Geweke And Porter-Hudak Research Articles

Modelling COVID-19 Fluctuation in Nigeria Using Fractional Integrated Garch Model

This study applied a fractionally integrated GARCH (FIGARCH) process in modelling daily cases of COVID-19 in Nigeria from 28 February 2020 to 23 March 2022. The time plot of the series showed the constant fluctuation in the study variable. The daily COVID-19 data was tested for stationarity using Augmented Dickey-Fuller (ADF), the series was not stationary. The Geweke and Porter-Hudak (GPH) method was used to estimate the long memory parameter d of the FIGARCH model. The daily series was stationary at a fractional differencing of order (d=0.97). The presence of long memory was also detected using the autocorrelation function. The fractionally integrated GARCH model was used to detect the period of high and low crisis. The crisis period was identified by volatility clustering and the leverage effect process. However, four models were estimated for FIGARCH models. The best model was selected based on the information criteria. Finally, the most adequate model for estimating the volatility of COVID-19 in Nigeria was the FIGARCH (1,0.97, 1) model.

Semiparametric nonlinear log-periodogram regression estimation for perturbed stationary anisotropic long memory random fields

In recent years, spatial statistics has been widely used in many fields. The applications of two-dimensional random fields to describe data in image processing, environment and earth science, space econometrics and other fields are ubiquitous. Considering the complexity of two-dimensional spatial data, two kinds of semiparametric nonlinear log-periodogram regression (NLPR) estimations are proposed to estimate memory parameters of perturbed two-dimensional anisotropic stationary long memory random fields. The long memory parameters d 1 in the “vertical” and d 2 in the “horizontal” direction respectively, and The anisotropic stationary long memory random field is disturbed by an independent, additive, and stationary Gaussian short memory noise field. The performance of the NLPR estimators is examined and compared with the performance of the GPH (Geweke and Porter-Hudak) estimators by simulation.

Long Memory in the Volatility of Selected Cryptocurrencies: Bitcoin, Ethereum and Ripple

This paper examines the volatility of cryptocurrencies, with particular attention to their potential long memory properties. Using daily data for the three major cryptocurrencies, namely Ripple, Ethereum, and Bitcoin, we test for the long memory property using, Rescaled Range Statistics (R/S), Gaussian Semi Parametric (GSP) and the Geweke and Porter-Hudak (GPH) Model Method. Our findings show that squared returns of three cryptocurrencies have a significant long memory, supporting the use of fractional Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) extensions as suitable modelling technique. Our findings indicate that the Hyperbolic GARCH (HYGARCH) model appears to be the best fitted model for Bitcoin. On the other hand, the Fractional Integrated GARCH (FIGARCH) model with skewed student distribution produces better estimations for Ethereum. Finally, FIGARCH model with student distribution appears to give a good fit for Ripple return. Based on Kupieck’s tests for Value at Risk (VaR) back-testing and expected shortfalls we can conclude that our models perform correctly in most of the cases for both the negative and positive returns.

Bootstrapping the log-periodogram estimator of the long-memory parameter: is it worth weighting

Estimation of the long-memory parameter from the log-periodogram (LP) regression, due to Geweke and Porter-Hudak (GPH), is a simple and frequently used method of semi-parametric estimation. However, the simple LP estimator suffers from a finite sample bias that increases with the dependency in the short-run component of the spectral density. In a modification of the GPH estimator, Andrews and Guggenberger, AG (2003) suggested a bias-reduced estimator, but this comes at the cost of inflating the variance. To avoid variance inflation, Guggenberger and Sun (2004, 2006) suggested a weighted LP (WLP) estimator using bands of frequencies, which potentially improves upon the simple LP estimator. In all cases a key parameter in these methods is the need to choose a frequency bandwidth, m, which confines the chosen frequencies to be in the ‘neighbourhood’ of zero. GPH suggested a ‘square-root’ rule of thumb that has been widely used, but has no optimality characteristics. An alternative, due to Hurvich and Deo (1999), is to derive the root mean square error (rmse) optimising value of m, which depends upon an unknown parameter, although that can be consistently estimated to make the method feasible. More recently, Arteche and Orbe (2009a,b), in the context of the GPH estimator, suggested a promising bootstrap method, based on the frequency domain, to obtain the rmse value of m that avoids estimating the unknown parameter. We extend this bootstrap method to the AG and WLP estimators and to consideration of bootstrapping in the frequency domain (FD) and the time domain (TD) and, in each case, to ‘blind’ and ‘local’ versions. We undertake a comparative simulation analysis of these methods for relative performance on the dimensions of bias, rmse, confidence interval width and fidelity.

Long Memory of NSE Indices

Long range memory in share indices show temporal dependence between observations spaced by long intervals of time and has distinct non-periodic cycles. This paper examines the presence of long memory of various indices of National Stock Exchange (NSE). The data consists of closing values of indices over different periods of time. The tests applied to examine long memory are Hurst exponent, Manderbolt-Hurst exponent, Lo’s rescaled-range analysis and Geweke and Porter-Hudak (GPH) test. The results of the estimated Hurst exponent, Manderbolt-Hurst exponent and GPH test show that invariably all NSE indices series have long memory. However, the results of Lo’s rescaled-range analysis indicate the absence of long memory for all indices. Key words: Long memory, rescaled range analysis, fractional dimension, Hurst exponent, GPH test, NSE indices

Long memory and fractional cointegration relationship between physical and financial oil markets

This paper investigates the relationship between spot-future oil volatility by examining the empirical evidence for the aspect followed by two process volatility. The analysis is undertaken using daily from January 2007 to March 2012 at the New York Mercantile Exchange (NYMEX) and International Petroleum Exchange (IPE). There is as yet little consensus on the methodology to test the fractional cointegration in crude oil markets. We consider semi-parametric frequency domain analysis of fractional cointegration between long memory processes. The estimation of predictive regression narrow band least square (NBLS) is based on the Fourier frequency number included in the spectral regression. Consistent with exploration the Geweke and Porter-Hudak (GPH) and local Whittle estimators, the results notice the non-stationary long memory in spot-future oil volatility and the mean reverting behaviour. An application to NBLS model, we indicate that futures oil volatilities are a consistent estimate of spots oil volatilities. The contribution of this paper is to demonstrate that oil futures prices display long memory and that form of long memory is persistence over the study period of 2007-2012 and proves the inter-relationship between financial and physical oil markets.

Monte Carlo simulation for comparison of different estimators of long memory parameter: An application of ARFIMA model for forecasting commodity price

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 inve stigated. 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.

Long Memory Properties in Return and Volatility: An Application of the Impact of Arab Spring in Turkey Financial Market

The Arab Spring which began on 17 December 2010 with the civil rebellions, revolutionary wave of demonstrations and protests in the Tunisia, Egypt, Libya, Yemen, Bahrain and Syria. The Arab Spring not only created a domino effect between Arabic countries but also it reflected a significant influence on the financial markets all over the world. The objective of this study is to analyze the impact of the Arab Spring in Turkey Financial Market in consideration of long memory. Long memory can be defined as the persistence of the unexpected shocks on the underlying has long lasting effects. Modeling long memory in stock returns and volatility has also attracted great deal of attention from finance literature recently. Existence of long memory is determined both for the returns and volatility of the time series by using different methods. Existence of long memory can be tested by Rescaled Range Statistics (R/S), Geweke and Porter-Hudak (GPH) Model and Gaussian Semi Parametric (GSP) Method. In consequence of these tests, if the stock returns have long memory affect then respectively Fractionally Integrated Autoregressive Moving Average Model (ARFIMA) and the Fractionally Integrated Generalized Autoregressive Conditional Heteroscedasticity (FIGARCH) model are used to detect the long memory in respectively return and volatility. In this study, the impact of the Arab Spring is investigated by modeled the long memory in Istanbul Stock Exchange using ISE 30 index prices in between December 17, 2010 and April 02, 2012.

Alternative Estimators of Long-Range Dependence

In this article, we concentrate on various techniques to quantify long-range dependence: wavelets, Geweke and Porter-Hudak (GPH)'s semi-parametric method, the periodogram method, rescaled range analysis (R/S) and a modification of it aimed at accommodating for short memory, quasi maximum likelihood (QML), de-trended fluctuation analysis (DFA), Modified DFA (MDFA), and Centered Moving Average (CMA) analysis.Based on Monte Carlo experiments, we conclude that if the data generating process (DGP) is an AR(1), MA(1) or ARMA(1, 1) process, with moderate parameter values, the periodogram, GPH, QML, and modified R/S methods, followed by the DFA, MDFA, and CMA ones, perform reasonably well as regards with bias, although some of these techniques exhibit a non-negligible size distortion. Moreover, the QML, the periodogram, DFA, MDFA, and CMA methods overall provide with powerful and low-bias estimators, under alternative ARFIMA (p, d, q)-DGPs. The wavelet-based estimator in turn has high power, but it is noticeably upward (downward) biased when the autoregressive (moving-average) coefficient of the DGP is large.Our Monte Carlo experiments are complemented with an application to Dow Jones AIG Gold Sub-index data, by means of bootstrap re-sampling.

Tests of Long Memory: A Bootstrap Approach

Many time series in diverse fields have been found to exhibit long memory. This paper analyzes the behaviour of some of the most used tests of long memory: the R/S analysis, the modified R/S, the Geweke and Porter-Hudak (GPH) test and the detrended fluctuation analysis (DFA). Some of these tests exhibit size distortions in small samples. It is well known that the bootstrap procedure may correct this fact. Here I examine the size and power of those tests for finite samples and different distributions, such as the normal, uniform, and lognormal. In the short-memory processes such as AR, MA and ARCH and long memory ones such as ARFIMA, p-values are calculated using the post-blackening moving-block bootstrap. The Monte Carlo study suggests that the bootstrap critical values perform better. The results are applied to financial return time series.

Stochastic chaos or ARCH effects in stock series?: A comparative study

Recent empirical studies have shown that the chaotic behaviour and excess volatility of financial series are the result of interactions between heterogeneous investors. In our article, we propose verifying this hypothesis. Thus, we use the Chen et al. [Testing for non-linear structure in an artificial financial market. Working Paper, University of Bonn (2000).] model to show that the modification of the agents' homogeneity hypothesis can drive to stochastic chaotic evolution of price series. Then, through an econometric procedure, we try to identify the underlying process of the Paris Stock Exchange returns series (CAC40). To this end, we apply several different tests: (1) dealing with long-memory components derives from the fractional integration test of Geweke and Porter-Hudak (GPH) [J. Time Ser. Anal. 4 (1983) 221.] and (2) dealing with chaotic structures comes from the work on correlation dimension of Grassberger and Procaccia [Physica 9D (1983) 189.] and the Lyapunov exponents method of Gençay and Dechert [Physica D (1992) 142.]. Finally, we forecast the CAC40 returns series using the recent methods of Principal Components Regression (PCR) and Radial Basis Functions (RBF). We conclude with the implications of the presence of chaotic structures in stock markets and future research on ARCH and chaotic models' relationships.

Estimation of the ARFIMA (p, d, q) fractional differencing parameter (d) using the classical rescaled adjusted range technique

Derived from the general ARMA (p, q) class of short-term dependent models, the Autoregressive Fractionally Integrated Moving Average (ARFIMA) specification provides a means of modelling long-term dependence in time-series data. In financial and economic time-series, the application of the ARFIMA model has been predominantly by the Maximum Likelihood (ML) methods, and the Geweke and Porter-Hudak (GPH) two step procedure. Extending the application of the classical rescaled adjusted range to long-term dependent ARFIMA (p, d, q) processes, estimates of the fractional differencing parameter (d) may also be derived by the Hurst exponent.

A fractional cointegration test of purchasing power parity: the case of selected members of OPEC

In recent years, analysts have used cointegration tests in determining whether the residuals of the purchasing power parity (PPP) model are mean-reverting. Cointegration methods, however, rest on the binary selection of the series as either stationary or integrated of degree one. This approach excludes a class of long-memory stochastic processes with a fractional differencing parameter which also have mean-reverting characteristics. Fractional cointegration method tests the mean-reverting property of a series which is based on this class of stochastic processes. This paper uses cointegration and fractional cointegration methods in determining the mean-reverting properties of the parallel market exchange rates for several members of the Organization of Petroleum Producing Countries. The Geweke and Porter-Hudak (GPH) test results suggest that the PPP models for Algeria, Ecuador, Saudi Arabia and Venezuela are fractionally cointegrated. Moreover, according to the Augmented Dickey-Fuller (ADF) test, the PPP models for all countries under study, appear not to have a cointegrating vector.

Fractional cointegration tests with GARCH

This paper examines the GARCH effects on the Geweke and Porter-Hudak (GPH) and modified rescaled range (MRR) tests for the analysis of the deviations from the cointegrating relationship among series. The Monte Carlo results show that the MRR test is very robust to the GARCH effects. The GPH test tends to over-reject the null hypothesis of no (fractional) cointegration. but the bias is not very serious except when the variance processes are integrated.

The distribution of the low frequency periodogram ordinates of fractionally differenced series and their inclusion in two estimators of the differencing parameter

The commonly held belief that the low freqrency ordinates of the periodogram of fractionally differenced models are unbiased for the spectral density, independent and exponentially distributed gives rise to some methods of estimating the differencing parameter d, in paricular Geweke and porter-Hudak (GPH),(1983) and Janacek(1994). Hurvich and Beltrao (1993) and Hurvich and Ray (1995) gave results on the bias ane expressions for the distribution under certain conditions which led them to suggest using a tapered periodogram and omitting the first orkinate for the GPH estimatot. In this paper we make further empirical investigations into the distribuion of both tapered and tntapered low frequency periodogram ordinates for vlues of d in the range {-2.25,2}.We then investigate which range of ordinates should be incuded in the GPH and Janacek estimators for models with a variety of short term componcnts and values of d, including nonstationary and noninvertible. Surprisingly we find that these estimators are usually better when the initial ordinates are included.We report the mean errors and root mean square errors obtained from these simulations and use these to compare the two estimators and to assess their performance.