Fractionally Integrated Moving Average Research Articles

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.

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.

Identifying diffusive motions in single-particle trajectories on the plasma membrane via fractional time-series models.

In this paper we show that an autoregressive fractionally integrated moving average time-series model can identify two types of motion of membrane proteins on the surface of mammalian cells. Specifically we analyze the motion of the voltage-gated sodium channel Nav1.6 and beta-2 adrenergic receptors. We find that the autoregressive (AR) part models well the confined dynamics whereas the fractionally integrated moving average (FIMA) model describes the nonconfined periods of the trajectories. Since the Ornstein-Uhlenbeck process is a continuous counterpart of the AR model, we are also able to calculate its physical parameters and show their biological relevance. The fitted FIMA and AR parameters show marked differences in the dynamics of the two studied molecules.

Estimation of a stationary multivariate ARFIMA process

In this note, we consider an m-dimensional stationary multivariate long memory ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process, which is defined as : A ( L ) D ( L ) ( y 1 ( t ),..., y m ( t ))' = B ( L ) ( ∈ 1 ( t ),..., ∈ m ( t ))', where M ' denotes the transpose of the matrix M . We determine the minimum Hellinger distance estimator (MHDE) of the parameters of a stationary multivariate long memory ARFIMA. This method is based on the minimization of the Hellinger distance between the random function of f n (.) and a theoretical probability density f θ (.). We establish, under some assumptions, the almost sure convergence of the estimator and its asymptotic normality. Keywords: Stationary Multivariate ARFIMA process; Estimation; Long memory; Minimum Hellinger distance AMS 2010 Mathematics Subject Classification: 62F12, 62H12

PERAMALAN JUMLAH PENUMPANG KERETA API MENGGUNAKAN METODE ARIMA, INTERVENSI DAN ARFIMA (Studi Kasus : Penumpang Kereta Api Kelas Lokal EkonomiDAOP IV Semarang)

Autoregressive Integrated Moving Average (ARIMA) is stationary time series model after differentiation. Differentiation value of ARIMA method is an integer so it is only able to model in the short term. The best model using ARIMA method is ARIMA([13]; 1; 0) with an MSE value of 1,870844. The Intervention method is a model for time series data which in practice has extreme fluctuations both up and down. In the data plot the number of train passengers was found to be extreme fluctuation. The data used was from January 2009 to June 2017 where fluctuation up significantly in January 2016 (T=85 to T=102) so the intervention model that was suspected was a step function. The best model uses the Intervention step function is ARIMA ([13]; 1; 1) (b=0; s=18; r=0) with MSE of 1124. Autoregressive Fractionally Integrated Moving Average (ARFIMA) method is a development of the ARIMA method. The advantage of the ARFIMA method is the non-integer differentiation value so that it can overcome long memory effect that can not be solve with the ARIMA method. ARFIMA model is capable of modeling high changes in the long term (long term persistence) and explain long-term and short-term correlation structures at the same time. The number of local economy class train passengers in DAOP IV Semarang contains long memory effects, so the ARFIMA method is used to obtain the best model. The best model obtained is the ARMA(0; [1,13]) model with the differential value is 0,367546, then the model can be written into ARFIMA (0; d; [1,13]) with an MSE value of 0,00964. Based on the analysis of the three methods, the best method of analyzing the number of local economy class train passengers in DAOP IV Semarang is the ARFIMA method with the model is ARFIMA (0; 0,367546; [1,13]). Keywords: Train Passengers, ARIMA, Intervention, ARFIMA, Forecasting

The impact of inflation rate on stock market returns: evidence from Kenya

This study examined the stochastic properties of inflation rate, stock market returns and their cointegrating residuals using monthly data for the period 1993 to 2015. The Autoregressive Fractionally Integrated Moving Average (ARFIMA)-based exact maximum likelihood estimation was employed to determine the integration orders of the individual variables as well as the cointegrating residuals. Results from the ARFIMA model indicate that the month-on-month inflation rate, year-on-year inflation rate and stock market returns have non-integer orders of integration. This is inconsistent with the stationary/nonstationary results often obtained from the conventional unit root tests and implies that any shocks to the variables are highly persistent but eventually disappear. The results also reveal that the cointegrating residuals have non-integer orders of integration, suggesting that deviations from the long run equilibrium are prolonged, contrary to the assumption held under the conventional cointegration framework. The Fractionally Integrated Error Correction Model (FIECM) reveals that the year-on-year inflation rate positively granger causes stock market returns. This supports Fisher Effect and implies that stock market returns in Kenya provide shelter against inflationary pressures. This is the first study to empirically examine fractional cointegration and ARFIMA-based Granger Causality between inflation rate and stock market returns in Kenya.

Predictability of monthly temperature and precipitation using automatic time series forecasting methods

We investigate the predictability of monthly temperature and precipitation by applying automatic univariate time series forecasting methods to a sample of 985 40-year-long monthly temperature and 1552 40-year-long monthly precipitation time series. The methods include a naive one based on the monthly values of the last year, as well as the random walk (with drift), AutoRegressive Fractionally Integrated Moving Average (ARFIMA), exponential smoothing state-space model with Box–Cox transformation, ARMA errors, Trend and Seasonal components (BATS), simple exponential smoothing, Theta and Prophet methods. Prophet is a recently introduced model inspired by the nature of time series forecasted at Facebook and has not been applied to hydrometeorological time series before, while the use of random walk, BATS, simple exponential smoothing and Theta is rare in hydrology. The methods are tested in performing multi-step ahead forecasts for the last 48 months of the data. We further investigate how different choices of handling the seasonality and non-normality affect the performance of the models. The results indicate that: (a) all the examined methods apart from the naive and random walk ones are accurate enough to be used in long-term applications; (b) monthly temperature and precipitation can be forecasted to a level of accuracy which can barely be improved using other methods; (c) the externally applied classical seasonal decomposition results mostly in better forecasts compared to the automatic seasonal decomposition used by the BATS and Prophet methods; and (d) Prophet is competitive, especially when it is combined with externally applied classical seasonal decomposition.

Variable Selection in Time Series Forecasting Using Random Forests

Time series forecasting using machine learning algorithms has gained popularity recently. Random forest is a machine learning algorithm implemented in time series forecasting; however, most of its forecasting properties have remained unexplored. Here we focus on assessing the performance of random forests in one-step forecasting using two large datasets of short time series with the aim to suggest an optimal set of predictor variables. Furthermore, we compare its performance to benchmarking methods. The first dataset is composed by 16,000 simulated time series from a variety of Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. The second dataset consists of 135 mean annual temperature time series. The highest predictive performance of RF is observed when using a low number of recent lagged predictor variables. This outcome could be useful in relevant future applications, with the prospect to achieve higher predictive accuracy.

Estimating Perturbation and Meta-Stability in the Daily Attendance Rates of Six Small High Schools

This paper discusses the daily attendance rates in six small high schools over a ten-year period and evaluates how stable those rates are. “Stability” is approached from two vantage points: pulse models are fitted to estimate the impact of sudden perturbations and their reverberation through the series, and Autoregressive Fractionally Integrated Moving Average (ARFIMA) techniques are used to detect dependencies over the long range of the series. The analyses are meant to (1) exemplify the utility of time series approaches in educational research, which lacks a time series tradition, (2) discuss some time series features that seem to be particular to daily attendance rate trajectories such as the distinct downward pull coming from extreme observations, and (3) present an analytical approach to handle the important yet distinct patterns of variability that can be found in these data. The analysis also illustrates why the assumption of stability that underlies the habitual reporting of weekly, monthly and yearly averages in the educational literature is questionable, as it reveals dynamical processes (perturbation, meta-stability) that remain hidden in such summaries.

Long Memory Models for Financial Time Series of Counts and Evidence of Systematic Market Participant Trading Behaviour Patterns in Futures on US Treasuries

This paper propose to incorporate the family of Gegenbauer Autoregressive Moving Average (GARMA) models and a special sub family called the Autoregressive Fractionally Integrated Moving Average (ARFIMA) models into the mean functions of count distributions, including Poisson, Negative Binomial (NB), Generalized Poisson (GP) and Double Poisson (DP). These distributions display equi-, over- and under-dispersion features and the additional long memory structure enhances modelling flexibility. Furthermore, we define the error terms of the GARMA family under two different approaches, the parameter-driven and observation-driven approaches. To estimate these models, we adopt a Bayesian approach implemented using R package Rstan. Then Deviance Information Criterion is evaluated to select some best-fitting models to undertake forecasting of these different classes of long memory count time series. The models are applied to analyse 136 individual U.S. Commodity Futures Trading Commission (CFTC) time series of counts which are each related to trade volume for futures-only and futures-and-options crossed classified with four fixed income securities provided by the U.S. federal government: Treasury notes (T-notes) at 2, 5 and 10 years and Treasury bonds (T-bonds) at marturities of 20 or 30 year terms. These represent some of the most active futures contracts traded in financial markets. The analysis developed provides the first detailed study of this kind undertaken by market participant type according to the categories of reportables and non-reportables and sub-categories of positions of their trading behaviours categorised by the buy and sell sides of long-call, short-put and spread being the difference between long-call and short-put. Furthermore, we study the disaggregated reportables data according to the CFTC four categories of traders, namely, dealers, asset managers, leveraged funds and other reportables. The studies performed demonstrate particular long-memory structures are consistently observed in these highly liquid and important financial instruments and in particular demonstrate systematic forecastable patterns in trading behaviour and liquidity by market participant type, which is as yet not reported or identified in financial literature. Such findings are then directly used as forecasting tools to study further relationships between price discovery and price volatility dynamics.

Using the hybrid Phillips curve with memory to forecast US inflation

AbstractThis paper adopts the Caputo fractional derivative to re-specify the hybrid Phillips curve as a dynamic process of inflation with memory. The Caputo fractional derivative contains a non-integer differencing order, providing the same insight for persistence as emphasized in the Autoregressive Fractionally Integrated Moving Average (ARFIMA) time series models. We utilize the hybrid Phillips curve with memory to forecast US inflation during 1967–2014. The results indicate that our model performs well against a traditional hybrid Phillips curve, an integrated moving average model and a naive random walk model in quasi-in-sample forecasts. In out-of-sample forecasts based on Consumer Price Index (CPI) and Personal Consumption Expenditure (PCE) data, we find that the forecasting performance of Phillips curve models depends on the sample period. Our model with CPI data can outperform others in out-of-sample forecasts during and after the most recent financial crisis (2006–2014).

Average run length of the long-memory autoregressive fractionally integrated moving average process of the exponential weighted moving average control chart

AbstractMeasurement of control chart efficiency by comparison of average run length (ARL) is widely implemented in quality control. The aim of this study is to evaluate the ARL, which is a solution of the integral equation obtained from the Exponential Weighted Moving Average (EWMA) statistic with a long-memory Autoregressive Fractionally Integrated Moving Average (ARFIMA) process. The derivation of the analytical ARL of the EWMA control chart and proof of the existence and uniqueness of the analytical ARL by Fixed Point theory are shown. Moreover, the numerical ARL carried out by the Composite Midpoint Rule technique of the EWMA control chart is demonstrated. A comparison between the analytical and numerical ARL is also illustrated. The findings indicated that analytical ARL of the EWMA control chart is more quickly computational than the numerical ARL. Therefore, the analytical ARL is an alternative method for measuring the efficiency of the EWMA control chart with the long-memory ARFIMA process.

Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model

Abstract Recent research argues that if the cause of confusion between long memory and regime switching were properly controlled for, they could be effectively distinguished. Motivated by this idea, our study aims to distinguish between them of financial series. We firstly model long memory and regime switching via the Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Markov Regime-Switching (MRS) models, respectively. Their finite-sample properties and the confusion are investigated via simulations. To control for the cause of this confusion, we propose the MRS–ARFIMA model. A Monte Carlo study shows that this framework can effectively distinguish between the pure ARFIMA and pure MRS processes. Furthermore, MRS–ARFIMA outperforms the ordinary ARFIMA model for data simulated from the MRS–ARFIMA process. Finally, empirical studies of hourly and five-minute Garman–Klass and realized volatility of the FTSE index is conducted to demonstrate the advantages and usefulness of the proposed MRS–ARFIMA framework compared with the ARFIMA and MRS models in practice.

Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors - An alternative approach.

Accurately characterizing the anomalous diffusion of a tracer particle has become a central issue in biophysics. However, measurement errors raise difficulty in the characterization of single trajectories, which is usually performed through the time-averaged mean square displacement (TAMSD). In this paper, we study a fractionally integrated moving average (FIMA) process as an appropriate model for anomalous diffusion data with measurement errors. We compare FIMA and traditional TAMSD estimators for the anomalous diffusion exponent. The ability of the FIMA framework to characterize dynamics in a wide range of anomalous exponents and noise levels through the simulation of a toy model (fractional Brownian motion disturbed by Gaussian white noise) is discussed. Comparison to the TAMSD technique, shows that FIMA estimation is superior in many scenarios. This is expected to enable new measurement regimes for single particle tracking (SPT) experiments even in the presence of high measurement errors.

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

The quasi maximum likelihood approach to statistical inference on a nonstationary multivariate ARFIMA process

We estimate the parameters of a nonstationary multivariate ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process by the quasi likelihood approach. Then, we define the pseudo-spectral density of the process. Under some assumptions, we establish consistency, asymptotic normality.

Stock index realized volatility forecasting in the presence of heterogeneous leverage effects and long range dependence in the volatility of realized volatility

In this article, we account for the presence of heterogeneous leverage effects and the persistence in the volatility of stock index realized volatility. The Heterogeneous Autoregressive (HAR) Realized Volatility (RV) model is extended in order to account for asymmetric responses to negative and positive shocks occurring at distinct frequencies, as well as, for the long range dependence in the heteroscedastic variance of the residuals. Compared with established HAR and Autoregressive Fractionally Integrated Moving Average (ARFIMA) realized volatility models, the proposed model exhibits superior in sample fitting, as well as, out of sample volatility forecasting performance. The latter is further improved when the Realized Power Variation (RPV) is used as a regressor, while we show that our analysis is also robust against microstructure noise.

Studying Long Memory of Tehran Stock Exchange

According to the efficient market hypothesis, prices in stock market follow the random walk theory. In such a market, data is published rapidly and affect the stock price. Thus a large proportion of financial theory is extended based on random walk models for assets prices and returns. Long memory is one of violation of efficient market that tells time series of capital market index does not follow the random walk theory. This study examined long memory as one of the properties of time series for Tehran dividend stock price index and industrial index to test the assumptions, Autoregressive Fractionally Integrated Moving Average (ARFIMA) model is used. The results indicated that the concept of long memory existed for two index in Tehran stock exchange. The result of this research shows that there is a conception of long memory in Capital Market of Iran. Not only capital market efficiency does not obey the random walk as Dickey Fuller test, but also it has long memory. Also its time series is not unstable, in other words it is steady.

Estimation par le minimum de distance de Hellinger dʼun processus ARFIMA

In this Note, we determine the minimum Hellinger distance estimate of an ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process. The estimate minimizes the Hellinger distance between the probability density function of the innovation of the process and a parameterized random function. Under some assumptions, we establish the asymptotic properties of this estimate.

The dynamics of inflation: a study of a large number of countries

Over the last twenty years the statistical properties of inflation persistence has been the subject of intense investigation and debate without reaching a unanimous conclusion yet. In this article we attempt to shed further light to this debate using a battery of econometric techniques in order to provide robust evidence on the degree of inflation persistence and whether this has changed during the period in which several countries have followed inflation-targeting regimes or new monetary regimes. We consider the inflation rates of thirty developed and emerging economies using quarterly data for the period 1958 to 2007 which include alternative monetary policy regimes. The coefficient of the inflation parameter is estimated by Ordinary Least Squares (OLS), Autoregressive Moving Average (ARMA) and Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. Furthermore, the grid-bootstrap Median Unbiased (MUB) estimator approach developed by Hansen (1999) is used to estimate the finite sample OLS estimates coupled with the 95% symmetric confidence interval. We also examine parameter stability of persistence coefficients by estimating a model with time-varying parameters.