ARFIMA Model Research Articles

The Economic Importance of Rare Earth Elements Volatility Forecasts

We compare the suitability of short-memory (ARMA models), long-memory (ARFIMA models), and a GARCH model to describe the volatility of rare earth elements (REEs). We find strong support for the existence of long-memory effects. A simple long-memory ARFIMA(0,

Econometric testing of unemployment hysteresis in selected CEE countries: Lessons for the Serbian economy

The paper investigates the empirical relevance of the unemployment hysteresis hypothesis in the following CEE countries: Bulgaria, Croatia, Romania, Hungary and Slovenia. Monthly time series are considered over the 2004-2015 period. The econometric analysis is based on several techniques. Apart from employing conventional unit root tests, the Fourier ADF test is computed to capture non-linear pattern of the deterministic component, and the Lee-Strazicich test to control for up to two endogenously determined structural breaks. These two tests are also used in the two-step approach to increase testing efficiency. Finally, to allow for more flexible treatment of the unemployment rate dynamics, the ARFIMA models are estimated. The unit root presence was clearly detected in Hungary and Slovenia, supporting the empirical validity of the unemployment hysteresis hypothesis and suggesting that random shocks have permanent impact on the evolution of unemployment rates. The unit root is rejected in the unemployment rates of Bulgaria, Croatia and Romania, but their trend components were under the long-lasting influence of great shocks. Impulse responses of these variables are more persistent than in purely stationary cases. Results for the analyzed CEE countries which have been part of the EU for a longer time indicate the necessity of implementing demand-side policies in order to reduce unemployment. New EU members in the same region may achieve satisfactory results in lowering their unemployment rates by combining supply-side and demand-side measures. Given the similar institutional background of the Serbian economy, we would expect that our results might be useful in considering the issue of reducing the unemployment rate in Serbia.

Forecasting Load Using Continuous-time Fractionally Auto-Regressive Integrated Moving-Average Models with Discrete Data

In a deregulated economy, it is important to forecast load on daily. It has many applications including energy purchasing and generation, load switching, contract evaluation, and infrastructure development. A large variety of mathematical methods have been developed for load forecasting. In this paper, we used a continuous-time autoregressive fractionally integrated moving average (CRAFIMA) model, which is defined as the stationary solution of a stochastic differential equation driven by a standard fractional Brownian motion. Like the discrete-time ARFIMA model, the CRAFIMA model is useful for studying time series with short memory, long memory and anti-persistence. Optimization issues including hyper-parameter selection and feature selection are also discussed. The study found that all three coefficients of the Hurst parameters are positive which is an advantage of using CRAFIMA algorithm. Based on this observations we conclude that self-similarity of the deseasonalized load Y(t) plays an important role in load prediction problems. The study also shows that the higher the Hurst exponent H , the bigger the range of short-term forecasting time horizons where the CRAFIMA model yields more accurate results than fitted ARIMA and f ARIMA models.

Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox

AbstractThis paper details particle Markov chain Monte Carlo (PMCMC) techniques for analysis of unobserved component time series models using several economic data sets. The objective of this paper is to explain the basics of the methodology and provide computational applications that justify applying PMCMC in practice. For instance, we use PMCMC to estimate a stochastic volatility model with a leverage effect, Student-t distributed errors or serial dependence. We also model time series characteristics of monthly US inflation rate by considering a heteroskedastic ARFIMA model where heteroskedasticity is specified by means of a Gaussian stochastic volatility process.

English

We extend the rational speculative bubbles literature to the frontier emerging stock markets. For this purpose, this paper employs fractional integration tests and duration dependence tests based on the ARFIMA models and nonparametric smoothed hazard functions. Unlike traditional bubble tests, fractional integration tests and duration dependence tests do not show strong evidence of rational speculative bubbles in the frontier emerging stock markets.

An alternative reference scenario for global CO2 emissions from fuel consumption: An ARFIMA approach

In this note, we establish an alternative reference scenario based on an ARFIMA model estimated using global CO2 emissions from 1750 to 2013. These new reference forecasts are free from additional assumptions on demographic and economic variables, often used in most reference forecasts. Instead, we only rely on the properties of the underlying stochastic process for global CO2 emissions that are, in this sense, closer to fundamentals. Our reference forecasts are clearly below the levels proposed by other reference scenarios available in the literature. This is important, as it suggests that the ongoing policy goals are actually easier to reach than what is implied by the standard reference scenarios. Having lower and more realistic reference emissions projections gives a truer assessment of the policy efforts that are needed, and highlights the lower costs involved in mitigation efforts, thereby maximizing the likelihood of more widespread environmental policy efforts.

Conditional Heteroskedasticity in Long Memory Model 'FIMACH' for Return Volatilities in BRICS Equity Markets

This paper introduces a new class of long memory model for volatility of stock returns, and applies the model on squared returns for BRICS (Brazil, Russia, India, China, and South Africa) countries. The conditional first- and second-order moments are provided. The CLS, FGLS and QML estimators are discussed. Empirically, we find evidence of long memory for squared return series for BRICS countries. In its estimation, the FIMACH model outperforms the FIGARCH and ARFIMA models.

Liquidity and Volatility in the Chinese Commodity Futures Market: Evidence from Intraday Data

This paper systematically explores liquidity and volatility forecasting for Aluminum, Copper, Fuel Oil, and Sugar futures contracts in China using intraday and daily data. Adopting three popular liquidity estimators, we first show that contracts with three months to delivery enjoy the best liquidity for all commodities under scrutiny. The finding that nearby contracts are less liquid than the more distant contracts is novel and contrary to the pattern in other major futures markets, and it results from unique institutional regulation in the Chinese futures markets. Utilizing more distant contracts and implementing four widely adopted volatility models for forecasting against alternative true volatility proxies, we provide strong evidence that the ARFIMA model consistently produces the best forecasts or forecasts not inferior to the best. This is robust for contracts with different liquidity levels.

Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets

Empirical evidence from time series methods which assume the usual I(0)/I(1) paradigm suggests that the efficient market hypothesis, stating that spot and futures prices of a commodity should co-integrate with a unit slope on futures prices, does not hold. However, these statistical methods are known to be unreliable if the data are fractionally integrated. Moreover, spot and futures price data tend to display clear patterns of time-varying volatility which also has the potential to invalidate the use of these methods. Using new tests constructed within a more general heteroskedastic fractionally integrated model we are able to find a body of evidence in support of the efficient market hypothesis for a number of commodities. Our new tests are wild bootstrap implementations of score-based tests for the order of integration of a fractionally integrated time series. These tests are designed to be robust to both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that the asymptotic tests do not admit pivotal asymptotic null distributions in the presence of heteroskedasticity, but that the corresponding tests based on the wild bootstrap principle do. A Monte Carlo simulation study demonstrates that very significant improvements in finite sample behaviour can be obtained by the bootstrap vis-à-vis the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments.

Forecasting High-Frequency Long Memory Series with Long Periods Using the SARFIMA Model

This paper evaluates the efficiency of the SARFIMA model at forecasting high-frequency long memory series with especially long periods. Three other models, the ARFIMA, ARMA and PAR models, are also included to compare their forecasting performances with that of the SARFIMA model. For the artificial SARFIMA series, if the correct parameters are used for estimating and forecasting, the model performs as well as the other three models. However, if the parameters obtained by the WHI estimation are used, the performance of the SARFIMA model falls far behind that of the other models. For the empirical intraday volume series, the SARFIMA model produces the worst performance of all of the models, and the ARFIMA model performs best. The ARMA and PAR models perform very well both for the artificial series and for the intraday volume series. This result indicates that short memory models are competent in forecasting periodic long memory series.

Stock returns, inflation, and real activity in developing countries: A Markov-switching approach

This paper empirically investigates the relationship between real stock returns, inflation, and real activity using the Markov-switching dynamic regression (MS-DR) approach. The MS-DR allows multiple structural breaks in the estimation, and we can check regression coefficients separately in the recession and expansion periods. We selected two major developing countries (Mexico and South Africa) in order to reduce location bias. We use real stock returns, expected inflation, unexpected inflation, and real GDP growth in the estimations, and the ARFIMA model is used for unexpected inflation. The empirical results show that the relationship between real stock returns and inflation is negative only in the recession period. This regime-dependency is also tested with Eugene F. Fama?s (1981) proxy effect hypothesis, and it is found that the stock returns respond differently to inflation in a regime according to the regime-dependent proxy effect hypothesis. These findings suggest that the negative relationship puzzle in the empirical finance literature can be explained with the regime-dependency effect.

Arfima-Figarch vs. Arfima-Hygarch: Case Study ETF Returns of Emerging Asian Countries

This research investigate the long memory returns for ETF returns index of seven Asian countries in Emerging Markets Equities during 2008-2013 periods. Those ETFs are Wisdom Tree Indian Rupee Fund (ICN), Market Vectors Indonesia Index (IDX), iShares MSCI Malaysia Index Fund (EWM), Market Vectors Russia ETF (RSX), and iShares MSCI Thailand Investable Market Index Fund (THD), SPDR S&P China ETF (GXC), and Market Vectors Vietnam ETF (VNM). The ARFIMA, ARFIMA-FIGARCH, and ARFIMA-HYGARCH models were estimated. The empirical results of log-likelihood information criterion analyses, the statistics supports ARFIMA-HYGARCH model instead of ARFIMA and ARFIMA-FIGARCH models.

Least absolute deviation estimation for general fractionally integrated autoregressive moving average time series models

We introduce a new class of ARFIMA models, which removes the restrictions that the roots of AR and MA polynomials are outside the unit circle. We establish consistency and asymptotic normality of the least absolute deviation estimator under non-Gaussian setting.

A Comparative Note about Estimation of the Fractional Parameter under Additive Outliers

In recent articles, Fajardo et al. (2009) and Reisen and Fajardo (2012) propose an alternative semiparametric estimator of the fractional parameter in ARFIMA models which is robust to the presence of additive outliers. The results are very interesting, however, they use samples of 300 or 800 observations which are rarely found in macroeconomics. In order to perform a comparison, I estimate the fractional parameter using the procedure of Geweke and Porter-Hudak (1983) augmented with dummy variables associated with the (previously) detected outliers using the statistic τd suggested by Perron and Rodríguez (2003). Comparing with Fajardo et al. (2009) and Reisen and Fajardo (2012), I found better results for the mean and bias of the fractional parameter when T = 100 and the results in terms of the standard deviation and the MSE are very similar. However, for higher sample sizes such as 300 or 800, the robust procedure performs better. Empirical applications for seven monthly Latin-American inflation series with very small sample sizes contaminated by additive outliers are discussed.

Can a simple structural time series model beat the random walk?

This paper tries to address the question that if the long run PPP holds, then there should exist a structural model which can outperform the random walk in out of sample forecasting. We propose an ARFIMA based model with log of the independent variable as an explanatory variable and make a comparison study of this structural model with the benchmark random walk model. Then, we compare our results with that as obtained by Engel and Hamilton, and by Clarida, Sarno, Taylor and Valente. We present the standard ARFIMA model and show how can make an extension of it so that it becomes a variant of ARFIMA and name it as YQ-ARFIMA, then construct a bivariate model relating the dependent variable yt and ln yt , and with that, perform an impulse response function analysis of the predictive ability of ln yt . We also transform the YQ-ARFIMA into a moving average representation, and thereafter perform the impulse response function analysis again, then make a comparison study between the standard ARFIMA and the YQARFIMA by comparing the out of sample forecasting ability of each one of them with the benchmark random walk model. After that, compare the performance of YQ-ARFIMA with that of the Markov switching model put forward by Engel and Hamilton, and the MSIH(3)-VECM as put forward by CSTV. Last, we test the robustness of the YQ-ARFIMA by fitting it into different exchange rate series spanning the five continents of the globe, then, test the consistency of the forecast by YQ-ARFIMA by a cointegration technique. By using the loss functions RMSE and MAPE, cointegration consistency in forecasts and impulse response function analysis, we have shown beyond doubt that theYQ-ARFIMA model is very much superior in forecasting ability.

Predicting air quality using ARIMA, ARFIMA and HW smoothing

Air quality indices (AQIs), used to classify and report the ambient air quality all across the world, computed for pol- lutants SPM, RSPM, NO2 and SO2 for the city Chandigarh using 24-hourly data revealed, RSPM as one of the main responsible air pollutants. Three time series models viz. ARIMA, ARFIMA and Holt and Winters (HW) smoothing techniques are employed to assess and predict the air quality status with respect to responsible pollutant RSPM. Various model selection criteria like Mean Absolute Error, Mean Absolute Percentage Error, Root Mean Square Error, and Bias corrected Akaike's information criterion (AICC) suggested ARFIMA as the appropriate model. Different long memory tests also justify the use of ARFIMA model and its comparison with ARIMA and HW smoothing techniques yield improved estimators/predictors for the responsible pollutant RSPM.

A comment on “Measuring fractality” by Stadnitski (2012)

A comment on “Measuring fractality” by Stadnitski (2012)

Are Central Bankers Inflation Nutters? A Bayesian MCMC Estimator of the Long Memory Parameter in a State Space Model

Several central banks have adopted inflation targets. The implementation of these targets is flexible; the central banks aim to meet the target over the long term but allow inflation to deviate from the target in the short-term in order to avoid unnecessary volatility in the real economy. In this paper, we propose modeling the degree of flexibility using an ARFIMA model. Under the assumption that the central bankers control the long-run inflation rates, the fractional integration order captures the flexibility of the inflation targets. A higher integration order is associated with a more flexible target. Several estimators of the fractional integration order have been proposed in the literature. Grassi and Magistris (2011) show that a state-based maximum likelihood estimator is superior to other estimators, but our simulations show that their finding is over-biased for a nearly non-stationary time series. We resolve this issue by using a Bayesian Monte Carlo Markov Chain (MCMC) estimator. Applying this estimator to inflation from six inflation-targeting countries for the period 1999 M1 to 2013 M3, we find that inflation is integrated of order 0.8 to 0.9 depending on the country. The inflation targets are thus implemented with a high degree of flexibility.

Modelling and forecasting international interest rate spreads: UK, Germany, Japan and the USA

The interest rate spread is of importance to policy-makers and finance professionals in asset allocation and is a common measure of financial market stress. In this paper, we model and forecast the interest rate spreads for a number of countries using two well-known continuous time models and discrete time ARMA and ARFIMA models. We use monthly and weekly data which cover the recent global financial market crisis of 2007-2009 for Germany, Japan, UK and the USA. We find that the Merton's continuous-time model outperforms all other model specifications in terms of the mean of the forecast errors, MAPE and RMSE.

Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox

This paper details particle Markov chain Monte Carlo (PMCMC) techniques for analysis of unobserved component time series models using several economic data sets. The objective of this paper is to explain the basics of the methodology and provide computational applications that justify applying PMCMC in practice. For instance, we use PMCMC to estimate a stochastic volatility model with a leverage effect, Student-t distributed errors or serial dependence. We also model time series characteristics of monthly US inflation rate by considering a heteroskedastic ARFIMA model where heteroskedasticity is specified by means of a Gaussian stochastic volatility process.