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Given observations X1 = 1, X2 = 1.5, X3 = 1.2 and X4 calculate the residuals at times t = 1 and t = 2. (b) Consider a SARMA(1,0) × (1,1)4 process. State the condit on the model parameters so that the process is stationary. (c) A researcher attempts to fit a zero-mean ARMA(1, 1) model time series of T = 100 data points. The analysis gives that 100

Given observations X1 = 1, X2 = 1.5, X3 = 1.2 and X4 calculate the residuals at times t = 1 and t = 2. (b) Consider a SARMA(1,0) × (1,1)4 process. State the condit on the model parameters so that the process is stationary. (c) A researcher attempts to fit a zero-mean ARMA(1, 1) model time series of T = 100 data points. The analysis gives that 100

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Q3 (a) Consider the ARMA(2, 1) model X; = X,-1 -X1-2+ €4 + &4-1 %3D Given observations X1 = 1, X2 = 1.5, X3 = 1.2 and X4 = 2, [3] calculate the residuals at times t = 1 and t = 2. (b) Consider a SARMA(1,0) × (1, 1)4 process. State the conditions on the model parameters so that the process is stationary. [3] (c) A researcher attempts to fit a zero-mean ARMA(1, 1) model to a time series of T = 100 data points. The analysis gives that 100 Ele - ē)? = 50.5 t=1 where e, is the estimated residual at time t, and ē = E et/100. This sum of squares is found to be 48.5 when attempting to fit a zero-mean ARMA(2,2) model at the same data. Which of the two models, ARMA(1, 1) and ARMA(2,2), provides a better fit to the data according to the AIC criterion? You are reminded of the formula AIC = TIn(s) + 2k from the course notes with appropriately defined terms. You may also use some of the following logarithms: In(50.5) = 3.92, In(48.5) = 3.88, In(95) = 4.55, In(97) = 4.57, In(99) = 4.60, In(100) = 4.61. [5]
Transcribed Image Text:Q3 (a) Consider the ARMA(2, 1) model X; = X,-1 -X1-2+ €4 + &4-1 %3D Given observations X1 = 1, X2 = 1.5, X3 = 1.2 and X4 = 2, [3] calculate the residuals at times t = 1 and t = 2. (b) Consider a SARMA(1,0) × (1, 1)4 process. State the conditions on the model parameters so that the process is stationary. [3] (c) A researcher attempts to fit a zero-mean ARMA(1, 1) model to a time series of T = 100 data points. The analysis gives that 100 Ele - ē)? = 50.5 t=1 where e, is the estimated residual at time t, and ē = E et/100. This sum of squares is found to be 48.5 when attempting to fit a zero-mean ARMA(2,2) model at the same data. Which of the two models, ARMA(1, 1) and ARMA(2,2), provides a better fit to the data according to the AIC criterion? You are reminded of the formula AIC = TIn(s) + 2k from the course notes with appropriately defined terms. You may also use some of the following logarithms: In(50.5) = 3.92, In(48.5) = 3.88, In(95) = 4.55, In(97) = 4.57, In(99) = 4.60, In(100) = 4.61. [5]
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