Loading in 5 sec....

Smooth Transition Autoregressive ModelPowerPoint Presentation

Smooth Transition Autoregressive Model

- By
**sarah** - Follow User

- 137 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Smooth Transition Autoregressive Model' - sarah

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Smooth Transition Autoregressive Model

- For some process, it may not seem reasonable to assume that the threshold is sharp
- Smooth Transition Autoregressive (STAR) Model allow the autoregressive parameters to change slowly.

Eni Sumarminingsih, SSi, MM

- Consider the special NLAR model given by
- If f() is a smooth continuous function, the autoregressive coefficient (α1 + β1) will change smoothly along with the value of Yt-1
- There are two particularly useful forms of the STAR model : the Logistic STAR and the Exponential STAR

Eni Sumarminingsih, SSi, MM

- The LSTAR Model generalizes the standard AR model such that the AR coefficient is a logistic function :
- where
- is called the smoothness parameter
- In the limit, as --> 0 or ∞, LSTAR become an AR(p) model since the value of is constant.

Eni Sumarminingsih, SSi, MM

- For intermediate value of the AR coefficient is a logistic function :, the degree of autoregressive decay depends on the value of Yt-1
- As Yt-1 -, 0 so that the behavior of Ytis given by
- As Yt-1 +, 1 so that the behavior of Ytis given by
- Thus the intercept and the AR coefficient smoothly change between these two extremes as the value of Yt-1 changes.

EniSumarminingsih, SSi, MM

- The ESTAR model uses the AR coefficient is a logistic function :
, > 0

- As approach zero or infinity, the model becomes an AR(p) model since is constant
- Otherwise, the model display nonlinear behavior
- As Yt-1 approach c, approach 0 behavior of Yt is given by

Eni Sumarminingsih, SSi, MM

- As Y the AR coefficient is a logistic function :t-1 moves further from c, approach 1 behavior of Yt is given by

Eni Sumarminingsih, SSi, MM

Test for STAR Model the AR coefficient is a logistic function :

Step 1 : Estimate the linear portion of the AR(p) model to determine the order and to obtain the residual {et}

Step 2 : Estimate the auxiliary equation

Eni Sumarminingsih, SSi, MM

Test the AR coefficient is a logistic function :the significance of the entire regression by comparing TR2 to the critical value of 2.

If the calculated value of TR2 exceed the critical value from a 2 table, reject the null hypothesis of linearity and accept the alternative hypothesis of a smooth transition model.

Alternatively, you can perform an F test

Eni Sumarminingsih, SSi, MM

Step 3 : If you accept the alternative hypothesis (i.e., if the model is nonlinear), test tre restriction a31 = a32 = … = a3p = 0 using an F test. If you reject the a31 = a32 = … = a3p = 0, the model has LSTAR form. If you accept the restriction, conclude that the model has the ESTAR form

Eni Sumarminingsih, SSi, MM

Uji the model is nonlinear), test F

JKGR: JK galat restricted model

JKGU: JK galat unrestricted model

kU: jumlahpeubaheksogen (termasukkonstanta) pada unrestricted model

kR: jumlahpeubaheksogen (termasukkonstanta) pada restricted model

Hipotesisnol: restricted model valid

Mendugarestricted model danunrestricted model

Memperoleh JK Galatuntukrestricted modeldan JK Galatuntuk unrestricted model, danmenghitungstatistikuji F.

Download Presentation

Connecting to Server..