ARFIMA Research Articles

Pattern interdependent network of cross-correlation in multivariate time series

Cross-correlation of a bivariate time series induces interdependencies between local patterns in the two series, which cooperatively exhibit in turn the structure of the cross-correlation. However, this structure is lost in the procedure of statistical average in time series analysis. In this paper a new concept called pattern interdependent network is proposed to display the structure of cross-correlation, in which the nodes are unique local patterns and the linkages are co-occurring frequencies of the unique local patterns in the series. The performance is illustrated by the bivariate series generated with the Gaussian process and the auto-regressive fractionally integrated moving average (ARFIMA) model. It is found that the cross-correlation and the scaling behaviors dominate the pattern of backbone structure (the set of the nodes and the set of linkages) and the symmetry of the network, respectively. The ARFIMA model can reproduce the structural behaviors of cross-correlations in U.S. stock markets. This concept provides us with a new method for detecting the structure of couplings between time series in various fields, such as clinical pathological signals.

Fractional ARIMA with an improved cuckoo search optimization for the efficient Short-term power load forecasting

Short-term power load forecasting plays a key role in power supply systems. Many methods have been used in short-term power load forecasting during the past years. A new short-term power load forecasting method is proposed in this study. First, the study represents a Fractional Auto-regressive Integrated Moving Average (FARIMA) model based on long-range dependence (LRD). The LRD model is governed by the Hurst exponent, which shows whether the model exhibits the LRD or not. Then, the study employs Cuckoo Search (CS) algorithm based on two parameters dynamic adjustment for parameter optimization of the forecasting model. As test problem, we use the real power consumption data, and test it for different forecasting models. Our results indicate that the FARIMA model and the improved optimization algorithm show relatively high accuracy and effectiveness in forecasting short-term power load.

Long memory investigation during demonetization in India

Long-range dependence (LRD) in financial markets remains a key factor in determining whether there is market memory, herding traces, or a bubble in the economy. Usually referred to as ‘Long Memory’, LRD has remained a key parameter even today since the mid-1970s. In November 2016, a sudden and drastic demonetization measure took place in the Indian market, aimed at curbing money laundering and terrorist funding. This study is an attempt to identify market behavior using long-range dependence during those few days in demonetization. Besides, it tries to identify nascent traces of bubble and embedded herding during that time. Auto Regressive Fractionally Integrated Moving Average (ARFIMA) is used for three consecutive days around the event. Tick-by-tick data from CNX Nifty High Frequency Trading (CNX Nifty HFT) is used for three consecutive days around demonetization (approximately, 5000 data points from morning trading sessions on each of the three days). The results show a clear and profound presence of herd behavior in all three data sets. The herd intensity remained similar, indicating a unique mixture of both ‘Noah Effect’ and ‘Joseph Effect’, proving a clear regime switch. However, the results on the event day show stable and prominent herding. Mandelbrot’s specified effects were tested on an uncertain and sudden financial event in India and proved to function perfectly.

Long-Range Dependence in Financial Markets: A Moving Average Cluster Entropy Approach.

A perspective is taken on the intangible complexity of economic and social systems by investigating the dynamical processes producing, storing and transmitting information in financial time series. An extensive analysis based on the moving average cluster entropy approach has evidenced market and horizon dependence in highest-frequency data of real world financial assets. The behavior is scrutinized by applying the moving average cluster entropy approach to long-range correlated stochastic processes as the Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Fractional Brownian motion (FBM). An extensive set of series is generated with a broad range of values of the Hurst exponent H and of the autoregressive, differencing and moving average parameters . A systematic relation between moving average cluster entropy and long-range correlation parameters H, d is observed. This study shows that the characteristic behaviour exhibited by the horizon dependence of the cluster entropy is related to long-range positive correlation in financial markets. Specifically, long range positively correlated ARFIMA processes with differencing parameter , and are consistent with moving average cluster entropy results obtained in time series of DJIA, S&P500 and NASDAQ. The findings clearly point to a variability of price returns, consistently with a price dynamics involving multiple temporal scales and, thus, short- and long-run volatility components. An important aspect of the proposed approach is the ability to capture detailed horizon dependence over relatively short horizons (one to twelve months) and thus its relevance to define risk analysis indices.

A Comparison of Hurst Exponent Estimators in Long-range Dependent Curve Time Series

Abstract The Hurst exponent is the simplest numerical summary of self-similar long-range dependent stochastic processes. We consider the estimation of Hurst exponent in long-range dependent curve time series. Our estimation method begins by constructing an estimate of the long-run covariance function, which we use, via dynamic functional principal component analysis, in estimating the orthonormal functions spanning the dominant sub-space of functional time series. Within the context of functional autoregressive fractionally integrated moving average (ARFIMA) models, we compare finite-sample bias, variance and mean square error among some time- and frequency-domain Hurst exponent estimators and make our recommendations.

Time Series Clustering of Electricity Demand for Industrial Areas on Smart Grid

This study forecasts electricity demand in a smart grid environment. We present a prediction method that uses a combination of forecasting values based on time-series clustering. The clustering of normalized periodogram-based distances and autocorrelation-based distances are proposed as the time-series clustering methods. Trigonometrical transformation, Box–Cox transformation, autoregressive moving average (ARMA) errors, trend and seasonal components (TBATS), double seasonal Holt–Winters (DSHW), fractional autoregressive integrated moving average (FARIMA), ARIMA with regression (Reg-ARIMA), and neural network nonlinear autoregressive (NN-AR) are used for demand forecasting based on clustering. The results show that the time-series clustering method performs better than the method using the total amount of electricity demand in terms of the mean absolute percentage error (MAPE).

A new hybrid model for forecasting Brent crude oil price

Received a plethora of attention by both practitioners and researchers, oil price forecasting remains a challenging issue due to the particular characteristics of oil price and its prodigious impact on various economic sectors. Motivated by this issue, the authors aim to introduce a robust hybrid model for reliable forecasting of Brent oil price. For this purpose, the Adaptive Neuro Fuzzy Inference System (ANFIS), Autoregressive Fractionally Integrated Moving Average (ARFIMA), and Markov-switching models are employed in the proposed hybrid model. The cardinal merit of this hybridization lies in the fact that the constituent models are capable of capturing particular features like nonlinearity, lag, and market interrelationships existing in oil price time series. Then, specific weights are assigned to each model to achieve an accurate prediction of the empirical time series. Three weighting scenarios, namely equal weights, error-value-based weights, and genetic algorithm weighting function, are applied. The authors use root mean square error, mean absolute error, and mean absolute percentage error to measure errors. Robustness of results and prediction quality of the hybrid model compared with counterparts are also investigated by Diebold-Mariano test. Finally, numerical results reveal that the hybrid model weighted by genetic algorithm generally outperforms the constituent models, hybrid model with equal weights, and hybrid model weighted based on the error values. Reliable forecasting of crude oil prices is especially beneficial to producer and importer nations to optimize their production and order rates and mitigate the adverse effect of possible shocks.

The Dynamics of India’s Major Exchange Rates

In this article, we analyze the dynamic properties of India’s major exchange rates, both in the short and the long runs. The particular issue of our concern is to find whether present values of the exchange rates depend (a) on their own past values and (b) on the past values of India’s other exchange rates. Since the series exhibit long memory, the autoregressive fractionally integrated moving average (ARFIMA) model is used for the first purpose and the cross-correlation, entropy transfer and vector auto regression (VAR) models are used for the later purpose. Combining the results of these models, we conclude that, in general, the Indian exchange rates are persistent and depend only on their immediate past values. In particular, past values, older than two periods (days in this case), do not appear to be consistently relevant in modelling the current value. These observations have clear implications for exchange rate trades using technical analysis (TA) and for exporters and importers.

On long memory origins and forecast horizons

AbstractMost long memory forecasting studies assume that long memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator and assess the performance of the autoregressive fractionally integrated moving average (ARFIMA) model when forecasting series with long memory generated by nonfractional models. We find that ARFIMA models dominate in forecast performance regardless of the long memory generating mechanism and forecast horizon. Nonetheless, forecasting uncertainty at the shortest forecast horizon could make short memory models provide suitable forecast performance, particularly for smaller degrees of memory. Additionally, we analyze the forecasting performance of the heterogeneous autoregressive (HAR) model, which imposes restrictions on high‐order AR models. We find that the structure imposed by the HAR model produces better short and medium horizon forecasts than unconstrained AR models of the same order. Our results have implications for, among others, climate econometrics and financial econometrics models dealing with long memory series at different forecast horizons.

ARFIMA Model for Short Term Forecasting of New Death Cases COVID-19

COVID-19 is an infectious disease that can spread from one person to another and has a high potential for death. The infection of COVID-19 is spreading massive and fast that causes the extreme fluctuating data spread and long memory effects. One of the ways in which the death of COVID-19 can be reduce is to produce a prediction model that could be used as a reference in taking countermeasures. There are various prediction models, from regression to Autoregressive Fractional Integrated Moving Average (ARIMA), but it still shows shortcomings when disturbances occur from extreme fluctuations and the existence of long memory effects in the form of analysis of a series of data becomes biased, and the power of statistical tests generated for identification become weak. Therefore, the prediction model with the Autoregressive Fractional Integrated Moving Average (ARFIMA) approach was used in this study to accommodate these weaknesses because of their flexible nature and high accuracy. The results of this study prove that ARFIMA (1,0,431.0) with an RMSE of 2,853 is the best model to predict data on the addition of new cases of patients dying from COVID-19.

Forecasting Diabetes Patients Attendance at Al-Baha Hospitals Using Autoregressive Fractional Integrated Moving Average (ARFIMA) Models

Diabetes has become a concern in the developed and developing countries with its growing number of patients reported to the ministry of health records. This paper discusses the use of the Autoregressive Fractional Moving Average (ARFIMA) technique to modeling the diabetes patient’s attendance at Al-Baha hospitals using monthly time series data. The data used in the analysis of this paper are monthly readings of diabetes patients data covered the period January 2006-December 2016. The data were collected from the General Directorate of Health Affairs, Al-Baha region. The autoregressive fractional moving average approach was applied to the data through the model identification, estimation, diagnostic checking and forecasting. Hurst test results and ACF confirmed that there is a long memory behavior in diabetic patient’s data. Also, the fractional difference to diabetes series data revealed that (d = 0.44). Moreover, unit root tests indicated that the fractional difference of diabetes series level is stationary. Furthermore, according to AIC and BIC of model selection criteria ARFIMA (1, 0.44, 0) model shown the smallest values, hence this model was chosen as an adequate represents the data. Also, a diagnostic check confirmed that ARFIMA was appropriate and highly recommended in modeling and forecasting this type of data.

Fractional Neuro-Sequential ARFIMA-LSTM for Financial Market Forecasting

Forecasting of fast fluctuated and high-frequency financial data is always a challenging problem in the field of economics and modelling. In this study, a novel hybrid model with the strength of fractional order derivative is presented with their dynamical features of deep learning, long-short term memory (LSTM) networks, to predict the abrupt stochastic variation of the financial market. Stock market prices are dynamic, highly sensitive, nonlinear and chaotic. There are different techniques for forecast prices in the time-variant domain and due to variability and uncertain behavior in stock prices, traditional methods, such as data mining, statistical approaches, and non-deep neural networks models are not suited for prediction and generalized forecasting stock prices. While autoregressive fractional integrated moving average (ARFIMA) model provides a flexible tool for classes of long-memory models. The advancement of machine learning-based deep non-linear modelling confirms that the hybrid model efficiently extracts profound features and model non-linear functions. LSTM networks are a special kind of recurrent neural network (RNN) that map sequences of input observations to output observations with capabilities of long-term dependencies. A novel ARFIMA-LSTM hybrid recurrent network is presented in which ARFIMA model-based filters having the linear tendencies better than ARIMA model in the data and passes the residual to the LSTM model that captures nonlinearity in the residual values with the help of exogenous dependent variables. The model not only minimizes the volatility problem but also overcome the over fitting problem of neural networks. The model is evaluated using PSX company data of the stock market based on RMSE, MSE and MAPE along with a comparison of ARIMA, LSTM model and generalized regression radial basis neural network (GRNN) ensemble method independently. The forecasting performance indicates the effectiveness of the proposed AFRIMA-LSTM hybrid model to improve around 80% accuracy on RMSE as compared to traditional forecasting counterparts.

Modelling Loans to Non-Financial Corporations within the Eurozone: A Long-Memory Approach

This paper uses fractional integration and cointegration methods to analyse the determinants of the amount of loans provided to non-financial corporations (NFCs) during the last three decades in four Eurozone countries, namely Germany, France, Italy and Spain. More specifically, ARFIMA (AutoRegressive Fractionally Integrated Moving Average) and FCVAR (Fractionally Cointegrated Vector Autoregression) models are estimated and then forecasts are also produced. All series are found to be highly persistent and long-run equilibrium relationships between them are also identified, confirming the role of real GDP and real gross investment as determinants of loans to NFCs. The forecasting accuracy of the FCVAR was also assessed by comparing it to that of the ARFIMA specifications, and the former were found to outperform the latter in all cases.

Generalized multivariate multiscale sample entropy for detecting the complexity in complex systems

Using the first moment in coarse-graining the original time series in different time scales will lose some important information of the complexity. In this paper, we propose the generalized multivariate multiscale sample entropy (GMMSE) to analyze the complexity for multivariate time series. Before empirical analysis, numerical simulation is conducted by applying GMMSE1 (mean), GMMSE2 (variance), GMMSE3 (skewness) to the autoregressive fractionally integrated moving average (ARFIMA) processes. The simulated results illustrate that GMMSE2 is more appropriate to analyze the complexity of ARFIMA time series. Then we apply GMMSE method to traffic multivariate time series and discuss their complexities over different time scales. Comparing the GMMSE1, GMMSE2 and GMMSE3 results for different detectors, GMMSE2 and GMMSE3 can clearly differentiate the detectors with different complexity and reflect the characteristics and similarities of the complexity of traffic data between different locations. Besides, both the effect of traffic accident and the effect of the weekday and weekend patterns containing in traffic signals on the complexity can be detected by GMMSE2 and GMMSE3 methods. GMMSE2 and GMMSE3 are capable of providing more important information and knowledge concerning the complexity of traffic time series and will bring enhanced understanding of the properties of traffic system.

Correlation Structures of PM2.5 Concentration Series in the Korean Peninsula

In this paper, the authors investigate the idiosyncratic features of auto- and cross-correlation structures of PM2.5 (particulate matter of diameter less than 2.5 μ m ) mass concentrations using DFA (detrended fluctuation analysis) methodologies. Since air pollutant mass concentrations are greatly affected by geographical, topographical, and meteorological conditions, their correlation structures can have non-universal properties. To this end, the authors firstly examine the spatio-temporal statistics of PM2.5 daily average concentrations collected from 18 monitoring stations in Korea, and then select five sites from those stations with overall lower and higher concentration levels in order to make up two groups, namely, G1 and G2, respectively. Firstly, to compare characteristic behaviors of the auto-correlation structures of the two groups, we performed DFA and MFDFA (multifractal DFA) analyses on both and then confirmed that the G2 group shows a clear crossover behavior in DFA and MFDFA analyses, while G1 shows no crossover. This finding implies that there are possibly two different scale-dependent underlying dynamics in G2. Furthermore, in order to confirm that different underlying dynamics govern G1 and G2, the authors conducted DCCA (detrended cross-correlation analysis) analysis on the same and different groups. As a result, in the same group, coupling behavior became more prominent between two series as the scale increased, while, in the different group, decoupling behavior was observed. This result also implies that different dynamics govern G1 and G2. Lastly, we presented a stochastic model, namely, ARFIMA (auto-regressive fractionally integrated moving average) with periodic trends, to reproduce behaviors of correlation structures from real PM2.5 concentration time series. Although those models succeeded in reproducing crossover behaviors in the auto-correlation structure, they yielded no valid results in decoupling behavior among heterogeneous groups.

Modeling the Ongoing Dynamics of Short and Long-Range Temporal Correlations in Broadband EEG During Movement.

Electroencephalogram (EEG) undergoes complex temporal and spectral changes during voluntary movement intention. Characterization of such changes has focused mostly on narrowband spectral processes such as Event-Related Desynchronization (ERD) in the sensorimotor rhythms because EEG is mostly considered as emerging from oscillations of the neuronal populations. However, the changes in the temporal dynamics, especially in the broadband arrhythmic EEG have not been investigated for movement intention detection. The Long-Range Temporal Correlations (LRTC) are ubiquitously present in several neuronal processes, typically requiring longer timescales to detect. In this paper, we study the ongoing changes in the dynamics of long- as well as short-range temporal dependencies in the single trial broadband EEG during movement intention. We obtained LRTC in 2 s windows of broadband EEG and modeled it using the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model which allowed simultaneous modeling of short- and long-range temporal correlations. There were significant (p < 0.05) changes in both broadband long- and short-range temporal correlations during movement intention and execution. We discovered that the broadband LRTC and narrowband ERD are complementary processes providing distinct information about movement because eliminating LRTC from the signal did not affect the ERD and conversely, eliminating ERD from the signal did not affect LRTC. Exploring the possibility of applications in Brain Computer Interfaces (BCI), we used hybrid features with combinations of LRTC, ARFIMA, and ERD to detect movement intention. A significantly higher (p < 0.05) classification accuracy of 88.3 ± 4.2% was obtained using the combination of ARFIMA and ERD features together, which also predicted the earliest movement at 1 s before its onset. The ongoing changes in the long- and short-range temporal correlations in broadband EEG contribute to effectively capturing the motor command generation and can be used to detect movement successfully. These temporal dependencies provide different and additional information about the movement.

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

Inflation targeting is a common monetary policy regime. Inflation targets are often flexible in the sense that the central bank allows inflation to temporarily deviate from the target to avoid causing unnecessary volatility in the real economy. In this paper, we propose modeling the degree of flexibility using an autoregressive fractionally integrated moving average (ARFIMA) model. Assuming that the central bank controls the long-run inflation rate, the fractional integration order becomes a measure of how flexible the inflation target is. A higher integration order implies that inflation deviates from the target for longer periods of time and consequently, that the target is flexible. Several estimators of the fractional integration order have been proposed in the literature. Grassi and Magistris (2014) 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. To resolve this issue, we first proposed a Bayesian Monte Carlo Markov Chain (MCMC) estimator for fractional integration parameters. This estimator resolves the problem of over-bias. We estimate the fractional integration order for 6 countries for the period 1993M1 to 2017M9. We found that inflation was integrated to an order of 0.8 to 0.9 indicating that the inflation targets are implemented with a high degree of flexibility.

A wavelet-based hybrid neural network for short-term electricity prices forecasting

Forecasting is a very important and difficult task for various economic activities. Despite the great evolution of time series modeling, forecasters are still in the hunt for better strategies to improve mathematical models and come up with more accurate predictions. In this respect, several new models, mixing autoregressive processes to artificial neural networks (ANNs), have recently emerged. This is particularly the case for energy economics, where old forecasting tools are replaced by new hybrid strategies. Along the same lines, this paper aims to define a wavelet-based hybridization, involving nonlinear smooth functions, autoregressive fractionally integrated moving average (ARFIMA) model and feedforward ANNs, for electricity spot prices forecasting. The use of the wavelet decomposition in this model allows to characterize certain patterns of power time series, such as the nonlinear trend and multiple seasonal effects, and to exactly extrapolate them over the time scale. In fact, such patterns have already been pointed out as potential causes of the ANN’s inaccuracy. An ARFIMA–ANN model is then used to forecast the resulting irregular component. In the last stage, the smooth and irregular components are recombined to constitute the forecasted price. We will demonstrate the cost-effectiveness of the proposed method using hourly power prices from the Nord Pool Exchange. The testing time series consists of 52,614 observations and corresponds to the period ranging from 2012 to 2017. The results show that the new method is able to provide better interval forecasting than four benchmark models.

Bayesian Inference for ARFIMA Models

This article develops practical methods for Bayesian inference in the autoregressive fractionally integrated moving average (ARFIMA) model using the exact likelihood function, any proper prior distribution, and time series that may have thousands of observations. These methods utilize sequentially adaptive Bayesian learning, a sequential Monte Carlo algorithm that can exploit massively parallel desktop computing with graphics processing units (GPUs). The article identifies and solves several problems in the computation of the likelihood function that apparently have not been addressed in the literature. Four applications illustrate the utility of the approach. The most ambitious is an ARFIMA(2,d,2) model for the Campito tree ring time series (length 5405), for which the methods developed in the article provide an essentially uncorrelated sample of size 16,384 from the exact posterior distribution in under four hours. Less ambitious applications take as little as 4 minutes without exploiting GPUs.

Inhomogeneous membrane receptor diffusion explained by a fractional heteroscedastic time series model.

Single particle tracking experiments have recently uncovered that the motion of cell membrane components can undergo changes of diffusivity as a result of the heterogeneous environment, producing subdiffusion and nonergodic behavior. In this paper, we show that an autoregressive fractionally integrated moving average (ARFIMA) with noise given by generalized autoregressive conditional heteroscedasticity (GARCH) can describe inhomogeneous diffusion in the cell membrane, where the ARFIMA process models anomalous diffusion and the GARCH process explains a fluctuating diffusion parameter.