Showing papers on "Partial autocorrelation function published in 2002"
Journal Article•
TL;DR: In this article, a time series of loliginid and ommastrephid landings was analyzed taking into account spatio-temporal descriptors of sea surface temperature (SST).
Abstract: Time series of loliginid and ommastrephid landings were analysed taking into account spatio-temporal descriptors of sea surface temperature (SST). The data are based on fisheries statistics recorded from the three most important fishing ports in the Northern Aegean Sea (1984-1999) and NOAA satellite images processed using GIS and image analysis tools. Autocorrelation (AC) and partial autocorrelation (PAC) functions were estimated leading to the identification and construction of seasonal ARIMA models, suitable for explaining the time series and forecasting future abundance values. The performance of the models was tested by comparing the predicted against the observed data of the last year (1999) and by examining the distribution and the AC of the residuals. The analysis provided results characterizing the different fishing patterns in each geographic area, as well as new series containing seasonally adjusted values, trend, cycle and error components of the model. Time series of several statistical parameters describing spatio-temporal variations of the SST were estimated and analysed aiming at the detection of anomalies and possible stock-environment relationships. Cross-correlation analysis between SST parameters and stock biomass indexes showed significant correlation coefficients, before and after compensation of the seasonal fluctuations by seasonal differencing. The results suggest that SST can be a leading indicator for stock prediction of the target species in the survey area.
27 citations
1 Jan 2002
TL;DR: By means of a large-scale simulation study, the performance of some information criteria, such as AIC, AICC, BIC and HIC, when the true model is an ARF IMA and the alternatives of interest are ARFIMA is assesed.
Abstract: Summary: For an ARFIMA model it is not possible to identify the order of the short memory polynomials by using autocorrelation and partial autocorrelation functions as for the ARMA model. Indeed when both long and short memory components are present in the data, their behavior is hard to distinguish and the model selection becomes very difficult. In this paper, by means of a large-scale simulation study, we asses the performance of some information criteria, such as AIC, AICC, BIC and HIC, when the true model is an ARFIMA and the alternatives of interest are ARFIMA The probability of successful identification increases with the sample size and depends on the values of the short memory parameters. Moreover, it varies across the different selection criteria.
12 citations
TL;DR: In this article, the authors discuss the reasons why the residual ACF and portmanteau statistic give different sensitivities in terms of testing model adequacy and hence of detecting changes in stochastic behavior of a process.
Abstract: Most statistical process control (SPC) methods for detecting the presence of special causes of variation when process observations are inherently autocorrelated are focused on studying changes in the mean or variance of a time series. It is seldom emphasized in the quality literature that the presence of special causes of variation is manifested not only by the changes in mean or variance of a time series but also by the changes in its stochastic behavior. An approach to detect this type of change can be based on the sample autocorrelation function (ACF) or the Ljung–Box–Pierce portmanteau statistic applied to the residuals of the chosen time series model. In this article, we discuss the reasons why the residual ACF and portmanteau statistic give different sensitivities in terms of testing model adequacy and, hence, of detecting changes in stochastic behavior of a process. The problem is shown to be related to the multivariate SPC problem of deciding whether to monitor the individual observations using se...
11 citations
TL;DR: In this paper, a new simple and efficient technique to identify the parameters of the moving average (MA) process using the technique of higher order cumulants was developed for modelling half-hour solar radiation recorded in Marrakesh.
Abstract: In this investigation we have two objectives. In the first one, we have developed a new simple and efficient technique to identify the parameters of the moving average (MA) process using the technique of higher order cumulants. The simulation for different orders of MA in the presence of Gaussian noise, for SNR lower than 20 dB, gives satisfactory results. In the second objective, the proposed method was adopted for modelling half-hour solar radiation recorded in Marrakesh. Accurate design and optimisation of short response time solar energy systems with storage are sensitive to the stationary and sequential characteristics of half-hourly solar radiation. So, in order to benefit from some characteristics of stationary processes, a preliminary transformation was performed on the original data. The proposed method was used to look for a simple and efficient model to represent solar half-hourly radiation sequences needed for many applications in the solar energy field. The Giannakis technique based on cumulant diagonal slices and the partial autocorrelation function of Box & Jenkins and Brockwell & Davis are used for selection of the model order.
11 citations
TL;DR: In this article, it was shown that the null distribution of the F-test in a linear regression is rather non-robust to spatial autocorrelation among the regression disturbances.
Abstract: It is shown that the null distribution of the F-test in a linear regression is rather non-robust to spatial autocorrelation among the regression disturbances. In particular, the true size of the test tends to either zero or unity when the spatial autocorrelation coefficient approaches the boundary of the parameter space.
11 citations
10 Dec 2002
TL;DR: This paper looks at the possibility of modelling MPEG4 traffic at the group of picture (GoP) level with autoregressive models, and found that the mean, variance and autocorrelation structure could be matched closely provided the right order autore progressive model was used.
Abstract: This paper looks at the possibility of modelling MPEG4 traffic at the group of picture (GoP) level with autoregressive models. Even though these models are short-range dependent the autocorrelation structure of the traffic can be matched up to an arbitrary lag by using the right order of the autoregressive process. No attempt is made to capture the long-range dependence in the traffic. A procedure to build such an autoregressive model of any order is described. Koenen (see ISO/IEC 14496, May/June 2000) found that the autocorrelation structure of GoPs decays almost exponentially for certain MPEG-4 traffic traces. Consequently, the use of autoregressive models for such traces seemed appropriate. It was found that the mean, variance and autocorrelation structure could be matched closely provided the right order autoregressive model was used. However, the empirical distribution function could not be matched closely. A distortion of the marginal distribution function was required to match that of the empirical sequence. A gamma distribution approximation was used. As this was not very successful the empirical distribution function itself was used to distort the marginal distribution.
10 citations
29 Jan 2002
2 citations
1 Jan 2002
TL;DR: In this paper, the authors extended the Box-Jenkins approach to the building of seasonal time series model and used it to model seasonally integrated time series, which allows to describe time series integrated at a few of the seasonal frequencies.
Abstract: In this paper the Box-Jenkins approach to the building of seasonal time series model is extended so that it is adequate to model seasonally integrated time series. To this end, the class of multiplicative ARIMA models is broadened in such a way that it allows to describe time series integrated at a few of the seasonal frequencies. Thus, tests for seasonal unit roots are not considered as a rival modeling approach, but can be used in the identification stage to decide the transformation inducing stationarity. The fit model is used to generate forecasts and to estimate unobservable components. The enhanced Box-Jenkins approach is illustrated modeling the Spanish Industrial Production Index.
1 Jan 2002
TL;DR: In this article, a new time-dependent power spectrum for non-stationary processes is introduced, which is in a one-to-one correspondence with the autocovariance function.
Abstract: Several approaches have been developed for the spectral analysis of nonstationary processes in the literature. Otherwise, it has been shown recently that, as in the stationary case, the partial autocorrelation function characterizes, like the autocovariance function, the second-order properties of the process. Our main result is the introduction of a new time-dependent power spectrum clearly related to this function. At each time, this spectrum describes a stationary situation in which the present is correlated with the past in the same way as our nonstationary process at this time. The properties of this spectrum are analysed. In particular, it is defined for all nonstationary processes and is in a one-to-one correspondence with the autocovariance function. Unfortunately, no spectral representation of the process is actually associated with it. This spectrum is also compared with two similar other spectra. Some examples of theoretical spectra and an estimated spectrum are considered for illustration.
TL;DR: The result is then used to derive the partial autocorrelation function of a first order non-invertible moving average process.
Abstract: In this paper an expression is obtained for the determinant of a particular patterned matrix. The result is then used to derive the partial autocorrelation function of a first order non-invertible moving average process.
TL;DR: This study reviewed on the estimation methods of preventing spurious correlation in the presence of autocorrelation and applied the former three methods, Yule-Walker, nonlinear least squares and maximum likelihood method, to a 20-year real data set.
Abstract: Autocorrelation in time series data can affect statistical inference in correlation or regression analyses. To improve a regression model from which the residuals are autocorrelated, Yule-Walker method, nonlinear least squares estimation, maximum likelihood method and `prewhitening` method have been used to estimate the parameters in a regression equation. This study reviewed on the estimation methods of preventing spurious correlation in the presence of autocorrelation and applied the former three methods, Yule-Walker, nonlinear least squares and maximum likelihood method, to a 20-year real data set. Monte carlo simulation was used to compare the three parameter estimation methods. However, the simulation results showed that the mean squared error distributions from the three methods simulated do not differ significantly.
TL;DR: In this paper, a new portmanteau test for time series, more powerful than the tests of Ljung and Box and Monti, is proposed, based on the mth root of the determinant of the mst autocorrelation matrix.
Abstract: A new portmanteau test for time series, more powerful than the tests of Ljung and Box and Monti, is proposed. The test is based on the mth root of the determinant of the mth autocorrelation matrix. It is shown that the proposed statistic is a function of all of the squared multiple correlation coefficients of the regressions of the residuals on their lags when the number of lags goes from 1 to m. It can also be written as a function of the first m partial autocorrelation coefficients. The asymptotic distribution of the test statistic is a linear combination of chi-squared distributions and can be approximated by a gamma distribution. It is shown, depending on the model and sample size, that this test can be up to 50% more powerful than the Ljung and Box and Monti tests. The test is applied to the detection of several types of nonlinearity by using the autocorrelation matrix of the squared residuals, and it is shown that, in general, the new test is more powerful than the test of McLeod and Li. An example ...
TL;DR: In this paper, a simple asymptotic formula for partial autocorrelation functions of fractional ARIMA processes is given for the case where the autocorerelation function is independent of the autoregressive function.
Abstract: We prove a simple asymptotic formula for partial autocorrelation functions of fractional ARIMA processes.