时间序列分析代写 Time Series Analysis代写 Exam代写

STAD57 Time Series Analysis

Final Examination

时间序列分析代写 Duration: 3hours Examination aids allowed: Non-programmable scientific calculator, open book/notes Instructions: • Read the questions carefully and

Duration: 3hours

Examination aids allowed: Non-programmable scientific calculator, open book/notes

Instructions:

• Read the questions carefully and answer only what is being asked.

• Answer all questions directly on the examination paper; use the last pages if you need more space, and provide clear pointers to your work.

• Show your intermediate work, and write clearly and legibly.

1. 时间序列分析代写

Consider the time series X_t = 5 + W_t + .5W_t−1 − .25W_t−2, where W_t ∼ WN(0, 1).

(a) (4 points) The series follows an ARMA(p, q) model. Find the order of the model (i.e. p, q) and determine whether it is stationary and/or invertible.

(b) (4 points) Find the ACF of the series.

3. 时间序列分析代写

The time series {X_t} follows a zero-mean SARIMA(0, 1, 0) × (1, 0, 0)_[3] model with a single parameter Φ and an i.i.d. Normal(0, σ² ) white noise sequence {W_t}.

(a) (4 points) Write down the linear equation describing the evolution of X_t based on its past (X_t−1, X_t−2, . . .) and the white noise (W_t , W_t−1, . . .).

(b) (4 points) Can you find a causal representation for X_t ? (If yes, provide the representation; if no, explain why not.)

(c) (4 points) Find the ACF of ∇X_t = X_t − X_t−1 .

(d) (8 points) Write the conditional likelihood, given X₀ = 0, of the first 4 observations of the series (x₁, . . . , x₄), expressed as a function of the parameters Φ, σ² and the values x₁, . . . , x₄.

4. 时间序列分析代写

Consider two jointly stationary time series {X_t , Y_t}, with individual auto-covariance functions γX(h),γY (h), ∀h ≥ 0 and cross-covariance function γX,Y (h), ∀h ∈ Z.

(a) (7 points) Find the Best Linear Predictor (BLP) of Y_t given X_t , and its Mean Square Prediction Error (MSPE), expressed in terms of γX(h),γY (h), γX,Y (h).

(b) (13 points) Find the BLP of Y_t given X_t , X_t−1, Y_t−1, and its MSPE, expressed in terms of γX(h),γY (h), γX,Y (h).

(Note: you don’t need to solve the system of equations defining the BLP coefficients.)

5. 时间序列分析代写

Consider a zero-mean (i.e. no drift) random walk X_t = X_t−1 + W_t , t ≥ 1, where X₀ = 0 and W_t ∼WN(0,σ² ).

更多代写：新加坡CS Course代写  槍手代考英文  英国心理学网课代修  香港作业代写  新加坡Sociology论文代写 优秀论文代写

合作平台：essay代写 论文代写 写手招聘 英国留学生代写