SAS/ETS. Séries Temporais Usando o SAS. Kim Samejima. November 4, 2018 UFBA. Kim Samejima (UFBA) SAS/ETS November 4, / 22

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1 SAS/ETS Séries Temporais Usando o SAS Kim Samejima UFBA November 4, 2018 Kim Samejima (UFBA) SAS/ETS November 4, / 22

2 SAS Datasets Criando libnames e tabelas SAS (datasets) data lib.dboutput(keep= drop= rename=(old=new) ); set lib.dbinput; variavel=conta; if condicao then ; where ; keep var1 var2...; drop var1 var2...; Kim Samejima (UFBA) SAS/ETS November 4, / 22

3 SAS Datasets Dataset a partir de um datalines libname matd51 '/courses/dbedd0adba27fe300'; data matd51.pibbr; input ano pibbruto pibpcap ; /*ano $char5.;*/ format ano $char5. pibbruto 8.3 pibpcap 5.; datalines; ; Kim Samejima (UFBA) SAS/ETS November 4, / 22

4 SAS Datasets /* USANDO OPÇÃO PARA MULTIPLAS ENTRADAS EM UMA SO LINHA */ data body_fat; input Gender $ datalines; m 13.3 f 22 m 22 f 23.2 m 16 m 12 ; proc print data=body_fat; title 'Results of Body Fat Testing'; Kim Samejima (UFBA) SAS/ETS November 4, / 22

5 SAS Datasets Criando datasets a partir de um arquivo texto DATA matd51.desemprego1; infile '/home/samejimal0/my_content/unemployed1.txt'; input month $ t unemplyd; proc print data = matd51.desemprego1(obs=10); /*'noobs' : nao imprimir numero das linhas*/ proc contents; /*data=matd51.desemprego1;*/ Kim Samejima (UFBA) SAS/ETS November 4, / 22

6 SAS Datasets Manipulação dos dados /*Ordenação dos dados*/ proc sort data=a; by var; *desc; Subset dos dados a partir de uma tabela existente data subset; set full; where date >= '1jan2001'd; if UF = 'BA'; where date >= '1jan2001'd & UF = 'BA'; Kim Samejima (UFBA) SAS/ETS November 4, / 22

7 SAS Gráficos Gráficos /* Graphical Options */ AXIS1 LABEL=(ANGLE=90 'unemployed'); AXIS2 LABEL=('t'); SYMBOL1 V=DOT C=GREEN I=JOIN H=0.4 W=1; PROC GPLOT DATA=matd51.desemprego1; PLOT unemplyd*t / VAXIS=AXIS1 HAXIS=AXIS2; RUN; Figure: Série de Desemprego Kim Samejima (UFBA) SAS/ETS November 4, / 22

8 Modelos de tendência e sazonalidade no SAS Tendência: Regressão Linear Figure: Série do PIB Kim Samejima (UFBA) SAS/ETS November 4, / 22 Série de PIB Brasileiro DATA matd51.pibbr2; set matd51.pibbr2; date=intnx('year','01jan01'd,_n_-1); FORMAT date yymon.; AXIS1 LABEL=(ANGLE=90 'pib bruto'); AXIS2 LABEL=('t'); SYMBOL1 V= star C=blue I=JOIN; PROC GPLOT DATA=matd51.pibbr2; PLOT pibbruto*date/ VAXIS=AXIS1 HAXIS=AXIS2; RUN;

9 Modelos de tendência e sazonalidade no SAS Tendência: Regressão Linear Figure: Ajuste de Regressão linear para a Série do PIB Kim Samejima (UFBA) SAS/ETS November 4, / 22 Ajustes de tendência PROC REG DATA=matd51.pibbr2; MODEL pibbruto=date; OUTPUT OUT=regdat P=predi; RUN; AXIS1 LABEL=(ANGLE=90 'temperatures'); AXIS2 LABEL=('Date'); SYMBOL1 V=DOT C=blue H=1 W=1; SYMBOL2 V=STAR C=GREEN I=JOIN H=1 W=1; /* Plot data and seasonally adjusted series */ PROC GPLOT data=regdat ; PLOT pibbruto*date=1 predi*date=2 /OVERLAY VAXIS=AXIS1 HAXIS=AXIS2; RUN;

10 Modelos de tendência e sazonalidade no SAS Sazonalidade Dados de Temperatura TITLE1 'Original and seasonally adjusted data'; TITLE2 'Temperatures data'; DATA temperatures; INFILE '/home/samejimal0/my_content/temperatures.txt'; INPUT matd51.temperature; date=intnx('month','01jan95'd,_n_-1); FORMAT date yymon.; Kim Samejima (UFBA) SAS/ETS November 4, / 22

11 Modelos de tendência e sazonalidade no SAS Sazonalidade Ajustes de sazonalidade /* Make seasonal adjustment */ PROC TIMESERIES DATA=matd51.temperatures OUT=matd51.series_temp SEASONALITY=12 OUTDECOMP=matd51.deseason_temp; VAR temperature; DECOMP /MODE=ADD; /* Merge necessary data for plot */ DATA matd51.plotseries_temp; MERGE matd51.temperatures matd51.deseason_temp(keep=sa); by date; Kim Samejima (UFBA) SAS/ETS November 4, / 22

12 Modelos de tendência e sazonalidade no SAS Sazonalidade Gráfico da série e do ajuste /* Graphical options */ AXIS1 LABEL=(ANGLE=90 'temperatures'); AXIS2 LABEL=('Date'); SYMBOL1 V=DOT C=GREEN I=JOIN H=1 W=1; SYMBOL2 V=STAR C=GREEN I=JOIN H=1 W=1; /* Plot data and seasonally adjusted series */ PROC GPLOT data=plotseries; PLOT temperature*date=1 SA*date=2 /OVERLAY VAXIS=AXIS1 HAXIS=AXIS2; RUN; Figure: Ajuste de sazonalidade para a série de temperaturas Kim Samejima (UFBA) SAS/ETS November 4, / 22

13 ACF e PACF Filtro Diferença e ACF /* Read in the data, generate year of observation and compute first order differences */ DATA matd51.sunspots; set matd51.sunspots; date=1748+_n_; diff1=dif(n_spots); /* Compute autocorrelation function */ PROC ARIMA DATA=matd51.sunspots_2; IDENTIFY VAR= n_spots NLAG=49 OUTCOV=dbcorr_nspots NOPRINT; PROC ARIMA DATA=matd51.sunspots_2; IDENTIFY VAR= diff1 NLAG=49 OUTCOV=dbcorr_dif NOPRINT; data matd51.corr_nspots (keep = lag corr_dif corr_nspots partcorr_dif partcorr_nspots); merge dbcorr_dif (rename = (corr = corr_dif partcorr = partcorr_dif )) dbcorr_nspots (rename = (corr = corr_nspots partcorr = partcorr_nspots)); by lag; Kim Samejima (UFBA) SAS/ETS November 4, / 22

14 ACF e PACF Figure: ACF para série de manchas solares Kim Samejima (UFBA) SAS/ETS November 4, / 22 Plotagem da ACF TITLE1 'Correlogram of first order differences'; TITLE2 'Sunspot Data'; /* Graphical options */ AXIS1 LABEL=('r(k)'); AXIS2 LABEL=('k') ORDER=( ) MINOR=(N=11); SYMBOL1 V=DOT C=GREEN I=JOIN H=0.5 W=1; SYMBOL2 V=star C=blue I=JOIN H=0.5 W=1; /* Plot autocorrelation function */ PROC GPLOT DATA=matd51.corr_nspots; PLOT corr_nspots*lag corr_dif*lag / overlay VAXIS=AXIS1 HAXIS=AXIS2 VREF=0; RUN;

15 ACF e PACF Figure: PACF para série de manchas solares Kim Samejima (UFBA) SAS/ETS November 4, / 22 Plotagem da PACF TITLE1 'Correlogram of first order differences'; TITLE2 'Sunspot Data'; /* Graphical options */ AXIS1 LABEL=('r(k)'); AXIS2 LABEL=('k') ORDER=( ) MINOR=(N=11); SYMBOL1 V=DOT C=GREEN I=JOIN H=0.5 W=1; SYMBOL2 V=star C=blue I=JOIN H=0.5 W=1; /* Plot autocorrelation function */ PROC GPLOT DATA=matd51.corr_nspots; PLOT partcorr_nspots*lag partcorr_dif*lag / overlay VAXIS=AXIS1 HAXIS=AXIS2 VREF=0; RUN;

16 Análise Espectral Periodograma Série Star /* star_periodogram.sas */ TITLE1 'Star Data plot'; /* Read in the data */ DATA data1; INFILE '/home/samejimal0/my_content/star.txt'; INPUT lumen Kim Samejima (UFBA) SAS/ETS November 4, / 22

17 Análise Espectral Periodograma Calculando o Periodograma /* Compute the periodogram */ PROC SPECTRA DATA=MATD51.star P OUT=MATD51.periodograma_star; /*'p' é a opção para calcular o periodograma*/ VAR lumen; /* Adjusting different periodogram definitions */ DATA periodograma_star;/*pp.146*/ SET MATD51.periodograma_star(FIRSTOBS=2); /*FIRSTOBS=k ignora as k lambda=freq/(2*constant('pi'));/* corrigindo a definicao para freq DROP FREQ; Kim Samejima (UFBA) SAS/ETS November 4, / 22

18 Análise Espectral Periodograma Plotando o Periodograma /* Graphical options */ SYMBOL1 V=NONE C=GREEN I=JOIN; AXIS1 LABEL=('I(' F=CGREEK 'l)'); AXIS2 LABEL=(F=CGREEK 'l'); /* Plot the periodogram */ PROC GPLOT DATA=periodograma_star(OBS=50); PLOT P_01*lambda / VAXIS=AXIS1 HAXIS=AXIS2; /* Sort by periodogram values */ PROC SORT DATA=periodograma_star OUT=periodograma_star_sorted; BY DESCENDING P_01; PROC PRINT DATA=periodograma_star_sorted(OBS=6) NOOBS; RUN; Kim Samejima (UFBA) SAS/ETS November 4, / 22

19 Análise Espectral Periodograma DATA matd51.sunspots; INFILE '/home/samejimal0/my_content/sunspot_orig.txt'; INPUT n_spots /* Computation of peridogram and estimation of spectral density11*/ PROC SPECTRA DATA=matd51.sunspots P S OUT=per_sunspots; VAR n_spots; WEIGHTS ; DATA per_sunspots; SET per_sunspots(firstobs=2); lambda=freq/(2*constant('pi')); p=p_01/2; s=s_01/2*4*constant('pi'); Kim Samejima (UFBA) SAS/ETS November 4, / 22

20 Análise Espectral Periodograma /* Graphical options */ SYMBOL1 I=JOIN C=RED V=NONE L=1; SYMBOL2 I=JOIN C=blue V=NONE L=1; AXIS1 LABEL=(F=CGREEK 'l') ORDER=(0 TO.5 BY.05); AXIS2 LABEL=NONE; /* Plot periodogram and estimated spectral density */ PROC GPLOT DATA=per_sunspots; PLOT p*lambda s*lambda / overlay HAXIS=AXIS1 VAXIS=AXIS2; RUN; Figure: Periodograma da Série Sunspot Kim Samejima (UFBA) SAS/ETS November 4, / 22

21 Modelagem Ajustando modelos ARIMA /* donauwoerth_firstanalysis.sas */ /* donauwoerth_adjustedment.sas */ Kim Samejima (UFBA) SAS/ETS November 4, / 22

22 Referências Referências Falk, M. at al. (2012). A First Course on Time Series Analysis - Examples with SAS. Chair of Statistics, University of Würzburg. Shumway, R.H. and Stoffer D.S. (2016). Time Series Analysis and Its Applications With R Examples, 4th Ed. Brockwell, P.J., and Davis, R.A. (2002), Introduction Time Series and Forecasting, 2 ed. New York: Springer. Morettin, P.A. e Toloi, C.M.C. (2004) Análise de Séries Temporais. Edgard Blücher. Kim Samejima (UFBA) SAS/ETS November 4, / 22