求助－数据建模的困惑－模型复杂了好吗

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具体数据见附件， 40226.rar (3.99 KB) 本附件包括：

• sunpots.xls

2006-2-19 17:22:00 上传

求助－数据建模的困惑－模型复杂了好吗

太阳黑子1700-1997年数据资料

如何建立模型进行拟和：

我采用的ARIMA(2,0,1)是否可以

模拟图见

如果采用ARIMA(2,0,1)-GARCH(1,1)是否更好

回答切合实际者，或能够提供更好的拟和模型的，奖励50论坛币

[此贴子已经被作者于2006-2-19 20:59:19编辑过]

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关键词：数据建模 ARIMA GARCH 50论坛币 如何建立 数据 建模 模型 困惑

对比结果O

-----------------------------------------------------------------------
Dependent Variable is Svar2
296 observations (3-298, Dates 1702 to 1997) used for estimation
Estimation Method: Conditional ML (Time Domain)
Gaussian Likelihood
ARIMA(2,0,1)

Estimate Std. Err. t Ratio p-Value
Trend 0.27684 0.02266 12.217 0
AR1 1.44678 0.05845 24.752 0
AR2 -0.7062 0.05332 -13.245 0
MA1 0.07206 0.06899 1.045 0.297
Error Variance^(1/2) 17.1681 0.9508 ------ ------
Log Likelihood = -1261.55
Schwarz Criterion = -1275.78
Sum of Squares = 87244.2
R-Squared = 0.8263
Residual SD = 17.1581
Residual skewness = 0.9076
Residual kurtosis = 4.7394
Jarque-Bera Test = 77.9566 {0}
Box-Pierce (residuals): Q(12) = 56.5027 {0}
Box-Pierce (squared residuals): Q(12) = 25.2682 {0.014}
-----------------------------------------------------------------------
Dependent Variable is Svar2
296 observations (3-298, Dates 1702 to 1997) used for estimation
with 2 pre-sample observations.
Estimation Method: Conditional ML (Time Domain)
Gaussian Likelihood
ARIMA(2,0,1) with GARCH(1,1)

Estimate Std. Err. t Ratio p-Value
Trend 0.21132 0.03342 6.323 0
AR1 1.47323 0.04253 34.64 0
AR2 -0.68724 0.04043 -16.998 0
MA1 0.11231 0.08942 1.256 0.21
GARCH Intercept^(1/2) 11.7474 1.3947 ------ ------
GARCH AR1 0.69857 0.22104 3.16 0.002
GARCH MA1 0.0704 0.09109 0.773 0.44
Log Likelihood = -1241.22
Sum of Squares = 90634.2
R-Squared = 0.8289
Residual SD = 17.1503
Residual skewness = 1.5023
Residual kurtosis = 5.0603
Jarque-Bera Test = 163.696 {0}
Box-Pierce (residuals): Q(12) = 55.8259 {0}
Box-Pierce (squared residuals): Q(12) = 35.2946 {0}

另外hansen采用two-threshold TAR model,下面是GAUSS程序，是否更好

/* SUNSPOT3.PRG */

/* This replicates some of the empirical work reported in
"Testing for Linearity" by Bruce E. Hansen.
For updates and contact information, see my webpage
www.ssc.wisc.edu/~bhansen
*/

/* This program estimates a two-threshold TAR model, and tests the null of a
one-threshold TAR against the alternative of a two-threshold TAR */

[此贴子已经被作者于2006-2-19 20:35:40编辑过]

I did not read your data.

--------------------------

If you start from the linear model(ARMA type), you need to test against non-linearity. Such as nonlinearity in the second moment(ARCH effect), or linearity in the first moment (TAR, STAR).

--------------------------

for model selection, you can compare the likelihood, or AIC, BIC. When using information criteria for nonlinear model, please use appropriate IC, because the usual AIC or BIC tends to be unfair for nonlinear model.

You may also want to compare the model's forecasting performance.[It turns out that in most of the published articles, forecasting comparison is not in much favorable to nonlinear models]. {But if you think of threshold cointegration, nonlinear model is more intuitively appealing}

Remember that in case when nonlinear models lose the horse race of prediction, you can still argue that,nonlinear model can be useful when there is rich-enough structure in the forecasting period.

-------------------------

when it comes to TAR or STAR (Smooth transition, such as LSTAR: Logistic STAR), you may choose TAR if you have strong economic argument for the data generating mechanism (such as the Iceland river flow data, in this case clear physical reasoning is in order). Otherwise STAR model can be a good choice since the LF is continuously differentiable. Furthermore, STAR reduces to TAR when the Smoothness parameter (gamma) tends to infinity.

Also note that it is possible that gamma_hat turns out to be insignificant when looking at the t-value. this is possible because normally the data can not provide enough information regarding whether gamma=50 or gamma=100.(in some published papers, some economists missed this point)

----------------------------

for linearity test in STAR models, Hansen's method is reliable, but really time consuming. moon method(m out of n bootstrap, published in Statistica sinica, Taiwanese Journal) is also applicable. the most widely applied method is the Taylor expansion (but note that when using Taylor expansion, you actually test another H0, not the original one), either first order or thrid order depending on the specific situation.

---------------------------

For serious parametric econometric modeling, better to put your estimated model in various misspecification tests.

such as additional nonlirearity,..... Bai (Jun Shan)'s LR test can help choose the number of regimes.

----------------------------

The above is just some general comments.

[此贴子已经被作者于2006-2-19 19:18:33编辑过]

To:数据建模的困惑－模型复杂了好吗

For forecasting purpose, simple model wins in general.

很好的见解，奖励您50论坛币。谢谢！

另外，

If you start from the linear model(ARMA type), you need to test against non-linearity. Such as nonlinearity in the second moment(ARCH effect), 比较好做到。

or linearity in the first moment (TAR, STAR). 是如何进行的呢

[此贴子已经被作者于2006-2-19 20:52:41编辑过]

Note that with STAR model, there is a nuisance parameter only identified under H1.

Hansen1996, Econometrica, 64,413-30 to obain the C.V.

Dvies 1977, Biometrika, 64,247-54-------------(2)

Dvies 1977, Biometrika, 64,247-54--------------(3)....(2)/(3) was the first that dicussed the topic and proposed some solution.

Bickel, Götze and van Zwet (1997), Statistica Sinica discussed the bootstrap method.

Horowitz (2001), Handbook of Econometrics Vol V is a nice reference for general application of bootstrap in Econometrics

the bootstrap method is also discussed in Skalin 1998, (SSE/EFI working paper series in Economics and Finance, 276, Stockholm School of Economics)

Saikkonen and Luukkonen 1988, Scandinavian J of Statistics,15,55-68, for the LM type test(Taylor expansion.)

van Dijk, Teräsvirta and Franses, Econometric Reviews 21,1-47, (and reference therein)discuss how to build a STAR model, excellent for practitioners

Bai, J. 1999, LR tests for multiple structural changes, J of Econometrics, 91,299-323... for TAR mdoel

Bai and Perron 2003, J of applied Econometrics, 18, 1-22, may aslo be informative.

十二分的感谢，您对STR模型太在行了。

俺正在看Helmut Lütkepohl 和Markus Krätzig 写的

Applied Time Series Econometrics

里面对STR介绍详细，只是估计方法不容易掌握

尤其是

转换变量的选择和检验

[此贴子已经被作者于2006-2-20 20:36:07编辑过]

没有其他人知道吗[em06][em06][em06][em06]

If you concentrate the likelihood, you may estimate it with OLS. then the point estimate of the transition variable should be the one minimize the SSR.

Teräsvirta 1994, JASA paper is a standard paper for choosing y(t-d).

The idea is you compute the F statistics of testing linearity(large value is critical).

The correct one should be the one with largest F value.

The intuition is the correct specification (you correctly chose the transition variable) should be the most revealing w.r.t. the misspecification.

Better Read the article I recommanded. Franses and van Dijk "Nonlinear models in empirical finance" is also a good reference.

[此贴子已经被作者于2006-2-22 5:12:27编辑过]