A time series {yt} follows an MA(2) model: Yt = 2 + Ut +0.54t-1 + 0.4ut-2. Assume that ut is a white noise series with a mean of O and a variance of 2. Please calculate Var(yt) (i.e. the varianc
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A time series {yt} follows an MA(2) model: Yt = 2 + Ut +0.54t-1 + 0.4ut-2. Assume that ut is a white noise series with a mean of O and a variance of 2. Please calculate Var(yt) (i.e. the variance of) 2.96 1.41 2.82 O 1.98
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- A time series {yt} follows an MA(2) model: Yt = 2 + Ut +0.54t-1 + 0.4ut-2. Assume that ut is a white noise series with a mean of O and a variance of 2. Please calculate Var(yt) (i.e. the variance of) 2.96 1.41 2.82 O 1.98 Please give me typed answer sirsolveIn random sampling from the exponential distribution, f(x) =1 θθe x− , x > 0, θ> 0, find the maximum likelihood estimator of θ and obtain the asymptotic distribution of this estimatorIf X is a uniformly distributed random varibale with a=9 and b=16, then Calculate the variance of X? Round to three decimal places
- Let i_t denote the effective annual return achieved on an equity fund achieved between time (t -1) and time t. Annual log-returns on the fund, denoted by In(1 + i_t) , are assumed to form a series of independent and identically distributed Normal random variables with parameters u = 6% and o = 14%.An investor has a liability of £10,000 payable at time 15. Calculate the amount of money that should be invested now so that the probability that the investor will be unable to meet the liability as it falls due is only 5%. Using only formulas, no tablesThe lifetime of an inexpensive light bulb is an exponential random variable with a mean of 36 hours. Suppose 16 light bulbs are tested in order to have their lifetime measured. Use the central limit theorem to estimate the probability that the sum of the lifetimes is less than 600 hours. Hint: the mean m in the proof of the central limit theorem is given by myn = nm, where n is the number of tests. The variance is given by σyn = σ √ n.Consider a cohort of patients receiving an experimental two-year treatment for a serious disease. Suppose that only 20% of the patients survive to the end of the second year. Assume CFM (constant force of mortality) within each year of treatment. Find the probability that a patient who survives the first four months dies by the end of the 20th month. Round to 4 decimal places.
- The distance between two subsequent rust attacks is exponentially distributed with parameter λ (the distancebetween subsequent events in a Poisson process is exponentially distributed), and we still assumethat λ = 5 per kilometer.What is the probability that the distance between two consecutive rust attacks is between 200and 300 meters ?Consider a process consisting of a linear trend with an additive noise termconsisting of independent random variables wt with zero means and variancesσ2w, that is,xt = β0 + β1t + wt,where β0, β1 are fixed constants.(a) Prove xt is nonstationary.(b) Prove that the first difference series ∇xt = xt − xt−1 is stationary byfinding its mean and autocovariance function.(c) Repeat part (b) if wt is replaced by a general stationary process, say yt,with mean function µy and autocovariance function γy(h)
