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on Econometric Time Series |
| By: | Monfort, A.; Renne, J.-P.; Roussellet, G. |
| Abstract: | We propose a new filtering and smoothing technique for non-linear state-space models. Observed variables are quadratic functions of latent factors following a Gaussian VAR. Stacking the vector of factors with its vectorized outer-product, we form an augmented state vector whose first two conditional moments are known in closed-form. We also provide analytical formulae for the unconditional moments of this augmented vector. Our new quadratic Kalman filter (Qkf) exploits these properties to formulate fast and simple filtering and smoothing algorithms. A first simulation study emphasizes that the Qkf outperforms the extended and unscented approaches in the filtering exercise showing up to 70% RMSEs improvement of filtered values. Second, we provide evidence that Qkf-based maximum-likelihood estimates of model parameters always possess lower bias or lower RMSEs that the alternative estimators. |
| Keywords: | non-linear filtering, non-linear smoothing, quadratic model, Kalman filter, pseudo-maximum likelihood. |
| JEL: | C32 C46 C53 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:bfr:banfra:486&r=ets |
| By: | Michael McAleer (University of Canterbury); Christian M. Hafner |
| Abstract: | One of the most popular univariate asymmetric conditional volatility models is the exponential GARCH (or EGARCH) specification. In addition to asymmetry, which captures the different effects on conditional volatility of positive and negative effects of equal magnitude, EGARCH can also accommodate leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. However, there are as yet no statistical properties available for the (quasi-) maximum likelihood estimator of the EGARCH parameters. It is often argued heuristically that the reason for the lack of statistical properties arises from the presence in the model of an absolute value of a function of the parameters, which does not permit analytical derivatives or the derivation of statistical properties. It is shown in this paper that: (i) the EGARCH model can be derived from a random coefficient complex nonlinear moving average (RCCNMA) process; and (ii) the reason for the lack of statistical properties of the estimators of EGARCH is that the stationarity and invertibility conditions for the RCCNMA process are not known. |
| Keywords: | Leverage, asymmetry, existence, random coefficient models, complex nonlinear moving average process |
| JEL: | C22 C52 C58 G32 |
| Date: | 2014–06–16 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:14/16&r=ets |
| By: | Varang Wiriyawit; Benjamin Wong |
| Abstract: | We highlight how detrending within Structural Vector Autoregressions (SVAR) is directly linked to the shock identification. Consequences of trend misspecification are investigated using a prototypical Real Business Cycle model as the Data Generating Process. Decomposing the different sources of biases in the estimated impulse response functions, we find the biases arising directly from trend misspecification are not trivial when compared to other widely studied misspecifications. Our example also illustrates how misspecifying the trend can also distort impulse response functions of even the correctly detrended variable within the SVAR system. |
| Keywords: | Structural VAR, Identification, Detrending, Bias |
| JEL: | C15 C32 C51 E37 |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2014-46&r=ets |
| By: | Anton Skrobotov (Gaidar Institute for Economic Policy) |
| Abstract: | Recent approaches in unit root testing that take into account the influences of the initial condition, trend, and breaks in the data using pre-testing and performing the union of rejection testing strategies based on the information obtained. This allows for the use of more powerful tests, if there is uncertainty about some of the parameters in the model. This paper proposes the extension of the Harvey et al. (2012b) approach to the case of uncertainty over the initial condition. It has been shown that the procedures of Harvey et al. (2012b) have low power under a large initial condition because they include GLS-based tests. Therefore, the efficiency of some ADF-type unit root tests with breaks under various magnitudes of initial condition will be investigated, and the decision rule based on pre-testing for a magnitude of the initial condition and simultaneous use of tests based on both GLS and OLS detrending is proposed. Additionally, the modification of the proposed algorithm using pre-testing for the trend coefficient will be analyzed. Analysis of a situation with the possible presence of multiple structural breaks in trend will also be conducted in the paper. Two algorithms are proposed: the first involves only pre-testing the initial condition, while the second involves pre-testing the number of breaks based on the Kejriwal and Perron (2010) test. The asymptotic behavior of all tests is analyzed under both a local-to-unity representation of the autoregressive root and a local-to- zero representation of trend and breaks magnitudes. The proposed modifications save the high power for small initial conditions/trend/breaks and at the same time lead to the power close to one of the effective tests for large initial condition/trend/breaks. |
| Keywords: | unit root test, infimum Dickey-Fuller tests, local trend, local trend break, asymptotic local power, union of rejection, pre-testing, multiple breaks in trend. |
| JEL: | C12 C22 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:gai:wpaper:0097&r=ets |
| By: | Helmut Lütkepohl; Aleksei Netsunajev; ; |
| Abstract: | In structural vector autoregressive analysis identifying the shocks of interest via heteroskedasticity has become a standard tool. Unfortunately, the approaches currently used for modelling heteroskedasticity all have drawbacks. For instance, assuming known dates for variance changes is often unrealistic while more exible models based on GARCH or Markov switching residuals are dicult to handle from a statistical and computational point of view. Therefore we propose a model based on a smooth change in variance that is exible as well as relatively easy to estimate. The model is applied to a five-dimensional system of U.S. variables to explore the interaction between monetary policy and the stock market. It is found that previously used conventional identification schemes in this context are rejected by the data if heteroskedasticity is allowed for. Shocks identified via heteroskedasticity have a different economic interpretation than the shocks identified using conventional methods. |
| Keywords: | Structural vector autoregressions, heteroskedasticity, smooth transition VAR models, identification via heteroskedasticity |
| JEL: | C32 |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2014-031&r=ets |
| By: | Giuseppe Cavaliere (University of Bologna); Morten Ørregaard Nielsen (Queen's University and CREATES); A. M. Robert Taylor (University of Essex) |
| Abstract: | In a recent paper Hualde and Robinson (2011) establish consistency and asymptotic normality for conditional sum-of-squares estimators, which are equivalent to conditional quasi-maximum likelihood estimators, in parametric fractional time series models driven by conditionally homoskedastic shocks. In contrast to earlier results in the literature, their results apply over an arbitrarily large set of admissible parameter values for the (unknown) memory parameter covering both stationary and non-stationary processes and invertible and non-invertible processes. In this paper we extend their results to the case where the shocks can display conditional and unconditional heteroskedasticity of a quite general and unknown form. We establish that the consistency result presented in Hualde and Robinson (2011) continues to hold under heteroskedasticity as does asymptotic normality. However, we demonstrate that the covariance matrix of the limiting distribution of the estimator now depends on nuisance parameters which derive both from the weak dependence in the process (as is also the case for the corresponding result in Hualde and Robinson, 2011) but additionally from the heteroskedasticity present in the shocks. Asymptotically pivotal inference can be performed on the parameters of the heteroskedastic model, provided a conventional "sandwich" estimator of the variance is employed. |
| Keywords: | (un)conditional heteroskedasticity, conditional sum-of-squares, fractional integration, quasi-maximum likelihood estimation |
| JEL: | C13 C22 |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1324&r=ets |