Journal of Water Resources Research
Vol.3 No.04(2014), Article ID:13947,6 pages
DOI:10.12677/JWRR.2014.34041

Threshold Autoregressive Model in Rainfall Forecasting—A Case Study in Yiwu

Lingzi Zhu, Lihua Feng*, Qiong Huang

Department of Geography, Zhejiang Normal University, Jinhua

Email: *309442308@qq.com

Received: Jul. 16th, 2014; revised: Jul. 23rd, 2014; accepted: Aug. 8th, 2014

ABSTRACT

The meteorological elements are not only combined effected by the impact factors, but also their own evolution. Multivariate analysis ignores the evolution of meteorological elements themselves, and the time-series analysis did not take full advantage of the implicit information about the impact factor. This article uses threshold autoregressive model by piecewise linearization method of nonlinear problem to deal with the meteorological elements, both considering influence factors of superimposition, and balancing the evolution law of meteorological elements themselves; the fitting and forecasting effect is relatively good. But now the time sequence of the meteorological elements is generally short, usually around 40 to 60 years, which belongs to the incomplete information system, the extrapolation value should not be too long. It would be best to gradually replenish the new information in a timely manner to improve the fitting and forecasting results.

Keywords:Precipitation, Impact Factor, Threshold Autoregressive, Forecasting

——以中国义乌市为例

Email: *309442308@qq.com

1. 引言

Box和Jenkins在1970年提出了处理线性时间序列的自回归模型AR(p)、自回归滑动平均模型ARMA(p, q) (Autoregressive and Moving Average)以及自回归求和滑动平均模型ARIMA(p, d, q) (Autoregressive Integrated Moving Average)[5] 。这些模型为处理线性时间序列提供了有力的数学工具。但是，实际工作中所遇到的数据序列往往非常复杂，有时候不能用线性模型来描述。因此，非线性模型的研究和应用越来越为人们所关注。Tong H于1972年提出的门限自回归(Threshold Autoregressive, 简称为TAR)模型就是一种处理非线性系统变化的时间序列模型[6] ，已经在气象学、水文学和地质学等领域获得了广泛的应用[7] [8] 。

2. 方法

2.1. 单一门限自回归模型

(1)

2.2. 混合门限自回归模型

(2)

1) 延迟步长d；

2) 门限值r；

3) 自回归阶数，以及相应的自回归系数，其中

3. 参数确定

3.1. 确定最大延迟步长D

3.2. 确定门限值r

(3)

3.3. 确定模型系数及阶数

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

3.4. 确定延迟步长d

(14)

(15)

4. 结果与讨论

(16)

(17)

5. 结语

Table 1. The forecast values and error of TAR(2, 1, 1), TARSO(2, (1, 1), (1, 1)) on June 21-July 5

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NOTES

*通讯作者。