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Econometrics, Volume 1, Issue 1 (June 2013), Pages 1-140

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Research

Open AccessArticle On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations
Econometrics 2013, 1(1), 1-31; doi:10.3390/econometrics1010001
Received: 15 January 2013 / Revised: 9 March 2013 / Accepted: 14 March 2013 / Published: 4 April 2013
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Abstract
This paper focuses on the diagnostic checking of vector ARMA (VARMA) models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This [...] Read more.
This paper focuses on the diagnostic checking of vector ARMA (VARMA) models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This is different from the traditional approach that employs only the squared series of standardized residuals. We then study two portmanteau statistics, called Q1(M) and Q2(M), for model checking. A residual-based bootstrap method is provided and demonstrated as an effective way to approximate the diagnostic checking statistics. Simulations are used to compare the performance of the proposed statistics with other methods available in the literature. In addition, we also investigate the effect of GARCH shocks on checking a fitted VARMA model. Empirical sizes and powers of the proposed statistics are investigated and the results suggest a procedure of using jointly Q1(M) and Q2(M) in diagnostic checking. The bivariate time series of FTSE 100 and DAX index returns is used to illustrate the performance of the proposed portmanteau statistics. The results show that it is important to consider the cross-product series of standardized residuals and GARCH effects in model checking. Full article
(This article belongs to the Special Issue Econometric Model Selection)
Open AccessArticle Constructing U.K. Core Inflation
Econometrics 2013, 1(1), 32-52; doi:10.3390/econometrics1010032
Received: 28 February 2013 / Revised: 12 March 2013 / Accepted: 12 March 2013 / Published: 25 April 2013
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Abstract
The recent volatile behaviour of U.K. inflation has been officially attributed to a sequence of “unusual” price changes, prompting renewed interest in the construction of measures of “core inflation”, from which such unusual price changes may be down-weighted or even excluded. This [...] Read more.
The recent volatile behaviour of U.K. inflation has been officially attributed to a sequence of “unusual” price changes, prompting renewed interest in the construction of measures of “core inflation”, from which such unusual price changes may be down-weighted or even excluded. This paper proposes a new approach to constructing core inflation based on detailed analysis of the temporal stochastic structure of the individual prices underlying a particular index. This approach is illustrated using the section structure of the U.K. retail price index (RPI), providing a number of measures of core inflation that can be automatically calculated and updated to provide both a current assessment and forecasts of the underlying inflation rate in the U.K. Full article
Open AccessArticle Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator
Econometrics 2013, 1(1), 53-70; doi:10.3390/econometrics1010053
Received: 28 January 2013 / Revised: 3 April 2013 / Accepted: 3 April 2013 / Published: 13 May 2013
Cited by 6 | PDF Full-text (315 KB) | HTML Full-text | XML Full-text
Abstract
In regression we can delete outliers based upon a preliminary estimator and re-estimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence [...] Read more.
In regression we can delete outliers based upon a preliminary estimator and re-estimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber-skip estimator. We provide a stochastic recursion equation for the estimation error in terms of a kernel, the previous estimation error and a uniformly small error term. The main contribution is the analysis of the solution of the stochastic recursion equation as a fixed point, and the results that the normalized estimation errors are tight and are close to a linear function of the kernel, thus providing a stochastic expansion of the estimators, which is the same as for the Huber-skip. This implies that the iterated estimator is a close approximation of the Huber-skip. Full article
Figures

Open AccessArticle Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments
Econometrics 2013, 1(1), 71-114; doi:10.3390/econometrics1010071
Received: 25 March 2013 / Revised: 25 April 2013 / Accepted: 25 April 2013 / Published: 27 May 2013
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Abstract
This paper studies the generalized spatial two stage least squares (GS2SLS) estimation of spatial autoregressive models with autoregressive disturbances when there are endogenous regressors with many valid instruments. Using many instruments may improve the efficiency of estimators asymptotically, but the bias might [...] Read more.
This paper studies the generalized spatial two stage least squares (GS2SLS) estimation of spatial autoregressive models with autoregressive disturbances when there are endogenous regressors with many valid instruments. Using many instruments may improve the efficiency of estimators asymptotically, but the bias might be large in finite samples, making the inference inaccurate. We consider the case that the number of instruments K increases with, but at a rate slower than, the sample size, and derive the approximate mean square errors (MSE) that account for the trade-offs between the bias and variance, for both the GS2SLS estimator and a bias-corrected GS2SLS estimator. A criterion function for the optimal K selection can be based on the approximate MSEs. Monte Carlo experiments are provided to show the performance of our procedure of choosing K. Full article
Open AccessArticle Ten Things You Should Know about the Dynamic Conditional Correlation Representation
Econometrics 2013, 1(1), 115-126; doi:10.3390/econometrics1010115
Received: 13 May 2013 / Revised: 7 June 2013 / Accepted: 14 June 2013 / Published: 21 June 2013
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Abstract
The purpose of the paper is to discuss ten things potential users should know about the limits of the Dynamic Conditional Correlation (DCC) representation for estimating and forecasting time-varying conditional correlations. The reasons given for caution about the use of DCC include [...] Read more.
The purpose of the paper is to discuss ten things potential users should know about the limits of the Dynamic Conditional Correlation (DCC) representation for estimating and forecasting time-varying conditional correlations. The reasons given for caution about the use of DCC include the following: DCC represents the dynamic conditional covariances of the standardized residuals, and hence does not yield dynamic conditional correlations; DCC is stated rather than derived; DCC has no moments; DCC does not have testable regularity conditions; DCC yields inconsistent two step estimators; DCC has no asymptotic properties; DCC is not a special case of Generalized Autoregressive Conditional Correlation (GARCC), which has testable regularity conditions and standard asymptotic properties; DCC is not dynamic empirically as the effect of news is typically extremely small; DCC cannot be distinguished empirically from diagonal Baba, Engle, Kraft and Kroner (BEKK) in small systems; and DCC may be a useful filter or a diagnostic check, but it is not a model. Full article
Open AccessArticle Forecasting Value-at-Risk Using High-Frequency Information
Econometrics 2013, 1(1), 127-140; doi:10.3390/econometrics1010127
Received: 7 March 2013 / Accepted: 22 April 2013 / Published: 21 June 2013
Cited by 2 | PDF Full-text (247 KB) | HTML Full-text | XML Full-text
Abstract
in the prediction of quantiles of daily Standard&Poor’s 500 (S&P 500) returns we consider how to use high-frequency 5-minute data. We examine methods that incorporate the high frequency information either indirectly, through combining forecasts (using forecasts generated from returns sampled at different [...] Read more.
in the prediction of quantiles of daily Standard&Poor’s 500 (S&P 500) returns we consider how to use high-frequency 5-minute data. We examine methods that incorporate the high frequency information either indirectly, through combining forecasts (using forecasts generated from returns sampled at different intraday interval), or directly, through combining high frequency information into one model. We consider subsample averaging, bootstrap averaging, forecast averaging methods for the indirect case, and factor models with principal component approach, for both direct and indirect cases. We show that in forecasting the daily S&P 500 index return quantile (Value-at-Risk or VaR is simply the negative of it), using high-frequency information is beneficial, often substantially and particularly so, in forecasting downside risk. Our empirical results show that the averaging methods (subsample averaging, bootstrap averaging, forecast averaging), which serve as different ways of forming the ensemble average from using high-frequency intraday information, provide an excellent forecasting performance compared to using just low-frequency daily information. Full article

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