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on Econometric Time Series |
| By: | Jinyuan Chang; Yue Du; Guanglin Huang; Qiwei Yao |
| Abstract: | We investigate the identification and the estimation for matrix time series CP-factor models. Unlike the generalized eigenanalysis-based method of Chang et al. (2023) which requires the two factor loading matrices to be full-ranked, the newly proposed estimation can handle rank-deficient factor loading matrices. The estimation procedure consists of the spectral decomposition of several matrices and a matrix joint diagonalization algorithm, resulting in low computational cost. The theoretical guarantee established without the stationarity assumption shows that the proposed estimation exhibits a faster convergence rate than that of Chang et al. (2023). In fact the new estimator is free from the adverse impact of any eigen-gaps, unlike most eigenanalysis-based methods such as that of Chang et al. (2023). Furthermore, in terms of the error rates of the estimation, the proposed procedure is equivalent to handling a vector time series of dimension $\max(p, q)$ instead of $p \times q$, where $(p, q)$ are the dimensions of the matrix time series concerned. We have achieved this without assuming the "near orthogonality" of the loadings under various incoherence conditions often imposed in the CP-decomposition literature, see Han and Zhang (2022), Han et al. (2024) and the references within. Illustration with both simulated and real matrix time series data shows the usefulness of the proposed approach. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.05634 |
| By: | Liudas Giraitis (Queen Mary University of London); Fulvia Marotta (De Nederlandsche Bank, University of Oxford); Peter C B Phillips (Yale University) |
| Abstract: | This paper builds on methodology that corrects for irregular spacing between realizations of unevenly spaced time series and provides appropriately corrected estimates of autoregressive model parameters. Using these methods for dealing with missing data, we develop time series tools for forecasting and estimation of autoregressions with cyclically varying parameters in which periodicity is assumed. To illustrate the robustness and flexibility of the methodology, an application is conducted to model daily temperature data. The approach helps to uncover cyclical (daily as well as annual) patterns in the data without imposing restrictive assumptions. Using the Central England Temperature (CET) time series (1772 - present) we find with a high level of accuracy that temperature intra-year averages and persistence have increased in the later sample 1850-2020 compared to 1772 - 1850, especially for the winter months, whereas the estimated variance of the random shocks in the autoregression seems to have decreased over time. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2409 |
| By: | Zongwu Cai (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA); Gunawan (Faculty of Economics and Business, Universitas Gadjah Mada, Yogyakarta 55281, Indonesia); Yuying Sun (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China) |
| Abstract: | This paper proposes a new nonparametric forecasting procedure based on a weighted local linear estimator for a nonparametric model with structural breaks. The proposed method assigns a weight based on both the distance of observations to the predictor covariates and their location in time and the weight is chosen using multifold forward-validation to account for time series data. We investigate the asymptotic properties of the proposed estimator and show that the weight estimated by the multifold forward-validation is asymptotically optimal in the sense of achieving the lowest possible out-of-sample prediction risk. Additionally, a nonparametric method is adopted to estimate the break date and the proposed approach allows for different features of predictors before and after break. A Monte Carlo simulation study is conducted to provide evidence for the forecasting outperformance of the proposed method over the regular nonparametric post-break and full-sample estimators. Finally, an empirical application to volatility forecasting compares several popular parametric and nonparametric methods, including the proposed weighted local linear estimator, demonstrating its superiority over other alternative methods. |
| Keywords: | Combination Forecasting; Model Averaging; multifold forward-validation; Nonparametric Model; Structural Break Model; Weighted Local Linear Fitting |
| JEL: | C14 C22 C53 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:kan:wpaper:202412 |
| By: | Ali Mehrabani (Department of Economics, University of Kansas, Lawrence, KS 66045); Shahnaz Parsaeian (Department of Economics, University of Kansas, Lawrence, KS 66045); Aman Ullah (Department of Economics, University of California at Riverside, CA 92521) |
| Abstract: | This paper introduces a Stein-like shrinkage method for estimating slope coefficients and forecasting in first order dynamic regression models under structural breaks. The model allows for unit root and non-stationary regressors. The proposed shrinkage estimator is a weighted average of a restricted estimator that ignores the break in the slope coefficients, and an unrestricted estimator that uses the observations within each regime. The restricted estimator is the most efficient estimator but inconsistent when there is a break. However, the unrestricted estimator is consistent but not efficient. Therefore, the proposed shrinkage estimator balances the trade-off between the bias and variance efficiency of the restricted estimator. The averaging weight is proportional to the weighted distance of the restricted estimator, and the unrestricted estimator. We derive the analytical large-sample approximation of the bias, mean squared error, and risk for the shrinkage estimator, the unrestricted estimator, and the restricted estimator. We show that the risk of the shrinkage estimator is lower than the risk of the unrestricted estimator under any break size and break points. Moreover, we extend the results for the model with a unit root and non-stationary regressors. We evaluate the finite sample performance of our proposed method via extensive simulation study, and empirically in forecasting output growth |
| Keywords: | ARX-model; Asymptotic approximation; Dynamic regressions; Forecasting; Moment approximation; Non-stationary regressors; Structural breaks; Unit root. |
| JEL: | C13 C22 C53 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:kan:wpaper:202410 |
| By: | Yixiao Sun (University of California, San Diego); Peter C. B. Phillips (Yale University); Igor L. Kheifets (University of North Carolina at Charlotte) |
| Abstract: | This note shows that the mixed normal asymptotic limit of the trend IV estimator with a fixed number of deterministic instruments (fTIV) holds in both singular (multicointegrated) and nonsingular cointegration systems, thereby relaxing the exogeneity condition in (Phillips and Kheifets, 2024, Theorem 1(ii)). The mixed normality of the limiting distribution of fTIV allows for asymptotically pivotal F tests about the cointegration parameters and for simple efficiency comparisons of the estimators for different numbers K of instruments, as well as comparisons with the trend IV estimator when K → ∞ with the sample size. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2410 |
| By: | Shahnaz Parsaeian (Department of Economics, University of Kansas, Lawrence, KS 66045) |
| Abstract: | This paper develops a Stein-like combined estimator for large heterogeneous panel data models under common structural breaks. The model allows for cross-sectional dependence through a general multifactor error structure. By utilizing the common correlated effects (CCE) estimation technique, we propose a Stein-like combined estimator of the CCE full-sample estimator (i.e., estimation using both the pre-break and post-break observations) and the CCE post-break estimator (i.e., estimation using only the post-break sample observations). The proposed Stein-like combined estimator benefits from exploiting the pre-break sample observations. We derive the optimal combination weight by minimizing the asymptotic risk. We show the superiority of the CCE Stein-like combined estimator over the CCE post-break estimator in terms of the asymptotic risk. Further, we establish the asymptotic properties of the CCE mean group Stein-like combined estimator. The finite sample performance of our proposed estimator is investigated using Monte Carlo experiments and an empirical application of predicting the output growth of industrialized countries. |
| Keywords: | Common correlated effects, Cross-sectional dependence, Heterogeneous panels, Structural breaks. |
| JEL: | C13 C23 C33 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:kan:wpaper:202409 |
| By: | Liu, Yirui; Qiao, Xinghao; Pei, Yulong; Wang, Liying |
| Abstract: | This paper introduces the Deep Functional Factor Model (DF2M), a Bayesian nonparametric model designed for analysis of high-dimensional functional time series. DF2M is built upon the Indian Buffet Process and the multi-task Gaussian Process, incorporating a deep kernel function that captures non-Markovian and nonlinear temporal dynamics. Unlike many black-box deep learning models, DF2M offers an explainable approach to utilizing neural networks by constructing a factor model and integrating deep neural networks within the kernel function. Additionally, we develop a computationally efficient variational inference algorithm to infer DF2M. Empirical results from four real-world datasets demonstrate that DF2M provides better explainability and superior predictive accuracy compared to conventional deep learning models for high-dimensional functional time series. |
| JEL: | C1 |
| Date: | 2024–07–21 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:125587 |
| By: | Gabriele Fiorentini; Alessio Moneta; Francesca Papagni |
| Abstract: | We establish the identification of a specific shock in a structural vector autoregressive model under the assumption that this shock is independent of the other shocks in the system, without requiring the latter shocks to be mutually independent, unlike the typical assumptions in the independent component analysis literature. The shock of interest can be either non-Gaussian or Gaussian, but, in the latter case, the other shocks must be jointly non-Gaussian. We formally prove the global identification of the shock and the associated column of the impact multiplier matrix, and discuss parameter estimation by maximum likelihood. We conduct a detailed Monte Carlo simulation to illustrate the finite sample behavior of our identification and estimation procedure. Finally, we estimate the dynamic effect of a contraction in economic activity on some measures of economic policy uncertainty. |
| Keywords: | Independent component analysis, Non-Gaussian maximum likelihood, Impact multipliers, Economic policy uncertainty |
| Date: | 2024–10–31 |
| URL: | https://d.repec.org/n?u=RePEc:ssa:lemwps:2024/28 |
| By: | Siyu Bie (City University of Hong Kong); Francis X. Diebold (University of Pennsylvania); Jingyu He (City University of Hong Kong); Junye Li (Fudan University) |
| Abstract: | We explore tree-based macroeconomic regime-switching in the context of the dynamic Nelson-Siegel (DNS) yield-curve model. In particular, we customize the treegrowing algorithm to partition macroeconomic variables based on the DNS model’s marginal likelihood, thereby identifying regime-shifting patterns in the yield curve. Compared to traditional Markov-switching models, our model offers clear economic interpretation via macroeconomic linkages and ensures computational simplicity. In an empirical application to U.S. Treasury bond yields, we find (1) important yield curve regime switching, and (2) evidence that macroeconomic variables have predictive power for the yield curve when the short rate is high, but not in other regimes, thereby refining the notion of yield curve “macro-spanning”. |
| Keywords: | Decision Tree; Macro-Finance; Term Structure; Regime Switching; Dynamic Nelson-Siegel Model; Bayesian Estimation |
| JEL: | C11 E43 G12 |
| Date: | 2024–10–08 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:24-028 |