Question: The SAS regression output for an AR(2)-TGARCH(1,1) model is given below for the Chinese stock market return data. Answer the questions below using this SAS

The SAS regression output for an AR(2)-TGARCH(1,1) model is given below for the Chinese stock market return data. Answer the questions below using this SAS output.

‘Estimation results for the AR(2)-TGARCH(1,1)-in-Mean model’

The AUTOREG Procedure

Dependent Variable: chinaret

Threshold GARCH Estimates

SSE

0.16165748

Observations

1500

MSE

0.0001078

Uncond Var

.

Log Likelihood

4825.87984

Total R-Square

0.3526

SBC

-9593.2539

AIC

-9635.7597

MAE

0.00752851

AICC

-9635.6631

MAPE

235.223423

HQC

-9619.9247

Parameter Estimates

Variable

DF

Estimate

Standard
Error

t Value

Approx
Pr > |t|

Intercept

1

0.0009

0.0002

3.57

0.0004

AR1

1

-0.0535

0.0268

-1.99

0.0462

AR2

1

0.0363

0.0255

1.42

0.1552

TARCHA0

1

0.2718

    0.0659

4.12

<.0001

TARCHA1

1

0.0400

0.0126

3.18

0.0015

TARCHB1

1

-0.0774

0.0171

-4.52

0.0048

TGARCH1

1

0.8959

0.0155

57.78

0.0022



a. Based on the SAS output, is there evidence of a significant ARCH effect? Write down the relevant p-value and answer this question using the p-value method.

b. Is there evidence of a significant leverage effect for the Chinese stock market return data? Write down the relevant p-value and answer this question using the p-value method. If significant, then also discuss the coefficient estimate on the leverage effect variable.

c. Is the TGARCH model stationary? In order to answer this question, a relevant hypothesis test was conducted. The resulting SAS output with the test statistic and p-value are given below. Based on this output, do you conclude that the model is stationary or not? Explain clearly.

Test STATIONARITY

Source

DF

F Value

Pr > F

Numerator

1

12.58

0.0160

Denominator

1492

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