时间序列实验题目

实验七 Unit root test

Case 1 : check whether the series in unit root1.xls is stationary or not by ADF-test ,if the series is nonstationary, then consider the nonsationarity and establish suitable model

◆ create a new integer-data workfile named unit root1; import data series

named y

◆ Check series-- long-run trend----unit root test(trend stationary or unit

root process)

◆ Uint root test--ADF

◆ Case3(including a constant and a linear time trend in the test

regression)---- H0 is rejected ： series is trend stationary

◆ Establish trend equation(we usually term the‘‘ trend equation”)

—eq01: y c t (t=@trend+1)

Eliminate nonstationarity( long-run trend component) ,get new

series X=y-c-at ，

x=y-eq01.@coefs(1)-eq01.@coefs(2)*@trend

i.e. residuals of eq01 in fact, which can be obtained from equation

Proc —make residual(show name)

◆ Obviously , new series x is stationary ，we can establish ARmodel for

series x by correlogram ，lag length p=1

◆ X ar(1)-------eq02，

◆ write the model (eq02)： ◆ In fact , we can establish combined model for original series y,

future value of y can be by the equation directly

y c @trend ar(1)

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Exercise 1 : check whether the series in test1.xls is stationary or not by ADF-test ,if the series is nonstationary, then consider the nonstationarity and establish suitable model

◆ create a new integer-data workfile named test1; import data series

named y

◆ Check series-- long-run trend----unit root test(trend stationary or unit

root process)

◆ Uint root test —ADF, give your reason or how do you get your result

◆ If the series y is nonstationary , please eliminate the nonstarionarity and

establish suitable model for original series , the equation should be

stored in the workfile and give name eq01

◆ write out the equation ：

10.32t t t x x ε-=+10.32((1))(10.32)()t t t t t y c bt y c b t L y c bt εε---=---+---=

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Case 2 : check whether the series in unit root2.xls is stationary or not by ADF-test ,if the series is nonstationary, then consider the nonsationarity and establish suitable model

◆ create a new integer-data workfile named unit root2; import data series

named y

◆ Check series-- long-run trend----unit root test(trend stationary or unit

root process)

◆ Uint root test--ADF

◆ Case3(including a constant and a linear time trend in the test

regression)---- H0 can not be rejected ：perhaps irrelevant

regressors are included

◆ Case2(including a constant in the test regression)---- H0 can

not be rejected ：perhaps irrelevant regressors are included ，

◆ Case1: --- H0 can not be rejected ：series y has unit root

◆ You should carry out unit root test for the first difference of y, case3: H0

can be rejected ---y is I(1)

◆ Establish ARIMA model for series y

◆ Generate the first difference series of y named x,x=d(y)

◆ we can establish AR model for series x by correlogram ，lag

length p=1

◆ establish ARIMA model for original series y —eq01, future

value of y can be forecasted by the equation directly

d(y) c ar(1)

◆ write out the final equation(eq01) ：

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Exercise 2: check whether the series in test22.xls is stationary or not by ADF-test,if the series is nonstationary, then consider the nonsationarity and establish suitable model

◆ create a new integer-data workfile named test22; import data series

named y

◆ Check series is stationary, trend stationary or unit root process by

ADF-test, give your reason or how do you get your result

◆ establish suitable model （eq01） for original series y based on

your conclusion in question 2

Write out the model ： 1()0.9020.43(()0.902)(10.43)(()0.902)t t t t t d y d y L d y εε--=-+--=