|
on Econometric Time Series |
| By: | Yoosoon Chang (Indiana University); Junior Maih (Norges Bank and BI Norwegian Business School); Fei Tan (Department of Economics, Chaifetz School of Business, Saint Louis University and Center for Economic Behavior and Decision-Making, Zhejiang University of Finance and Economics) |
| Abstract: | This article studies the estimation of state space models whose parameters are switching endogenously between two regimes, depending on whether an autoregressive latent factor crosses some threshold level. Endogeneity stems from the sustained impacts of transition innovations on the latent factor, absent from which our model reduces to one with exogenous Markov switching. Due to the flexible form of state space representation, this class of models is vastly broad, including classical regression models and the popular dynamic stochastic general equilibrium (DSGE) models as special cases. We develop a computationally efficient filtering algorithm to estimate the non-linear model. Calculations are greatly simplified by appropriate augmentation of the transition equation and exploiting the conditionally linear and Gaussian structure. The algorithm is shown to be accurate in approximating both the likelihood function and filtered state variables. We also apply the filter to estimate a small-scale DSGE model with threshold-type switching in monetary policy rule, and find apparent empirical evidence of endogeneity in the U.S. monetary policy shifts. Overall, our approach provides a greater scope for understanding the complex interaction between regime switching and measured economic behavior. |
| Keywords: | state space model; regime switching; endogenous feedback; filtering; DSGE model |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:inu:caeprp:2018011&r=ets |
| By: | Eric Benhamou |
| Abstract: | In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using graphical models. This enables us to establish the connection between Kalman filter and Hidden Markov Models. We then look at their application in financial markets and provide various intuitions in terms of their applicability for complex systems such as financial markets. Although this paper has been written more like a self contained work connecting Kalman filter to Hidden Markov Models and hence revisiting well known and establish results, it contains new results and brings additional contributions to the field. First, leveraging on the link between Kalman filter and HMM, it gives new algorithms for inference for extended Kalman filters. Second, it presents an alternative to the traditional estimation of parameters using EM algorithm thanks to the usage of CMA-ES optimization. Third, it examines the application of Kalman filter and its Hidden Markov models version to financial markets, providing various dynamics assumptions and tests. We conclude by connecting Kalman filter approach to trend following technical analysis system and showing their superior performances for trend following detection. |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1811.11618&r=ets |
| By: | Yukai Yang (Uppsala University); Luc Bauwens (Université catholique de Louvain) |
| Abstract: | We develop novel multivariate state-space models wherein the latent states evolve on the Stiefel manifold and follow a conditional matrix Langevin distribution. The latent states correspond to time-varying reduced rank parameter matrices, like the loadings in dynamic factor models and the parameters of cointegrating relations in vector error-correction models. The corresponding nonlinear filtering algorithms are developed and evaluated by means of simulation experiments. |
| Keywords: | State-space models, Stiefel manifold, matrix Langevin distribution, filtering, smoothing, Laplace method, dynamic factor model, cointegration |
| JEL: | C32 C51 |
| Date: | 2411 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2018-30&r=ets |
| By: | Chang, Yoosoon; Lu, Ye; Park, Joon Y. |
| Abstract: | In this paper, we analyze regressions with observations collected at small time interval over long period of time. For the formal asymptotic analysis, we assume that samples are obtained from continuous time stochastic processes, and let the sampling interval δ shrink down to zero and the sample span T increase up to infinity. In this setup, we show that the standard Wald statistic diverges to infinity and the regression becomes spurious as long as δ → 0 sufficiently fast relative to T → ∞. Such a phenomenon is indeed what is frequently observed in practice for the type of regressions considered in the paper. In contrast, our asymptotic theory predicts that the spuriousness disappears if we use the robust version of the Wald test with an appropriate longrun variance estimate. This is supported, strongly and unambiguously, by our empirical illustration. |
| Keywords: | high frequency regression; spurious regression; continuous time model; asymptotics; longrun variance estimation |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:syd:wpaper:2018-10&r=ets |
| By: | Jiang, Bibo; Lu, Ye; Park, Joon Y. |
| Abstract: | The high frequency behavior of the KPSS test, which is most commonly used to test for stationarity, is analyzed in a continuous time framework. Our asymptotics show that the test has no discriminatory power at high frequency: It either always rejects stationarity or has no nontrivial power at high frequency. The test becomes valid at high frequency only when the bandwidth of its longrun variance estimate is chosen suitably in our framework. We also analyze the residual-based KPSS test for cointegration. |
| Keywords: | KPSS test; testing for stationarity; testing for cointegration; continuous time process; high frequency observation |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:syd:wpaper:2018-09&r=ets |
| By: | Anne Lundgaard Hansen (Department of Economics, University of Copenhagen, Denmark) |
| Abstract: | It is well-known that interest rates and inflation rates are extremely persistent, yet they are best modeled and understood as stationary processes. These properties are contradictory in the workhorse Gaussian affine term structure model in which the persistent data often result in unit roots that imply non-stationarity. We resolve this puzzle by proposing a macro-finance term structure model with volatility-induced stationarity. Our model employs a level-dependent conditional volatility that maintains stationarity despite presence of unit roots in the characteristic polynomial corresponding to the conditional mean. Compared to the Gaussian affine term structure model, we improve out-of-sample forecasting of the yield curve and estimate term premia that are economically plausible and consistent with survey data. Moreover, we show that volatility-induced stationarity affects the error-correcting mechanism in a system of interest rates, inflation, and real activity. |
| Keywords: | Yield curve, error-correction, unit root, volatility-induced stationarity, macro-finance term structure model, level-dependent conditional volatility |
| JEL: | E43 E44 G12 |
| Date: | 2018–12–03 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1812&r=ets |
| By: | Jackson, Laura E. (Bentley University, Department of Economics); Kliesen, Kevin L. (Federal Reserve Bank of St. Louis); Owyang, Michael T. (Federal Reserve Bank of St. Louis) |
| Abstract: | We consider the effects of uncertainty shocks in a nonlinear VAR that allows uncertainty to have amplification effects. When uncertainty is relatively low, fluctuations in uncertainty have small, linear effects. In periods of high uncertainty, the effect of a further increase in uncertainty is magnified. We find that uncertainty shocks in this environment have a more pronounced effect on real economic variables. We also conduct counterfactual experiments to determine the channels through which uncertainty acts. Uncertainty propagates through both the household consumption channel and through businesses delaying investment, providing substantial contributions to the decline in GDP observed after uncertainty shocks. Finally, we find evidence of the ability of systematic monetary policy to mitigate the adverse effects of uncertainty shocks. |
| Keywords: | uncertainty; time-varying threshold VAR; monetary policy; generalized impulse response functions |
| JEL: | C34 E2 E32 |
| Date: | 2018–11–16 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:2018-035&r=ets |
| By: | Gabriel Rodríguez (Departamento de Economía de la Pontificia Universidad Católica del Perú); Carlos Guevara (Departamento de Economía de la Pontificia Universidad Católica del Perú) |
| Abstract: | This paper analyzes the effect of loan supply shocks on the real economic activity of Pacific Alliance countries. The econometric approach is a Time-Varying Parameter VAR with Stochastic Volatility (TVP-VAR-SV), which is identified by sign restrictions. Results of a trace test, t-tests and the Kolmogorov-Smirnov test reveal the existence of significant changes in the distribution of parameters over time, which supports the use of time-varying parameters. The results indicate that loan supply shocks have an important impact on real economic activity in all Pacific Alliance countries: about 1% in Colombia, Mexico, and Peru, and about 0.5% in Chile. Moreover, loan supply shocks have a considerable role in driving business cycle fluctuations, not only in crisis periods, but also in stability periods. Their contribution to GDP growth is higher than that of aggregate supply shocks and as high as that of aggregate demand and monetary policy shocks. The evolution of the impact of loan supply shocks on real economic activity shows evidence of cross-country heterogeneity, reflecting different financial structures among Pacific Alliance countries. Furthermore, by assessing the effects on different measures of economic activity, it is estimated that loan supply shocks have a higher impact on domestic demand, while the impact is similar when the model is estimated for non-primary activities. Finally, the sensitivity analysis indicates that the results of the model are robust to different priors specifications, to different measures of external variables, and to multiple sets of sign restrictions. Moreover, by applying an agnostic identification, the results indicate that even letting the response of GDP unrestricted, its response to loan supply shocks remains positive and significant. With this multiple specification, the impact of loan supply shocks on GDP growth ranges between 0.8% and 1.2% in Peru and Colombia, and between 0.5% and 0.8% in Chile. These results are close to the baseline estimation and show robustness. Regarding Mexico, it is estimated that the impact of loan supply shocks varies between 0.8%-3.5%. JEL Classification-JEL: C32, E32, E51 |
| Keywords: | Loan Supply Shocks, Variance Decomposition, Historical Decomposition, Time-Varying Parameter VAR with Stochastic Volatility, Sign Restrictions |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:pcp:pucwps:wp00467&r=ets |