统计时间序列代考 Stat 4603-5504代写 统计代考 时间序列代写

Stat 4603-5504 midterm test

统计时间序列代考 1. Let xt = 3.5 + 1.2xt−1 − .8xt−2 + wt where wt is a white noise with variance 5.5. (a) [5 marks] Identify xt as an ARMA(p, q). (i.e. find p, q and

1.

Let x_t = 3.5 + 1.2x_t−1 − .8x_t−2 + w_t where w_t is a white noise with variance 5.5.

(a) [5 marks] Identify x_t as an ARMA(p, q). (i.e. find p, q and the values of the parameters including the mean of this process).

(b) [5 marks] Assume that x₁₉₈ = 1.9 and x₁₉₉ = 2.8 and x₂₀₀ = 3.1. Compute 统计时间序列代考

point forecasts for x₂₀₁ and x₂₀₂. Find interval forecast for x₂₀₁.

(c) [5 marks] Generate 100 observations from the ARMA model x_t above using set.seed(1692) (to have the same numbers). Use this sample to estimate the model and write down the estimated parameters.

2. 统计时间序列代考

[10 marks] (only for Stat4603) data in the column x in the csv file test-data represent monthly sales for certain product. What ARMA model would you suggest for the data x_t? (You will write down the numerical values of the estimates). Comment on the diagnostic checking of your tentative model. Use it to forecast the next sale.

3. 统计时间序列代考

[10 marks] Data in column y of the csv file test-data contains some signal perturbed by a noise. Use a sinewave function (trigonometric) to estimate the signal. Write down your estimated model and use it to predict the next value.

5. 统计时间序列代考

[10 marks] Let s_t = x_t + y_t where x_t and y_t are two AR(1) models independent from each other with covariance functions γ_x and γ_y. Let φ₁ and φ₂ be the AR(1) coefficients of x_t and y_t respectively. Find the covariance function γ_s(h) of the sum s_t (in terms of γ_x and γ_y) as well as its autocorrelation function ρ_s(h). In case φ₁ = φ₂, what model does s_t follow?

6. 统计时间序列代考

(For stat 5504 only). Let Y = X²+XZ where X and Z are independent, normally distributed and E(Z) = E(X) = 2 and E(Z² ) = E(X² ) = 3,

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