Name and discuss the four. methods of measuring cyclic variation
2.define a moving average process of order p and show that it is second stationary.Find it's autocorrelation function.
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where at is a white noise process with unit variance. It is known that the above process is overestimated.(a) Suggest a parismony model ARMA(2,1) for the above process.(b) Hence, determine the stationarity and invertibility of the process.(c) Find the mean, the variance and the first two lags of the autocovariance function of theprocess.(d) Find the first three lags of the autocorrelation function (ACF) for the process.(e) Find the first three lags of the partial autocorrelation coefficients.
True or false? You do not have to provide explanations. (a) Any moving average (MA) process is covariance stationary. (b) Any autoregressive (AR) process is invertible. (c) The autocorrelation function of an MA process decays gradually while the partial autocorrelation function exhibits a sharp cut-off. (d) Suppose yt is a general linear process. The optimal 2-step-ahead prediction error follows MA(2) process. (e) Any autoregressive moving average (ARMA) process is invertible because any moving average (MA) process is invertible. (f) The...
Use your knowledge of the relationship between spectral density and autocorrelation function in order to answer the following questions. Show your work for full credit. Determine the spectral density of a process with autocorrelation function Rx(t) = 3e-2t a) Determine the spectral density of a process with autocorrelation function Rx(t)-2 sinc(0.51) b) c) Determine the autocorrelation function of a process with spectral density Sx (f) 2 sinc2(f/2) 12 Determine the autocorrelation function ofa process with spectral density Sx(a)-A+ d) Use...
Below you are given the first four values of a time series. Time Period Time Series Value 1 18 2 20 25 17 Using a fourth-order moving average, the forecasted value for period 5 is 2.5 20 O 17 10
(1) Explain smoothing methods in time series. How to find the opti- mal value of the smoothing parameter in an exponentially weighted moving average. (2) Prove that ARCH(1) process is leptokurtic. Also establish its equiv- alence to AR process. (3) Prove that exponentially weighted moving average model is a special case of GARCH(1,1) processes. Also establish its equivalence to ARMA(1,1) process. (4) Find the minimum mean square error (MMSE) forecast of AR(2) process and then obtain the variance of the...
Recall that a time series {εt} is called a white noise process if i. E[εt] = 0 t ; ii. Cov(εs, εt) = 0 s ≠ t ; iii. Var(εt) = σ2 < ∞ Construct the autocorrelation function f(h), h=0,-+1,-+2,… for the white noise process.
The time series {} is said to be an AR(2) process if , where {} is a white noise process with variance < a) For what values of is the process weakly stationary? b) Select in the range where the process is weakly stationary and plot the autocorrelation function for the chosen We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
1. [30 pts! Let Yǐ follow a moving average process of order 1 (ie, MA(1): where e is a white noise process with N(0,1). Suppose that you estimate the model using STATA. You obtain ê-1, ê-0.5 and ớ2-1. You also know e,-2 and E1-1-3. (a) Obtain the unconditional mean and variance of Y (b) Obtain Cor(Y, Yi-1). (c) Obtain the autocorrelation of order 1 for Y 1. [30 pts! Let Yǐ follow a moving average process of order 1 (ie,...
3. (10 points) The Hamiltonian for a particle moving in a vertical uniform gravitational field g is 2 Hmgq where q is the altitude above the ground. We want to find any canonical transformation from old variables (q,p) to new variables (Q,P) which provides a cyclic coordinate. To do this, define new variables as where a, b are constants. a) Determine any combination of constants a and b, which provides a canonical transformation b) Find the type 1 generating function,...
2. Let G {g, g. . . , gn-le} be a cyclic group of order n, H a group, and h є H. Define a function φ : G → H by φ(gi-hi for all 0 < i n-1. Show that φ is a group homomor- phism if and only if o(h) divides o(g). Warning: mind your modular arithmetic! [10]