Abstract: In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the classical Box-Jenkins approach to quantile autoregressive models. Specifically, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the fitted model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR, QPCOR, QACF, and PQACF, but also show the large sample results of the QAR estimates and the quantile version of the Ljung-Box test. Simulation studies indicate that the proposed methods perform well in finite samples, and an empirical example is presented to illustrate usefulness.

Abstract: This paper proposes the autocorrelation function (acf) and partial autocorrelation function (pacf) as tools to help and improve the construction of the input layer for univariate time series artificial neural network (ANN) models, as used in classical time series analysis. Especially reducing the number of input layer neurons, and also helping the user to understand the behaviour of the series. Although the acf and pacf are considered linear functions, this paper shows that they can be used even in non linear time series. The ANNs used in this work are the Incremental Gaussian Mixture Network (IGMN), because it is a deterministic model, and the multilayer perceptron (MLP), the most used ANN model for time series forecasting.

Abstract: In this paper, the partial Hamming correlation properties of frequency-hopping sequences (FHSs) are discussed. The Peng-Fan bounds on sets of FHSs are generalized to the case of partial correlation. Both individual FHSs with optimal partial autocorrelation and sets of FHSs with optimal partial correlation are presented. The former has more new parameters compared with the known individual FHSs with optimal partial autocorrelation, while the later is obtained in the literature for the first time.

Abstract: The studies of spatial complexity have resulted in new understanding of the distance-decay functions of geography. The weight functions of spatial autocorrelation should be consistent with the functions of spatial distribution and interaction. This paper is on “spatial autocorrelation analysis” of spatial autocorrelation. The 1-dimension spatial autocorrelation function (ACF) and partial autocorrelation function (PACF) of space series are employed to analyze four kinds of weight function in common use for the 2-dimensional spatial autocorrelation model. The aim of this study is at how to select a proper weight function to construct a spatial contiguity matrix for spatial analysis. The scopes of application of different weight functions are defined in terms of the characters of their ACFs and PACFs.

Abstract: The detection of long-range dependence in time series analysis is an important task to which this paper contributes by showing that whilst the theoretical definition of a long-memory (or long-range dependent) process is based on the autocorrelation function, it is not possible for long memory to be identified using the sum of the sample autocorrelations, as usually defined The reason for this is that the sample sum is a predetermined constant for any stationary time series; a result that is independent of the sample size Diagnostic or estimation procedures, such as those in the frequency domain, that embed this sum are equally open to this criticism We develop this result in the context of long memory, extending it to the implications for the spectral density function and the variance of partial sums of a stationary stochastic process The results are further extended to higher order sample autocorrelations and the bispectral density The corresponding result is that the sum of the third order sample (auto) bicorrelations at lags h,k≥1, is also a predetermined constant, different from that in the second order case, for any stationary time series of arbitrary length

Abstract: In business, dynamic models often provide valuable insights into the complex interactions between variablesover time. But recent research contends that the lagged dependent variable specification is too problematic foruse in most situations. More specifically, if residuals autocorrelation is present in a dynamic equation wherelagged values of the dependent variable appear as regressors, Ordinary least squares (OLS) estimates are biasedand generally inconsistent. For this reason it is important to have available tests against autocorrelation,particularly when it is a dynamic model. The Breusch-Godfrey (BG) test is the most appropriate test in thepresence of stochastic regressors such as lagged values of the dependent variable for higher order autocorrelation,which is asymptotically equivalent to the Durbin-Watson h test for first order autocorrelation. But Durbin htest is not applicable for second or higher order autocorrelation. Moreover these existing tests are not suitable forone-sided higher order autoregressive schemes. Whenever the sign of the parameters are known of aneconometric model, usual two-sided tests are no longer valid. In this situation, we propose a distance-basedone-sided Lagrange Multiplier (DLM) test, a likelihood based test, to test one-sided alternative. Monte Carlosimulations are conducted to compare power properties of the proposed DLM test with the BG test. It is foundthat the DLM test shows substantially improved power than two-sided counterparts for most of the casesconsidered.

Abstract: Molecular dynamics simulation of nanofluid system composed of argon liquid and copper nanoparticle was carried out in this paper. To ensure the interatomic force gradually decreases to zero at the cut-off distance, Stoddard and Ford potential function was employed. Green–Kubo method was used to obtain the thermal conductivity. The characteristics of the heat current were measured by its mean value, variance, third moment, and the Shannon entropy. It was found that the thermal conductivity increases as the nanoparticle volume fraction increases, and so do the variance and the Shannon entropy of the heat current. The third moment of the heat current was almost zero, indicating that the probability distribution of the heat current is nearly symmetric about its mean value. Autocorrelation and partial autocorrelation functions of the heat current were used to investigate the correlation between the discrete heat current value and different lags.

Abstract: The present study revisits the statistical modeling of typhoon transition. The objective of the study is to provide insights on plausible statistical typhoon transition models based on extensive statistical analysis. First, the correlation structures of the typhoon transition are estimated in terms of autocorrelation function (ACF) and partial autocorrelation function (PACF). This facilitates to specify a set of plausible models for further investigation. Then, the corrected Akaike Information Criterion (cAIC) is applied to investigate the relative goodness of fit of these models. The spatial inhomogeneity and the seasonality are taken into account by developing the models for different spatial grids and seasons separately. An appropriate size of spatial grids is investigated. The statistical characteristics of the random residual terms in the models are also examined. Finally, Monte Carlo simulations are performed to investigate the overall performance of the proposed model.

Abstract: The correlation of data contained in a series of signal sample values makes the estimation of the statistical characteristics describing such a random sample difficult. The positive correlation of data increases the arithmetic mean variance in relation to the series of uncorrelated results. If the normalized autocorrelation function of the positively correlated observations and their variance are known, then the effect of the correlation can be taken into consideration in the estimation process computationally. A significant hindrance to the assessment of the estimation process appears when the autocorrelation function is unknown. This study describes an application of the conditional averaging of the positively correlated data with the Gaussian distribution for the assessment of the correlation of an observation series, and the determination of the standard uncertainty of the arithmetic mean. The method presented here can be particularly useful for high values of correlation (when the value of the normalized autocorrelation function is higher than 0.5), and for the number of data higher than 50. In the paper the results of theoretical research are presented, as well as those of the selected experiments of the processing and analysis of physical signals.

Abstract: To study the potential impact of the ever-increasing wind farm on future power grid, realistic long term time series of future wind generation at individual sites as well as for the system as a whole are required. This paper proposes a method to simulate time series of hourly wind speed. An ARMA(p, q) model with transformation procedure to a stationary process is chose to simulate the hourly wind speed for it can reflect the time sequential, statistical and stochastic characteristics. Ten years of hourly wind speed data are used to collect characteristic indices such as seasonal and diurnal patterns, autocorrelation and partial autocorrelation parameters. Wind farm output data in a whole year are reconstructed with diurnal and monthly pattern features. Comparison is made between the generated and real series of wind power in an aspect of probability distribution. The result demonstrates that the method is proper.

Abstract: One of the most popular models that usually be used to predict time series data is Autoregressive Integrated Moving Average (ARIMA) model. The most crucial steps in ARIMA modeling are identification and selection the best model based on available data. These steps require a good understanding about the characteristics of the process in terms of their theoretical autocorrelation function (ACF) and partial autocorrelation function (PACF). In identification step, the goal is to match the patterns of the sample ACF and PACF with the patterns of theoretical ACF and PACF for determining an appropriate order of ARIMA, including order of subset ARIMA. In this paper, we propose the new procedure for determining the order of ARIMA based on over-fitting concept. The process is started from the simplest ARIMA model that all of parameters are statistically significant and determination of an additional order AR or MA is based on over-fitting concept, i.e. based on ACF of the residual model. This new proposed procedure is applied for constructing a subset ARIMA model of Indonesia's inflation data. The results show that the proposed procedure yields an appropriate order of subset ARIMA model for Indonesia's inflation data.

Abstract: Generalized fractional processes in terms of Gegenbauer polynomials and GARCH (Generalized Autoregressive Conditional Heteroscedastic) errors is introduced and derived as a time series model. A related simulation study of the proposed model depicts statistical properties of the new class established in terms of the realization, sample autocorrelation function, the- oretical autocorrelation function, partial autocorrelation function and the spectral density function. DOI: http://dx.doi.org/10.4038/sljastats.v12i0.4964 Sri Lankan Journal of Applied Statistics Vol.12 2011 pp.1-12

Abstract: The invention relates to a modeling method for a quartz flexible accelerometer starting model, and belongs to the field of navigation and control research of delivery vehicles The method comprises the following steps of: performing data sampling on a quartz flexible accelerometer starting process; de-noising the sampled quartz flexible accelerometer starting process data by using Daubechies wavelet to acquire time sequence data; extracting an exponential tread term and a linear trend term of the time sequence data; standardizing the time sequence data after the trend term is extracted; determining category of the time sequence model according to characteristics of an autocorrelation function and a partial autocorrelation function of the time sequence data and modeling by using a proper model; and estimating parameters of the time sequence data model and establishing the time sequence analysis-based quartz flexible accelerometer starting model The invention provides the modeling method for the time sequence analysis-based quartz flexible accelerometer starting model Research personnel are helped to more deeply analyze the accelerometer starting process

Abstract: The seasonal dependency or seasonality is a general component of the time series pattern that can be examined via correlograms, where the correlogram displays graphical and numerical information in an autocorrelation function. This paper discusses the use of an autocorrelation function in the seasonality analysis for the fatigue strain data to help identify the seasonal pattern. The objective of this study is to determine the capability of this time domain method in detecting the seasonality component in the fatigue time series. A set of case study data consisting of the non-stationary variable amplitude loading strain data that exhibits random behaviour was used. This random data was collected in the unit of micro-strain on a lower suspension arm of a mid-sedan car. The data was measured for 60 seconds at the sampling rate of 500 Hz, which gave 30,000 discrete data points. The collected data was then analysed in the form of an auto-correlogram shape and characteristics. As a result, an autocorrelation plot is weak in identifying the seasonal pattern, but the autocorrelation coefficient values are statistically significant and have shown a positive serial correlation. Thus, the finding of this characteristic is expected for a non-stationary signal.

Abstract: In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the classical Box-Jenkins approach to quantile autoregressive models. Speci cally, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the tted model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR, QPCOR, QACF, and PQACF, but also show the large sample results of the QAR estimates and the quantile version of the Ljung-Box test. Simulation studies indicate that the proposed methods perform well in nite samples, and an empirical example is presented to illustrate usefulness.

Abstract: We reconsider the classical problem of estimating the autocorrelation sequence of a stationary time-series from the viewpoint of multitaper spectrum estimates. This results in estimates of the autocorrelation that have both lower variance and, in particular, do not have the very slow decay that is characteristic of ordinary autocorrelation estimates.

Abstract: Traumatic brain injury (TBI) endangers many patients and lays great burden on the neural intensive-care units in the whole world. To improve the outcome of TBI patients, it is desirable to forecast the intracranial Pressure (ICP) so to enable timely or early interventions to control the ICP level. Past research mainly focused on ICP pulse morphology analysis and ICP waveform forecast, but results were not satisfactory. In this paper, to forecast ICP continuous trends, we propose an autoregressive integrated moving average (ARIMA) ICP forecast online application with orders selection predicated on autocorrelation function (ACF) and partial autocorrelation function (PACF). Results show that the accuracy of ICP forecast improves significantly with our forecast model, compared with ARIMA based on Akaike information criterion (AIC) and artificial neural network approach. Besides, the forecast processing time of ARIMA model predicated on PACF and ACF is much shorter than ANN and ARIMA predicated on AIC.

Abstract: BACKGROUND Seasonal patterns are assumed in many fields of medicine. However, biological processes are full of variations and the possibility of chance findings can often not be ruled out. METHODS Using simulated data we assess whether auto correlation is helpful to minimize chance findings and test to support the presence of seasonality. RESULTS Autocorrelation required to cut time curves into pieces. These pieces were compared with one another using linear regression analysis. Four examples with imperfect data are given. In spite of substantial differences in the data between the first and second year of observation, and in spite of otherwise inconsistent patterns, significant positive autocorrelations were constantly demonstrated with correlation coefficients around 0.40 (SE 0.14). CONCLUSIONS Our data suggest that autocorrelation is helpful to support the presence of seasonality of disease, and that it does so even with imperfect data.

Abstract: The non linear part of a mixed bilinear time series structure seems to pose difficulty if we are to extract the pure autoregressive (AR) bilinear form from the mixed process with the condition that the outcome of such extraction clearly defines itself as an extension from its parent linear AR model. It is therefore of immense interest to address a ‘ bilinear’ situation where the same “order” identified in the linear AR processes are extended to cover the linear and non linear components of a bilinear process with an exception that the lagged white noise process is allowed to remain in its present state. This research focused on these two innovations where the white noise is lagged zero to isolate a pure vector AR bilinear model from a mixed process based on the distribution of autocorrelation and partial autocorrelation function of the different series involved in a vector process, and the extension of the linear ‘orders’ to bilinear ‘orders’. To achieve the aforementioned, we formulated a matrix for a general case of n-dimensional vector for an AR process and then considered a special case of zero lag of white noise. With given conditions, and introduction of diagonal matrix of lagged vector elements, special bilinear expressions reflecting the same ‘orders’ of the corresponding linear forms emerged. The zero lagged white noise denoted by it-0 clearly defined our models as pure AR bilinear models since the lag l = 0 and is equivalent to the current state white noise t of the linear AR process. These gave a brilliant meaning to vector bilinear AR processes in terms of linear AR ‘orders’. The workability of these special bilinear models was assessed by applying them to revenue series and the result showed that the models gave a good fit, in support of our idea.

Abstract: Since the oilfield water development system is complex and there are numerous characterization indices, it is quite necessary to simplify the index system. This paper deals with the similarity analysis problem of oilfield development indices. At first, from the perspective of time series, 11 numerical characteristics of historical data of oilfield development indices are found, including statistical features, trend features, autocorrelation and partial autocorrelation coefficient, nonlinear features and spectral characteristics. Then based on these numerical characteristics, a new algorithm is proposed to make similarity analysis for oilfield development indices by fuzzy c-means clustering. In the end, a practical example is given, successfully solved, and the computational results are presented.

Abstract: In order to extract cloud cover feature from ISCCP D2 dataset, a method of feature extraction using wavelet and statistics was used. This method concerned the characteristic of the cloud cover and the applications requirement, and combined the autocorrelation function, partial autocorrelation function with the wavelet method. We can get the conclusion from the features: (1) the features from wavelet analysis are more evident than the features from original series; (2) most of the cloud amount series in ISCCP D2 dataset are stationary series, and the autocorrelation functions (AF) and partial autocorrelation functions (PAF) shows there are diurnal cycle in these series. As a result, it is possible to establish ARIMA model to estimate the cloud amount for a small region in the world.

Abstract: This paper addresses the problem of forecasting for monthly mean streamflow series, in which we call the forecast horizon (h), the interval of time between the last observation used in fitting the model prediction and the future value being predicted. The analysis of the forecast error is made on the basis of the forecast horizon. These series have a periodic behavior on average, ariance and autocorrelation function. Therefore, we consider the widely used approach to modeling these series that initially consists of removing the periodicity in mean and variance of the streamflow series and then calculating a standardized series for which stochastic models are adjusted. In this study we consider the series to the standard periodic autoregressive models PAR (pm). Orders pm of the adjusted models for each month are determined from the analysis of periodic partial autocorrelation function (PePACF), using the Bayesian Information Criterion (BIC) applied to PAR models, proposed in (MecLeod, 1994) and analysis of PePACF proposed in (Stedinger, 2001). The forecast errors are calculated on the basis of parameters adjusted and evaluated for forecasting horizons h, ranging from 1 to 12 months on the original scale of the flow series. These errors are compared with estimates of the variances of the flows for the month being predicted. As a result we have an evaluation of the predictive performance in months of the adjusted models for each month.

Abstract: Based on China railway freight volume statistics from 1978 to 2010, this paper analyzes railway freight time series' numeral characteristic with the using of econometrics method. According to freight time series unit root test, it is proved that freight time series is a two-order fractional integration serial. Observing the residual of freight time series after two differences, the paper got autocorrelation and partial autocorrelation, then established China railway freight volume autoregressive integrated moving average (ARIMA) forecasting model. Through testing the forecasting modal, it was found that the result is satisfactory. Finally, the paper forecasts the railway freight volume of 2012 and 2013 and the precision is high.

Abstract: There are several ways to compute the autocorrelation and autocovariance matrixs of causal ARMA(p, q) process[1], The multiple time series analysis[2] shows that the computing process is very complicated in the multiple cases, in practice, with the backward shift operator, the autoregressive operator and moving average operator, time series can be transformed into polynomial which are usually related to the power series, in this paper, we demonstrate the approaches to use the geometrics series to compute autocorrelation function.

Abstract: Binomial thinning operator has a major role in modeling one-dimensional integer-valued autoregressive time series models. The purpose of this article is to extend the use of such operator to define a new stationary first-order spatial non negative, integer-valued autoregressive SINAR(1, 1) model. We study some properties of this model like the mean, variance and autocorrelation function. Yule-Walker estimator of the model parameters is also obtained. Some numerical results of the model are presented and, moreover, this model is applied to a real data set.