## 这个Assignment是完成股票数据的建模，并进行数据分析

Assignment 2
1. Use the attached data of daily equity prices of Bank of America (BAC) starting in 1990. In each case estimate the model with an intercept.
a) Estimate an ARCH(1) model and report the Schwarz information criterion
b) Estimate an ARCH(9) model and report the Schwarz information criterion
c) Estimate a GARCH(1,1) model and report the Schwarz information criterion
d) Estimate a GARCH(1,2) model (one GARCH and two ARCH terms) and report the Schwarz information criterion
e) Pick another order GARCH model and report the Schwarz criterion
f) Introduce another lagged or deterministic variable to see if it is significant.
Which is preferred?
Do all of these models satisfy the basic criteria for a good model?
2. For the GARCH(1,2) model(one GARCH and two ARCH terms), calculate the time series of annualized volatilities. What was the maximum conditional volatility and when did this occur?
3. Test the autocorrelation of the standardized residuals and the squared standardized residuals with 10 lags. Does this model pass both tests? Explain.
4. Report the skewness and kurtosis of the standardized residuals. Compare these with the BAC returns.
5. Forecast the next year of daily volatility for BAC and plot the result.
6. Reestimate the GARCH(1,2) with student-t distribution. Now what is the Schwarz criterion? Does it find this estimate preferable?
7. Describe the volatility pattern of a GARCH(1,1):
a. When the sum of alpha plus beta is small?
b. When the sum of alpha plus beta is bigger than one?
c. When alpha is small and beta is big with a sum slightly less than one?
d. When alpha is big and beta is small with a sum slightly less than one?

1. 使用随附的美国银行 (BAC) 从 1990 年开始的每日股票价格数据。在每种情况下用截距估计模型。
a) 估计 ARCH(1) 模型并报告 Schwarz 信息准则
b) 估计 ARCH(9) 模型并报告 Schwarz 信息准则
c) 估计 GARCH(1,1) 模型并报告 Schwarz 信息准则
d) 估计 GARCH(1,2) 模型（一个 GARCH 和两个 ARCH 项）并报告 Schwarz 信息准则
e) 选择另一个阶 GARCH 模型并报告 Schwarz 准则
f) 引入另一个滞后或确定性变量，看它是否显着。

2. 对于GARCH(1,2)模型（一个GARCH和两个ARCH项），计算年化波动率的时间序列。 最大条件波动率是多少，何时发生？
3. 用 10 个滞后检验标准化残差和平方标准化残差的自相关性。 这个模型是否通过了这两个测试？ 解释。
4. 报告标准化残差的偏度和峰度。 将这些与 BAC 回报进行比较。
5. 预测下一年 BAC 的每日波动并绘制结果。
6. 重新估计具有学生 t 分布的 GARCH(1,2)。 现在什么是 Schwarz 标准？ 它觉得这个估计更可取吗？
7. 描述 GARCH(1,1) 的波动率模式：
A。 什么时候alpha加beta的和很小？
b. 当 alpha 加 beta 的总和大于 1 时？
C。 当 alpha 小而 beta 大且总和略小于 1 时？
d. 当 alpha 大而 beta 小且总和略小于 1 时？