventions cause structural breaks in the factor loadings for the treated units. The method allows heterogeneous trends and is easy to implement. We compare our method with the synthetic control methods of Abadie, et al (2010, 2015), and obtain similar results. Additionally, we provide confidence intervals for the causal effects. Our approach expands the toolset for causal inference. |
| Keywords: | synthetic control, difference-in-differences, structural breaks, latent factors. |
| JEL: | C1 C23 C33 C51 |
| Date: | 2024–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:120585&r=ets |
| By: | Jiatong Li; Hongqiang Yan |
| Abstract: | We develop uniform inference for high-dimensional threshold regression parameters and valid inference for the threshold parameter in this paper. We first establish oracle inequalities for prediction errors and $\ell_1$ estimation errors for the Lasso estimator of the slope parameters and the threshold parameter, allowing for heteroskedastic non-subgaussian error terms and non-subgaussian covariates. Next, we derive the asymptotic distribution of tests involving an increasing number of slope parameters by debiasing (or desparsifying) the scaled Lasso estimator. The asymptotic distribution of tests without the threshold effect is identical to that with a fixed effect. Moreover, we perform valid inference for the threshold parameter using subsampling method. Finally, we conduct simulation studies to demonstrate the performance of our method in finite samples. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.08105&r=ets |
| By: | Peter Reinhard Hansen; Chen Tong |
| Abstract: | We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody cluster structures with flexible nonlinear dependencies and heterogeneous marginal distributions. Importantly, convolution-t distributions have simple density functions that facilitate estimation and likelihood-based inference. The characteristic features of convolution-t distributions are found to be important in an empirical analysis of realized volatility measures and help identify their underlying factor structure. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2404.00864&r=ets |