Suppose now the time series is linear trend + cycle processYt = c + Bt + Ct + €tE4 ~ WN(0, o²)(a) Suppose the Cţ is as in MA(1) process. Which process does the first difference follow ?(b) Suppose the Cţ is as in AR(1) process. Which process does the first difference follow ?(c) Extend this reasoning for the case of Ct following ARMA(p,q).(d) What effect does taking differences have on time series dynamics ?

Answered: Image /qna-images/answer/98b85b82-53e4-4bf6-8b03-6572d7971106.jpg

Answered: Suppose now the time series is linear…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the time series data for the real consumption of households and government from year 1950 to year 2019. Five autoregressive models, AR(1) to AR(5), are estimated as follows, where the t statistics for the corresponding estimated coefficients are in the parentheses, and the size of the samples, n, used for each estimation is also shown in the table. According to the significant lag approach, which model is the optimal under the 5% significance level? AR(1) AR(2) AR(3) AR(4) AR(5) 5365.55 7681.51 intercept t stat 5854.66 5041.07 5689.50 (2.44) (2.05) (2.13) 0.92 (2.13) (2.82) rcont-1 0.82 0.92 0.92 0.92 t stat (315.53) (9.49) (9.41) (9.33) (9.57) -0.26 rcont-2 -0.18 -0.28 -0.27 t stat (-1.38) (-1.38) (-1.31) (-1.32) rcon-s 0.08 0.02 0.07 t stat (0.64) (0.09) (0.32) rcont-4 0.06 -0.32 t stat (0.38) (-1.47) rcont-s 0.34 t stat (2.32) 65 65 65 65 65 AIC 18.30 18.30 18.33 18.36 18.29 BIC 18.37 18.40 18.46 18.52 18.50 O A. AR(2). O B. AR(1). O C. none. D. AR(5).
(a) Every working day, Alan reverses his car from his driveway on to the road in such a way that there is a very small probability p that his car will be involved in a collision. (i) Show that the probability that there will be no collision in a five-day week is (1– p)³. (ii) State one assumption that is made in your answer above. (iii) Let p 0.001. Check that the Poisson approximation can be used, and find the approximate probability that Alan will avoid a collision in 500 working days. Round your answer to 4 decimal places. (b) Organisms are present in ballast water discharged from a ship according to a Poisson pro- cess with a concentration of 4 organisms per cubic meter. Find the probability that the number of organisms in 1.5 cubic meter of discharge exceeds its mean value by more than one standard deviation. Round your answer to 4 decimal places. (c) The number of times that a person gets a cold in a given year is a Poisson random variable with parameter A = 5. Suppose that a new…
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Pedestrians approach a crossing from the left and right sides following independent Poisson processes withaverage arrival rates of λL = 5 and λR = 1 arrivals per minute. Each pedestrian then waits until a lightis flashed, at which time all waiting pedestrians must cross to the opposite side (either from left to right orfrom right to left). Assume that the left and right arrival processes are independent, that the light flashesevery T = 2 minutes, and that crossing takes zero time – it is instantaneous.1. What is the probability that in a particular crossing, there are total 10 pedestrian and they are allcrossing from left to right?
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