Abstract: We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.

Abstract: We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.

Abstract: This paper focuses on the general determinants of autocorrelation and the relationship between autocorrelation and volatility in particular. Using UK stock market index and individual stock price data, a multivariate generalized autoregressive conditional heteroskedasticity (M-GARCH) model is used to generate estimates of conditional autocorrelation. The covariance equation of this model is modified to include the potential determinants of autocorrelation including volatility, which is proxied using the time series of filtered probabilities of a Markov regime switching model. Consistent with the previous literature, this paper documents a negative relationship between volatility and autocorrelation. The results suggest that an asymmetry exists in this relationship which is attributed to the constraints placed on short selling.

Abstract: We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.

Abstract: Partial autocorrelation and partial rate correlation functions are frequently used to detect the order of the endogenous process generating an observed population time series. Here we uncover a problem with this approach: the diagnosis of spurious second order autocorrelation due to strong nonlinearity in a first order endogenous process, as exemplified by time series data from a population of Soay sheep. Causes and a possible solution are discussed.

Abstract: The autoregressive method of spectral analysis is widely used in diverse areas for its solid theoretical foundation. Various aspects of its statistical performance have been investigated. People assume the times series xn to be samples from a zero-mean distribution whose variance remains constant in time. However, it is not available in fact. In this paper, by formulating the resolution event in the framework of statistical autocorrelation theory and directly determining its value from its center-autocorrelation function and statistical autocorrelation function, we obtain a power spectral density formula for the statistical resolution. On this basis, we determine the limiting resolving behavior of the sample autoregressive spectrum and develop the corresponding statistical insight in the time series. Simulation results are also presented to confirm and illustrate the effectiveness of the theory.

Abstract: GPS positioning accuracy in indoor and urban canyons environments is greatly affected by multipaths due to distortions in its autocorrelation function. In this paper, the first sidelobe of Pseudorandom Noise (PN) code autocorrelation is studied and a new multipath mitigation technique based on PN code autocorrelation function is presented. This new technique relies on the detection of the partial autocorrelation function that is affected by multipath signals. The increase in fractional delay of the line-of-sight (LOS) signal is calculated. Simulation results indicate that the proposed technique has superior performance compared with the 0.1-chip-spacing narrow correlator on mitigating multipath signals, especially the short-delay multipath signals.

Abstract: A new method of state recognition of milling tool wear was presented based on time series analysis and fuzzy cluster analysis. After calculating, verifying liberation signal of tool state, and analyzing cutoff property, trailing property, periodicity of the sample autocorrelation function and partial autocorrelation function as well as estimating parameter of model. It can be decided that dynamic data serial is suit AR(p) (autoregression) model. Taking p equal to 12 as a feature vector extraction, based on the fuzzy cluster analysis the similarity relation between the feature vector of the tool working state and the sample feature vector was obtained. Working state of tool wear was determined according to the similarity relation of feature vector. This method was used to recognize initial wear state, normal wear state and acute wear state of milling tool. The result indicates that this method of tool wear recognition based on time series analysis and fuzzy cluster is effective.

Abstract: The maximum entropy (ME) principle, as it is often invoked in the context of time-series analysis, suggests the selection of a power spectrum which is consistent with autocorrelation data and corresponds to a random process least predictable from past observations. We introduce and compare a class of spectra with the property that the underlying random process is least predictable at any given point from the complete set of past and future observations. In this context, randomness is quantified by the size of the corresponding smoothing error and deterministic processes are characterized by integrability of the inverse of their power spectral densities - as opposed to the log-integrability in the classical setting. The power spectrum which is consistent with a partial autocorrelation sequence and corresponds to the most random (MR) process in this new sense, is no longer rational but generated by finitely many fractional-poles.

Abstract: An example from economics is used to show how regression analysis can be misleading if the assumption of independence of the errors is violated. The issue of autocorrelation is of importance when regression is used to estimate input-output relationships..

Abstract: Frequency estimators based on the argument of the sample autocorrelation function outperform those based on the phase of the samples of the sinusoid signal in additive white Gaussian noise background.The expression of the noise in the argument of the sample autocorrelation function was given to investigate the performance of these estimators.And formulas for evaluating the variance of sample autocorrelation argument noise and the variance of frequency estimation based on the sample autocorrelation argument were derived.The relations among frequency estimation variance and signal-to-noise ratio,length of the measurement time,and sample numbers used in smoothing the autocorrelation function can be determined using these formulas.Computer simulation results confirm the correctness of the proposed formulas.

Abstract: The dependence structure of a family of self exciting threshold autoregressive moving average (SETARMA) models, is investigated. An alternative representation for this class of models is proposed and the exact autocorrelation function is derived in the case of two regimes. Some practical implications of the theoretical results are analysed and discussed via several examples of SETARMA structures of fixed orders

Abstract: China′s urbanization cannot be modeled by the logistic equation,which is followed by the USA′s urbanization process.In order to reveal the features and property of China′s urbanization,the auto-correlation and spectral analysis are employed to make a multifold study on time series of urbanization from 1949 to 2000.(1) An autocorrelation analysis is implemented,and partial autocorrelation function(PACF) has a first order cutoff.This implies that the urbanization process of China possesses a locality: a change in the i-th year only affects that in the(i+1)th year directly,but cannot affect the changes in and after the(i+2)th year.However,the auto-correlation function(ACF) suggests that a change perhaps influence a change ten years later indirectly.(2) An autoregressive analysis is made and an autoregressive moving-average(ARMA) model is built such as Lt=μ+Lt-1+limq→∞∑qj=0φjet-j=0.510+Lt-1+limq→∞∑qj=00.439jet-jwhere Lt is the i-th year's urbanization level,e is an innovation or "random shock"(white noise),φ is a parameter,and q the order of moving average.(3) A spectral analysis is made based on the residuals of the logistic model,that is,the logistic trend of urbanization level is removed from the time series,and the result shows that there exists a periodic change behind the trend change.The wavelength(cycle length) is about 30 years.The Hurst exponent of the urbanization data is estimated to interpret the periodic behavior.The value of the Hurst exponent,H=0.37,suggests anti-persistence in the urbanization process of China.Based on the above analyses,the process of urbanization is divided into three parts: random process,periodic process,and trend process.Among the three different components of change in urbanization,trend is a basic process,cycle is an accessorial process,and random change is a complex process.The future of China′s urbanization is hard to be predicted using the common methods because of auto-correlation and random disturbance,so new approaches should be found to conduct a convincing prediction.

Abstract: The sample autocorrelation function is defined with the mean lagged products of random observations. It is the inverse Fourier transform of the raw periodogram. Both contain the same information and the quality of the sample autocorrelation, as a representation of data, is as poor as that of a raw periodogram. The autocorrelation function can be estimated much more accurately with a parametric time series method. A MATLABreg computer program automatically selects the type and the order of the best time series model for stochastic observations with unknown characteristics. The parametric estimate of the autocorrelation function has always a better accuracy than the mean-lagged-product estimates. Parametric estimates will die out eventually. They allow an objective answer to the question how long the autocorrelation function really is.

Abstract: Based on time series analysis and fuzzy cluster analysis,a new method of state recognition of milling tool wear was set up.After calculating,verifying liberation signal of tool state,and analyzing cutoff property,trailing property,periodicity of the sample autocorrelation function and partial autocorrelation function as well as estimating parameter of model.It can be decided that dynamic data serial is suit AR(p)(autoregression) model.Taking p equal to 12 as a feature vector extraction,based on the fuzzy cluster analysis the similarity relation between the feature vector of the tool working state and the sample feature vector was obtained.Working state of tool wear was determined according to the similarity relation of feature vector.This method was used to recognize initial wear state,normal wear state and acute wear state of milling tool.The result indicates that this method of tool wear recognition based on time series analysis and fuzzy cluster is effective.

Abstract: We develop a stochastic process with two coupled variables where the absolute values of each variable exhibit long-range power-law autocorrelations and are also long-range cross-correlated. We investigate how the scaling exponents characterizing power-law autocorrelation and long-range cross-correlation behavior in the absolute values of the generated variables depend on the two parameters in our model. In particular, if the autocorrelation is stronger, the cross-correlation is also stronger. We test the utility of our approach by comparing the autocorrelation and cross-correlation properties of the time series generated by our model with data on daily returns over ten years for two major financial indices, the Dow Jones and the S&P500, and on daily returns of two well-known company stocks, IBM and Microsoft, over five years.

Abstract: Univariate and multivariate autoregressive integrated moving average (ARIMA) models were used to model and forecast the monthly pelagic production of fish species in the Mediterranean Sea during 1990–2005. Autocorrelation (AC) and partial autocorrelation (PAC) functions were estimated, which led to the identification and construction of seasonal ARIMA models, suitable in explaining the time series and forecasting the future catch per unit of effort (CPUE) values. Univariate and multivariate ARIMA models satisfactorily predicted the total pelagic fish production and the production of anchovy, sardine, and horse mackerel. The univariate ARIMA models demonstrated a good perpormance in terms of explained variability and predicting power. The current findings revealed a strong autoregressive character providing relatively high R 2 and satisfactory forecasts that were close to the recorded CPUE values. The present results also indicated that the multivariate ARIMA outperformed the univariate ARIMA models in terms of fitting accuracy. The opposite was evidenced when testing the forecasting accuracy of the two methods, where the univariate ARIMA models overall performed better than the multivariate models. The observed seasonal pattern in the monthly production series was attributed to the intrinsic nature of the pelagic fishery. As anchovy, sardine, and horse mackerel represent main target species in the Mediterranean pelagic fishery, the findings of the present study provided direct support for the potential use of accurate forecasts in decision making and fisheries management in the Mediterranean Sea.