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on Econometric Time Series |
| By: | Paul Ho (Princeton University) |
| Abstract: | This paper develops tools for global prior sensitivity analysis in large Bayesian models. Without imposing parametric restrictions, the framework provides bounds for a wide range of posterior statistics given any prior that is close to the original in relative entropy. The methodology also reveals parts of the prior that are important for the posterior statistics of interest. To implement these calculations in large models, we develop a sequential Monte Carlo algorithm and use approximations to the likelihood and statistic of interest. We use the framework to study error bands for the impulse response of output to a monetary policy shock in the New Keynesian model of Smets and Wouters (2007). The error bands depend asymmetrically on the prior through features of the likelihood that are hard to detect without this formal prior sensitivity analysis. |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:red:sed019:390&r=all |
| By: | Matteo Barigozzi; Matteo Luciani |
| Abstract: | This paper studies Quasi Maximum Likelihood estimation of dynamic factor models for large panels of time series. Specifically, we consider the case in which the autocorrelation of the factors is explicitly accounted for and therefore the factor model has a state-space form. Estimation of the factors and their loadings is implemented by means of the Expectation Maximization algorithm, jointly with the Kalman smoother. We prove that, as both the dimension of the panel $n$ and the sample size $T$ diverge to infinity, the estimated loadings, factors, and common components are $\min(\sqrt n,\sqrt T)$-consistent and asymptotically normal. Although the model is estimated under the unrealistic constraint of independent idiosyncratic errors, this mis-specification does not affect consistency. Moreover, we give conditions under which the derived asymptotic distribution can still be used for inference even in case of mis-specifications. Our results are confirmed by a MonteCarlo simulation exercise where we compare the performance of our estimators with Principal Components. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.03821&r=all |
| By: | Kashif Yousuf; Serena Ng |
| Abstract: | High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for parameter instability in economic time series, but theories for parameter instability are mainly developed for models with a small number of covariates. In this paper, we present two $L_2$ boosting algorithms for estimating high dimensional models in which the coefficients are modeled as functions evolving smoothly over time and the predictors are locally stationary. The first method uses componentwise local constant estimators as base learner, while the second relies on componentwise local linear estimators. We establish consistency of both methods, and address the practical issues of choosing the bandwidth for the base learners and the number of boosting iterations. In an extensive application to macroeconomic forecasting with many potential predictors, we find that the benefits to modeling time variation are substantial and they increase with the forecast horizon. Furthermore, the timing of the benefits suggests that the Great Moderation is associated with substantial instability in the conditional mean of various economic series. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.03109&r=all |
| By: | Beaumont, Paul; Smallwood, Aaron |
| Abstract: | We review the multiple frequency Gegenbauer autoregressive moving average model, which is able to reproduce a wide range of autocorrelation functions. Extending the result of Chung (1996a), we propose the asymptotic distributions for a conditional sum of squares estimator of the model parameters. The parameters that determine the cycle lengths are asymptotically independent, converging at rate T for finite cycles. This result does not hold generally, most notably for the differencing parameters associated with the cycle lengths. Remaining parameters are typically not independent and converge at the standard rate of T1/2. We present simulation results to explore small sample properties of the estimator, which strongly support most distributional results while also highlighting areas that merit additional exploration. We demonstrate the applicability of the theory and estimator with an application to IBM trading volume. |
| Keywords: | k-factor Gegenbauer processes, Asymptotic distributions, ARFIMA, Conditional sum of squares |
| JEL: | C22 C40 C5 C58 G1 G12 |
| Date: | 2019–09–29 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:96314&r=all |
| By: | Bernd Funovits |
| Abstract: | This paper analyzes identifiability properties of structural vector autoregressive moving average (SVARMA) models driven by independent and non-Gaussian shocks. It is well known, that SVARMA models driven by Gaussian errors are not identified without imposing further identifying restrictions on the parameters. Even in reduced form and assuming stability and invertibility, vector autoregressive moving average models are in general not identified without requiring certain parameter matrices to be non-singular. Independence and non-Gaussianity of the shocks is used to show that they are identified up to permutations and scalings. In this way, typically imposed identifying restrictions are made testable. Furthermore, we introduce a maximum-likelihood estimator of the non-Gaussian SVARMA model which is consistent and asymptotically normally distributed. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.04087&r=all |
| By: | Bernd Funovits; Alexander Braumann |
| Abstract: | We generalize well-known results on structural identifiability of vector autoregressive models (VAR) to the case where the innovation covariance matrix has reduced rank. Structural singular VAR models appear, for example, as solutions of rational expectation models where the number of shocks is usually smaller than the number of endogenous variables, and as an essential building block in dynamic factor models. We show that order conditions for identifiability are misleading in the singular case and provide a rank condition for identifiability of the noise parameters. Since the Yule-Walker equations may have multiple solutions, we analyze the effect of restrictions on the system parameters on over- and underidentification in detail and provide easily verifiable conditions. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.04096&r=all |
| By: | Du Nguyen |
| Abstract: | We introduce a concept of $autoregressive$ (AR)state-space realization that could be applied to all transfer functions $\boldsymbol{T}(L)$ with $\boldsymbol{T}(0)$ invertible. We show that a theorem of Kalman implies each Vector Autoregressive model (with exogenous variables) has a minimal $AR$-state-space realization of form $\boldsymbol{y}_t = \sum_{i=1}^p\boldsymbol{H}\boldsymbol{F}^{i-1}\boldsymbol{G}\boldsymbol{x}_{t-i}+\boldsymbol{\epsilon}_t$ where $\boldsymbol{F}$ is a nilpotent Jordan matrix and $\boldsymbol{H}, \boldsymbol{G}$ satisfy certain rank conditions. The case $VARX(1)$ corresponds to reduced-rank regression. Similar to that case, for a fixed Jordan form $\boldsymbol{F}$, $\boldsymbol{H}$ could be estimated by least square as a function of $\boldsymbol{G}$. The likelihood function is a determinant ratio generalizing the Rayleigh quotient. It is unchanged if $\boldsymbol{G}$ is replaced by $\boldsymbol{S}\boldsymbol{G}$ for an invertible matrix $\boldsymbol{S}$ commuting with $\boldsymbol{F}$. Using this invariant property, the search space for maximum likelihood estimate could be constrained to equivalent classes of matrices satisfying a number of orthogonal relations, extending the results in reduced-rank analysis. Our results could be considered a multi-lag canonical-correlation-analysis. The method considered here provides a solution in the general case to the polynomial product regression model of Velu et. al. We provide estimation examples. We also explore how the estimates vary with different Jordan matrix configurations and discuss methods to select a configuration. Our approach could provide an important dimensional reduction technique with potential applications in time series analysis and linear system identification. In the appendix, we link the reduced configuration space of $\boldsymbol{G}$ with a geometric object called a vector bundle. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.02546&r=all |
| By: | Kley, Tobias; Preuss, Philip; Fryzlewicz, Piotr |
| Abstract: | In statistical research there usually exists a choice between structurally simpler or more complex models. We argue that, even if a more complex, locally stationary time series model were true, then a simple, stationary time series model may be advantageous to work with under parameter uncertainty. We present a new model choice methodology, where one of two competing approaches is chosen based on its empirical, finite-sample performance with respect to prediction, in a manner that ensures interpretability. A rigorous, theoretical analysis of the procedure is provided. As an important side result we prove, for possibly diverging model order, that the localised Yule-Walker estimator is strongly, uniformly consistent under local stationarity. An R package, forecastSNSTS, is provided and used to apply the methodology to financial and meteorological data in empirical examples. We further provide an extensive simulation study and discuss when it is preferable to base forecasts on the more volatile time-varying estimates and when it is advantageous to forecast as if the data were from a stationary process, even though they might not be. |
| Keywords: | forecasting; Yule-Walker estimate; local stationarity; covariance stationarity; EP/L014246/1 |
| JEL: | C1 |
| Date: | 2019–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:101748&r=all |
| By: | Kristoffer Pons Bertelsen (Aarhus University and CREATES) |
| Abstract: | This paper compares the log periodic power law (LPPL) and the supremum augmented Dickey Fuller (supremum ADF) procedures considering bubble detection and time stamping capabilities in a thorough analysis based on simulated data. A generalized formulation of the LPPL procedure is derived and analysed demonstrating performance improvements. |
| Keywords: | Rational bubbles, explosive processes, log periodic power law, critical points theory |
| JEL: | C01 C02 C12 C13 C22 C52 C53 C58 C61 G01 |
| Date: | 2019–10–11 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2019-16&r=all |