Abstract: We classify some p/sup k/-ary (p prime, k integer) generalized m-sequences and generalized Gordon-Mills-Welch (GMW) sequences of period p/sup 2k/-1 over a residue class ring R=GF(p)[/spl xi/]/(/spl xi//sup k/) having optimal partial Hamming autocorrelation properties. In frequency hopping (FH) spread-spectrum systems, these sequences are useful for synchronizing process. Suppose, for example, that a transmitting p/sup k/-ary FH patterns of period p/sup 2k/-1 are correlated at a receiver. Usually, the length of a correlation window, denoted by L, is shorter than the pattern's overall period. In that case, the maximum value of the out-of-phase Hamming autocorrelation is lower-bounded by /spl lceil/L/p/sup k/+1/spl rceil/ but the classified sequences achieve this bound with equality for any positive integer L.

Abstract: This paper studies correlation and partial autocorrelation properties of periodic autoregressive moving-average (PARMA) time series models. An efficient algorithm to compute PARMA autocovariances is first derived. An innovations based algorithm to compute partial autocorrelations for a general periodic series is then developed. Finally, periodic moving averages and autoregressions are characterized as periodically stationary series whose autocovariances and partial autocorrelations, respectively, are zero at all lags that exceed some periodically varying threshold.

Abstract: This paper studies correlation and partial autocorrelation properties of periodic autoregressive moving-average (PARMA) time series models. An efficient algorithm to compute PARMA autocovariances is first derived. An innovations based algorithm to compute partial autocorrelations for a general periodic series is then developed. Finally, periodic moving averages and autoregressions are characterized as periodically stationary series whose autocovariances and partial autocorrelations, respectively, are zero at all lags that exceed some periodically varying threshold.

Abstract: We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof involves the alternate iteration of projection operators associated with the infinite past and the infinite future. We provide several applications, which include rates of convergence of the finite predictor coefficients, an equality of Baxter-type for long memory processes, and a simple representation of the partial autocorrelation function (PACF). We use the last result to obtain the precise asymptotic behavior of PACF with remainder, for the fractional ARIMA processes.

Abstract: This paper presents an application of lazy learning algorithms in the domain of industrial processes. These processes are described by a set of variables, each corresponding a time series. Each variable plays a different role in the process and some mutual influences can be discovered. A methodology to study the different variables and their roles in the process are described. This methodology allows the structuration of the study of the time series. The prediction methodology is based on a k-nearest neighbour algorithm. A complete study of the different parameters of this kind of algorithm is done, including data preprocessing, neighbour distance, and weighting strategies. An alternative to Euclidean distance called shape distance is presented, this distance is insensitive to scaling and translation. Alternative weighting strategies based on time series autocorrelation and partial autocorrelation are also presented. Experiments using autorregresive models, simulated data and real data obtained from an industrial process (Waste water treatment plants) are presented to show the feasabilty of our approach.

Abstract: The exponentially weighted moving average (EWMA) controller has been proven to be an effective algorithm in the control the modern manufacturing system. The performance of the EWMA controlled process is based on choosing the correct EWMA gain. Most related research has focused on analysing the optimal EWMA gain in the static condition. The objective was to propose an approach based on the neural technique for on-line tuning of the single EWMA gain. The underlying approach indicated that the network learns very quickly when taking autocorrelation function and sample partial autocorrelation function patterns as the input features. It is shown that the sequence of the EWMA gains, generated by the proposed adaptive approach, converges close to the optimal controller value under several disturbance models, including IMA(1,1), and step and small ramp disturbances. In addition, the approach possesses a superior controlled output performance compared with the previous adaptive system.

Abstract: Time series regression models have been widely studied in the literature by several authors. However, statistical analysis of replicated time series regression models has received little attention. In this paper, we study the application of the quasi-least squares method to estimate the parameters in a replicated time series model with errors that follow an autoregressive process of order p. We also discuss two other established methods for estimating the parameters: maximum likelihood assuming normality and the Yule-Walker method. When the number of repeated measurements is bounded and the number of replications n goes to infinity, the regression and the autocorrelation parameters are consistent and asymptotically normal for all three methods of estimation. Basically, the three methods estimate the regression parameter efficiently and differ in how they estimate the autocorrelation. When p=2, for normal data we use simulations to show that the quasi-least squares estimate of the autocorrelation is undoub...

Abstract: The environment is friable and the drought is a serious in summer in the Three Gorges Reservoir Area.Changjiang is a serious disaster area of drought, of which frequency is 80%～90% and duration are 30～50 days. Drought has a serious impact on planting and growth of spring crops. In addition, soil sluice is low, soil layers of upland is weak, ability of fighting a drought is feeble, the contained water of soil planting layer can not satisfy the needs of crops. All of these influence agriculture production seriously and make for low economy benefit of agriculture and graze. Soil water movement is a complex time series system. Its variety has a close relationship with regional climate conditions and environment and has obvious random undulation. In using AR method of time series analysis to constitute forecast model, the most important is that datum must accord with balance and normal distribution. By proper transformation(for example standardization, one or many times difference etc), AR model can be constituted. The test of AR model uses residual and An Information Criterion. From November 1998 to April 2001, by measuring soil water of soil surface layer(0～30 cm) every six days, we worked out mensal average soil water of purple soil in hilly region. Using 36 months soil water data, adopting time series analysis method(AR model), we studied soil water dynamic trend. Firstly, we normalized raw data. After the standardization of raw datum, its autocorrelation and partial autocorrelation coefficients gradually trend to zero along with lags. It showed that managed data is a series accorded with zero average, balance, normal distribution and needs of AR model. Secondly, using former 28 months data as model simulating point, we calculated parameters of AR model and using the subsequent 8 months data as detecting stylebook, we tested model and forecasted the anaphase(4 months)trend of soil water at the same time. The results showed that the AIC of order 10 AR model is least and its standard deviation is also least. So we considered to use AR(10) to constitute soil water forecast model. By validating residual of AR(10) model statistically, we found that model residual fluctuated surround zero and the first residual autocorrelation coefficient ρ1 equaled to -0.001, which showed that there was no obvious autocorrelation among residuals. The simulated showed that model could preferably fit the soil water time series.

Abstract: This paper, after providing an introduction to the operating context of low cost carriers in Europe, examines the competitive pricing behaviour of airlines. Data is collected by route for cases where more than one airline is in direct competition. Data on fares is obtained from the internet for two airlines with competing services to Alicante, Prague and Malaga, departing from Nottingham East Midlands Airport in the UK, for the six working weeks up to and including the actual departure. These destinations represent leisure traffic. Two domestic business destinations were also selected to illustrate price competition on business demand where departure times were within a maximum of 20 minutes of each other and a further examination of competing services from London Gatwick (LGW) was made. Cross Correlation Analysis is used to examine whether, subject to a variety of lags, the prices offered by one airline can be seen to be both correlated with the other price series and to lead it. This provides some insight into the pricing strategy adopted by the competitors. Autocorrelation Functions (ACFs) and Partial Autocorrelation Functions (PACFs) can also be produced on the prices offered by each airline. These suggest the nature of the ARIMA model that can be fitted to the series and these models can show the degree to which series values are correlated with their own past values and whether a reasonable model could be based on an ARIMA approach. The relative strength of these two relationships is examined; are prices more closely explained by the competitor's actions or the airlines own past price setting?

Abstract: We characterize pk-ary (p prime, k integer) generalized m-sequences and generalized GMW sequences of period p2k-1 over a residue class ring R=GF(p)[xi]/(xik) with the "strictly" optimal partial Hamming autocorrelation function (HAF)

Abstract: The presence of autocorrelation in a regression model requires the use of the generalized least-squares technique in estimating the regression coefficients. To study the diagnostics of such a model it is therefore necessary to take account of the autocorrelation while re-estimating the parameters after the deletion of an observation. In this paper we look into this problem assuming that the disturbances follow a first-order autoregressive process.

Abstract: Two extension tools for enhancing the compression performance of prediction-based lossless audio coding are proposed. One is progressive-order prediction of the starting samples at the random access points, where the information of previous samples is not available. The first sample is coded as is, the second is predicted by first-order prediction, the third is predicted by second-order prediction, and so on. This can be efficiently carried out with PAR-COR (PARtial autoCORrelation) coefficients. The second tool is interchannel joint coding. Both predictive coefficients and prediction error signals are efficiently coded by interchannel differential or three-tap adaptive prediction. These new prediction tools lead to a steady reduction in bit rate when random access is activated and the interchannel correlation is strong.