Analysis of time series data

Time series data is a sequence of observations collected over intervals of time. Each time series describes a phenomenon as a function of time. For example, daily stock prices can be used to describe the movements of the stock market. In general, the time series X with n observations, X is represented as

,

where VI and I, 1 £ i £ n, the observation value and its time stamp, respectively. A time series [7, 11, 13, 14] can be regular or irregular. In regular time series, data are collected periodically in a certain time points, while in irregular time series, data arrives at indeterminist time points. Irregular time series may have long periods of time without any data, and short periods of bursts of data.

Analysis of time series data includes detecting trends (or patterns) in a time series sequence [7, 13]. Time series models are classified as either systematic patterns, where patterns can be established at certain points of time, or non-systematic patterns. Many researchers working on different algorithms of time series analysis. Two main lines of research are considered to achieve this goal,

(A) Identification and description of the pattern of observed time series data. Once the model is established, can be interpreted and integrated with other data. The identified pattern can be extrapolated to predict future events [11, 13].

(B) Determining whether two or more defined time series display similar behavior or not. Similar time series can be grouped or classified into similar groups. Due to the inherent high data dimensions, the problem of similarity search in large time series databases is a non-trivial problems [7, 14].

Most solutions [7, 10, 15] Size of data reduction performed, then indexing the reduced data with a spatial access method. Singular Value Decomposition (SVD), Discrete Fourier transform (DFT), Discrete wave transform (DWT), and Piecewise Aggregate Approximation (Paa) is used to reduce dimensions.

Discovering patterns in time series data will tell us that the models are mostly likely to happen, but in some cases and in non-systematic models, would not say when these models will occur. Predicting Sun systematic patterns needs applying some techniques to detect similarity between two or more time series sequences. While studying the similarity between models is an important topic, but it only covers a narrow class of time series applications. To extend the range of applications that could benefit from the time series analysis,

new look of the term "similarity" should be considered. In fact, using the word "similarity" does not reflect the true meaning of synchronized or behavior depends on two time series sequences. Two sequences can be quite different (in values, forms, ... etc.), but they still react the same way depending on conditions.

In recent years, data mining appeared and was recognized as a new technology for data analysis. Data mining is the process of discovering potentially valuable patterns, associations, movements, sequences and dependencies in the data [1-6, 9, 12]. Key examples include business analysis for improvements in the environment, e-commerce, fraud detection, screening and verification, and product analysis. Extraction techniques may reveal information that many traditional business analysis and statistical techniques fail to deliver. Data mining, advanced features that enable energy users to seek more sophisticated and relevant questions are provided.

The past trend patterns in a time series can be used to predict future sequences in the same time series, we'll call this local prediction, and this trend models are called local patterns. Predicting the future sequences using only local models might work, but only for certain types of time series sequences, for example, regular or cyclical. For most real-life time series data, prediction of sequences using only a local trend models will tell us what sequences are mostly likely to happen, but it will not tell us when they will happen. In this paper, we introduce the idea of ​​a global prediction. The global prediction, we do not use just past the local models, but we also use in other forms past "dependent" time sequences, these models are called global patterns. For every trend pattern, pattern vector is generated to hold information about these sequences have a pattern.

In this paper, we propose a generic technique that can be used in predicting time series data. The proposed technique consists of three phases:

(A) Generate trend sequences for all time series sequences under consideration.
(B) Discover frequent sequential patterns and generate maximum frequent trend pattern vectors.
(C) predict future time series sequences, which refer to the maximum frequent trend pattern vectors.

In section 2, formal definition of the problem is given. The approach is introduced in Section 3. In item 4, the approach is assessed. The paper is summarized and concluded in section 5.