|
on Econometric Time Series |
| By: | Jinyuan Chang; Qin Fang; Xinghao Qiao; Qiwei Yao |
| Abstract: | We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series $p$ is large in relation to the length of time series $n$. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from any two different groups are uncorrelated both contemporaneously and serially. Consequently in our second step those groups are handled separately without the information loss on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for all the transformed functional time series within each group. Furthermore the finite-dimensional structure is represented by that of a vector time series. Modelling and forecasting for the original high-dimensional functional time series are realized via those for the vector time series in all the groups. We investigate the theoretical properties of our proposed methods, and illustrate the finite-sample performance through both extensive simulation and two real datasets. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.00700&r= |
| By: | Massimiliano MARCELLINO; Michael PFARRHOFER |
| Abstract: | We review specification and estimation of multivariate Bayesian nonparametric models for forecasting (possibly large sets of) macroeconomic and financial variables. The focus is on Bayesian Additive Regression Trees and Gaussian Processes. We then apply various versions of these models for point, density and tail forecasting using datasets for the euro area and the US. The performance is compared with that of several variants of Bayesian VARs to assess the relevance of accounting for general forms of nonlinearities. We find that medium-scale linear VARs with stochastic volatility are tough benchmarks to beat. Some gains in predictive accuracy arise for nonparametric approaches, most notably for short-run forecasts of unemployment and longer-run predictions of inflation, and during recessionary or otherwise non-standard economic episodes |
| Keywords: | United States, euro area, Bayesian Additive Regression Trees, Gaussian Processes, multivariate time series analysis, structural breaks |
| JEL: | C11 C32 C53 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:baf:cbafwp:cbafwp24224&r= |
| By: | Roberto Leon-Gonzalez (National Graduate Institute for Policy Studies, Tokyo, Japan); Blessings Majon (National Graduate Institute for Policy Studies, Tokyo, Japan) |
| Abstract: | Common factor stochastic volatility (CSV) models capture the commonality that is often observed in volatility patterns. However, they assume that all the time variation in volatility is driven by a single multiplicative factor. This paper has two contributions. Firstly we develop a novel CSV model in which the volatility follows an inverse gamma process (CSV-IG), which implies fat Student’s t tails for the observed data. We obtain an analytic expression for the likelihood of this CSV model, which facilitates the numerical calculation of the marginal and predictive likelihood for model comparison. We also show that it is possible to simulate exactly from the posterior distribution of the volatilities using mixtures of gammas. Secondly, we generalize this CSV-IG model by parsimoniously substituting conditionally homoscedastic shocks with heteroscedastic factors which interact multiplicatively with the common factor in an approximate factor model (CSV-IG-AF). In empirical applications we compare these models to other multivariate stochastic volatility models, including different types of CSV models and exact factor stochastic volatility (FSV) models. The models are estimated using daily exchange rate returns of 8 currencies. A second application estimates the models using 20 macroeconomic variables for each of four countries: US, UK, Japan and Brazil. The comparison method is based on the predictive likelihood. In the application to exchange rate data we find strong evidence of CSV and that the best model is the IG-CSV-AF. In the Macro application we find that 1) the CSV-IG model performs better than all other CSV models, 2) the CSV-IG-AF is the best model for the US, 3) the CSV-IG is the best model for Brazil and 4) exact factor SV models are the best for UK and JP. |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:ngi:dpaper:24-02&r= |
| By: | Roberto Leon-Gonzalez (National Graduate Institute for Policy Studies, Tokyo, Japan; The Rimini Centre for Economic Analysis); Blessings Majoni (National Graduate Institute for Policy Studies, Tokyo, Japan) |
| Abstract: | We obtain a novel analytic expression of the likelihood for a stationary inverse gamma Stochastic Volatility (SV) model. This allows us to obtain the Maximum Likelihood Estimator for this non linear non gaussian state space model. Further, we obtain both the filtering and smoothing distributions for the inverse volatilities as mixture of gammas and therefore we can provide the smoothed estimates of the volatility. We show that by integrating out the volatilities the model that we obtain has the resemblance of a GARCH in the sense that the formulas are similar, which simplifies computations significantly. The model allows for fat tails in the observed data. We provide empirical applications using exchange rates data for 7 currencies and quarterly inflation data for four countries. We find that the empirical fit of our proposed model is overall better than alternative models for 4 countries currency data and for 2 countries inflation data. |
| Keywords: | Hypergeometric Function, Particle Filter, Parallel Computing, Euler Acceleration. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:ngi:dpaper:23-07&r= |
| By: | Siddhartha Chib; Simon C. Smith |
| Abstract: | We develop a new approach to select risk factors in an asset pricing model that allows the set to change at multiple unknown break dates. Using the six factors displayed in Table 1 since 1963, we document a marked shift towards parsimonious models in the last two decades. Prior to 2005, five or six factors are selected, but just two are selected thereafter. This finding offers a simple implication for the factor zoo literature: ignoring breaks detects additional factors that are no longer relevant. Moreover, all omitted factors are priced by the selected factors in every regime. Finally, the selected factors outperform popular factor models as an investment strategy. |
| Keywords: | Model comparison; Factor models; Structural breaks; Anomaly; Bayesian analysis; Discount factor; Portfolio analysis; Sparsity |
| JEL: | G12 C11 C12 C52 C58 |
| Date: | 2024–05–31 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2024-37&r= |