Computational Aspects of Maximum Likelihood Estimation of Autoregressive Fractionally Integrated Moving Average Models

We discuss computational aspects of likelihood-based estimation of univariate ARFIMA (p,d,q) models. We show how efficient computation and simulation is feasible, even for large samples. We also discuss the implementation of analytical bias corrections.Long memory, Bias, Modified profile likelihood, Restricted maximum likelihood estimator, Time-series regression model likelihood

Multimodality in the GARCH Regression Model

Several aspects of GARCH(p,q) models that are relevant for empirical applications are investigated. In particular, it is noted that the inclusion of dummy variables as regressors can lead to multimodality in the GARCH likelihood. This invalidates standard inference on the estimated coefficients. Next, the implementation of different restrictions on the GARCH parameter space is considered. A refinement to the Nelson and Cao (1992) conditions for a GARCH(2,q) model is presented, and it is shown how these can then be implemented by parameter transformations. It is argued that these conditions may also be too restrictive, and a simpler alternative is introduced which is formulated in terms of the unconditional variance. Finally, examples show that multimodality is a real concern for models of the £/$ exchange rate, especially when p>2.Dummy variable, EGARCH, GARCH, Multimodality.

Multimodality and the GARCH Likelihood

We investigate several aspects of GARCH models which are relevant for empirical applications. In particular, we note that the inclusion of a dummy variable as regressor can lead to multimodality in the GARCH likelihood. This makes standard inference on the estimated coefficient impossible. Next, we investigate the implementation of different restrictions on the GARCH parameter space. We present a small refinement to the Nelson and Cao (1992) conditions for a GARCH(2,q) model, and show how these can be implemented by parameter transformations. We argue that these conditions are also too restrictive, and consider restrictions which are formulated in terms of the unconditional variance. These are easier to work with and understand. Finally, we show that multimodality is a real concern for models of the pound/dollar exchange rate, and should be taken account of, especially when p>=2.

Outlier Detection in GARCH Models

We present a new procedure for detecting multiple additive outliers in GARCH(1,1) models at unknown dates. The outlier candidates are the observations with the largest standardized residual. First, a likelihood-ratio based test determines the presence and timing of an outlier. Next, a second test determines the type of additive outlier (volatility or level). The tests are shown to be similar with respect to the GARCH parameters. Their null distribution can be easily approximated from an extreme value distribution, so that computation of p-values does not require simulation. The procedure outperforms alternative methods, especially when it comes to determining the date of the outlier. We apply the method to returns of the Dow Jones index, using monthly, weekly, and daily data. The procedure is extended and applied to GARCH models with Student-t distributed errors.

Computationally-intensive Econometrics using a Distributed Matrix-programming Language

This paper reviews the need for powerful facilities in econometrics, focusing on concrete problems which arise in financial economics and in macroeconomics. We argue that the profession is being held back by the lack of easy to use generic software which is able to exploit the availability of cheap clusters of distributed computers. Our response is to extend, in a number of directions, the well known matrix-programming interpreted language Ox developed by the first author. We note three possible levels of extensions: (i) Ox with parallelization explicit in the Ox code; (ii) Ox with a parallelized run-time library; (iii) Ox with a parallelized interpreter. This paper studies and implements the first case, emphasizing the need for deterministic computing in science. We give examples in the context of financial economics and time-series modelling.Distributed computing; Econometrics; High-performance computing; Matrix-programming language

Parallel Computation in Econometrics: A Simplified Approach

Parallel computation has a long history in econometric computing, but is not at all wide spread. We believe that a major impediment is the labour cost of coding for parallel architectures. Moreover, programs for specific hardware often become obsolete quite quickly. Our approach is to take a popular matrix programming language (Ox), and implement a message-passing interface using MPI. Next, object-oriented programming allows us to hide the specific parallelization code, so that a program does not need to be rewritten when it is ported from the desktop to a distributed network of computers. Our focus is on so-called embarrassingly parallel computations, and we address the issue of parallel random number generation.Code optimization; Econometrics; High-performance computing; Matrix-programming language; Monte Carlo; MPI; Ox; Parallel computing; Random number generation.