我已经知道数据{Si},并对其进行非线性回归.

设非线性自回归模型为：Si+1=a*Si^2+b*Si+c(其中i+1,i均是S的下标)

条件是使该拟合曲线于表中的数据误差最小,怎么算出a,b,c呢?

郁闷.

>>设非线性自回归模型为：Si+1=a*Si^2+b*Si+c(其中i+1,i均是S的下标)

>>条件是使该拟合曲线于表中的数据误差最小,怎么算出a,b,c呢?

If you provide more details, I might be able to help you. Autoregression is mainly used for the analysis of time-series data, your notations "S_i+1" and "S_i" suggest that your dataset {Si} is indeed a time series.

First, tell me why you chose a quadratic model rather than a linear model. Keep in mind that higher model complexity would more likely lead to overfitting. Non-linear dependence on previous data points is only of interest if you have a chaotic time-series dataset. So please describe your dataset in more details (the scientific background information) for me to make relevant suggestions.

Second, the computation of "a,b,c" is still based on the method of least squares. If you are not comfortable to use the R programming language, you want to try the autoregression procedure within SAS.

Third, tell me how many time points (i.e., how many i's) do you have in this dataset. It seems to me that you might want to try a "moving average" type of models such as ARMA or ARIMA.

The following paragraphs from Wikipedia may also help you understand autoregression better ---

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Time series

In statistics and signal processing, a time series is a sequence of data points, measured typically at successive times, spaced at (often uniform) time intervals. Time series analysis comprises methods that attempt to understand such time series, often either to understand the underlying theory of the data points (where did they come from? what generated them?), or to make forecasts (predictions). Time series prediction is the use of a model to predict future events based on known past events: to predict future data points before they are measured. The standard example is the opening price of a share of stock based on its past performance.

Models for time series data can have many forms. Three broad classes of practical importance are the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models. These three classes depend linearly on previous data points and are treated in more detail in the articles autoregressive moving average models (ARMA) and autoregressive integrated moving average (ARIMA). Non-linear dependence on previous data points is of interest because of the possibility of producing a chaotic time series.

References

* An open source book on time series analysis with SAS:

http://statistik.mathematik.uni-wuerzburg.de/timeseries/

* George Box and F.M. Jenkins. Time Series Analysis: Forecasting and Control, second edition. Oakland, CA: Holden-Day, 1976.
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我是在看一篇文章《因特网拓扑演化及其节点平均连接度的分形研究》，电子学报第8期.
其中S_i+1和S_i，没错，指的是时间序列。
你问我为什么选择二次模型而非选择线性模型，对此我也很奇怪。文章里没有做任何解释，
就选择了这个二次模型，但是做出的结果倒是还不错。
其中这个参数的选取是关键。
下午去书店翻了spss和sas的书,没有找到类似的,你确定是可以通过这些软件可以求出来
吗?

再问件事,对混沌时间序列进行预测是不是件几乎没有什么意义的事啊?

时序分析通常都有意义