Homework 6

Ulziibat Tserenbat

#install.packages("fpp")
#library(fpp)
data(ausbeer)
timeserie_beer = tail(head(ausbeer, 17*4+2),17*4-4)
plot(as.ts(timeserie_beer))

#install.packages("Ecdat")
#library(Ecdat)
data(AirPassengers)
timeserie_air = AirPassengers
plot(as.ts(timeserie_air))

#install.packages("forecast")
#library(forecast)
trend_beer = ma(timeserie_beer, order = 4, centre = T)
plot(as.ts(timeserie_beer))
lines(trend_beer)

plot(as.ts(trend_beer))

#install.packages("forecast")
#library(forecast)
trend_air = ma(timeserie_air, order = 12, centre = T)
plot(as.ts(timeserie_air))
lines(trend_air)

plot(as.ts(trend_air))

detrend_beer = timeserie_beer - trend_beer
plot(as.ts(detrend_beer))

detrend_air = timeserie_air / trend_air
plot(as.ts(detrend_air))

m_beer = t(matrix(data = detrend_beer, nrow = 4))
seasonal_beer = colMeans(m_beer, na.rm = T)
plot(as.ts(rep(seasonal_beer,16)))

m_air = t(matrix(data = detrend_air, nrow = 12))
seasonal_air = colMeans(m_air, na.rm = T)
plot(as.ts(rep(seasonal_air,12)))

random_beer = timeserie_beer - trend_beer - seasonal_beer
plot(as.ts(random_beer))

random_air = timeserie_air / (trend_air * seasonal_air)
plot(as.ts(random_air))

recomposed_beer = trend_beer+seasonal_beer+random_beer
plot(as.ts(recomposed_beer))

recomposed_air = trend_air*seasonal_air*random_air
plot(as.ts(recomposed_air))

ts_beer = ts(timeserie_beer, frequency = 4)
decompose_beer = decompose(ts_beer, "additive")
 
plot(as.ts(decompose_beer$seasonal))

plot(as.ts(decompose_beer$trend))

plot(as.ts(decompose_beer$random))

plot(decompose_beer)

ts_air = ts(timeserie_air, frequency = 12)
decompose_air = decompose(ts_air, "multiplicative")
 
plot(as.ts(decompose_air$seasonal))

plot(as.ts(decompose_air$trend))

plot(as.ts(decompose_air$random))

plot(decompose_air)

ts_beer = ts(timeserie_beer, frequency = 4)
stl_beer = stl(ts_beer, "periodic")
seasonal_stl_beer   <- stl_beer$time.series[,1]
trend_stl_beer     <- stl_beer$time.series[,2]
random_stl_beer  <- stl_beer$time.series[,3]
 
plot(ts_beer)

plot(as.ts(seasonal_stl_beer))

plot(trend_stl_beer)

plot(random_stl_beer)

plot(stl_beer)

Flu plots

decompose(flu, "additive")

$x
           Jan       Feb       Mar       Apr       May       Jun
1968 0.8113721 0.4458291 0.3415985 0.2774243 0.2484958 0.2525427
1969 0.8192756 0.4376872 0.3834813 0.2919304 0.2556420 0.2369918
1970 0.4932865 0.5692177 0.3593959 0.2741868 0.2424912 0.2241473
1971 0.3743171 0.3746391 0.3398281 0.2909505 0.2403667 0.2269297
1972 0.6381312 0.5195216 0.2968231 0.2514277 0.2144966 0.1964111
1973 0.5968794 0.5156948 0.3085772 0.2569596 0.2194814 0.2158074
1974 0.3096678 0.3330646 0.3497020 0.3066515 0.2238370 0.2030033
1975 0.4937200 0.4728154 0.3094317 0.2343683 0.2007220 0.1906996
1976 0.2902977 0.5702096 0.6384278 0.3135166 0.2047724 0.1885323
1977 0.2817310 0.3030367 0.2915253 0.2453148 0.2051037 0.1845583
1978 0.5712671 0.4351815 0.2825850 0.2381904 0.2196089 0.1904820
           Jul       Aug       Sep       Oct       Nov       Dec
1968 0.2466902 0.2452006 0.2279679 0.2610293 0.3177998 0.7298681
1969 0.2495123 0.2280816 0.2335083 0.2679917 0.3030445 0.3594536
1970 0.2280840 0.2283657 0.2282342 0.2579092 0.2909701 0.3113483
1971 0.2134564 0.2074597 0.2099793 0.2464345 0.2768291 0.3359459
1972 0.2343862 0.2095384 0.2177600 0.2450697 0.2554203 0.3357194
1973 0.2240929 0.2217431 0.2388084 0.2528328 0.2605210 0.2822165
1974 0.2231299 0.1891271 0.1997522 0.2269953 0.2295186 0.3198083
1975 0.1877136 0.1990874 0.1908602 0.2111834 0.2084524 0.2510464
1976 0.1798065 0.1867087 0.1871117 0.2157304 0.2385934 0.2572363
1977 0.2046436 0.1828399 0.1960763 0.2203844 0.2249940 0.3036654
1978 0.1926964 0.1853681 0.1943872 0.2290728 0.2253550 0.2569408

$seasonal
             Jan         Feb         Mar         Apr         May
1968  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1969  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1970  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1971  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1972  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1973  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1974  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1975  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1976  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1977  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
1978  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
             Jun         Jul         Aug         Sep         Oct
1968 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1969 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1970 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1971 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1972 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1973 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1974 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1975 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1976 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1977 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
1978 -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
             Nov         Dec
1968 -0.03073393  0.05766152
1969 -0.03073393  0.05766152
1970 -0.03073393  0.05766152
1971 -0.03073393  0.05766152
1972 -0.03073393  0.05766152
1973 -0.03073393  0.05766152
1974 -0.03073393  0.05766152
1975 -0.03073393  0.05766152
1976 -0.03073393  0.05766152
1977 -0.03073393  0.05766152
1978 -0.03073393  0.05766152

$trend
           Jan       Feb       Mar       Apr       May       Jun
1968        NA        NA        NA        NA        NA        NA
1969 0.3712479 0.3706522 0.3701698 0.3706907 0.3703660 0.3543173
1970 0.3161336 0.3152526 0.3150447 0.3144048 0.3134816 0.3109741
1971 0.2820524 0.2805718 0.2789401 0.2777014 0.2766341 0.2770698
1972 0.3014484 0.3024071 0.3028179 0.3030852 0.3021363 0.3012349
1973 0.3005123 0.3005919 0.3019774 0.3031779 0.3037139 0.3016972
1974 0.2671383 0.2657392 0.2627528 0.2600489 0.2576806 0.2579551
1975 0.2726984 0.2716377 0.2716822 0.2706529 0.2691163 0.2653734
1976 0.2875122 0.2866669 0.2859950 0.2860282 0.2874736 0.2889874
1977 0.2324063 0.2332800 0.2334923 0.2340597 0.2336870 0.2350549
1978 0.2719954 0.2716030 0.2716379 0.2719295 0.2723066 0.2703748
           Jul       Aug       Sep       Oct       Nov       Dec
1968 0.3674808 0.3674709 0.3688768 0.3712263 0.3721285 0.3717783
1969 0.3253005 0.3171980 0.3216749 0.3199320 0.3186448 0.3175616
1970 0.3040127 0.2909482 0.2820254 0.2819086 0.2825185 0.2825460
1971 0.2890869 0.3061160 0.3103609 0.3069222 0.3041975 0.3018480
1972 0.2995066 0.2976283 0.2979586 0.2986789 0.2991171 0.3001330
1973 0.2875007 0.2679240 0.2620279 0.2658120 0.2680639 0.2677119
1974 0.2671903 0.2806821 0.2848271 0.2801374 0.2761625 0.2746867
1975 0.2540324 0.2496146 0.2673809 0.2843869 0.2878535 0.2879320
1976 0.2888883 0.2773992 0.2518127 0.2345167 0.2316888 0.2315370
1977 0.2490535 0.2666235 0.2717570 0.2710876 0.2713952 0.2722464
1978        NA        NA        NA        NA        NA        NA

$random
               Jan           Feb           Mar           Apr
1968            NA            NA            NA            NA
1969  0.2516560635 -0.0960603885 -0.0530439885 -0.0597608302
1970 -0.0192187031  0.0908697490 -0.0220042760 -0.0212185094
1971 -0.1041069073 -0.0690280969 -0.0054675344  0.0322486073
1972  0.1403111760  0.0540191323 -0.0723503177 -0.0326580385
1973  0.0999955385  0.0520075406 -0.0597557469 -0.0272188177
1974 -0.1538420823 -0.0957699135  0.0205936865  0.0656020990
1975  0.0246500469  0.0380823573 -0.0286059969 -0.0172850594
1976 -0.1935860865  0.1204472990  0.2860773240  0.0464878615
1977 -0.1470468781 -0.0933386135 -0.0083224802  0.0302545865
1978  0.1029000927  0.0004831948 -0.0554084094 -0.0147396385
               May           Jun           Jul           Aug
1968            NA            NA -0.0465656981 -0.0397538273
1969 -0.0485453948 -0.0366066602 -0.0015632315 -0.0065999523
1970 -0.0048117740 -0.0061079935 -0.0017037356  0.0199340019
1971  0.0299112594  0.0305787606 -0.0014055815 -0.0161397690
1972 -0.0214611073 -0.0241049435  0.0091045310 -0.0055734565
1973 -0.0180538781 -0.0051709269  0.0108171227  0.0363356019
1974  0.0323350594  0.0257669940  0.0301645394 -0.0090385148
1975 -0.0022156406  0.0060449898  0.0079061102  0.0319892852
1976 -0.0165225406 -0.0197362352 -0.0348568898 -0.0081740023
1977  0.0375953427  0.0302222315  0.0298150935 -0.0012671065
1978  0.0134809344  0.0008260440            NA            NA
               Sep           Oct           Nov           Dec
1968 -0.0618732827 -0.0591210044 -0.0235947702  0.3004282773
1969 -0.0091310160 -0.0008643252  0.0151336548 -0.0157695560
1970  0.0252443840  0.0270766373  0.0391854840 -0.0288591769
1971 -0.0213459494 -0.0094116752  0.0033655423 -0.0235635769
1972 -0.0011630452 -0.0025331794 -0.0129628619 -0.0220750894
1973  0.0558160756  0.0380968623  0.0231909965 -0.0431569310
1974 -0.0060393202 -0.0020660752 -0.0159099369 -0.0125399060
1975  0.0025149381 -0.0221274627 -0.0486671619 -0.0945470727
1976  0.0143345881  0.0322897165  0.0376385673 -0.0319622019
1977  0.0033548881  0.0003727665 -0.0156672535 -0.0262425060
1978            NA            NA            NA            NA

$figure
 [1]  0.19637160  0.16309536  0.06635550 -0.01899951 -0.06617864
 [6] -0.08071884 -0.07422495 -0.08251649 -0.07903560 -0.05107602
[11] -0.03073393  0.05766152

$type
[1] "additive"

attr(,"class")
[1] "decomposed.ts"

plot(decompose(flu, "additive"))

plot(decompose(flu, "multiplicative"))

plot(decompose(log(flu), "additive"))

scatter.smooth(x=1:length(unemployment$Value), y=unemployment$Value, ylim=c(0,11), degree=2, col="lightblue", span=0.3)

Changing a x axis

scatter.smooth(unemployment$Year, unemployment$Value, ylim=c(0,11), degree=2, col="lightblue", span=0.3)