From a time series
[x.sub.i] (1 [less than or equal to] i [less than or equal to] N), we can construct an L x K * (K=N-L+1) trajectory matrix X with a window size L (Vautard et al., 1992) as follows,
Although the quantization of SAX can be advantageous for retrieval purposes, it is not suitable for finding clusters of time series
having similar shapes, since it is not sufficiently accurate for measuring distances among time series
in the clustering problem .
Considering hydrological time series
, the monthly streamflow series typically have a periodic behavior in the mean and variance and in general, periodic autoregressive models are used in de analysis of the data (see, for example, Modal & Wasimi, 2006).
Mehta says that, when using time series
data for machine learning, the only way to determine the future state of a system for throughput improvement, downtime reduction, operator safety or product quality is to examine multiple signals over a period of time.
Tests are performed on time series
from M2-Competition  and SSS model has shown more reliable forecasts even SSS model is simpler than HW model.
In Section 5, we evaluate the performance of our proposed algorithm on both synthetic data and real time series
. Finally, Section 6 concludes our work and discusses some future work.
Recently, a multiscale entropy (MSE) technique was proposed for coarse-grained time-scaling procedures to offer more robust determination of the complexity of time series
Two famous econometricians formulated the strategy of forecasting a times series called the Box-Jenkins method named after the statisticians George Box and Gwilym Jenkins,  this method applies autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) models to find the best fit of a time-series model to past values of a time series
. The Box-Jenkins method (ARIMA) is one of the most widely used time series
forecasting methods in practice .
Future strategies based on time series
modeling techniques should be developed to meet the demand for oil seed crops, which are rich sources of energy and protein for human nourishment and important feedstuff for livestock and aquaculture, as well as being a source for biodiesel (Masuda and Goldsmith, 2009).
This study on time series
of prices for agricultural products was performed based on the commodities identified bellow as SUG (sugar), COT (cotton) COR (corn), COF (coffee), and SOY (soy).
These continuous time series
- help to estimate pollutant concentrations in sewer systems and offer real-time control applicability -.
Taking the monitoring data time series
of one seawall project in Zhejiang, China, as an example, after analyzing the seawall settlement variation and its inducing factors, a combined LS-ARIMA forecasting model that is composed of the least-square method (LS) and the autoregressive integrated moving average (ARIMA) model was proposed in this study.