## 这是一篇关于GARCH模型代写

1.(50 points) Group project.

2.(25 points) The fifile d-gmsp9908.txt contains the daily sample returns of GM stock and the S&P composite index from 1999 to 2008. It has three columns denoting date, GM return, and S&P return. https://faculty.chicagobooth.edu/-/media/faculty/ruey-s-tsay/teaching/fts3/d-gmsp9908.txt

(a) Compute the daily log returns of GM stock. Is there any evidence of ARCH effffects in the log returns? You may use 10 lags of the squared returns and 5% signifificance level to perform the test.

(b) Compute the ACF and PACF of the squared log returns (10 lags).

(c) Specify a GARCH model for the GM log return using a normal distribution for the innovations. Perform model checking and write down the fifitted model.

(d) Derive multistep-ahead forecasts for your GARCH model specifified in part (c) at the forecast origin *h*.

(e) Compute 1-step- to 4-step-ahead forecasts of the GM return and it volatility based on the fifitted model.

3.(25 points) Consider the monthly log stock returns, in percentages and including dividends, of Merck & Company, Johnson & Johnson, General Electric, General Motors, Ford Motor Company, and value-weighted index from January 1960 to December 2008; see the fifile m-mrk2vw.txt.

https://faculty.chicagobooth.edu/-/media/faculty/ruey-s-tsay/teaching/fts3/m-mrk2vw.txt

(a) Perform a principal component analysis of the data using the sample covariance matrix.

(b) Perform a principal component analysis of the data using the sample correlation matrix.

(c) Perform a statistical factor analysis on the data. Identify the number of common factors.

How many common factors are there? Why?

(d) Obtain estimates of factor loadings using both the principal component and maximum-likelihood methods. Interpret the common factors.

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