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.

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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).

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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.

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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]