ISYEl 6402l Finall Examl (Latestl 2025/l
2026l Update)l Review|l Q/Al |l Gradel A|l
100%l Correctl (Verifiedl Answers)
Q:l wherel isl stationarityl requiredl forl applicationl ofl models?
Answer:
MAl modelsl arel alwaysl stationary,l butl therel arel stilll spikesl inl thel earlyl
lags.
Bothl ARIMAl andl VARl modelsl canl onlyl fitl stationaryl residuals.
ARCHl andl GARCHl modelsl canl bel fitl onl datal withl non-constantl variancel
(andl thereforel they'rel notl stationary),l butl thel datal theyl fitl shouldl havel
constantl mean.
Q:l Checkingl residualsl ofl anl ARIMAl model
Answer:
Afterl fittingl anl ARIMAl model,l youl mustl checkl forl constantl variancel andl
normalityl ofl residuals.
Howl tol telll ifl normallyl distributedl noise?l Checkl Q-Ql plot/histogram.
Also,l canl usel JBl testl onl normality
, Wel canl alsol evaluatel whetherl thel residualsl havel constantl variancel byl
applyingl thel arch.testl Rl command,l whichl isl al hypothesisl testingl procedurel
wherel thel nulll hypothesisl isl thatl thel residualsl havel constantl variance.
Q:l Specifyingl lagl andl fitdfl inl thel Box.test
Answer:
Thel ACFl plotl suggestsl nol significantl autocorrelationl asl spikesl arel alll either
insignificantl orl closel tol 0.l Thel highl p-valuel froml thel Boxl testl confirmsl
this.
Box.test(resid(model.c),lag=24,type="Ljung",fitdf=5)
Lagl inl thel Box.testl -l lagl =l 2l xl seasonall differencingl e.g.l 12l forl monthly
Rememberl lagl mustl bel fitdfl +1l atl least
Forl fitdfl -l it'sl thel suml ofl Psl +l Qsl (bothl littlel andl bigl Psl andl Qs)
Q:l Isl ARCH-GARCHl al goodl candidatel forl al fat-tailedl QQl plot?
Answer:
Ideallyl GARCHl modelsl arel fitl tol residualsl thatl don'tl havel fatl tailsl inl theirl
Q-Ql plot.l Therel arel otherl betterl modelsl forl thisl case.
Q:l Isl anyl MAl modell stationary?
Answer:
2026l Update)l Review|l Q/Al |l Gradel A|l
100%l Correctl (Verifiedl Answers)
Q:l wherel isl stationarityl requiredl forl applicationl ofl models?
Answer:
MAl modelsl arel alwaysl stationary,l butl therel arel stilll spikesl inl thel earlyl
lags.
Bothl ARIMAl andl VARl modelsl canl onlyl fitl stationaryl residuals.
ARCHl andl GARCHl modelsl canl bel fitl onl datal withl non-constantl variancel
(andl thereforel they'rel notl stationary),l butl thel datal theyl fitl shouldl havel
constantl mean.
Q:l Checkingl residualsl ofl anl ARIMAl model
Answer:
Afterl fittingl anl ARIMAl model,l youl mustl checkl forl constantl variancel andl
normalityl ofl residuals.
Howl tol telll ifl normallyl distributedl noise?l Checkl Q-Ql plot/histogram.
Also,l canl usel JBl testl onl normality
, Wel canl alsol evaluatel whetherl thel residualsl havel constantl variancel byl
applyingl thel arch.testl Rl command,l whichl isl al hypothesisl testingl procedurel
wherel thel nulll hypothesisl isl thatl thel residualsl havel constantl variance.
Q:l Specifyingl lagl andl fitdfl inl thel Box.test
Answer:
Thel ACFl plotl suggestsl nol significantl autocorrelationl asl spikesl arel alll either
insignificantl orl closel tol 0.l Thel highl p-valuel froml thel Boxl testl confirmsl
this.
Box.test(resid(model.c),lag=24,type="Ljung",fitdf=5)
Lagl inl thel Box.testl -l lagl =l 2l xl seasonall differencingl e.g.l 12l forl monthly
Rememberl lagl mustl bel fitdfl +1l atl least
Forl fitdfl -l it'sl thel suml ofl Psl +l Qsl (bothl littlel andl bigl Psl andl Qs)
Q:l Isl ARCH-GARCHl al goodl candidatel forl al fat-tailedl QQl plot?
Answer:
Ideallyl GARCHl modelsl arel fitl tol residualsl thatl don'tl havel fatl tailsl inl theirl
Q-Ql plot.l Therel arel otherl betterl modelsl forl thisl case.
Q:l Isl anyl MAl modell stationary?
Answer:
