ECON-4200_Assignment_3_Winter_2022TRENT UNIVERSITY DEPARTMENT OF ECONOMICS ECON-4200H: TOPICS IN...

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ECON-4200_Assignment_3_Winter_2022TRENT UNIVERSITY DEPARTMENT OF ECONOMICS ECON-4200H: TOPICS IN ECONOMETRICS ASSIGNMENT 3 DUE: APRIL 12, 2022 Question 1: The posted dataset contains information on the daily returns of the DOW Index for the period March 2010 to March 2020.  (a) Test for the presence of ARCH effects in the daily returns (variable r).  What do you conclude? (b) Plot the daily returns.  What do you observe? (c) Estimate an ARCH(1) model on the daily return series. Interpret the results.  (d)  Estimate a GARCH(1,1) model on the daily return series. Interpret the results. (e)  Estimate a T-GARCH(1,1) model on the daily return series.  Interpret the results. (f)  Of the models estimated in parts (c), (d), and (e), which provides the best fit?

Manoj · Accepted Answer

Question 1.
a.  
R- Output:
##  ARCH LM-test; Null hypothesis: no ARCH effects
## 
## data:  dt$r
## Chi-squared = 259.23, df = 1, p-value 
##  [data = dt$r]
## 
## Conditional Distribution:
##  norm 
## 
## Coefficient(s):
##       mu     omega    alpha1  
## 0.056573  0.607614  0.316754  
## 
## Std. Errors:
##  based on Hessian 
## 
## Error Analysis:
##         Estimate  Std. Error  t value Pr(>|t|)    
## mu       0.05657     0.01651    3.427 0.000609 ***
## omega    0.60761     0.02286   26.585  |t|)
## mu      0.000000          NA       NA       NA
## omega   0.034954    0.005537   6.3124        0
## alpha1  0.168595    0.017706   9.5221        0
## beta1   0.794274    0.019044  41.7074        0
## 
## Robust Standard Errors:
##         Estimate  Std. Error  t value Pr(>|t|)
## mu      0.000000          NA       NA       NA
## omega   0.034954    0.007607    4.595    4e-06
## alpha1  0.168595    0.023773    7.092    0e+00
## beta1   0.794274    0.024767   32.070    0e+00
## 
## LogLikelihood : -2956.501 
## 
## Information Criteria
## ------------------------------------
##                    
## Akaike       2.3525
## Bayes        2.3595
## Shibata      2.3525
## Hannan-Quinn 2.3551
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.3888  0.5329
## Lag[2*(p+q)+(p+q)-1][2]    1.0116  0.4945
## Lag[4*(p+q)+(p+q)-1][5]    3.2026  0.3713
## d.o.f=0
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                    0.05442  0.8155
## Lag[2*(p+q)+(p+q)-1][5]   1.93507  0.6339
## Lag[4*(p+q)+(p+q)-1][9]   2.89826  0.7756
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]   0.07716 0.500 2.000  0.7812
## ARCH Lag[5]   1.69028 1.440 1.667  0.5438
## ARCH Lag[7]   1.

ECON-4200_Assignment_3_Winter_2022 TRENT UNIVERSITY DEPARTMENT OF ECONOMICS ECON-4200H: TOPICS IN ECONOMETRICS ASSIGNMENT 3 DUE: APRIL 12, 2022 Question 1: The posted dataset contains information on...

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