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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- Q2B. Which of the following are limitations of using Impulse Response Functions(IRFs) in time series analysis?i. IRFs are only valid for linear time series models.ii. IRFs assume that the underlying time series is stationary.iii. IRFs can provide information about the short-term dynamics of the relationshipbetween variables, but they do not capture longer-term effects or otherimportant aspects of the relationship.iv. IRFs depend on the specification of the model used to estimate the relationshipbetween variables.Why is base 10 logarithm (log) derived as a natural logarithm (1/x2)? Please confirm that derivate of logarithm of base 10 is in this case 1/[x2*log(10)] to modify your answer. Thank youFor arithmetic gradient solutions, the gradient starts _______ periods from Period 0. a N b 0 c 2 d 1
- Q6 Suppose that at time t=0, half of a "logistic" population of 100000 persons have heard a certain rumor and that the number of those who have heard it is then increasing at the rate of 500 persons per day. How long will it take for this rumor to spread to 80% of the population? ( Suggestion: Find the value of k by substituting P(0) and P'(0) in the logistic equation) a. About 98 days b. About 34 days c. About 19 days d. About 69 days e. About 119 daysSediment buildup behind a dam can adversely affect a reservoir's storage capacity. Measurements of a reservoir in 1988 showed it had a capacity of 500,000 acre-feet of water. Measurements in 2018 showed that the reservoir's capacity has been decreasing at a rate of 2,000 acre-feet per year. Find a linear model of the number of acre-feet A of water in the reservoir n years after 1988.Define the Ordinary Least Square estimator is linear and conditionally unbiased?
- With respect to a given product, describe the connection that exists between equalibrium/disequalibrium and prediction. cite an unique exampleThe demand function for Newton’s Donuts has been estimated as follows:Qx = -14 – 54Px + 45Py + 0.62Ax where Qx represents thousands of donuts; Px is the price per donut; Py is the average price per donut of other brands of donuts; and Ax represents thousands of dollars spent on advertising Newton’s Donuts. The current values of the independent variables are Ax=120, Px=0.95, and Py=0.64.Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary. Calculate the price elasticity of demand for Newton’s Donuts and describe what it means. Describe your answer and show your calculations. Derive an expression for the inverse demand curve for Newton’s Donuts. Describe your answer and show your calculations. If the cost of producing Newton’s Donuts is constant at $0.15 per donut, should they reduce the price and thereafter, sell more donuts (assuming profit maximization is the company’s goal)? Should Newton’s Donuts spend…Explain why the variables move together on this time trend. (Please see attachment and give proper correct explanation in typed format step by step within 40 min . Will give you thumbs up only for the correct answer . Thank you .)
- It is projected that in the future, the population of a certain country in millions will be P(t)= 85e^.05t, where t is is time in years since 2022. Round all answers to the nearest whole number a. What is the projected population of the town in 2026 b. Find the simplified derivative function c. At what rate will the population be changing in 2026 d. In what year was the population increasing at a rate of 5 million people per year e. When will the population reach 160 millionHello. May I ask how did you get the values? Were those only assumed values? Can you also explain how did you make the normal form thoroughly?A researcher has a sample of 6 annual observations {94, 104, 102, 99, 111 and 107} for the CPI in country Z for the period 2015 to 2020, and wants to forecast CPI for the years 2021, 2022 and 2023. The researcher uses 3 different forecasting models: A, B and C. Model A is an AR(1) model with no drift and with an estimated autoregressive coefficient = 0.7. Model B is a MA(1) model with no constant and with an estimated MA coefficient = -0.4 (note the minus !). Model C is a random walk model with no drift. The error terms over the 2015-2020 period were estimated to have the values: {3, -1, 2, 4, -3, 1}. a. Compute the 2021, 2022 and 2023 forecasted values for the consumer price index based on the three models. Show the formulas and the details of your calculations, and explain all the related symbols. b. Suppose that the actual values of the CPI over the 2021, 2022 and 2023 were {108, 114, 105}. Calculate the Root mean square error of the three model forecasts over the 2021-2023…