Short Memory Component Research Articles

Dual memory scale network for multi-step time series forecasting in thermal environment of aquaculture facility: A case study of recirculating aquaculture water temperature

Multi-step time series forecasting is essential in engineering. However, effective time series prediction of the agricultural environment is still a challenge due to the disturbance of external factors and the complexity of temporal patterns. The objective of this work is to provide an intelligent prediction system with field priori-knowledge for aquaculture facility thermal environment. Specifically, we present a novel network framework that considers the spatial correlation of exogenous environmental factors, the short-term and long-term temporal dependence of the sequence, and the spatio-temporal fusion correlation at different times. Among them, the dual-scale memory components focus on long-term seasonal and trend memory patterns as well as short-term fluctuation memory patterns, respectively. Besides, the attention mechanism coordinates the information flow between the long and short memory components. We applied the model to recirculating water temperature forecasting in the aquaponics greenhouse. The empirical results of global and local metrics indicate that our proposed model outperforms benchmark models. The RMSE of the proposed dual memory scale network (DMSNet) is 0.1631, 0.3206, and 0.3761, respectively, in the next 6 h, 12 h, and 24 h water temperature prediction. Ablation study proved that the components of our proposed network could be targeted to extract different information patterns from aquaponics environmental sequence data. Experimental results show that the thermal environment prediction based on DMSNet has higher precision in short-term and long-term forecasting multi-step prediction.

Combining Long and Short Memory in Time Series Models: the Role of Asymptotic Correlations of the [formula omitted

A major practical problem in the application of the long memory ARFIMA model has been distinguishing between the long memory and short memory components and subsequent estimation of the model. The asymptotic correlations between the Maximum Likelihood Estimators (MLE) of the long memory parameter, d, and the short memory parameters within an ARFIMA estimation are derived. The correlation in an ARFIMA(1,d,0) model can be as large as −0.95. However, MLE still works well in these high correlation cases; even for non stationary situations. Similarly, QMLE also performs well in simulations where the innovations have t or skewed t densities. MLE also performs very well for ARFIMA(3,d,0) models when there is a moderate level of persistence in the short memory part. However, MLE can perform extremely poorly when there is a combination of long memory and substantial persistence in the short memory component. Some of these points are illustrated in the analysis of some Realized Volatility time series which contain long memory. The correlation in “gap ARFIMA” models is comparatively low which indicates that MLE is quite stable in this case. Some suggestions and recommendations for applied work are provided.

Multivariate Fractional Components Analysis

Abstract We propose a setup for fractionally cointegrated time series which is formulated in terms of latent integrated and short-memory components. It accommodates nonstationary processes with different fractional orders and cointegration of different strengths and is applicable in high-dimensional settings. In an application to realized covariance matrices, we find that orthogonal short- and long-memory components provide a reasonable fit and competitive out-of-sample performance compared with several competing methods.

A harmonically weighted filter for cyclical long memory processes

The estimation of the long memory parameter d is a widely discussed issue in the literature. The harmonically weighted (HW) process was recently introduced for long memory time series with an unbounded spectral density at the origin. In contrast to the most famous fractionally integrated process, the HW approach does not require the estimation of the d parameter, but it may be just as able to capture long memory as the fractionally integrated model, if the sample size is not too large. Our contribution is a generalization of the HW model, denominated the Generalized harmonically weighted (GHW) process, which allows for an unbounded spectral density at k ge 1 frequencies away from the origin. The convergence in probability of the Whittle estimator is provided for the GHW process, along with a discussion on simulation methods. Fit and forecast performances are evaluated via an empirical application on paleoclimatic data. Our main conclusion is that the above generalization is able to model long memory, as well as its classical competitor, the fractionally differenced Gegenbauer process, does. In addition, the GHW process does not require the estimation of the memory parameter, simplifying the issue of how to disentangle long memory from a (moderately persistent) short memory component. This leads to a clear advantage of our formulation over the fractional long memory approach.

Long memory and ARFIMA modelling: The case of CPI inflation rate in Ghana

In macroeconomic theory and economic policy, changes in the general price level or the rate of inflation plays an essential role. Hence, for example, one of the motives behind the adoption of Inflation Targeting policy (IT) by Ghana and the treaty espoused by the European Monetary Union, known as the Maastricht Treaty, was the convergence of inflation rates. On the other hand there is a controversy about which is the order of integration in the inflation rates, some authors arguing that this variable is stationary I(0) Whittle others saying it is nonstationary I(1). In this study we examine the CPI inflation rates of Ghana from a different perspective allowing for fractional degrees of differentiation. Thus, the methodology is based on long memory or long-range dependence processes, using fractional integration and employing techniques based on Whittle parametric and semiparametric methods and autoregressive fractionally integrated moving average (ARFIMA) models. Standard I(0)/I(1) methods were also employed. Our findings indicate that long memory exists in the CPI inflation rate of Ghana. After processing fractional differencing and determining the short memory components, the following two models, ARFIMA(3,0.427,1) and ARFIMA(2,0.499,1) were respectively specified to describe the pre and post introduction of IT policy in May 2007. Consequently, the CPI inflation rate of Ghana is fractionally integrated and mean reverting. Long memory in financial time series has important implications for the critical explanation of financial time series behaviour, as it could provide an opportunity to earn speculative profits in financial markets and cast disbelief on the correctness of the EMH. For instance, when price changes exhibit long memory or long-range dependence, asset pricing models based on the Efficient Market Hypothesis (EMH) may overestimate or underestimate investment risk. Furthermore, the presence of long memory in inflation rates can provide vital information about the likely impact of shocks (e.g. demand/supply) on the economy with respect to time. The results obtained in this study would be very useful in setting up monetary policies or consolidating previous policies such as IT in order to enhance economic growth. Moreover, estimation of long memory in inflation rates can serve as an evaluation tool to assess the performance of monetary policy under different dispensations. Lastly, the presence of long memory can assist in identifying inflationary pressures in the economy.

On the estimation of short memory components in long memory time series models

AbstractA substantial amount of recent time series research has emphasized semi-parameteric estimators of a long memory parameter and we provide a selective review of the literature on this issue. We consider such estimators applied to the issue of estimating the parameters relating to a short memory process which is embedded within the long memory process. We consider the fractional differencing filter and the subsequent properties of a two step estimator of the short memory parameters. We conclude that while the semi-parametric estimators can have excellent properties in terms of estimating the long memory parameter, they do not have good properties when applied to the two step estimator of short memory

A New Test for Short Memory in Long Memory Time Series

This article considers short memory characteristics in a long memory process. We derive new asymptotic results for the sample autocorrelation difference ratios. We used these results to develop a new portmanteau test that determines if short memory parameters are statistically significant. In simulations, the new test can detect short memory components more often than the Ljung-Box test when these short memory components are in fact within a long memory process. Interestingly, our test finds short memory autocorrelations in U.S. inflation rate data, whereas the Ljung-Box test fails to find these autocorrelations. Modeling these short memory autocorrelations of the inflation rate data leads to improved model accuracy and more precise prediction.

Scaling symmetry, renormalization, and time series modeling: The case of financial assets dynamics

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous autoregressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power-law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal, and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance, in terms of obtaining closed formulas for derivative pricing. Further important features are the possibility of making contact, in certain limits, with autoregressive models widely used in finance and the possibility of partially resolving the long- and short-memory components of the volatility, with consistent results when applied to historical series.

A semiparametric approach to estimate two seasonal fractional parameters in the SARFIMA model

This paper explores seasonal and long-memory time series properties by using the fractional ARIMA model when the data have one and two seasonal periods and short-memory components. The stationarity and invertibility parameter conditions are established for the model studied. To estimate the seasonal fractional long-memory parameters, a semiparametric estimation method is proposed. The asymptotic properties of the estimator are established and the accuracy of the method is investigated through Monte Carlo experiments. The good performance of the estimator indicates that it can be an alternative procedure to estimate long-memory time series data with two seasonal periods. Series of PM10 concentrations and electricity hourly demand are considered as examples of applications of the proposed estimation method.

Multivariate limits of multilinear polynomial-form processes with long memory

Consider a vector of multilinear polynomial-form processes with either short or long memory components. The components have possibly different coefficients but same noise elements. We study the limit of the normalized partial sums of the vector and identify the independent components.

Inference of seasonal long-memory aggregate time series

Time-series data with regular and/or seasonal long-memory are often aggregated before analysis. Often, the aggregation scale is large enough to remove any short-memory components of the underlying process but too short to eliminate seasonal patterns of much longer periods. In this paper, we investigate the limiting correlation structure of aggregate time series within an intermediate asymptotic framework that attempts to capture the aforementioned sampling scheme. In particular, we study the autocorrelation structure and the spectral density function of aggregates from a discrete-time process. The underlying discrete-time process is assumed to be a stationary Seasonal AutoRegressive Fractionally Integrated Moving-Average (SARFIMA) process, after suitable number of differencing if necessary, and the seasonal periods of the underlying process are multiples of the aggregation size. We derive the limit of the normalized spectral density function of the aggregates, with increasing aggregation. The limiting aggregate (seasonal) long-memory model may then be useful for analyzing aggregate time-series data, which can be estimated by maximizing the Whittle likelihood. We prove that the maximum Whittle likelihood estimator (spectral maximum likelihood estimator) is consistent and asymptotically normal, and study its finite-sample properties through simulation. The efficacy of the proposed approach is illustrated by a real-life internet traffic example.

Cointegrating rank selection in models with time-varying variance

Reduced rank regression (RRR) models with time varying heterogeneity are considered. Standard information criteria for selecting cointegrating rank are shown to be weakly consistent in semiparametric RRR models in which the errors have general nonparametric short memory components and shifting volatility provided the penalty coefficient Cn→∞ and Cn/n→0 as n→∞. The AIC criterion is inconsistent and its limit distribution is given. The results extend those in Cheng and Phillips (2009a) and are useful in empirical work where structural breaks or time evolution in the error variances is present. An empirical application to exchange rate data is provided.

Local polynomial Whittle estimation of perturbed fractional processes

We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also inflate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d∈(0,1), asymptotically normal for d∈(0,3/4), and if the spectral density is sufficiently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, n. A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator.

Clustering streamflow time series for regional classification

The article aims to show how some dissimilarity criteria, the Mahalanobis distance between regression coefficients and the Euclidean distance between Autoregressive weights, can be applied to hydrologic time series clustering. Specifically, the temporal dynamics of streamflow time series are compared through the estimated parameters of the corresponding linear models which may include both short and long memory components. The performance of the proposed technique is assessed by means of an empirical study concerning a set of daily streamflow series recorded at sites in Oregon and Washington State.

A dual-pass error-correction technique for forecasting streamflow

Summary This study reports the development and testing of a “dual-pass” method for correcting slowly varying errors in simulations of streamflow. Error correction is a form of data assimilation used to improve streamflow forecasts. The dual-pass method is ideally suited for catchments with long-lasting shifts in runoff efficiency that the hydrologic model poorly simulates. In a first pass, the simulation is rescaled (i.e. multiplicative correction is applied), based on the cumulative error over the prior 365 days. In a second pass, a correction is added to the adjusted series, based on the error from the most recent timestep. When tested on 330 Australian and 183 United States catchments, the dual-pass approach improved the median four-measure validation skill score from 0.83 to 0.89 for the GR4J model and from 0.56 to 0.79 for a naive coefficient model. The majority of improvement comes from the second pass (the short-memory component). The magnitudes of correction at each pass are controlled by two tuneable parameters; a global sensitivity analysis determined that satisfactory performance could be had without tuning of the long-memory (first pass) error-correction parameter. For most catchments, the use of the long-memory error-correction neither degrades nor significantly improves performance. International hydrological modeling datasets have relatively fewer catchments with slowly varying errors than might be encountered in operational forecasting environments, therefore, there is a need for better identification and study of such problem catchments.

Bootstrap-based bandwidth choice for log-periodogram regression

The choice of the bandwidth in the local log-periodogram regression is of crucial importance for estimation of the memory parameter of a long memory time series. Different choices may give rise to completely different estimates, which may lead to contradictory conclusions, for example about the stationarity of the series. We propose here a data-driven bandwidth selection strategy that is based on minimizing a bootstrap approximation of the mean-squared error (MSE). Its behaviour is compared with other existing techniques for optimal bandwidth selection in a MSE sense, revealing its better performance in a wider class of models. The empirical applicability of the proposed strategy is shown with two examples: the widely analysed in a long memory context Nile river annual minimum levels and the input gas rate series of Box and Jenkins. Over the last years, the log-periodogram regression, first proposed by Geweke and Porter-Hudak (1983) and analysed in detail by Robinson (1995a), has become one of the most popular tools for the estimation of the memory parameter d in long memory time series. It has been widely applied for statistical inference in empirical research owing to its simple implementation, pivotal asymptotic normality and robustness as a result of the local condition. The log- periodogram regression estimation in the version of Robinson (1995a; LPE hereafter) is based on a simple least squares regression of the logarithm of the periodogram over the logarithm of the m Fourier frequencies closest to the origin, providing that m goes to infinity but more slowly than the sample size such that the band of frequencies used in the estimation shrinks to zero. The parameter m, known as the bandwidth in a local or semi-parametric memory parameter estimation context, plays an important role on the performance of the LPE. A large m reduces the variance at the cost of a higher bias, which in some situations can render meaningless estimates, as for example in the presence of a significant short memory component. On the contrary a low m guarantees a small bias but with larger variability. From an empirical perspective, the estimates of the memory parameter usually vary significantly with the choice of m. Figures 9b and

Seasonal Mackey–Glass–GARCH process and short-term dynamics

The aim of this article is the study of complex structures which are behind the short-term predictability of stock returns series. In this regard, we employ a seasonal version of the Mackey–Glass–GARCH(p,q) model, initially proposed by Kyrtsou and Terraza (Computat Econ 21:257–276, 2003) and generalized by Kyrtsou (Int J Bifurcat Chaos 15(10):3391–3394, 2005). To unveil short or long memory components and non-linear structures in the French Stock Exchange (CAC40) returns series, we apply the test of Geweke and Porter-Hudak (J Time Ser Anal 4:221–238, 1983), the Brock et al. (Econom Rev 15:197–235, 1996) and Dechert (An application of chaos theory to stochastic and deterministic observations. Working paper, University of Houston, 1995) tests, the correlation-dimension method of Grassberger and Procaccia (Phys 9D:189–208, 1983), the Lyapunov exponents method of Gencay and Dechert (Phys D 59:142–157, 1992), and the Recurrence quantification analysis introduced by Webber and Zbilut (J Appl Physiol 76:965–973, 1994). As a confirmation procedure of the dynamics generating future movements in CAC40, we perform forecast with the use of a seasonal Mackey–Glass–GARCH(1,1) model. The interest of the forecasting exercise is found in the inclusion of high-dimensional non-linearities in the mean equation of returns.

Seasonal Mackey-Glass-Garch Process and Short-Term Dynamics

The aim of this article is the study of complex structures which are behind the short-term predictability of stock returns series. In this regard, we employ a seasonal version of the Mackey-Glass-GARCH(p,q) model, initially proposed by Kyrtsou and Terraza (2003) and generalized by Kyrtsou (2005, 2006). It has either negligible or significant autocorrelations in the conditional mean, and a rich structure in the conditional variance. To reveal short or long memory components and non-linear structures in the French Stock Exchange (CAC40) returns series, we apply the test of Geweke and Porter-Hudak (1983), the Brock et al. (1996) and Dechert (1995) tests, the correlation-dimension method of Grassberger and Procaccia (1983), the Lyapunov exponents method of Gen?ay and Dechert (1992), and the Recurrence Quantification Analysis introduced by Webber and Zbilut (1994). As a confirmation procedure of the dynamics generating future movements in CAC40, we forecast the return series using a seasonal Mackey-Glass-GARCH(1,1) model. The interest of the forecasting exercise is found in the inclusion of high-dimensional non-linearities in the mean equation of returns.

Semiparametric cointegrating rank selection

Some convenient limit properties of usual information criteria are given for cointegrating rank selection. Allowing for a non‐parametric short memory component and using a reduced rank regression with only a single lag, standard information criteria are shown to be weakly consistent in the choice of cointegrating rank provided the penalty coefficient Cn→∞ and Cn/n → 0 as n →∞. The limit distribution of the AIC criterion, which is inconsistent, is also obtained. The analysis provides a general limit theory for semiparametric reduced rank regression under weakly dependent errors. The method does not require the specification of a full model, is convenient for practical implementation in empirical work, and is sympathetic with semiparametric estimation approaches to co‐integration analysis. Some simulation results on the finite sample performance of the criteria are reported.

Local Polynomial Whittle Estimation of Perturbed Fractional Processes

We propose a semiparametric local polynomial Whittle with noise (LPWN) estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the spectrum of the perturbation as well as that of the short-memory component of the signal by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also inflate the asymptotic variance of the long memory estimate by a multiplicative constant. We show that the estimator is consistent for d ∈ (0, 1), asymptotically normal for d ∈ (0, 3/4), and if the spectral density is infinitely smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, square root of n. A Monte Carlo study reveals that the LPWN estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle estimator.