rstudio serie storiche, Tesine universitarie di Statistica

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> ###CARICAMENTI DATI

> library(readxl)

> Nat_nordest<-ts(Nat_nordest, start=2001, frequency=1)

> View(Nat_nordest)

> Nat_nordest

Time Series:

Start = 2001

End = 2014

Frequency = 1

Nordest

[1,] - 1.

[2,] - 1.

[3,] - 1.

[4,] - 0.

[5,] - 0.

[6,] - 0.

[7,] - 0.

[8,] - 0.

[9,] - 0.

[10,] - 0.

[11,] - 0.

[12,] - 1.

[13,] - 1.

[14,] - 1.

> plot(Nat_nordest, main= "Tasso di natalità nel Nord-est")

> ####STIMA TREND CON MM A 3 TERMINI

> Nat_nordest.fil2<-filter(Nat_nordest, filter=rep(1/3,3))

> plot(Nat_nordest.fil2, main="Trend stimato con media mobile - 'funzione

filter' ")

> ###DIFFERENZA SECONDA PER ELIMINARE IL TREND PARABOLICO

> Nat_nordest.diff<-diff(Nat_nordest,lag=1, differences=2)

> Nat_nordest.diff

Time Series:

Start = 2003

End = 2014

Frequency = 1

Nordest

[1,] - 0.

[2,] 1.

[3,] - 1.

[4,] 0.

[5,] - 0.

[6,] - 0.

[7,] 0.

[8,] - 0.

[9,] - 0.

[10,] - 0.

[11,] 0.

[12,] - 0.

> plot(Nat_nordest.diff, main= " Serie della natalità al Nord-est

detrendizzata")

> ##DECOMPOSIZIONE DELLA SERIE STORICA

> dec.fit<-decompose(natnordesttimeseries, type="multiplicative")

> stag.dec<-dec.fit$seasonal

> stag.dec

> trend.dec<-dec.fit$trend

> trend.dec

14 NA NA NA

> res.dec<-dec.fit$random

res.dec

14 1.0113009 1.0176101 1.0208431 1.0201087 1.0137623 0.9983872 NA NA NA NA NA

14 NA

• byrow = TRUE))/ > natnordest12=c(matrix(data=Nat_nordest,ncol=length(Nat_nordest),nrow=12,
• 1 - 0.08893843 - 0.08893843 - 0.08893843 - 0.08893843 - 0.08893843 - 0.08893843 - 0.08893843 - 0.08893843 - 0. Jan Feb Mar Apr May Jun Jul Aug Sep
• 2 - 0.08811368 - 0.08811368 - 0.08811368 - 0.08811368 - 0.08811368 - 0.08811368 - 0.08811368 - 0.08811368 - 0.
• 3 - 0.12032648 - 0.12032648 - 0.12032648 - 0.12032648 - 0.12032648 - 0.12032648 - 0.12032648 - 0.12032648 - 0.
• 4 - 0.02114133 - 0.02114133 - 0.02114133 - 0.02114133 - 0.02114133 - 0.02114133 - 0.02114133 - 0.02114133 - 0.
• 5 - 0.04306420 - 0.04306420 - 0.04306420 - 0.04306420 - 0.04306420 - 0.04306420 - 0.04306420 - 0.04306420 - 0.
• 6 - 0.01634642 - 0.01634642 - 0.01634642 - 0.01634642 - 0.01634642 - 0.01634642 - 0.01634642 - 0.01634642 - 0.
• 7 - 0.01861862 - 0.01861862 - 0.01861862 - 0.01861862 - 0.01861862 - 0.018618 62 - 0.01861862 - 0.01861862 - 0.
• 8 - 0.02584798 - 0.02584798 - 0.02584798 - 0.02584798 - 0.02584798 - 0.02584798 - 0.02584798 - 0.02584798 - 0.
• 9 - 0.02944902 - 0.02944902 - 0.02944902 - 0.02944902 - 0.02944902 - 0.02944902 - 0.02944902 - 0.02944902 - 0.0294
• 10 - 0.03768596 - 0.03768596 - 0.03768596 - 0.03768596 - 0.03768596 - 0.03768596 - 0.03768596 - 0.03768596 - 0.
• 11 - 0.06622735 - 0.06622735 - 0.06622735 - 0.06622735 - 0.06622735 - 0.06622735 - 0.06622735 - 0.06622735 - 0.
• 12 - 0.11174353 - 0.11174353 - 0 .11174353 - 0.11174353 - 0.11174353 - 0.11174353 - 0.11174353 - 0.11174353 - 0.
• 13 - 0.12500257 - 0.12500257 - 0.12500257 - 0.12500257 - 0.12500257 - 0.12500257 - 0.12500257 - 0.12500257 - 0.
• 14 - 0.13916263 - 0.13916263 - 0.13916263 - 0.13916263 - 0.13916263 - 0.13916263 - 0.13916263 - 0.13916263 - 0.
• 1 - 0.08893843 - 0.08893843 - 0. Oct Nov Dec
• 2 - 0.08811368 - 0.08811368 - 0.
• 3 - 0.12032648 - 0.12032648 - 0.
• 4 - 0.02114133 - 0.02114133 - 0.
• 5 - 0.0430642 0 - 0.04306420 - 0.
• 6 - 0.01634642 - 0.01634642 - 0.
• 7 - 0.01861862 - 0.01861862 - 0.
• 8 - 0.02584798 - 0.02584798 - 0.
• 9 - 0.02944902 - 0.02944902 - 0.
• 10 - 0.03768596 - 0.03768596 - 0.
• 11 - 0.06622735 - 0.06622735 - 0.06622
• 12 - 0.11174353 - 0.11174353 - 0.
• 13 - 0.12500257 - 0.12500257 - 0.
• 14 - 0.13916263 - 0.13916263 - 0.
• 1 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov
• 2 1.0371964 1.021 6788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 3 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 4 1.0371964 1.0216788 1.0095433 1.0015182 0.999 1325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 5 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 6 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 7 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 8 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 9 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 10 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 11 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 12 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 13 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 14 1.0371964 1.0216788 1.0095433 1.0015182 0.9991325 1.0058800 1.0073095 0.9943596 0.9850748 0.9795117 0.
• 1 0. Dec
• 2 0.
• 3 0.
• 4 0.
• 5 0.
• 6 0.
• 7 0.
• 8 0.
• 9 0.
• 10 0.
• 11 0.
• 12 0.
• 13 0.
• 14 0.
• 1 NA NA NA NA NA NA - 0.08890407 - 0.08883534 - 0. Jan Feb Mar Apr May Jun Jul Aug Sep
• 2 - 0.08849169 - 0.08842296 - 0.0883 5423 - 0.08828550 - 0.08821678 - 0.08814805 - 0.08945588 - 0.09214028 - 0.
• 3 - 0.10556228 - 0.10824668 - 0.11093108 - 0.11361548 - 0.11629988 - 0.11898428 - 0.11619377 - 0.10792834 - 0.
• 4 - 0.06660119 - 0.05833577 - 0.05007034 - 0.04180491 - 0.03353948 - 0.02 527405 - 0.02205479 - 0.02388169 - 0.
• 5 - 0.03301622 - 0.03484313 - 0.03667003 - 0.03849694 - 0.04032384 - 0.04215075 - 0.04195096 - 0.03972448 - 0.
• 6 - 0.02859207 - 0.02636558 - 0.02413910 - 0.02191262 - 0.01968614 - 0.01745966 - 0.01644109 - 0.01663044 - 0.
• 7 - 0.01757719 - 0.01776654 - 0.01795589 - 0.01814524 - 0.01833459 - 0.01852394 - 0.01891984 - 0.01952229 - 0.
• 8 - 0.02253452 - 0.02313697 - 0.02373942 - 0.02434186 - 0.02494431 - 0.02554676 - 0.02599802 - 0.02629811 - 0.
• 9 - 0.02779854 - 0.02809863 - 0.02839871 - 0.02869880 - 0.02899889 - 0.02929897 - 0.02979222 - 0.03047863 - 0.
• 10 - 0.03391069 - 0.03459711 - 0.03528352 - 0.03596993 - 0.03665634 - 0.03734275 - 0.03887518 - 0.04125363 - 0.
• 11 - 0.05314588 - 0.05552433 - 0.05790278 - 0.0602812 3 - 0.06265967 - 0.06503812 - 0.06812386 - 0.07191687 - 0.
• 12 - 0.09088194 - 0.09467496 - 0.09846797 - 0.10226099 - 0.10605400 - 0.10984702 - 0.11229599 - 0.11340091 - 0.
• 13 - 0.11892551 - 0.12003043 - 0.12113535 - 0.12224027 - 0.12334519 - 0.12445011 - 0.12559 258 - 0.12677258 - 0.
• 1 - 0.08869788 - 0.08862915 - 0. Oct Nov Dec
• 2 - 0.09750908 - 0.10019348 - 0.
• 3 - 0.09139748 - 0.08313205 - 0.
• 4 - 0.02753550 - 0.02936241 - 0.
• 5 - 0.03527151 - 0.03304503 - 0.
• 6 - 0.01700914 - 0.01719849 - 0.
• 7 - 0.02072718 - 0.02132963 - 0.
• 8 - 0.02689828 - 0.02719837 - 0.
• 9 - 0.03185146 - 0.0325 3787 - 0.
• 10 - 0.04601053 - 0.04838898 - 0.
• 11 - 0.07950290 - 0.08329591 - 0.
• 12 - 0.11561075 - 0.11671567 - 0.
• 13 - 0.12913259 - 0.13031260 - 0.
• 1 NA NA NA NA NA NA 0.9931272 1.0068395 1.0171163 1.0236856 1. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov
• 2 0.9600191 0.9753577 0.98785 01 0.9965408 0.9996986 0.9937668 0.9778483 0.9617237 0.9433063 0.9225473 0.
• 3 1.0989843 1.0880084 1.0744421 1.0574622 1.0355209 1.0053689 1.0280528 1.1211978 1.2256274 1.3440560 1.
• 4 0.3060479 0.3547179 0.4182413 0.5049476 0.6308891 0.83159 41 0.9516266 0.8902742 0.8348045 0.7838442 0.
• 5 1.2575581 1.2097201 1.1632690 1.1169439 1.0688860 1.0156987 1.0190877 1.0902214 1.1658405 1.2464724 1.
• 6 0.5512086 0.6068352 0.6707744 0.7448509 0.8310725 0.9307663 0.9870268 0.9884968 0.98658 09 0.9811390 0.
• 7 1.0212615 1.0257231 1.0271066 1.0245327 1.0163730 0.9992354 0.9769380 0.9591207 0.9391783 0.9170596 0.
• 8 1.1059036 1.0934672 1.0785285 1.0602638 1.0371272 1.0058765 0.9870140 0.9884589 0.9865185 0.9810529 0.
• 9 1.02 13811 1.0258203 1.0271815 1.0245855 1.0164041 0.9992455 0.9813071 0.9716991 0.9592544 0.9439128 0.
• 10 1.0714747 1.0661674 1.0579929 1.0461191 1.0289811 1.0032913 0.9623746 0.9187004 0.8768078 0.8362049 0.
• 11 1.2014530 1.1674537 1.1329560 1.09 69743 1.0578550 1.0123325 0.9651064 0.9261111 0.8880053 0.8504422 0.
• 12 1.1854515 1.1552417 1.1240935 1.0910723 1.0545623 1.0113184 0.9878595 0.9909742 0.9906622 0.9867668 0.
• 13 1.0134048 1.0193262 1.0221699 1.0210472 1.0143169 0.9985676 0.98 80798 0.9916311 0.9917465 0.9882651 0.
• 1 1. Dec
• 2 0.
• 3 1.
• 4 0.
• 5 1.
• 6 0.
• 7 0.
• 8 0.
• 9 0.
• 10 0.
• 11 0.
• 12 0.
• 13 0.

s9 1.001939e+

s10 1.002716e+

s11 1.003493e+

s12 1.004272e+

> plot(Nat_nordest.hw,main="Holt-Winters filtering Nord-est")

> #PREVISIONE CON HOLT-WINTERS

> prev<-predict(Nat_nordest.hw, n.ahead = 12)

> prev

Jan Feb Mar Apr May Jun Jul

Aug Sep Oct

Nov Dec

> plot(prev,main="Previsione 2015")

> #ISTOGRAMMA DEI RESIDUI

> hist(res.dec,main="Distribuzione dei residui: istogramma",xlab="Residui")

> abline(0,1)

> ##ANALISI PRELIMINARE PER VEDERE SE C'E' STAZIONARIETA'

> acf(Nat_nordest,main="Correlogramma globale Centro")

> pacf(Nat_nordest,main="Correlogramma parziale Centro")

> #VERIFICA DELLA STAZIONARIETA' DELLA SERIE DIFFERENZIATA

> acf(natnordest.diff.st,main="Correlogramma globale delle serie

differenziata")

> pacf(natnordest.diff.st,main="Correlogramma parziale delle serie

differenziata")

> #2^STIMA ARIMA

> stima2<-arima(Nat_nordest,order = c(2,2,1))

> stima

Call:

arima(x = Nat_nordest, order = c(2, 2, 1))

Coefficients:

ar1 ar2 ma

s.e. 0.6273 0.5741 0.

sigma^2 estimated as 0.1635: log likelihood = - 6.88, aic = 21.

> tsdiag(stima2)

> #3^STIMA ARIMA

> stima3<-arima(Nat_nordest,order = c(2,0,1))

> stima

Call:

arima(x = Nat_nordest, order = c(2, 0, 1))

Coefficients:

ar1 ar2 ma1 intercept

s.e. 0.5530 0.3919 0.5720 0.

sigma^2 estimated as 0.1374: log likelihood = - 6.37, aic = 22.

> tsdiag(stima3)

> ###TEST DI LJUNG-BOX

> lb<-Box.test(Nat_nordest,lag=1, type ="Ljung-Box")

> lb

Box-Ljung test

data: Nat_nordest

X-squared = 5.991, df = 1, p-value = 0.

> ###JARQUE E BERA

> library("normtest", lib.loc="~/R/win-library/3.3")

> jb.norm.test(Nat_nordest, nrepl=200)

Jarque-Bera test for normality

data: Nat_nordest

JB = 1.4857, p-value = 0.

> ###PREVISIONE CON t=

> previsioni<-arima(Nat_nordest, order=c(1,2,1))

> predict(previsioni, n.ahead=2)

$pred

Time Series:

Start = 2015

End = 2016

Frequency = 1

[1] - 1.929349 - 2.

$se

Time Series:

Start = 2015

End = 2016

Frequency = 1

[1] 0.4164981 0.