First, what is the time-series

1. Definitions

Chronological order of the process of development and change a random event record constitute a time series .

Time series to observe, study, look for changes in the development of its regularity, it forecast the future trend is the time series analysis .

2, chestnuts

7,000 years ago, ancient Egyptians the Nile case-by-day fluctuations recorded on a so-called time series.

Long-term observation of the time sequence so that they find very regular fluctuations of the Nile. After the first time Sirius and the sun rises at the same time that day, another about two hundred days, the Nile began to flood, flood period will last seven, eighty days after the flood, fertile land, there will be a huge random seeding harvest.

Due to the basics of what the Nile flood, making the rapid development of agriculture in ancient Egypt, the liberation of a large number of labor force to engage in non-agricultural production, creating a splendid prehistoric civilization of Egypt.

3, time series analysis methods:

Descriptive timing analysis: by visual observation or drawing data comparison, the law of development to find the sequence contains.
Statistical Timing Analysis: Using the basic principles of mathematical statistics, correlation analysis of the internal sequence value.

Second, the timing analysis of related concepts

Timing Analysis goal:

1) found that implicit dependencies and increase our understanding of such time series;

2) Not observed Not occurred or a time series forecast.

Stationary sequence : sequence substantially tendency does not exist. Each observed value is substantially fixed at a certain level fluctuations, although different degrees at different time periods of the fluctuation, and a single

Some kind of law does not exist, volatility can be seen as random.

Non-stationary sequence : comprising trends, seasonal or periodic sequence, it may contain only one ingredient, may contain several components, it is divided into a sequence of non-stationary trends

Potential sequence, and seasonality trend, complex sequences of several components are mixed.

Trend : a rising or declining volatility for some time series presented in the long term, also known as long-term trend. But linear time series, may be

Non-linear.

Seasonal , also known as seasonal variation, which is cyclical fluctuations time series within a year recurring.

Periodic : time series presentation of a wave-shaped or around the long-term trend of shock-style changes.

Randomness : removing trend in the time series, and chance fluctuations after seasonal periodicity.

Time series components : Trends T, seasonal or seasonal variation S, periodic or cyclic fluctuations C, irregular, or random fluctuations I, decomposing the multiplicative model.

Third, time series analysis and forecasting method is mainly classified

Time series prediction method can be used for short-term forecasting , medium-term projections and long-term forecasts . Depending on the data analysis method, can be divided into: Simple method chronological average , weighted average method sequence , moving average , weighted moving average process , trend prediction , exponential smoothing , seasonal trend forecasting method , market life cycle prediction method and so on.

　　Simple chronological average method , also known as the arithmetic average method . That is the statistic of several historical periods as observed values, and the arithmetic mean of the predicted value as the next stage. This method is based on the following assumptions: "In the past this way, the future will be like this," the short and long term data assimilation and averaged, it can only apply to little things change in trend forecasting. If some things trend up or down, we should not use this method.

　　Sequence weighted average method is the historical data of all periods and by long-term impact of recent weighted average value, as the value of the prediction.

　　Simple moving average is calculated several times successively moved as the arithmetic mean of the predicted value.

　　Weighted moving average method that simple, weighted moving average calculation. In determining the weights, weights recent observations should be bigger, long-term observations of the weights should be smaller.

Although the above-mentioned methods is simple, can quickly obtain predictive value, but does not consider the impact of new trends in the overall social and economic development and other factors, it is less accurate. It should be based on the new situation, to predict the results mutatis mutandis.

　　Exponential smoothing i.e., actual and predicted value of the historical data, with exponentially weighted prediction approach. This method is essentially a method comes evolved from the average within the weighted moving method, the advantage as long as the last of the actual number and the last of the predicted value, can be predicted value of the calculation, this can save a lot of time and processed data to reduce the amount of data stored, the method is simple. It is a widely used foreign short-term prediction method.

　　Seasonal trend forecasting changes in economic index based on the periodic season things are repeated every year, predict seasonal changes in trend. Seasonal index calculated using different methods, commonly used methods are season (monthly), and two kinds of methods do not average the moving average method: a. Season (May) do not average method. That is, the value of each year's quarterly (or monthly) are averaged, divided by the total average each quarter (or month), come each season (March) index. This method can be used to analyze the production, sales , raw material reserves, expected cash flow of seasonal change in the economic aspects of things and other requirements; b. Moving average method. That is calculated using the moving average ratio requirements typical seasonal index.

　　Market life cycle prediction method is the analysis of the product market life cycle. For example, in the growth stage of its product sales forecast, the most common method is based on statistics, time series plotted as a graph , then the curve extension, to obtain future sales trends. The simplest method is a straight extension of epitaxy, suitable for consumer durables prediction. This method is simple, intuitive and easy to master.

Fourth, the main steps of time series analysis

Investigation characteristic sequence of observations: Step
Step: Select the appropriate fitting characteristics model according to the sequence
The third step: determining the diameter of the observation model data sequence
Step four: test model, optimization model
Step five: Use a good fitting model to extrapolate the future development of other statistical properties of the sequence or sequences predicted