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# 统计时间序列代考 Stat 4603-5504代写 统计代考 时间序列代写

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## Stat 4603-5504 midterm test

### 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 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 xt 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 xt? (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 st = xt + yt where xt and yt are two AR(1) models independent from each other with covariance functions γx and γy. Let φ1 and φ2 be the AR(1) coefficients of xt and yt respectively. Find the covariance function γs(h) of the sum st (in terms of γx and γy) as well as its autocorrelation function ρs(h). In case φ1 = φ2, what model does st 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,

The prev:

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