Testovanie bieleho šumu
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- Ira Preston
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1 Beáta Stehlíková FMFI UK Bratislava
2 Opakovanie z prednášky
3 Vygenerujeme dáta Vygenerujeme dáta: N <- 250 # pocet dat set.seed(12345) # aby sme mali rovnake vysledky x <- rnorm(n, mean=10, sd=1) # nezavisle N(10,1) Budeme testovať, či sú bielym šumom. Aká je skutočnosť - sú alebo nie sú?
4 Priebeh dát Zobrazte priebeh vygenerovaných dát x Index
5 Úloha 1 Zobrazte výberovú autokorelačnú funkciu a interpretujte výstup. Series x ACF Lag
6 Úloha 2 Testujte Ljung-Boxovym testom hypotézu, že autokorelácie rádu 1, 2, 3, 4 sú súčasne nulové. ## ## Box-Ljung test ## ## data: x ## X-squared = , df = 4, p-value =
7 Úloha 2 - rozšírenie V cykle vypočítajte p-hodnoty zodpovedajúce testovaniu hypotézy, že prvých k autokorelácií je súčasne nulových, pre k od 1 do 20. # Postup: k.max <- 20 p.hodnoty <- rep(na, k.max) for (i in 1:k.max) { # doplnte priradenie do vektora p.hodnoty } # doplnte kreslenie grafu
8 Úloha 2 - rozšírenie p.hodnoty :k.max
9
10 Načítajte (ak treba, aj nainštalujte) knižnicu quantmod library(quantmod) Viac o tejto knižnici:
11 Ceny akcií - dáta Napríklad: getsymbols("amzn", from=" ", to=" ", auto.assign=true) ## [1] "AMZN" head(amzn) ## AMZN.Open AMZN.High AMZN.Low AMZN.Close AMZN. ## ## ## ## ## ## Beáta Stehlíková FMFI UK Bratislava Testovanie bieleho šumu
12 Ceny akcií - pekné grafy :) AMZN [ / ] Last Volume (millions): 2,048, Jan Mar May Jul Sep Nov Dec
13 Ceny akcií - grafy Na predchádzajúcom slajde: chartseries(amzn, theme="white") Skúste aj: # od januara do marca chartseries(amzn, subset=" :: ") # mesacne data AMZN.mesacne <- to.monthly(amzn) AMZN.mesacne # vypiseme chartseries(amzn.mesacne) # graf
14 Ceny akcií - grafy Nepovinné - pre záujemcov: Pozná napríklad aj Moving Average Convergence/Divergence Oscillator (MACD) php?id=chart_school:technical_indicators: moving_average_convergence_divergence_macd chartseries(amzn) addmacd()
15 Ceny akcií - grafy AMZN [ / ] Last Volume (millions): 2,048, Moving Average Convergence Divergence (12,26,9): MACD: Signal: Jan Mar May Jul Aug Oct Nov Dec
16
17 Výnosy Logaritmické výnosy z cien AMZN.Adjusted: # vynos_t = log(cena_t / cena_{t-1}) AMZN.vynosy <- diff(log(amzn$amzn.adjusted)) chartseries(amzn.vynosy, theme="white") Zistite, či ich môžeme považovať za biely šum (výberová ACF, Ljung-Boxov test).
18 Výnosy AMZN.vynosy [ / ] Last Jan Mar May Jul Sep Nov Dec
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