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ECMT 670 Econometric Analysis of Financial Data –
Problem Set 3

1.假设您有一个时间序列{Xt}
Ť

j = 1 j = 2 j = 3 j = 4 j = 5
ρˆj 0.78 0.0.61 0.52 0.35 0.10
πˆj 0.37 0.21 0.16 0.06 0.01
（a）如果您想通过MA（q）模型拟合数据，您会选择哪个q？

（b）如果您想通过AR（p）模型拟合数据，您会选择什么p？

2.（可选）从eCampus下载数据集MerckDaily.csv并使用每日

（a）绘制时间序列的ACVF和ACF。
（b）使用AIC将0≤p，q≤4模型的ARMA（p，q）拟合到数据

（c）使用BIC标准重复（b）部分。 将您的选择与零件进行比较
（b）。 您会从AIC和BIC选择的两个对中选择哪个？
3. Let {Xt} be a stationary time series in R.
(a) For µ = E[Xt
], γj = Cov(Xt
, Xt−j ) and ρj = γj/γ0, exploit Proposition 3.1.1
in the lecture notes to verify the following:
Π(Xt+1|1, Xt) = (1 − ρ1)µ + ρ1Xt
. (1)
(b) If Xt = µ + t + θt−1 for some white noise {t}, simplify (1) in terms of
primitive parameters of this model.
(c) Continue with part (b) and suppose Xt = x for some known number x. Propose an estimator for Π(Xt+1|1, Xt) and derive its asymptotic distribution.
4. Consider an investor whose utility function is: for some γ 6= 1,
u(ct) = (ct − st)
1−γ − 1
1 − γ
, (2)
where ct
is the consumption at time t, and st
is the habit consumption level at
time t. Let xt be the payoff of an asset at time t.
1
(a) Compute the stochastic discount factor mt+1, and write down the pricing
equation.
(b) Explain how you would estimate the parameter γ.
2

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