ARFIMA Research Articles

Prediction of Electricity Consumption in Ghana: Long or Short Memory

In this study, we explore both univariate and multivariate aspects of time series analysis. In the univariate aspect, we evaluated the predictive performance of three widely used univariate time series methods in forecasting the electricity consumption in Ghana during the 1980 – 2011 periods. The three univariate time series approaches are autoregressive integrated moving average (ARIMA), autoregressive fractional integrated moving average (ARFIMA) and exponential smoothing. In each approach, we examined competing models and the “best” model according to the minimum information criterion and diagnostic checking was selected. The forecast accuracy measure (i.e.; mean absolute forecast error, MAFE) was computed for each “best” model in the three different approaches. The empirical results revealed that the MAFE for ARIMA, ARFIMA and exponential smoothing were 31.3%, 9.4% and 41.6% respectively. Thus, the comparative analysis of the forecast performance of these methods clearly concluded that the ARFIMA method gives better forecast in predicting electricity consumption in Ghana. And, in the multivariate aspect, we examined whether GDP, export, import and population influences electricity consumption. The results revealed a feedback causality between electricity consumption and economic growth. Again, we established that there exists an uni-directional influence of import, export, population towards electricity consumption. The “best” model of the univariate approach is ARFIMA (2,0.31,1) with MAFE of 9.4% while the “best” model for the multivariate approach is vector error correction model VECM (3) with MAFE of 1.5%. Thus, the multivariate approach has a better predictive performance in forecasting electricity consumption in Ghana. This shows how superior the multivariate approach against the univariate time series approach.

Modelling and forecasting of retail price of arhar dal in Karnal, Haryana

Forecasting retail price of agricultural commodities is of utmost importance for planning in advance to resist any abnormalities. In this regard, the autoregressive fractionally integrated moving-average (ARFIMA) model is employed. ARFIMA model searches for a non-integer differencing parameter d to difference the data to capture long memory. The model is applied for modelling and forecasting of daily retail price of pigeonpea (Cajanas cajan) in Karnal during January, 2011 to July, 2013. Augmented Dickey-Fuller (ADF) test and Philips Peron (PP) test are used for testing the stationarity of the series. Autocorrelation (ACF) and partial autocorrelation (PACF) functions showed a slow hyperbolic decay indicating the presence of long memory. In the present price series, long memory parameter is found to be significant. On the basis of minimum AIC values, the best model is identified. To this end, 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. It is found that ARFIMA model has been able to capture the long memory present in the data set. The R software package has been used for data analysis.

Forecasting RMB Exchange Rate Based on a Nonlinear Combination Model of ARFIMA, SVM, and BPNN

There are various models to predict financial time series like the RMB exchange rate. In this paper, considering the complex characteristics of RMB exchange rate, we build a nonlinear combination model of the autoregressive fractionally integrated moving average (ARFIMA) model, the support vector machine (SVM) model, and the back-propagation neural network (BPNN) model to forecast the RMB exchange rate. The basic idea of the nonlinear combination model (NCM) is to make the prediction more effective by combining different models’ advantages, and the weight of the combination model is determined by a nonlinear weighted mechanism. The RMB exchange rate against US dollar (RMB/USD) and the RMB exchange rate against Euro (RMB/EUR) are used as the empirical examples to evaluate the performance of NCM. The results show that the prediction performance of the nonlinear combination model is better than the single models and the linear combination models, and the nonlinear combination model is suitable for the prediction of the special time series, such as the RMB exchange rate.

Particle Gibbs with ancestor sampling for stochastic volatility models with: heavy tails, in mean effects, leverage, serial dependence and structural breaks

AbstractParticle Gibbs with ancestor sampling (PG-AS) is a new tool in the family of sequential Monte Carlo methods. We apply PG-AS to the challenging class of stochastic volatility models with increasing complexity, including leverage and in mean effects. We provide applications that demonstrate the flexibility of PG-AS under these different circumstances and justify applying it in practice. We also combine discrete structural breaks within the stochastic volatility model framework. For instance, we model changing time series characteristics of monthly postwar US core inflation rate using a structural break autoregressive fractionally integrated moving average (ARFIMA) model with stochastic volatility. We allow for structural breaks in the level, long and short-memory parameters with simultaneous breaks in the level, persistence and the conditional volatility of the volatility of inflation.

Modeling Geodetic Processes with Levy $$\alpha $$ α -Stable Distribution and FARIMA

Over the last years the scientific community has been using the autoregressive moving average (ARMA) model in the modeling of the noise in global positioning system (GPS) time series (daily solution). This work starts with the investigation of the limit of the ARMA model which is widely used in signal processing when the measurement noise is white. Since a typical GPS time series consists of geophysical signals (e.g., seasonal signal) and stochastic processes (e.g., coloured and white noise), the ARMA model may be inappropriate. Therefore, the application of the fractional auto-regressive integrated moving average (FARIMA) model is investigated. The simulation results using simulated time series as well as real GPS time series from a few selected stations around Australia show that the FARIMA model fits the time series better than other models when the coloured noise is larger than the white noise. The second fold of this work focuses on fitting the GPS time series with the family of Levy \(\alpha \)-stable distributions. Using this distribution, a hypothesis test is developed to eliminate effectively coarse outliers from GPS time series, achieving better performance than using the rule of thumb of \(n\) standard deviations (with \(n\) chosen empirically).

Modeling and predicting measured response time of cloud-based web services using long-memory time series

Predicting cloud performance from user’s perspective is a complex task, because of several factors involved in providing the service to the consumer. In this work, the response time of 10 real-world services is analyzed. We have observed long memory in terms of the measured response time of the CPU-intensive services and statistically verified this observation using estimators of the Hurst exponent. Then, naïve, mean, autoregressive integrated moving average (ARIMA) and autoregressive fractionally integrated moving average (ARFIMA) methods are used to forecast the future values of quality of service (QoS) at runtime. Results of the cross-validation over the 10 datasets show that the long-memory ARFIMA model provides the mean of 37.5 % and the maximum of 57.8 % reduction in the forecast error when compared to the short-memory ARIMA model according to the standard error measure of mean absolute percentage error. Our work implies that consideration of the long-range dependence in QoS data can help to improve the selection of services according to their possible future QoS values.

Particle Gibbs with Ancestor Sampling Methods for Unobserved Component Time Series Models with Heavy Tails, Serial Dependence and Structural Breaks

Particle Gibbs with ancestor sampling (PG-AS) is a new tool in the family of sequential Monte Carlo methods. We apply PG-AS to the challenging class of stochastic volatility models with increasing complexity, including leverage and in mean effects. We provide applications that demonstrate the flexibility of PG-AS under these different circumstances and justify applying it in practice. We also combine discrete structural breaks within the stochastic volatility model framework. For instance, we model changing time series characteristics of monthly postwar US core inflation rate using a structural break autoregressive fractionally integrated moving average (ARFIMA) model with stochastic volatility. We allow for structural breaks in the level, long and short-memory parameters with simultaneous breaks in the level, persistence and the conditional volatility of the volatility of inflation.

Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling

In this survey paper we present a systematic methodology which demonstrates how to identify the origins of fractional dynamics. We consider three mechanisms which lead to it, namely fractional Brownian motion, fractional Lévy stable motion and an autoregressive fractionally integrated moving average (ARFIMA) process but we concentrate on the ARFIMA modelling. The methodology is based on statistical tools for identification and validation of the fractional dynamics, in particular on an ARFIMA parameter estimator, an ergodicity test, a self-similarity index estimator based on sample p-variation and a memory parameter estimator based on sample mean-squared displacement. A complete list of algorithms needed for this is provided in appendices –. Finally, we illustrate the methodology on various empirical data and show that ARFIMA can be considered as a universal model for fractional dynamics. Thus, we provide a practical guide for experimentalists on how to efficiently use ARFIMA modelling for a large class of anomalous diffusion data.

Predicting BRICS stock returns using ARFIMA models

This article examines the existence of long memory in daily stock market returns from Brazil, Russia, India, China and South Africa (BRICS) countries and also attempts to shed light on the efficacy of autoregressive fractionally integrated moving average (ARFIMA) models in predicting stock returns. We present evidence which suggests that ARFIMA models estimated using a variety of estimation procedures yield better forecasting results than the non-ARFIMA (AR, MA, ARMA and GARCH) models with regard to prediction of stock returns. These findings hold consistently for the different countries whose economies differ in size, nature and sophistication.

Detection of changes in hydrologic system memory associated with urbanization in the Great Lakes region

The change of long memory with urbanization in a regional hydrologic system was investigated using both stochastic time series models and a physically based hydrologic model. Based on observed streamflow at five USGS gauge stations in the Great Lakes region, objective fractional autoregressive integrated moving average (FARIMA) model identification and estimation procedures were used for daily streamflow. The recently improved Variable Infiltration Capacity (VIC) model with urban representation was applied to simulate the water and energy response in 16 basins in the region with various degrees of urbanization. The VIC model was driven by different years' land use/cover maps, including a year 1992 base map, and year 2010 and 2030 maps projected by the Land Transformation Model. The ability of the VIC model to capture long memory of observed daily streamflow was evaluated before applying the FARIMA model to all 16 basins. Overall, the northern portion of the domain generally has larger long-term hydrologic dependence than the southern portion. Simulated streamflow statistics show that the long memory in the hydrologic system has decreased with urbanization. In order to interpret the long memory change with urbanization from a physical point of view, spectral analysis was conducted to examine the spectrum change of soil moisture content with urbanization. The decrease in simulated streamflow long memory relates to the decreased low-frequency power and amplitude of soil moisture in the deep soil layer. The long-term response of surface water systems to urbanization should be considered by water resources and urban planners.

MODELLING FOR THE WAVELET COEFFICIENTS OF ARFIMA PROCESSES

AbstractWe consider a model for the discrete nonboundary wavelet coefficients of autoregressive fractionally integrated moving average (ARFIMA) processes in each scale. Because the utility of the wavelet transform for the long‐range dependent processes, which many authors have explained in semi‐parametrical literature, is approximating the transformed processes to white noise processes in each scale, there have been few studies in a parametric setting. In this article, we propose the model from the forms of the (generalized) spectral density functions (SDFs) of these coefficients. Since the discrete wavelet transform has the property of downsampling, we cannot directly represent these (generalized) SDFs. To overcome this problem, we define the discrete non‐decimated nonboundary wavelet coefficients and compute their (generalized) SDFs. Using these functions and restricting the wavelet filters to the Daubechies wavelets and least asymmetric filters, we make the (generalized) SDFs of the discrete nonboundary wavelet coefficients of ARFIMA processes in each scale clear. Additionally, we propose a model for the discrete nonboundary scaling coefficients in each scale.

Wavelet based deseasonalization for modelling and forecasting of daily discharge series considering long range dependence

Abstract Short term streamflow forecasting is important for operational control and risk management in hydrology. Despite a wide range of models available, the impact of long range dependence is often neglected when considering short term forecasting. In this paper, the forecasting performance of a new model combining a long range dependent autoregressive fractionally integrated moving average (ARFIMA) model with a wavelet transform used as a method of deseasonalization is examined. It is analysed, whether applying wavelets in order to model the seasonal component in a hydrological time series, is an alternative to moving average deseasonalization in combination with an ARFIMA model. The one-to-ten-steps-ahead forecasting performance of this model is compared with two other models, an ARFIMA model with moving average deseasonalization, and a multiresolution wavelet based model. All models are applied to a time series of mean daily discharge exhibiting long range dependence. For one and two day forecasting horizons, the combined wavelet - ARFIMA approach shows a similar performance as the other models tested. However, for longer forecasting horizons, the wavelet deseasonalization - ARFIMA combination outperforms the other two models. The results show that the wavelets provide an attractive alternative to the moving average deseasonalization.

Investigating the long memory property of the Hungarian market pig prices by using detrended fluctuation analys

Within the scope of this study we test the Long Memory property on monthly average pig market prices including piglet, young pig, sow and slaughter pig. We also calculate the Hurst exponent using Detrended Fluctuation Analysis (DFA) method. DFA is a method for determining the statistical self-affinity of a time serie. It is a useful technique for investigating time series with long memory (diverging correlation time and power-low decaying autocorrelation function. The obtained exponent by DFA is similar to those Hurst exponents estimated by other methods such as Rescaled Range (R/S) and AutoRegressive Fractionally Integrated Moving Average (ARFIMA), except the fact that DFA may also be applied to non-stacionary time series (mean and variance is changing with time) as in our case. We study the long memory property of the market pig prices. Data consist of four time series (piglet, young pig, sow, slaughter pig) between 1991 and 2013. Before the econometric analysis all the series were seasonally adjusted by using TRAMO/SEATS method. Data preparation was followed by differencing the time series and testing the normality and stationarity of them. In the next step we divided the analysed period to four parts and determined the Hurst exponent for each sub-period with the DFA method. So as to sum it up, slaughter pig prices are random, young pig and piglet prices developed similarly and have long memory, while sow price changes have definitely short memory

On the test and estimation of fractional parameter in ARFIMA model: bootstrap approach

One of the most important problems concerning Autoregressive Fractional Integrated Moving Average (AFRIMA) time series model is the estimation of the fractional parameter . This research work was aimed to show efficiency of the different methods used to test and estimate fractional parameter in the fractionally integrated autoregressive moving-average (AFRIMA) model. In this study, estimates were obtained by smoothed spectral regression method and truncated geometric bootstrap method which aid in the test and estimation of fractional parameter by obtaining estimates through regression estimation method. The results indicate that the semi-parametric methods outperformed the parametric method when elements of AR or MA components are involved. Performance of one of the semi-parametric method (Robinson estimator) usually is not as good as the other semiparametric method: it has large bias, standard deviation and mean square error. The use of smoothed periodogram in this method improves the estimate; however, they are still not as good as the usual semi-parametric methods. In the long run, having compared the result of the two estimates, it was discovered that the bootstrap approach that is, the stimulation obtained using the truncated geometric bootstrap method produced a set of

Forecasting Wholesale Price of Pigeon Pea Using Long Memory Time-Series Models

The fractional integration is a generalization of integer integration, under which time-series are usually presumed to be integrated of order zero or one. In this regard, the autoregressive fractionally integrated moving-average (ARFIMA) model along with its estimation procedure is investigated. ARFIMA model searches for a non-integer differencing parameter d to difference the data to capture long memory. The model has been applied for modelling and forecasting of daily wholesale price of pigeon pea (Cajanas cajan) in the Amritsar and Bhatinda markets and the all-India maximum, minimum and modal prices of pigeon pea. Augmented Dickey-Fuller (ADF) test and Philips Perron (PP) test have been used for testing the stationarity of the series. Autocorrelation (ACF) and partial autocorrelation (PACF) functions have shown a slow hyperbolic decay indicating the presence of long memory. In all the five price series, long memory parameters are found to be significant. On the basis of minimum AIC values, the best model was identified for each series. To this end, evaluation of forecasting was 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 have been used for diagnostic checking. Out-of sample forecast of wholesale prices of pigeon pea has been computed up to February, 2014. The R software package has been used for data analysis.

Análise da variabilidade da frequência cardíaca em indivíduos saudáveis, doentes com insuficiência cardíaca e doentes transplantados

This study aimed to find parameters to characterize heart rate variability (HRV) and discriminate healthy subjects and patients with heart diseases. The parameters used for discrimination characterize the different components of HRV memory (short and long) and are extracted from HRV recordings using parametric as well as non parametric methods. Thus, the parameters are: spectral components at low frequencies (LH) and high frequencies (HF) which are associated with the short memory of HRV and the long memory parameter (d) obtained from autoregressive fractionally integrated moving average (ARFIMA) models. In the non parametric context, short memory (α1) and long memory (α2) parameters are obtained from detrended fluctuation analysis (DFA). The sample used in this study contains 24-hour Holter HRV recordings of 30 subjects: 10 healthy individuals, 10 patients suffering from congestive heart failure and 10 heart transplanted patients from the Noltisalis database. It was found that short memory parameters present higher values for the healthy individuals whereas long memory parameters present higher values for the diseased individuals. Moreover, there is evidence that ARFIMA modeling allows the discrimination between the 3 groups under study, being advantageous over DFA.

A hybrid ARFIMA and neural network model for electricity price prediction

In the framework of competitive electricity market, prices forecasting has become a real challenge for all market participants. However, forecasting is a rather complex task since electricity prices involve many features comparably with those in financial markets. Electricity markets are more unpredictable than other commodities referred to as extreme volatile. Therefore, the choice of the forecasting model has become even more important. In this paper, a new hybrid model is proposed. This model exploits the feature and strength of the Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) model as well as the feedforward neural networks model. The expected prediction combination takes advantage of each model’s strength or unique capability. The proposed model is examined by using data from the Nordpool electricity market. Empirical results showed that the proposed method has the best prediction accuracy compared to other methods.

Realized stochastic volatility with leverage and long memory

The daily return and the realized volatility are simultaneously modeled in the stochastic volatility model with leverage and long memory. The dependent variable in the stochastic volatility model is the logarithm of the squared return, and its error distribution is approximated by a mixture of normals. In addition, the logarithm of the realized volatility is incorporated into the measurement equation, assuming that the latent log volatility follows an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process to describe its long memory property. The efficient Bayesian estimation method using Markov chain Monte Carlo method (MCMC) was proposed and implemented in the state space representation. Model comparisons are performed based on the marginal likelihood, and the volatility forecasting performances are investigated using S&P500 stock index returns.

Fractionally integrated ARMA for crude palm oil prices prediction: case of potentially overdifference

Dealing with stationarity remains an unsolved problem. Some of the time series data, especially crude palm oil (CPO) prices persist towards nonstationarity in the long-run data. This dilemma forces the researchers to conduct first-order difference. The basic idea is that to obtain the stationary data that is considered as a good strategy to overcome the nonstationary counterparts. An opportune remark as it is, this proxy may lead to overdifference. The CPO prices trend elements have not been attenuated but nearly annihilated. Therefore, this paper presents the usefulness of autoregressive fractionally integrated moving average (ARFIMA) model as the solution towards the nonstationary persistency of CPO prices in the long-run data. In this study, we employed daily historical Free-on-Board CPO prices in Malaysia. A comparison was made between the ARFIMA over the existing autoregressive-integrated moving average (ARIMA) model. Here, we employed three statistical evaluation criteria in order to measure the performance of the applied models. The general conclusion that can be derived from this paper is that the usefulness of the ARFIMA model outperformed the existing ARIMA model.

Asymptotic Decorrelation of Wavelet Packet Transform for Certain Long-Memory Processes

The asymptotic decorrelation of the discrete wavelet transform for long-memory processes (such as the fractionally differenced (FD) process, the autoregressive fractionally integrated moving average (ARFIMA) process, and the Gegenbauer autoregressive moving average (GARMA) process) as well as the statistical inference techniques based on this property, have received much attention nowadays. In this paper, we investigate the asymptotic decorrelation property of the discrete wavelet packet transform (DWPT) for two classes of discrete-time long-memory processes containing the ARFIMA and the GARMA processes. Especially, we prove theoretically that the covariance across between-packet DWPT coefficients decays hyperbolically or exponentially fast as the width of the underlying Daubechies scaling and wavelet filters to generate the DWPT gets large. Meanwhile, we show that the covariance between within-packet DWPT coefficients converges hyperbolically fast to its corresponding counterpart when the underlying scaling and wavelet filters to generate the DWPT are the Shannon's ideal low- and high-pass filters.