PLEASE ANSWER PART (A) AND (B) Problem 1. Let c, t = 1,...,n be the cmort time series from the astsapackage. Here n = 508. Let r, = Ve be the first differenced time series.(a) Plot both ct and rt. Discuss whether differencing seems a reasonabletransformation for cmort. What is the length of r;?(b) Show the sample ACF and PACF plots for r. Is an AR(1) model areasonable identification for r? Why?(c) Fit an AR(1) model to z4, t = 1,...,508, using the method of conditionalML, using(i) the ar.mle function(ii) the arima function(iii) sarima: astsa function.Make sure you can write out the fitted AR(1) model by pulling out relevantinformation from each function's output.(d) Is the AR(1) coefficient o significant? Discuss.(e) How will you determine whether the residuals from the AR(1) fit are WNor not?(f) For each case in (c), construct L = 4 step-ahead forecasts for a given allthe past data, and get the 95% forecast intervals. Make sure you learn touse the predict() function in R and the sarima.for() function in astsa.(g) From (f), and using the relation between a, and c, write down the forecastfor c509 from the fitted AR(1) model. That is, what is C508 (1) = ĉ509?(h) What ARIMA model does c; follow, when r; is an AR(1)?

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Description: PLEASE ANSWER PART (A) AND (B) Problem 1. Let c, t = 1,...,n be the cmort time series from the astsapackage. Here n = 508. Let r, = Ve be the first differenced time series.(a) Plot both ct and rt. Discuss whether differencing seems a reasonabletrans

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Problem 1. Let c, t 1,...,n be the cmort tine series from the astsa package. Here n = 508. Let z = Vc be the first differenced time series. (a) Plot both c and z. Discuss whether differencing seems a reasonable transformation for cmort. What is the length of r? (b) Show the sample ACF and PACF plots for rt. Is an AR(1) model a reasonable identification for r,? Why?

Problem 1. Let c, t 1,...,n be the cmort tine series from the astsa package. Here n = 508. Let z = Vc be the first differenced time series. (a) Plot both c and z. Discuss whether differencing seems a reasonable transformation for cmort. What is the length of r? (b) Show the sample ACF and PACF plots for rt. Is an AR(1) model a reasonable identification for r,? Why?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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PLEASE ANSWER PART (A) AND (B)

Problem 1. Let c, t = 1,...,n be the cmort time series from the astsa
package. Here n = 508. Let r, = Ve be the first differenced time series.
(a) Plot both ct and rt. Discuss whether differencing seems a reasonable
transformation for cmort. What is the length of r;?
(b) Show the sample ACF and PACF plots for r. Is an AR(1) model a
reasonable identification for r? Why?
(c) Fit an AR(1) model to z4, t = 1,...,508, using the method of conditional
ML, using
(i) the ar.mle function
(ii) the arima function
(iii) sarima: astsa function.
Make sure you can write out the fitted AR(1) model by pulling out relevant
information from each function's output.
(d) Is the AR(1) coefficient o significant? Discuss.
(e) How will you determine whether the residuals from the AR(1) fit are WN
or not?
(f) For each case in (c), construct L = 4 step-ahead forecasts for a given all
the past data, and get the 95% forecast intervals. Make sure you learn to
use the predict() function in R and the sarima.for() function in astsa.
(g) From (f), and using the relation between a, and c, write down the forecast
for c509 from the fitted AR(1) model. That is, what is C508 (1) = ĉ509?
(h) What ARIMA model does c; follow, when r; is an AR(1)?

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ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated