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on Econometric Time Series |
| By: | Younghoon Kim; Zachary F. Fisher; Vladas Pipiras |
| Abstract: | This work considers estimation and forecasting in a multivariate count time series model based on a copula-type transformation of a Gaussian dynamic factor model. The estimation is based on second-order properties of the count and underlying Gaussian models and applies to the case where the model dimension is larger than the sample length. In addition, novel cross-validation schemes are suggested for model selection. The forecasting is carried out through a particle-based sequential Monte Carlo, leveraging Kalman filtering techniques. A simulation study and an application are also considered. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.10454&r=ets |
| By: | Christis Katsouris |
| Abstract: | We establish the asymptotic validity of the bootstrap-based IVX estimator proposed by Phillips and Magdalinos (2009) for the predictive regression model parameter based on a local-to-unity specification of the autoregressive coefficient which covers both nearly nonstationary and nearly stationary processes. A mixed Gaussian limit distribution is obtained for the bootstrap-based IVX estimator. The statistical validity of the theoretical results are illustrated by Monte Carlo experiments for various statistical inference problems. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.14463&r=ets |
| By: | Paolo Andreini (Independent Researcher); Cosimo Izzo (Independent Researcher); Giovanni Ricco (CREST, Ecole Polytechnique, University of Warwick, OFCE-SciencesPo, CEPR) |
| Abstract: | A novel deep neural network framework – that we refer to as Deep Dynamic Factor Model (D2FM) –, is able to encode the information available, from hundreds of macroeconomic and financial time-series into a handful of unobserved latent states. While similar in spirit to traditional dynamic factor models (DFMs), differently from those, this new class of models allows for nonlinearities between factors and observables due to the autoencoder neural network structure. However, by design, the latent states of the model can still be interpreted as in a standard factor model. Both in a fully real-time out-of-sample nowcasting and forecasting exercise with US data and in a Monte Carlo experiment, the D2FM improves over the performances of a state-of-the-art DFM. |
| Keywords: | Machine Learning, Deep Learning, Autoencoders, Real-Time data, Time-Series, Forecasting, Nowcasting, Latent Component Models, Factor Models |
| JEL: | C22 C52 C53 C55 |
| Date: | 2023–05–20 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2023-08&r=ets |
| By: | Matteo Barigozzi |
| Abstract: | We prove that in an approximate factor model for an $n$-dimensional vector of stationary time series the factor loadings estimated via Principal Components are asymptotically equivalent, as $n\to\infty$, to those estimated by Quasi Maximum Likelihood. Both estimators are, in turn, also asymptotically equivalent, as $n\to\infty$, to the unfeasible Ordinary Least Squares estimator we would have if the factors were observed. We also show that the usual sandwich form of the asymptotic covariance matrix of the Quasi Maximum Likelihood estimator is asymptotically equivalent to the simpler asymptotic covariance matrix of the unfeasible Ordinary Least Squares. This provides a simple way to estimate asymptotic confidence intervals for the Quasi Maximum Likelihood estimator without the need of estimating the Hessian and Fisher information matrices whose expressions are very complex. All our results hold in the general case in which the idiosyncratic components are cross-sectionally heteroskedastic as well as serially and cross-sectionally weakly correlated. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.09864&r=ets |
| By: | Christis Katsouris |
| Abstract: | We consider Wald type statistics designed for joint predictability and structural break testing based on the instrumentation method of Phillips and Magdalinos (2009). We show that under the assumption of nonstationary predictors: (i) the tests based on the OLS estimators converge to a nonstandard limiting distribution which depends on the nuisance coefficient of persistence; and (ii) the tests based on the IVX estimators can filter out the persistence under certain parameter restrictions due to the supremum functional. These results contribute to the literature of joint predictability and parameter instability testing by providing analytical tractable asymptotic theory when taking into account nonstationary regressors. We compare the finite-sample size and power performance of the Wald tests under both estimators via extensive Monte Carlo experiments. Critical values are computed using standard bootstrap inference methodologies. We illustrate the usefulness of the proposed framework to test for predictability under the presence of parameter instability by examining the stock market predictability puzzle for the US equity premium. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.15151&r=ets |
| By: | Ping Wu (Department of Economics, University of Strathclyde); Gary Koop (Department of Economics, University of Strathclyde) |
| Abstract: | Bayesian inference in Vector Autoregressions (VARs) involves manipulating large matrices which appear in the posterior (or conditional posterior) of the VAR coe- cients. For large VARs, the computational time involved with these manipulations becomes so large as to make empirical work impractical. In response to this, many researchers transform their VARs so as to allow for Bayesian estimation to proceed one equation at a time. This leads to a massive reduction in the computational bur- den. This transformation involves taking the Cholesky decomposition for the error covariance matrix. However, this strategy implies that posterior inference depends on the order the variables enter the VAR. In this paper we develop an alternative transformation, based on the eigendecomposition, which does not lead to order de- pendence. Beginning with an inverse-Wishart prior on the error covariance matrix, we derive and discuss the properties of the prior it implies on the eigenmatrix and eigenvalues. We then show how an extension of the prior on the eigenmatrix can allow for greater exibility while maintaining many of the bene ts of conjugacy. We exploit this exibility in order to extend the prior on the eigenvalues to allow for stochastic volatility. The properties of the eigendecomposition approach are investigated in a macroeconomic forecasting exercise involving VARs with 20 variables. |
| Keywords: | Eigendecomposition, order invariance, large vector autoregression |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:str:wpaper:2310&r=ets |
| By: | Bruno Feunou |
| Abstract: | We introduce generalized autoregressive gamma (GARG) processes, a class of autoregressive and moving-average processes that extends the class of existing autoregressive gamma (ARG) processes in one important dimension: each conditional moment dynamic is driven by a different and identifiable moving average of the variable of interest. The paper provides ergodicity conditions for GARG processes and derives closed-form conditional and unconditional moments. The paper also presents estimation and inference methods, illustrated by an application to European option pricing where the daily realized variance follows a GARG dynamic. Our results show that using GARG processes reduces pricing errors by substantially more than using ARG processes does. |
| Keywords: | Econometric and statistical methods; Asset pricing |
| JEL: | C58 G12 |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:23-40&r=ets |
| By: | Jad Beyhum; Jonas Striaukas |
| Abstract: | This study introduces a bootstrap test of the validity of factor regression within a high-dimensional factor-augmented sparse regression model that integrates factor and sparse regression techniques. The test provides a means to assess the suitability of the classical (dense) factor regression model compared to alternative (sparse plus dense) factor-augmented sparse regression models. Our proposed test does not require tuning parameters, eliminates the need to estimate covariance matrices, and offers simplicity in implementation. The validity of the test is theoretically established under time-series dependence. Through simulation experiments, we demonstrate the favorable finite sample performance of our procedure. Moreover, using the FRED-MD dataset, we apply the test and reject the adequacy of the classical factor regression model when the dependent variable is inflation but not when it is industrial production. These findings offer insights into selecting appropriate models for high-dimensional datasets. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.13364&r=ets |
| By: | Kurt Graden Lunsford; Kenneth D. West |
| Abstract: | We study the use of a zero mean first difference model to forecast the level of a scalar time series that is stationary in levels. Let bias be the average value of a series of forecast errors. Then the bias of forecasts from a misspecified ARMA model for the first difference of the series will tend to be smaller in magnitude than the bias of forecasts from a correctly specified model for the level of the series. Formally, let P be the number of forecasts. Then the bias from the first difference model has expectation zero and a variance that is O(1/P-squared), while the variance of the bias from the levels model is generally O(1/P). With a driftless random walk as our first difference model, we confirm this theoretical result with simulations and empirical work: random walk bias is generally one-tenth to one-half that of an appropriately specified model fit to levels. |
| Keywords: | ARMA Models; Overdifferenced; Prediction; Macroeconomic Time Series; Simulation |
| JEL: | C22 C53 E37 E47 |
| Date: | 2023–08–03 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwq:96521&r=ets |
| By: | Lutz Kilian |
| Abstract: | It is common in applied work to estimate responses of macroeconomic aggregates to news shocks derived from surprise changes in daily futures prices around the date of policy announcements. This requires mapping the daily surprises into a monthly shock that may be used as an external instrument in a monthly VAR model or local projection. The standard approach has been to sum these daily surprises over the course of a given month when constructing the monthly proxy variable, ignoring the accounting relationship between daily and average monthly price data. In this paper, I provide a new approach to constructing monthly proxies from daily surprises that takes account of this link and revisit the question of how to use OPEC announcements to identify news shocks in VAR models of the global oil market. The proposed approach calls into question the interpretation of the identified shock as oil supply news and implies quantitatively and qualitatively different estimates of the macroeconomic impact of OPEC announcements. |
| Keywords: | Proxy VAR; instrumental variables; shock aggregation; time aggregation; identification; OPEC; supply news; storage demand; oil futures; oil price expectations |
| JEL: | C36 C51 E31 E32 E44 Q43 |
| Date: | 2023–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddwp:96517&r=ets |
| By: | Guido Ascari; Paolo Bonomolo; Qazi Haque |
| Abstract: | In U.S. data, inflation and output are negatively related in the long run. A Bayesian VAR with stochastic trends generalized to be piecewise linear provides robust reduced-form evidence in favor of a threshold level of trend inflation of around 4%, below which potential output is independent of trend inflation, and above which, instead, potential output is negatively affected by trend inflation. Moreover, this negative relationship is quite substantial: above the threshold every percentage point increase in trend inflation is related to about 1% decrease in potential output per year. A New Keynesian model generalized to admittime-varying trend inflation and estimated via particle filtering provides theoretical foundations to this reduced-form evidence. The structural long-run Phillips Curve implied by the estimated New Keynesian model is not statistically different from the one implied by the reduced-form piecewise linear BVAR model. |
| Keywords: | Long-Run Phillips Curve, Inflation, Bayesian VAR, DSGE, Particle Filter |
| JEL: | C32 C51 E30 E31 E52 |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2023-37&r=ets |