X(t) is a wide sense stationary stochastic process with autocorrelation function sin(271000T) R(T) 10. 271000T The process Y(t) is a version of X(t) delayed by 50 micro seconds. {Y(t) = X(t - t0)} (a) Derive the autocorrelation function of Y (t).
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- Find f'(x). T(x) = 2x° (x* - 2) 5 f'(x) =O5. Consider the process where S0 = 0 and {ut : t ∈ Z} is an i.i.d. random variable with N(0,σ2). a) DeterminethemeanandcovariancefunctionoftheprocessSt.Isthisprocessstrictlystationary?Second-order stationary? b) Show that the process Yt = (1 − L)St , t = 1,2,... is strictly stationary. Compute its mean and autocovariance function.Anation with fixed quantities of resources is able to produce any of the following combinations of carpet and carpet looms: Yards of Carpet (Millions) Carpet Looms (Thousands) 75 60 20 45 35 30 45 15 50 50 These figures assume that a certain number of previously produced looms are available in the current period for producing carpet. To answer this question, assume carpet looms is on the y-axis and yards of carpet is on the x-ais The plot of these points that make up the PPF has a vertical intercept of and a horizontal intercept of This PPF would be (Enter your responses as a wvhole number) bowed out a straight line
- The assumption that is required to shows the efficiency of the OLS estimator, consistency and unbiasedness is: i) Cov(u,,u-;) { A0 ii) Var(u,) =o? iii) E(u,) = 0 iv) u, ~ N(0,0²) a) (i), (ii) and (iii) only b) (i) and (iii) only c) (ii) and (iv) only d) (i), (ii) (iii) and (iv) Answer O A ODu (x1, x2) = x1x2 What is the value of MRS(4, 20)? (Don't forget to include a minus sign in your answer)If the annual rate of world oil consumption t years after 1970 is modeledby the equation R(t) = 16.1e^.07t (billions of barrels per year), how much total oil (net change) was used between 1976 and 1980?
- 5. Simulate the following AR(2) processes: Yt=1+0.3 Yt-1 +0.7 Yt-2+ɛtYt-1-0.3 Yt-1 -0.7 Yt-2+εt for øpt → N(0, 1). Comment on their differences: Contrast their time series and their autocorrelation functions. Comment on the covariance-stationary properties of both processes. 41%DEPENDENT VARIABLE Qc R- SQUARE P- VALUE ON F 64 0.8093 0.0001 INDEPENDENTVARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 8.20 4.01 2.04 0.0461 PC -3.54 1.64 -2.16 0.0357 M 0.64287 0.19 3.38 0.0014 PA 0.7854 0.38 2.07 0.0439 Explain the interceptand the coefficients of Pc, M, and PA.DEPENDENT VARIABLE Qc R- SQUARE P- VALUE ON F 64 0.8093 0.0001 INDEPENDENTVARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 8.20 4.01 2.04 0.0461 PC -3.54 1.64 -2.16 0.0357 M 0.64287 0.19 3.38 0.0014 PA 0.7854 0.38 2.07 0.0439 4. At the 5% level of significance, which variables are statistically significant?