Abstract: Fast retrieval of time series in terms of their contents is important in many application domains. This paper studies database techniques supporting fast searches for time series whose contents are similar to what users specify. The content types studied include shapes, trends, cyclic components, autocorrelation functions and partial autocorrelation functions. Due to the complex nature of the similarity searches involving such contents, traditional database techniques usually cannot provide a fast response when the involved data volume is high. This paper proposes to answer such content-based queries using appropriate approximation techniques. The paper then introduces two specific approximation methods, one is wavelet based and the other line-fitting based. Finally, the paper reports some experiments conducted on a stock price data set as well as a synthesized random walk data set, and shows that both approximation methods significantly reduce the query processing time without introducing intolerable errors.

Abstract: Recently, several researchers have attempted to use neural network approaches in conjunction with the extended sample autocorrelation function (ESACF) to automatically identify ARMA models. The work to date appears promising, but generalizations are limited by the fact that the test and training sets for the neural networks were generated from random perturbations of prototype ESACF tables. This paper develops test and training sets by varying the parameters of actual ARMA processes. The results show that the ability of neural networks to accurately identify the order of an ARMA(p,q) model from its transformed ESACF is much lower than reported by previous researchers, and is especially low for time series with fewer than 100 observations.

Abstract: Let {Xn: n ∈ Z} be a fractional ARIMA(p, d, q) process with partial autocorrelation function α(ċ). In this paper, we prove that if d ∈ (-1/2,0) then |α(n)| ∼ |d|/n as n → ∞ This extends the previous result for the case 0 < d < 1/2.

Abstract: Generalized autoregressive moving average (GARMA) models are fitted to the Leland et al. (1994) Bellcore Ethernet trace data. We find the time series to have long memory. In addition, we find evidence for self-similarity, as was also found in earlier studies. Our GARMA analysis shows the time series m-aggregated at 0.01, 10, 100 and 1000 seconds to be non-stationary. However, the first differences of these series are found to be stationary by the same analysis, and are represented well by GARMA models. Unlike in earlier studies, our estimation methodology can be extended to forecast the time series. We present GARMA model forecasts for the first difference of the m-aggregated data at 100, and compare with ARIMA forecasts. The fitted GARMA(0,0) model forecast is very good and tracks both the level and pattern in the time series with a negligible 95% confidence interval of 0.02. The ARIMA(15,1,5) model can track neither the level nor the pattern, and has a 95% confidence interval of 0.86 (nearly the same magnitude of the time series data) for the same 1000 predicted points. The fitted GARMA(0,0) model utilizes 4 parameters versus 23 for the ARIMA(15,1,5) model. The autocorrelation and partial autocorrelation functions indicate a very large number of parameters for the ARIMA model. Based on the similarity of the spectra of the time series data m-aggregated at various levels, we can expect similar quality of forecasts for those series using the GARMA framework.

Abstract: We consider the autoregressive estimation for periodically correlated processes, using the parametrization given by the partial autocorrelation function. We propose an estimation of these parameters by extending the sample partial autocorrelation method to this situation. A comparison with other methods is made. Relationships with the stationary multivariate case are discussed.

Abstract: In this paper the autocorrelation structure of the Exponential GARCH(p,q) process of Nelson (1991) is considered. Conditions for the existence of any arbitrary unconditional moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of squared observations are derived. The properties of the autocorrelation structure are discussed and compared to those of the standard GARCH(p,q) process. In particular, it is seen that, the EGARCH(p,q) model has a richer autocorrelation structure than the standard GARCH(p,q) one. The statistical theory is further illustrated by a few special cases such as the symmetric and the asymmetric EGARCH(2,2) models under the assumption of normal errors or non-normal errors. The autocorrelations computed from an estimated EGARCH(2,1) model of Nelson (1991) are highlighted.

Abstract: This paper discusses statistical properties of conditionally heteroskedastic in mean models. We derive the autocovariance function of an observed series under the assumption that the conditional variance follows a flexible parameterization, which nests a variety of specifications, including models for the variance, the standard deviation or their logarithm. Furthermore, the mean parameter can be timevarying. We also present the autocovariance function of the squared residuals. Our result can be applied so that the properties of the observed data can be compared with the theoretical properties of the models, thus facilitating model identification.

Abstract: We consider the autoregressive estimation for periodically correlated processes, using the parametrization given by the partial autocorrelation function. We propose an estimation of these parameter...

Abstract: In this paper we try to fit a threshold autoregressive (TAR) model to time series data of monthly coconut oil prices at Cochin market. The procedure proposed by Tsay [7] for fitting the TAR model is briefly presented. The fitted model is compared with a simple autoregressive (AR) model. The results are in favour of TAR process. Thus the monthly coconut oil prices exhibit a type of non-linearity which can be accounted for by a threshold model.

Abstract: Exploratory methods for determining appropriate lagged vsrlables in a vector nonlinear time series model are investigated. The first is a multivariate extension of the R statistic considered by Granger and Lin (1994), which is based on an estimate of the mutual information criterion. The second method uses Kendall's ρ and partial ρ statistics for lag determination. The methods provide nonlinear analogues of the autocorrelation and partial autocorrelation matrices for a vector time series. Simulation studies indicate that the R statistic reliabiy identifies appropriate lagged nonlinear moving average terms in a vector time series, while Kendall's ρ and partial ρ statistics have some power in identifying appropirate lagged nonlinear moving average and autoregressive terms, respectively, when the nonlinear relationship between lagged variables is monotonic. For illustration, the methods are applied to set of annual temperature and tree ring measurements at Campito Mountain In California.

Abstract: When studying a real-life time series, it is frequently reasonable to assume, possibly after a suitable transformation, that the data come from a stationary time series (Xt). This means that the finite-dimensional distributions of this sequence are invariant under shifts of time. Various stationary time series models have been studied in detail in the literature. A standard assumption is that the time series is Gaussian or, more generally, that it has a probability distribution with light tails, in the sense that P(lXtl > x) decays to zero at least exponentially. Zie: Summary

Abstract: This paper is devoted to the study of the second-order properties using partial autocorrelations of an instantaneous mixture of colored sources without additive noise. We introduce the notion of symmetric recursive canonical partial innovation. Then, their components, for the observation process, meet exactly with those of the source process from the order for which the autoregressive models underlying the sources are distinct. This property leads to a new separation method based on the sample counterpart of partial autocorrelation matrices associated with these innovations. Simulation results show a notable improvement of the achievements of such an approach with respect to those of similar methods. Two other separation methods related to partial autocorrelation are also discussed.

Abstract: The purpose of this paper is to study the long-time behaviour of the partial autocorrelation function of a stationary process. Let {Xn} = {Xn : n ∈ Z} be a real, zero-mean, weakly stationary process, defined on a probability space (Ω,F , P ), which we shall simply call a stationary process . Throughout this paper, we assume that {Xn} is purely nondeterministic (see §2). The autocovariance function γ(·) of {Xn} is defined by