FI4003 Empirical Methods in Finance
Coursework Assignment # 2

A部分
1.解释时间序列的以下特征并提供过程示例

•平均回归
•确定性趋势
•随机趋势
•协整
[25分]
2.讨论共同建模两个时间序列y1，t和y2，t的优缺点

[25分]
3.从财务中举一个例子，其中一组变量之间的协整可能是

[25分]
4.使用向量自回归（VAR）方法定义以下术语。使用公式

•结构形式
•简化形式
•格兰杰因果关系
•脉冲响应功能
[25分]
B部分

1.为了确定系列是否包含单位根，首先进行Dickey-Fuller-Test
（DF）进行。写下适当的DF检验和

[30分]
2. In addition to the simple Dickey-Fuller-test, several Augmented-Dickey-Fuller-tests
(ADF) have been conducted. Explain how the ADF-test differs from the DF-test. How
can you choose the number of lags in the ADF test?
[20 marks]
3. The results of these tests (value of the test statistic and p-value) are given in the first
row of Table B.1. Draw the appropriate conclusions from these tests using a
significance level of α=5%.
[10 marks]
4. Figure B.2 shows the correlogram for the first difference of the time series yt: Δyt.
The second row in Table B.1 gives results of the DF and ADF tests for the Δyt series.
Tables B.2 and B.3 show the regression outputs for an ARMA(2,1) and ARMA(2,0)
model. Explain which specification you prefer to model the time-series Δyt. Use all
figures and the output to justify your arguments.
[30 marks]
5. Briefly describe further diagnostic tests that should be conducted before using either
ARMA model for the purpose of forecasting.
[10 marks]
Part C
Consider two time-series yt and zt which are both integrated to order one.
1. Explain how you can test if yt and zt are cointegrated. Clearly describe the procedure,
the variables used, and the test statistic and its hypotheses.
[30 marks]
2. Assume that yt and zt are cointegrated and that the dynamics of yt follow the
autoregressive distributed lag (ADL) model:
𝑦𝑡 = 𝛼0 + 𝛼1 𝑧𝑡 + 𝛼2𝑧𝑡−1 + 𝛼3𝑦𝑡−1 + 𝜀𝑡
(C.1)
What is the error correction model (ECM) for yt? How can you estimate the ECM?
Why is the ECM of interest? Explain your answers.
[30 marks]
3. Assume that Δyt and Δzt follow the vector autoregressive (VAR) model

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