Minimum distance estimation of ARFIMA processes (original) (raw)
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A comparison of estimation methods in non-stationary ARFIMA processes
Journal of Statistical Computation and Simulation, 2004
This paper reports an extensive Monte Carlo simulation study based on six estimators for the long memory fractional parameter when the time series is non-stationary, i.e., ARF IM A(p, d, q) process for d > 0.5. Parametric and semiparametric methods are compared. In addition, the effect of the parameter estimation is investigated for small and large sample sizes and non-Gaussian error innovations. The methodology is applied to a well known data set, the so-called UK short interest rates.
Non-stationary Gaussian ARFIMA processes: Estimation and application
Brazilian Review of Econometrics, 2002
Recently, the study of time series turned the attention to the ones having long memory property. The ARFIMA (p,d,q) model shows this property when the degree of differencing d is in the interval (0.0,0.5), range where the process is stationary. In this work, we analyze the estimation of the degree d '" in ARFIMA (p,d'" ,q) processes when d" >0.5, that is, when the processes are non-stationary but still have the property of long memory. We present a simulation study for the estimators of d* with semi parametric and parametric methods and different sample sizes. The methodology is applied to the experimental data series of UK long interest gilts. Resumo Recentes estudos em Series Temporais tern dado atenc;ao aquelas com pro priedade de Zonga dependencia. Os modelos ARFIMA (p,d J q) evidenciam esta propriedade quando 0 grau de diferenciac;ao d esta no intervalo (0.0,0.5), regiao onde 0 processo e estacionario. Neste trabalho, nos analisamos a estima�ao do parametro d'" em processos ARFIMA (p,d'" ,q) quando d* >0.5, isto e, quando os processos sao nao-estaciomirios mas ainda possuem a propriedade de longa de pendencia. Apresentamos urn estudo de simulac;ao para estimadores de d'" com metodos semiparametricos e parametricos e diferentes tamanhos amostrais. A metodologia e aplicada para a serie temporal "UK long interest gilts" .
Processes with correlated errors have been widely used in economic time series. The fractionally integrated autoregressive moving-average processes-ARFIMA(p d q)- have been explored to model stationary and non stationary time series with long-memory property. This work uses the Monte Carlo simulation method to evaluate the performance of some parametric and semiparametric estimators for long and short-memory parameters of the ARFIMA model with conditional heteroskedastic (ARFIMA-GARCH model). The comparison is based on the empirical bias and the mean squared error of each estimator.
2003
We propose a detailed Monte Carlo study of model selection criteria when the exact maximum likelihood (EML) method is used to estimate ARFIMA processes. More specifically, our object is to assess the performance of two automatic selection criteria in the presence of long−term memory: Akaike and Schwarz information criteria. Two special processes are considered: a pure fractional noise model (ARFIMA(0,d,0)) and an ARFIMA(1,d,0) process. For each criterion, we compute bias and root mean squared error for various d and AR(1) parameter values. Obtained results suggest that the Schwarz information criterion frequently selects the right model. Moreover, this criterion outperforms the other one in terms of bias and RMSE, for both pure fractional noise and ARFIMA processes.
Autoregression-Based Estimators for ARFIMA Models
This paper describes a parameter estimation method for both stationary and non-stationary ARFIMA (p,d,q) models, based on autoregressive approximation. We demonstrate consistency of the estimator for -1/2 < d < 1, and in the stationary case we provide a Normal approximation to the finite-sample distribution which can be used for inference. The method provides good finite-sample performance, comparable with that of ML, and stable performance across a range of stationary and non-stationary values of the fractional differencing parameter. In addition, it appears to be relatively robust to mis-specification of the ARFIMA model to be estimated, and is computationally straightforward. Nous décrivons une méthode d'estimation pour les paramètres des modèles ARFIMA stationnaires ou non-stationnaires, basée sur l'approximation auto-régressive. Nous démontrons que la procédure est consistante pour -1/2 < d < 1, et dans le cas stationnaire nous donnons une approximation Norm...
Estimation of Long-Memory Time Series Models: a Survey of Different Likelihood-Based Methods
Advances in Econometrics
Since the seminal works by Granger and Joyeux (1980) and Hosking (1981), estimations of long-memory time series models have been receiving considerable attention and a number of parameter estimation procedures have been proposed. This paper gives an overview of this plethora of methodologies with special focus on likelihood-based techniques. Broadly speaking, likelihood-based techniques can be classified into the following categories: the exact maximum likelihood (ML) estimation (Sowell, 1992; Dahlhaus, 1989), ML estimates based on autoregressive approximations (Granger & Joyeux, 1980; Li & McLeod, 1986), Whittle estimates (Fox & Taqqu, 1986; Giraitis & Surgailis, 1990), Whittle estimates with autoregressive truncation (Beran, 1994a), approximate estimates based on the Durbin-Levinson algorithm (Haslett & Raftery, 1989), state-space-based maximum likelihood estimates for ARFIMA models (
2004
We propose a detailed Monte Carlo study of model selection criteria when the exact maximum likelihood (EML) method is used to estimate ARFIMA processes. More specifically, our object is to assess the performance of two automatic selection criteria in the presence of long-term memory: Akaike and Schwarz information criteria. Two special processes are considered: a pure fractional noise model (ARFIMA(0,d,0)) and an ARFIMA(1,d,0) process. For each criterion, we compute bias and root mean squared error for various d and AR(1) parameter values. Obtained results suggest that the Schwarz information criterion frequently selects the right model. Moreover, this criterion outperforms the other one in terms of bias and RMSE, for both pure fractional noise and ARFIMA processes.
Model Assisted Statistics and Applications, 2015
Time series with long memory or long-range dependence occurs frequently in agricultural commodity prices. For describing long memory, fractional integration is considered. The autoregressive fractionally integrated moving-average (ARFIMA) model along with its different estimation procedures is investigated. For the present investigation, the daily spot prices of mustard in Mumbai market are used. Autocorrelation (ACF) and partial autocorrelation (PACF) functions showed a slow hyperbolic decay indicating the presence of long memory. On the basis of minimum AIC values, the best model is identified for each series. Evaluation of forecasting is carried out with root mean squares prediction error (RMSPE), mean absolute prediction error (MAPE) and relative mean absolute prediction error (RMAPE). The residuals of the fitted models were used for diagnostic checking. Long memory parameter of ARFIMA model is computed by Geweke and Porter-Hudak (GPH), Gaussian semiparametric and wavelet method by using Maximal overlap discrete wavelet transform (MODWT). To this end, a comparison in the performance of different estimation procedures is carried out by Monte Carlo simulation technique. The R software package has been used for data analysis.
AnM-estimator for the long-memory parameter
Journal of Statistical Planning and Inference, 2017
This paper proposes an M-estimator for the fractional parameter of stationary long-range dependent processes as an alternative to the classical GPH (Geweke and Porter-Hudak (1983)) method. Under very general assumptions on the long-range dependent process the consistency and the asymptotic normal distribution are established for the proposed method. One of the main results is that the convergence rate of the M-estimator is N β/2 , for some positive β, which is the same rate as the standard GPH estimator. The asymptotic properties of the M-estimation method is investigated through Monte-Carlo simulations under the scenarios of ARFIMA models using contaminated with additive outliers and outlier-free data. The GPH approach is also considered in the study for comparison purposes, since this method is widely used in the literature of long-memory time series. The empirical investigation shows that M and GPH-estimator methods display standardized densities fairly close to the standard Gaussian density in the context of non-contaminated data. On the other hand, in the presence of additive outliers, the M-estimator remains unaffected with the presence of additive outliers while the GPH is totally corrupted, which was an expected performance of this estimator. Therefore, the M-estimator here proposed becomes an alternative method to estimate the long-memory parameter when dealing with long-memory time series with and without outliers.
Error and Model Misspecification in ARFIMA Process
Brazilian Review of Econometrics, 2001
In developing the long and short memory estimation, it is usually assumed that the innovations in the ARFIMA model are normally distributed. How ever, circumstances may occur where this assumption is not true. This paper uses Monte Carlo simulation to evaluate the robustness of different estimators of the fractional parameter in stationary and invertible ARFIMA processes to the misspecification of the error distribution. In particular, we consider misspecifi cation against heavy-tailed, skewed and bimodal distributions. The study is also extended for the incorrect ARFIMA specification. Resumo No processo de estima<;ao dos parametros de longa e curta memoria e usual mente assumido que os erros no modelo ARFIMA sao normalmente distribuidos. Entretanto pode ocorrer, em certas circunstancias, que esta suposi<;ao nao seja verdadeira. Este artigo utiliza simula<;ao de Monte Carlo para investigar a ro bustez de diferentes estimadores do parametro fraciomirio do processo ARFIMA, estaciomirio e invertivel, quando os erros nao sao normais. Em particular, con sideramos as distribui<;oes de caldas pesadas, assimetricas e bimodais. 0 estudo e tambem extendido para 0 caso de ordem incorreta do processo ARFIMA.