library(psych)library(seasonal)##
## Attaching package: 'seasonal'## The following object is masked from 'package:psych':
##
## outlierlibrary(Metrics)library(magrittr)library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tidyverse)## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.2 v stringr 1.4.0
## v tidyr 1.1.3 v forcats 0.5.1
## v readr 1.4.0## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x ggplot2::%+%() masks psych::%+%()
## x ggplot2::alpha() masks psych::alpha()
## x tidyr::extract() masks magrittr::extract()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x purrr::set_names() masks magrittr::set_names()
## x tibble::view() masks seasonal::view()library(forecast)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo##
## Attaching package: 'forecast'## The following object is masked from 'package:Metrics':
##
## accuracytrain = read.csv("C:\\\\Users\\\\cthom\\\\OneDrive\\\\Boston College\\\\Econometrics\\\\train.csv") %>%
mutate(store = as.factor(store), item = as.factor(item))
test = read.csv("C:\\\\Users\\\\cthom\\\\OneDrive\\\\Boston College\\\\Econometrics\\\\train.csv")%>%
mutate(store = as.factor(store), item = as.factor(item))describe(train)## vars n mean sd median trimmed mad min max range skew
## date* 1 913000 913.50 527.12 913.5 913.50 676.81 1 1826 1825 0.00
## store* 2 913000 5.50 2.87 5.5 5.50 3.71 1 10 9 0.00
## item* 3 913000 25.50 14.43 25.5 25.50 18.53 1 50 49 0.00
## sales 4 913000 52.25 28.80 47.0 49.48 28.17 0 231 231 0.87
## kurtosis se
## date* -1.20 0.55
## store* -1.22 0.00
## item* -1.20 0.02
## sales 0.51 0.03avg_daily <- train %>% group_by(date) %>% summarise(avg_sale = mean(sales))
avg_daily## # A tibble: 1,826 x 2
## date avg_sale
## <chr> <dbl>
## 1 2013-01-01 27.4
## 2 2013-01-02 27.4
## 3 2013-01-03 29.0
## 4 2013-01-04 31.4
## 5 2013-01-05 32.5
## 6 2013-01-06 34.6
## 7 2013-01-07 23.5
## 8 2013-01-08 27.1
## 9 2013-01-09 27.8
## 10 2013-01-10 29.3
## # ... with 1,816 more rows#Average sales for all stores
ggplot(avg_daily, aes(x= date, y= avg_sale, group=1))+
geom_line(size=1)+
geom_smooth(method = "loess", se = FALSE, span = 0.1, color = "springgreen", size = 0.5)## `geom_smooth()` using formula 'y ~ x'
avg_by_store <- train %>%
group_by(date, store) %>%
summarise(avg_store = mean(sales))## `summarise()` has grouped output by 'date'. You can override using the `.groups` argument.#Average Sales by store
avg_by_store %>%
ggplot( aes(x=date, y=avg_store, color=store))+
geom_line(aes(group = as.factor(store)))
#Average sales per item (over time)
avg_item <- train %>%
group_by(item, date) %>%
summarize(avg = mean(sales))## `summarise()` has grouped output by 'item'. You can override using the `.groups` argument.ggplot(avg_item, aes(date, avg, group=1)) +
geom_line() +
geom_smooth(method = "loess", se = FALSE, span = 0.1, color = "springgreen", size = 0.5) +
facet_wrap(~item, ncol = 10)## `geom_smooth()` using formula 'y ~ x'
#Utilizing weekly frequency and average of sales across all stores
avg_by_date<- train %>%
group_by(date) %>%
summarise(sales_by_date = mean(sales))
avg_sales_by_date <- avg_by_date$sales_by_date
avg_by_date_ts <- ts(avg_sales_by_date, frequency = 7, start=c(2013,1,1))forecast::autoplot(avg_by_date_ts)+ ylab("Average Sales across all stores")
model1 = ets(avg_by_date_ts)
summary(model1)## ETS(M,Ad,M)
##
## Call:
## ets(y = avg_by_date_ts)
##
## Smoothing parameters:
## alpha = 0.9432
## beta = 0.0056
## gamma = 1e-04
## phi = 0.9779
##
## Initial states:
## l = 29.183
## b = -0.0852
## s = 0.7923 1.1891 1.1228 1.0559 0.9897 0.9261
## 0.924
##
## sigma: 0.0256
##
## AIC AICc BIC
## 14667.17 14667.37 14738.80
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.007962439 1.316542 0.5346847 -0.00779551 1.064274 0.3360362
## ACF1
## Training set -0.01128009model1 %>% forecast(h=90) %>% autoplot()+ xlab("Year") + ylab("Average Sales across all stores")
checkresiduals(model1)
##
## Ljung-Box test
##
## data: Residuals from ETS(M,Ad,M)
## Q* = 2.8711, df = 3, p-value = 0.4119
##
## Model df: 12. Total lags used: 15#Utilizing daily frequency and average sales across all stores.
avg_by_date_ts_d <- ts(avg_sales_by_date, frequency = 365, start=c(2013,1,1))avg_by_date_ts_d %>% decompose(type="additive") %>%
autoplot()
avg_by_date_ts_d %>% decompose(type="multiplicative") %>%
autoplot()
#Simple Exponential Smoothing
model3<- ses(avg_by_date_ts_d)
summary(model3)##
## Forecast method: Simple exponential smoothing
##
## Model Information:
## Simple exponential smoothing
##
## Call:
## ses(y = avg_by_date_ts_d)
##
## Smoothing parameters:
## alpha = 0.134
##
## Initial states:
## l = 29.2878
##
## sigma: 7.5041
##
## AIC AICc BIC
## 21077.49 21077.50 21094.02
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.06887025 7.500038 6.091927 -1.799641 12.15033 0.7002368
## ACF1
## Training set 0.1906654
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2018.0027 46.13914 36.52218 55.75609 31.43128 60.84700
## 2018.0055 46.13914 36.43623 55.84204 31.29982 60.97845
## 2018.0082 46.13914 36.35103 55.92725 31.16951 61.10876
## 2018.0110 46.13914 36.26656 56.01171 31.04033 61.23794
## 2018.0137 46.13914 36.18281 56.09546 30.91225 61.36602
## 2018.0164 46.13914 36.09976 56.17851 30.78524 61.49304
## 2018.0192 46.13914 36.01739 56.26088 30.65926 61.61901
## 2018.0219 46.13914 35.93569 56.34259 30.53431 61.74396
## 2018.0247 46.13914 35.85463 56.42364 30.41034 61.86793
## 2018.0274 46.13914 35.77421 56.50406 30.28735 61.99092model3 %>% forecast() %>% autoplot()+ xlab("Year") + ylab("Average Sales across all stores")
checkresiduals(model3)
##
## Ljung-Box test
##
## data: Residuals from Simple exponential smoothing
## Q* = 93862, df = 363, p-value < 2.2e-16
##
## Model df: 2. Total lags used: 365#TBATS
model2 = tbats(avg_by_date_ts_d)
summary(model2)## Length Class Mode
## lambda 1 -none- numeric
## alpha 1 -none- numeric
## beta 0 -none- NULL
## damping.parameter 0 -none- NULL
## gamma.one.values 1 -none- numeric
## gamma.two.values 1 -none- numeric
## ar.coefficients 2 -none- numeric
## ma.coefficients 5 -none- numeric
## likelihood 1 -none- numeric
## optim.return.code 1 -none- numeric
## variance 1 -none- numeric
## AIC 1 -none- numeric
## parameters 2 -none- list
## seed.states 30 -none- numeric
## fitted.values 1826 ts numeric
## errors 1826 ts numeric
## x 54780 -none- numeric
## seasonal.periods 1 -none- numeric
## k.vector 1 -none- numeric
## y 1826 ts numeric
## p 1 -none- numeric
## q 1 -none- numeric
## call 2 -none- call
## series 1 -none- character
## method 1 -none- charactermodel2 %>% forecast(h=90) %>% autoplot()+ xlab("Year") + ylab("Average Sales across all stores")
checkresiduals(model2)
##
## Ljung-Box test
##
## data: Residuals from TBATS
## Q* = 77911, df = 324, p-value < 2.2e-16
##
## Model df: 41. Total lags used: 365#Tbats Forecast
model2_forecast = forecast(model2, h=90)#STLF
model5 = stlf(avg_by_date_ts_d, lambda=0, biasadj=TRUE)
summary(model5)##
## Forecast method: STL + ETS(A,Ad,N)
##
## Model Information:
## ETS(A,Ad,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.0024
## beta = 0.0024
## phi = 0.9605
##
## Initial states:
## l = 3.7181
## b = 0.0012
##
## sigma: 0.1167
##
## AIC AICc BIC
## 5874.900 5874.946 5907.959
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.5380809 6.07909 4.771846 -0.3673232 9.335984 0.5485 0.0283429
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2018.0027 45.99218 39.33570 53.05019 36.34163 57.42082
## 2018.0055 43.69997 37.37518 50.40629 34.53031 54.55915
## 2018.0082 42.94130 36.72617 49.53134 33.93063 53.61221
## 2018.0110 41.38374 35.39381 47.73501 32.69959 51.66805
## 2018.0137 40.63185 34.75040 46.86811 32.10500 50.72997
## 2018.0164 40.92609 35.00157 47.20805 32.33684 51.09826
## 2018.0192 43.80139 37.45998 50.52546 34.60778 54.68951
## 2018.0219 46.25636 39.55863 53.35830 36.54624 57.75645
## 2018.0247 44.02468 37.64905 50.78514 34.78161 54.97192
## 2018.0274 43.06497 36.82713 49.67941 34.02175 53.77589
## 2018.0301 41.32631 35.33896 47.67521 32.64634 51.60738
## 2018.0329 40.66811 34.77460 46.91760 32.12431 50.78836
## 2018.0356 41.37428 35.37670 47.73425 32.67973 51.67362
## 2018.0384 43.79974 37.44850 50.53487 34.59267 54.70683
## 2018.0411 46.25090 39.54182 53.36566 36.52527 57.77303
## 2018.0438 44.03609 37.64576 50.81297 34.77273 55.01130
## 2018.0466 42.80842 36.59358 49.39937 33.79965 53.48279
## 2018.0493 41.57450 35.53601 47.97863 32.82157 51.94660
## 2018.0521 40.78348 34.85693 47.06907 32.19304 50.96391
## 2018.0548 40.99268 35.03256 47.31408 32.35382 51.23145
## 2018.0575 44.00354 37.60204 50.79333 34.72521 55.00132
## 2018.0603 46.29217 39.55368 53.43964 36.52573 57.86973
## 2018.0630 44.08996 37.66798 50.90198 34.78257 55.12459
## 2018.0658 43.19819 36.90191 49.87713 34.07331 54.01769
## 2018.0685 41.58053 35.51582 48.01411 32.79157 52.00301
## 2018.0712 40.88386 34.91643 47.21454 32.23622 51.14009
## 2018.0740 41.29039 35.25906 47.68915 32.55050 51.65741
## 2018.0767 43.61317 37.23753 50.37754 34.37475 54.57306
## 2018.0795 46.32984 39.55154 53.52178 36.50839 57.98309
## 2018.0822 44.23547 37.75813 51.10844 34.85052 55.37246
## 2018.0849 46.70796 39.86263 53.97179 36.79030 58.47894
## 2018.0877 46.32521 39.52989 53.53638 36.48048 58.01149
## 2018.0904 45.36823 38.70715 52.43734 35.71846 56.82495
## 2018.0932 45.68162 38.96818 52.80671 35.95649 57.22975
## 2018.0959 48.90823 41.71363 56.54444 38.48665 61.28552
## 2018.0986 51.46134 43.88366 59.50466 40.48544 64.49929
## 2018.1014 48.87285 41.66902 56.51982 38.43903 61.26912
## 2018.1041 48.05424 40.96373 55.58139 37.78513 60.25707
## 2018.1068 46.28084 39.44479 53.53835 36.38083 58.04730
## 2018.1096 45.23011 38.54207 52.33095 35.54502 56.74334
## 2018.1123 45.91126 39.11507 53.12742 36.07014 57.61227
## 2018.1151 48.91632 41.66724 56.61390 38.42004 61.39882
## 2018.1178 51.46534 43.82989 59.57376 40.41030 64.61499
## 2018.1205 49.06199 41.77476 56.80118 38.51179 61.61375
## 2018.1233 47.75215 40.65123 55.29402 37.47233 59.98479
## 2018.1260 46.14080 39.27142 53.43730 36.19681 57.97633
## 2018.1288 45.30288 38.55021 52.47594 35.52848 56.93906
## 2018.1315 45.60651 38.80039 52.83690 35.75540 57.33658
## 2018.1342 49.10255 41.76577 56.89728 38.48408 61.74914
## 2018.1370 51.46301 43.76407 59.64313 40.32114 64.73591
## 2018.1397 48.98058 41.64391 56.77640 38.36372 61.63092
## 2018.1425 47.90754 40.72261 55.54274 37.51098 60.29823
## 2018.1452 46.09166 39.17032 53.44733 36.07722 58.02967
## 2018.1479 45.33329 38.51717 52.57774 35.47178 57.09175
## 2018.1507 45.72318 38.83961 53.03991 35.76479 57.59992
## 2018.1534 48.99278 41.60744 56.84349 38.30925 61.73735
## 2018.1562 51.45124 43.68521 59.70731 40.21784 64.85497
## 2018.1589 48.95947 41.55988 56.82664 38.25689 61.73289
## 2018.1616 52.58086 44.62349 61.04177 41.07236 66.31946
## 2018.1644 55.29071 46.91217 64.20019 43.17398 69.75892
## 2018.1671 54.26854 46.03397 63.02569 42.36089 68.49058
## 2018.1699 55.09462 46.72353 63.99770 42.99047 69.55492
## 2018.1726 58.45373 49.56035 67.91312 45.59534 73.81890
## 2018.1753 61.84898 52.42636 71.87216 48.22643 78.13134
## 2018.1781 58.80139 49.83096 68.34438 45.83357 74.30506
## 2018.1808 56.94812 48.24863 66.20368 44.37294 71.98615
## 2018.1836 55.31429 46.85290 64.31733 43.08422 69.94332
## 2018.1863 54.09004 45.80464 62.90660 42.11527 68.41734
## 2018.1890 54.62560 46.24673 63.54242 42.51666 69.11712
## 2018.1918 58.42601 49.45192 67.97711 45.45789 73.94973
## 2018.1945 61.85332 52.33976 71.97949 48.10670 78.31319
## 2018.1973 58.72439 49.67966 68.35239 45.65622 74.37592
## 2018.2000 57.49598 48.62825 66.93643 44.68455 72.84400
## 2018.2027 55.24005 46.70849 64.32342 42.91527 70.00888
## 2018.2055 54.04602 45.68735 62.94614 41.97194 68.51822
## 2018.2082 54.65698 46.19212 63.67098 42.43048 69.31568
## 2018.2110 58.28425 49.24513 67.91064 45.22933 73.94027
## 2018.2137 61.60618 52.03863 71.79626 47.78916 78.18047
## 2018.2164 58.51910 49.41838 68.21285 45.37729 74.28756
## 2018.2192 57.35010 48.41881 66.86426 44.45398 72.82784
## 2018.2219 55.31912 46.69216 64.50993 42.86344 70.27220
## 2018.2247 54.07732 45.63231 63.07510 41.88531 68.71771
## 2018.2274 54.39715 45.89041 63.46155 42.11700 69.14729
## 2018.2301 58.20409 49.08938 67.91720 45.04734 74.01132
## 2018.2329 61.44122 51.80623 71.70972 47.53458 78.15385
## 2018.2356 58.61376 49.40941 68.42421 45.32975 74.58236
## 2018.2384 57.27493 48.26835 66.87546 44.27739 72.90331
## 2018.2411 55.23957 46.54102 64.51263 42.68756 70.33626
## 2018.2438 54.25672 45.70111 63.37825 41.91197 69.10810
## 2018.2466 58.73937 49.46408 68.62910 45.35728 74.84300
## 2018.2493 67.92607 57.18531 79.37940 52.43090 86.57749
## 2018.2521 71.61044 60.27145 83.70282 55.25355 91.30437
## 2018.2548 68.33759 57.50189 79.89430 52.70798 87.16088
## 2018.2575 66.26058 55.73973 77.48254 51.08633 84.54034
## 2018.2603 64.18026 53.97569 75.06587 49.46337 81.91379
## 2018.2630 63.00478 52.97332 73.70671 48.53872 80.44072
## 2018.2658 63.40877 53.29912 74.19513 48.83113 80.98390
## 2018.2685 68.09151 57.22036 79.69141 52.41709 86.99398
## 2018.2712 71.44708 60.02457 83.63645 54.97902 91.31196
## 2018.2740 68.40337 57.45251 80.09051 52.61656 87.45157
## 2018.2767 66.46284 55.80810 77.83500 51.10417 84.99940
## 2018.2795 64.01424 53.73804 74.98340 49.20242 81.89558
## 2018.2822 62.79906 52.70421 73.57565 48.24980 80.36814
## 2018.2849 63.11672 52.95700 73.96355 48.47516 80.80197
## 2018.2877 67.83577 56.90162 79.51050 52.07941 86.87265
## 2018.2904 71.51851 59.97514 83.84489 54.88559 91.61984
## 2018.2932 68.32647 57.28338 80.11971 52.41570 87.56018
## 2018.2959 66.30811 55.57677 77.76950 50.84774 85.00235
## 2018.2986 64.00364 53.63129 75.08264 49.06167 82.07587
## 2018.3014 62.89689 52.69020 73.79997 48.19473 80.68382
## 2018.3041 63.55473 53.22743 74.58766 48.68004 81.55517
## 2018.3068 67.77833 56.74996 79.56132 51.89515 87.00431
## 2018.3096 71.36064 59.73386 83.78414 54.61696 91.63362
## 2018.3123 67.92157 56.84035 79.76323 51.96483 87.24689
## 2018.3151 66.28711 55.45814 77.86027 50.69486 85.17601
## 2018.3178 63.99516 53.52672 75.18406 48.92323 82.25859
## 2018.3205 62.80397 52.51676 73.80018 47.99416 80.75455
## 2018.3233 63.46276 53.05388 74.59005 48.47899 81.62901
## 2018.3260 67.87078 56.72422 79.78777 51.82638 87.32810
## 2018.3288 74.27238 62.05839 87.33177 56.69293 95.59692
## 2018.3315 72.83546 60.84202 85.66022 55.57482 93.77882
## 2018.3342 70.89110 59.20252 83.39104 54.07054 91.30590
## 2018.3370 68.50871 57.19815 80.60549 52.23344 88.26692
## 2018.3397 67.45614 56.30481 79.38373 51.41128 86.93980
## 2018.3425 68.14485 56.86499 80.21103 51.91634 87.85672
## 2018.3452 72.40332 60.40299 85.24138 55.13962 93.37812
## 2018.3479 76.23588 63.58393 89.77227 58.03621 98.35366
## 2018.3507 72.80230 60.70454 85.74695 55.40121 93.95516
## 2018.3534 70.96855 59.16028 83.60460 53.98520 91.61903
## 2018.3562 68.27638 56.90142 80.44986 51.91754 88.17275
## 2018.3589 67.32251 56.09205 79.34244 51.17275 86.96973
## 2018.3616 67.80892 56.48282 79.93234 51.52291 87.62711
## 2018.3644 72.55133 60.41760 85.54041 55.10540 93.78658
## 2018.3671 76.09902 63.35572 89.74188 57.77809 98.40516
## 2018.3699 72.44285 60.29636 85.44796 54.98131 93.70821
## 2018.3726 71.17362 59.22479 83.96827 53.99758 92.09678
## 2018.3753 68.18073 56.71984 80.45400 51.70739 88.25311
## 2018.3781 67.24433 55.92656 79.36544 50.97798 87.06968
## 2018.3808 67.96664 56.51288 80.23452 51.50612 88.03387
## 2018.3836 72.58732 60.33949 85.70689 54.98700 94.04968
## 2018.3863 76.10190 63.24493 89.87521 57.62769 98.63578
## 2018.3890 72.38414 60.13996 85.50218 54.79181 93.84791
## 2018.3918 70.67606 58.70588 83.50170 53.47876 91.66333
## 2018.3945 68.15368 56.59633 80.53812 51.55078 88.42082
## 2018.3973 67.35657 55.92020 79.61247 50.92873 87.41520
## 2018.4000 67.74445 56.22796 80.08732 51.20281 87.94725
## 2018.4027 72.19254 59.90470 85.36329 54.54435 93.75238
## 2018.4055 76.30864 63.30417 90.24876 57.63266 99.12996
## 2018.4082 72.53521 60.15860 85.80350 54.76228 94.25865
## 2018.4110 70.10599 58.12919 82.94681 52.90852 91.13146
## 2018.4137 70.31593 58.28855 83.21214 53.04717 91.43400
## 2018.4164 71.51587 59.26831 84.64936 53.93232 93.02444
## 2018.4192 71.72904 59.43000 84.91890 54.07295 93.33188
## 2018.4219 76.88686 63.68740 91.04361 57.93962 100.07541
## 2018.4247 81.00948 67.08541 95.94473 61.02363 105.47540
## 2018.4274 77.08892 63.82269 91.31982 58.04876 100.40312
## 2018.4301 75.45790 62.45669 89.40576 56.79953 98.31046
## 2018.4329 72.75002 60.20028 86.21474 54.74095 94.81296
## 2018.4356 71.51995 59.16759 84.77407 53.79548 93.23977
## 2018.4384 72.00148 59.55105 85.36200 54.13766 93.89763
## 2018.4411 76.95178 63.62946 91.24922 57.83842 100.38549
## 2018.4438 80.89091 66.86993 95.93947 60.77673 105.55794
## 2018.4466 77.09391 63.71518 91.45442 57.90254 100.63521
## 2018.4493 75.41282 62.31030 89.47810 56.61910 98.47220
## 2018.4521 72.85230 60.17967 86.45728 54.67658 95.15905
## 2018.4548 71.38774 58.95522 84.73614 53.55774 93.27573
## 2018.4575 71.72489 59.21894 85.15330 53.79094 93.74605
## 2018.4603 76.90225 63.47783 91.31815 57.65264 100.54489
## 2018.4630 80.66140 66.56427 95.80104 60.44869 105.49320
## 2018.4658 77.15257 63.65291 91.65182 57.79799 100.93612
## 2018.4685 75.21342 62.03771 89.36597 56.32472 98.43032
## 2018.4712 72.24614 59.57551 85.85736 54.08289 94.57698
## 2018.4740 71.53062 58.97092 85.02385 53.52774 93.66984
## 2018.4767 71.72035 59.11277 85.26622 53.65018 93.94790
## 2018.4795 76.34004 62.90487 90.77634 57.08516 100.03080
## 2018.4822 81.10217 66.81247 96.45802 60.62412 106.30419
## 2018.4849 77.31086 63.67351 91.96696 57.76913 101.36657
## 2018.4877 74.87941 61.65581 89.09208 55.93199 98.20935
## 2018.4904 72.43815 59.63104 86.20437 54.08887 95.03723
## 2018.4932 71.28634 58.66850 84.85030 53.20957 93.55535
## 2018.4959 73.71735 60.65436 87.76105 55.00424 96.77600
## 2018.4986 81.52433 67.06151 97.07430 60.80746 107.05839
## 2018.5014 85.85019 70.60269 102.24525 64.01095 112.77430
## 2018.5041 81.76359 67.22548 97.39721 60.94197 107.43950
## 2018.5068 79.48846 65.33896 94.70551 59.22490 104.48240
## 2018.5096 76.64639 62.98745 91.33714 57.08681 100.77798
## 2018.5123 75.30412 61.86933 89.75503 56.06694 99.04381
## 2018.5151 76.59799 62.91706 91.31491 57.00982 100.77678
## 2018.5178 80.54056 66.13940 96.03358 59.92268 105.99664
## 2018.5205 85.63112 70.30268 102.12315 63.68729 112.73099
## 2018.5233 81.76464 67.11206 97.53086 60.78989 107.67410
## 2018.5260 79.71887 65.41706 95.10897 59.24774 105.01243
## 2018.5288 76.73494 62.95323 91.56664 57.00971 101.11287
## 2018.5315 75.37952 61.82630 89.96655 55.98274 99.35739
## 2018.5342 76.19315 62.47856 90.95513 56.56686 100.46068
## 2018.5370 80.99323 66.39863 96.70377 60.10912 106.82236
## 2018.5397 85.48457 70.06377 102.08590 63.41982 112.78056
## 2018.5425 81.75738 66.99282 97.65359 60.63314 107.89626
## 2018.5452 79.22064 64.89858 94.64173 58.73100 104.58044
## 2018.5479 77.06002 63.11342 92.07812 57.10897 101.75923
## 2018.5507 75.45330 61.78266 90.17548 55.89844 99.66791
## 2018.5534 76.01576 62.22830 90.86501 56.29523 100.44146
## 2018.5562 80.95917 66.25923 96.79251 59.93501 107.00585
## 2018.5589 85.29343 69.78981 101.99382 63.12144 112.76881
## 2018.5616 81.57188 66.72877 97.56213 60.34603 107.88118
## 2018.5644 79.37296 64.91447 94.95016 58.69862 105.00485
## 2018.5671 76.71023 62.72183 91.78225 56.70951 101.51298
## 2018.5699 75.11457 61.40251 89.89008 55.51037 99.43145
## 2018.5726 75.51992 61.71917 90.39225 55.79034 99.99821
## 2018.5753 80.96876 66.15654 96.93243 59.79470 107.24553
## 2018.5781 85.36359 69.73083 102.21301 63.01816 113.10068
## 2018.5808 76.21221 62.24058 91.27247 56.24263 101.00614
## 2018.5836 70.09883 57.23437 83.96682 51.71304 92.93185
## 2018.5863 67.70804 55.26924 81.11828 49.93187 89.78926
## 2018.5890 66.09252 53.93775 79.19765 48.72349 87.67317
## 2018.5918 66.78585 54.49070 80.04345 49.21746 88.61943
## 2018.5945 71.46001 58.29058 85.66150 52.64372 94.85003
## 2018.5973 75.25607 61.37258 90.22882 55.42095 99.91844
## 2018.6000 71.84761 58.57912 86.15830 52.89247 95.42146
## 2018.6027 69.90520 56.98200 83.84463 51.44466 92.86941
## 2018.6055 67.38209 54.91242 80.83345 49.57066 89.54410
## 2018.6082 66.23278 53.96311 79.46948 48.70827 88.04297
## 2018.6110 66.54835 54.20750 79.86296 48.92341 88.48874
## 2018.6137 71.10392 57.90469 85.34581 52.25440 94.57429
## 2018.6164 75.25397 61.27000 90.34385 55.28518 100.12389
## 2018.6192 71.40477 58.12246 85.73867 52.43927 95.03073
## 2018.6219 69.73225 56.74778 83.74588 51.19334 92.83226
## 2018.6247 67.53920 54.95025 81.12709 49.56626 89.93928
## 2018.6274 66.22537 53.86873 79.56360 48.58533 88.21573
## 2018.6301 66.64032 54.19362 80.07687 48.87296 88.79462
## 2018.6329 71.34188 58.00353 85.74217 52.30304 95.08718
## 2018.6356 75.49783 61.36819 90.75367 55.33093 100.65598
## 2018.6384 71.31278 57.95291 85.73869 52.24588 95.10427
## 2018.6411 69.69002 56.62100 83.80302 51.03952 92.96738
## 2018.6438 67.18317 54.57160 80.80330 49.18673 89.64948
## 2018.6466 65.91581 53.52972 79.29349 48.24237 87.98404
## 2018.6493 66.60930 54.08038 80.14238 48.73329 88.93571
## 2018.6521 71.35292 57.91833 85.86542 52.18606 95.29713
## 2018.6548 75.14632 60.98340 90.44684 54.94176 100.39279
## 2018.6575 71.48415 57.99804 86.05468 52.24645 95.52808
## 2018.6603 69.81039 56.62698 84.05503 51.00578 93.31849
## 2018.6630 67.17331 54.47534 80.89455 49.06237 89.81950
## 2018.6658 63.78325 51.71420 76.82595 46.57052 85.31131
## 2018.6685 62.35356 50.54340 75.11751 45.51122 83.42326
## 2018.6712 66.41803 53.82565 80.02847 48.46141 88.88689
## 2018.6740 69.81797 56.56799 84.14034 50.92492 93.46406
## 2018.6767 66.68097 54.01393 80.37433 48.62037 89.29042
## 2018.6795 64.68139 52.38219 77.97818 47.14645 86.63786
## 2018.6822 62.65905 50.73277 75.55370 45.65695 83.95323
## 2018.6849 61.45368 49.74544 74.11362 44.76356 82.36195
## 2018.6877 62.20172 50.33945 75.02923 45.29319 83.38848
## 2018.6904 66.35572 53.68898 80.05425 48.30173 88.98297
## 2018.6932 69.86766 56.51763 84.30632 50.84106 93.71939
## 2018.6959 66.15703 53.50381 79.84316 48.12476 88.76746
## 2018.6986 64.77781 52.37644 78.19259 47.10566 86.94177
## 2018.7014 62.69761 50.68295 75.69513 45.57769 84.17392
## 2018.7041 61.70251 49.86719 74.50703 44.83929 82.86163
## 2018.7068 62.11312 50.18764 75.01623 45.12258 83.43688
## 2018.7096 66.14467 53.43301 79.89949 48.03527 88.87782
## 2018.7123 69.85868 56.42046 84.40084 50.71550 93.89504
## 2018.7151 66.78791 53.92818 80.70518 48.47004 89.79328
## 2018.7178 64.92042 52.40840 78.46246 47.09904 87.30734
## 2018.7205 62.85583 50.73024 75.98068 45.58602 84.55482
## 2018.7233 61.50848 49.63158 74.36515 44.59402 82.76581
## 2018.7260 61.96855 49.99153 74.93464 44.91264 83.40852
## 2018.7288 65.95946 53.19909 79.77468 47.78924 88.80534
## 2018.7315 69.72321 56.22203 84.34162 50.49941 93.89926
## 2018.7342 66.33599 53.47867 80.25837 48.03018 89.36279
## 2018.7370 64.58018 52.05146 78.14782 46.74342 87.02205
## 2018.7397 62.48537 50.35173 75.62621 45.21223 84.22303
## 2018.7425 61.56775 49.60115 74.52870 44.53354 83.00955
## 2018.7452 61.78794 49.76738 74.80836 44.67805 83.32986
## 2018.7479 63.35115 51.01503 76.71443 45.79328 85.46208
## 2018.7507 64.62448 52.02875 78.27005 46.69830 87.20431
## 2018.7534 61.67602 49.64385 74.71209 44.55304 83.24899
## 2018.7562 60.26286 48.49553 73.01298 43.51789 81.36432
## 2018.7589 58.02174 46.68160 70.30997 41.88573 78.36039
## 2018.7616 56.88381 45.75586 68.94305 41.05077 76.84504
## 2018.7644 57.18079 45.98448 69.31506 41.25155 77.26781
## 2018.7671 61.15791 49.17190 74.14905 44.10627 82.66511
## 2018.7699 64.48195 51.83293 78.19277 46.48829 87.18239
## 2018.7726 61.58911 49.49655 74.69778 44.38817 83.29433
## 2018.7753 59.71275 47.97793 72.43461 43.02178 80.77915
## 2018.7781 58.17217 46.72973 70.57803 41.89813 78.71693
## 2018.7808 56.95346 45.74059 69.11137 41.00698 77.08919
## 2018.7836 57.20531 45.93267 69.42897 41.17488 77.45155
## 2018.7863 61.13844 49.07988 74.21534 43.99150 82.79962
## 2018.7890 64.41331 51.69739 78.20416 46.33282 87.25890
## 2018.7918 61.66735 49.48257 74.88318 44.34321 83.56212
## 2018.7945 60.03007 48.15816 72.90756 43.15186 81.36599
## 2018.7973 57.85971 46.40677 70.28370 41.57822 78.44586
## 2018.8000 57.09031 45.77957 69.36099 41.01202 77.42404
## 2018.8027 57.52559 46.11844 69.90181 41.31132 78.03582
## 2018.8055 61.44484 49.24967 74.67705 44.11159 83.37536
## 2018.8082 64.62455 51.78689 78.55495 46.37931 87.71404
## 2018.8110 61.58310 49.33878 74.87069 44.18226 83.60886
## 2018.8137 59.94433 48.01529 72.89077 42.99265 81.40628
## 2018.8164 57.95529 46.41189 70.48417 41.55268 78.72665
## 2018.8192 56.54871 45.27554 68.78524 40.53112 76.83697
## 2018.8219 57.33046 45.89139 69.74801 41.07820 77.92047
## 2018.8247 61.02571 48.83863 74.25626 43.71184 82.96550
## 2018.8274 64.51713 51.62151 78.51797 46.19783 87.73607
## 2018.8301 61.27474 49.01649 74.58461 43.86200 83.34949
## 2018.8329 62.23384 49.77284 75.76487 44.53425 84.67714
## 2018.8356 62.02160 49.59228 75.51927 44.36813 84.41131
## 2018.8384 61.58795 49.23479 75.00393 44.04380 83.84388
## 2018.8411 61.52667 49.17509 74.94196 43.98588 83.78319
## 2018.8438 65.84857 52.61790 80.21974 47.06058 89.69279
## 2018.8466 69.46473 55.49542 84.63939 49.62911 94.64401
## 2018.8493 66.04106 52.74877 80.48136 47.16799 90.00368
## 2018.8521 64.32835 51.36963 78.40735 45.93008 87.69323
## 2018.8548 61.90370 49.42269 75.46471 44.18480 84.41070
## 2018.8575 60.98650 48.67987 74.35907 43.51626 83.18246
## 2018.8603 61.75516 49.28274 75.30891 44.05071 84.25357
## 2018.8630 65.66631 52.39262 80.09187 46.82568 89.61373
## 2018.8658 69.37884 55.34274 84.63414 49.45730 94.70562
## 2018.8685 66.21674 52.80896 80.79025 47.18819 90.41349
## 2018.8712 64.42250 51.36692 78.61424 45.89499 87.98721
## 2018.8740 62.14372 49.53926 75.84612 44.25754 84.89765
## 2018.8767 61.13199 48.72223 74.62375 43.52321 83.53785
## 2018.8795 61.49899 49.00417 75.08424 43.77064 84.06185
## 2018.8822 65.63963 52.29229 80.15289 46.70288 89.74560
## 2018.8849 69.13159 55.06235 84.43097 49.17189 94.54523
## 2018.8877 65.91383 52.48817 80.51447 46.86837 90.16864
## 2018.8904 64.43207 51.29720 78.71753 45.80030 88.16512
## 2018.8932 61.69887 49.11064 75.39083 43.84363 84.44765
## 2018.8959 61.27504 48.76282 74.88533 43.52874 83.88986
## 2018.8986 61.43717 48.88138 75.09589 43.63019 84.13419
## 2018.9014 65.85802 52.38753 80.51288 46.75499 90.21221
## 2018.9041 69.29876 55.11272 84.73324 49.18224 94.95051
## 2018.9068 65.75381 52.28228 80.41201 46.65170 90.11724
## 2018.9096 64.26018 51.08374 78.59834 45.57768 88.09350
## 2018.9123 61.94592 49.23351 75.78018 43.92249 84.94338
## 2018.9151 50.83264 40.39226 62.19521 36.03138 69.72271
## 2018.9178 44.03256 34.98138 53.88396 31.20156 60.41159
## 2018.9205 46.49337 36.92849 56.90466 32.93499 63.80458
## 2018.9233 49.32035 39.16555 60.37457 34.92665 67.70198
## 2018.9260 46.97101 37.29200 57.50809 33.25257 64.49403
## 2018.9288 45.83383 36.38143 56.12498 32.43739 62.94916
## 2018.9315 43.85492 34.80325 53.71052 31.02722 60.24712
## 2018.9342 43.39312 34.42946 53.15361 30.69093 59.62836
## 2018.9370 44.02733 34.92525 53.93926 31.12980 60.51571
## 2018.9397 46.66967 37.01349 57.18579 32.98783 64.16443
## 2018.9425 49.43558 39.19882 60.58480 34.93202 67.98498
## 2018.9452 46.96675 37.23335 57.56854 33.17721 64.60668
## 2018.9479 45.66559 36.19419 55.98275 32.24806 62.83324
## 2018.9507 44.35183 35.14549 54.38100 31.31061 61.04151
## 2018.9534 43.59072 34.53509 53.45645 30.76377 60.00965
## 2018.9562 44.08172 34.91673 54.06733 31.10066 60.70141
## 2018.9589 46.71895 36.99786 57.31122 32.95110 64.34967
## 2018.9616 49.28948 39.02531 60.47432 34.75337 67.90792
## 2018.9644 46.79411 37.04178 57.42196 32.98373 64.48671
## 2018.9671 45.61523 36.10101 55.98437 32.14286 62.87842
## 2018.9699 44.30143 35.05387 54.38068 31.20747 61.08326
## 2018.9726 43.36270 34.30389 53.23694 30.53678 59.80441
## 2018.9753 43.89041 34.71409 53.89349 30.89890 60.54790
## 2018.9781 46.52749 36.79211 57.14077 32.74533 64.20241
## 2018.9808 49.32765 38.99820 60.58938 34.70537 68.08388
## 2018.9836 46.84305 37.02614 57.54676 32.94717 64.67124
## 2018.9863 45.65832 36.08215 56.10031 32.10404 63.05188
## 2018.9890 43.87316 34.66416 53.91552 30.83937 60.60228
## 2018.9918 43.19781 34.12344 53.09407 30.35535 59.68477
## 2018.9945 43.69984 34.51281 53.71969 30.69874 60.39395
## 2018.9973 46.29744 36.55670 56.92197 32.51358 64.00031
## 2019.0000 47.77737 37.71740 58.75089 33.54264 66.06309
## 2019.0027 47.23186 37.27900 58.08934 33.14954 65.32556
## 2019.0055 44.84616 35.38865 55.16399 31.46554 62.04183
## 2019.0082 44.03770 34.74347 54.17815 30.88888 60.93898
## 2019.0110 42.41277 33.45453 52.18733 29.74005 58.70543
## 2019.0137 41.61619 32.81939 51.21530 29.17260 57.61757
## 2019.0164 41.89245 33.03040 51.56345 29.35733 58.01487
## 2019.0192 44.80988 35.32335 55.16312 31.39226 62.07092
## 2019.0219 47.29527 37.27485 58.23196 33.12337 65.53040
## 2019.0247 44.98964 35.45037 55.40193 31.49906 62.35169
## 2019.0274 43.98654 34.65280 54.17524 30.78741 60.97700
## 2019.0301 42.19010 33.23069 51.97087 29.52108 58.50152
## 2019.0329 41.49871 32.67937 51.12727 29.02851 57.55745
## 2019.0356 42.20035 33.22504 51.99989 29.51038 58.54546
## 2019.0384 44.65498 35.15037 55.03318 31.21744 61.96653
## 2019.0411 47.13450 37.09449 58.09809 32.94087 65.42386
## 2019.0438 44.85955 35.29685 55.30267 31.34151 62.28194
## 2019.0466 43.59230 34.29269 53.74884 30.44695 60.53783
## 2019.0493 42.32030 33.28520 52.18866 29.54961 58.78622
## 2019.0521 41.50051 32.63372 51.18572 28.96847 57.66201
## 2019.0548 41.69932 32.78332 51.43897 29.09849 57.95286
## 2019.0575 44.74760 35.17261 55.20786 31.21623 62.20497
## 2019.0603 47.06029 36.98286 58.07025 32.81972 65.43639
## 2019.0630 44.80817 35.20580 55.29986 31.23971 62.32054
## 2019.0658 43.88929 34.47677 54.17428 30.58990 61.05788
## 2019.0685 42.23414 33.16980 52.13937 29.42746 58.77002
## 2019.0712 41.51556 32.59878 51.26024 28.91811 57.78459
## 2019.0740 41.91774 32.90785 51.76487 29.18951 58.35901
## 2019.0767 44.26504 34.74352 54.67207 30.81483 61.64241
## 2019.0795 47.01132 36.89155 58.07304 32.71685 65.48321
## 2019.0822 44.87607 35.20876 55.44396 31.22152 62.52460
## 2019.0849 47.37416 37.16113 58.53940 32.94967 66.02161
## 2019.0877 46.97623 36.84149 58.05667 32.66316 65.48339
## 2019.0904 45.99666 36.06591 56.85483 31.97251 64.13389
## 2019.0932 46.30556 36.30074 57.24548 32.17764 64.58067
## 2019.0959 49.56716 38.84974 61.28712 34.43386 69.14672
## 2019.0986 52.14550 40.86230 64.48504 36.21423 72.76163
## 2019.1014 49.51423 38.79251 61.24054 34.37663 69.10724
## 2019.1041 48.67697 38.12882 60.21427 33.78531 67.95555
## 2019.1068 46.87330 36.70856 57.99201 32.52377 65.45376
## 2019.1096 45.80226 35.86252 56.67562 31.77118 63.97402
## 2019.1123 46.48535 36.39000 57.52970 32.23546 64.94421
## 2019.1151 49.52116 38.75868 61.29618 34.33048 69.20263
## 2019.1178 52.09479 40.76475 64.49165 36.10395 72.81711
## 2019.1205 49.65573 38.84831 61.48158 34.40340 69.42499
## 2019.1233 48.32413 37.79891 59.84201 33.47092 67.57993
## 2019.1260 46.68800 36.51177 57.82475 32.32813 65.30795
## 2019.1288 45.83497 35.83745 56.77691 31.72810 64.13053
## 2019.1315 46.13718 36.06647 57.15998 31.92787 64.56925
## 2019.1342 49.66874 38.81936 61.54465 34.36165 69.52879
## 2019.1370 52.05121 40.67324 64.50660 35.99928 72.88181
## 2019.1397 49.53566 38.69979 61.39844 34.24941 69.37659
## 2019.1425 48.44600 37.84090 60.05696 33.48615 67.86713
## 2019.1452 46.60558 36.39605 57.78423 32.20458 65.30493
## 2019.1479 45.83487 35.78700 56.83728 31.66271 64.24073
## 2019.1507 46.22530 36.08460 57.33012 31.92304 64.80379
## 2019.1534 49.52691 38.65418 61.43420 34.19310 69.44936
## 2019.1562 52.00827 40.58268 64.52188 35.89568 72.94667
## 2019.1589 49.48594 38.60676 61.40195 34.14479 69.42581
## 2019.1616 53.14258 41.45122 65.94906 36.65711 74.57405
## 2019.1644 55.87765 43.57587 69.35369 38.53245 78.43124
## 2019.1671 54.84112 42.75900 68.07745 37.80662 76.99509
## 2019.1699 55.67249 43.39855 69.11989 38.36854 78.18132
## 2019.1726 59.06334 46.03266 73.34083 40.69357 82.96330
## 2019.1753 62.49045 48.69397 77.60805 43.04223 87.79851
## 2019.1781 59.40801 46.28285 73.79099 40.90718 83.48797
## 2019.1808 57.53260 44.81286 71.47227 39.60427 80.87202
## 2019.1836 55.87919 43.51635 69.42867 38.45490 78.56690
## 2019.1863 54.63980 42.54271 67.89893 37.59103 76.84290
## 2019.1890 55.17824 42.95341 68.57830 37.95043 77.61892
## 2019.1918 59.01446 45.93059 73.35712 40.57711 83.03538
## 2019.1945 62.47361 48.61319 77.66859 42.94309 87.92377
## 2019.1973 59.31086 46.14298 73.74760 40.75725 83.49274
## 2019.2000 58.06789 45.16702 72.21285 39.89153 81.76271
## 2019.2027 55.78740 43.38460 69.38720 38.31378 78.57058
## 2019.2055 54.57955 42.43689 67.89501 37.47339 76.88797
## 2019.2082 55.19460 42.90662 68.67034 37.88471 77.77312
## 2019.2110 58.85557 45.74352 73.23603 40.38587 82.95163
## 2019.2137 62.20804 48.33957 77.41913 42.67396 87.69770
## 2019.2164 59.08896 45.90679 73.54829 40.52260 83.32057
## 2019.2192 57.90685 44.97953 72.08761 39.70046 81.67328
## 2019.2219 55.85455 43.37685 69.54303 38.28238 78.79755
## 2019.2247 54.59922 42.39361 67.99012 37.41120 77.04501
## 2019.2274 54.92069 42.63482 68.40055 37.62063 77.51718
## 2019.2301 58.76277 45.60845 73.19646 40.24087 82.95987
## 2019.2329 62.02945 48.13442 77.27695 42.46569 87.59262
## 2019.2356 59.17353 45.90923 73.72990 40.49887 83.57968
## 2019.2384 57.82061 44.85077 72.05478 39.56155 81.68821
## 2019.2411 55.76465 43.24750 69.50293 38.14389 78.80235
## 2019.2438 54.77132 42.46881 68.27494 37.45369 77.41709
## 2019.2466 59.29529 45.96763 73.92515 40.53565 83.83149
## 2019.2493 68.56762 53.14543 85.49780 46.86101 96.96372
## 2019.2521 72.28545 56.01609 90.14685 49.38773 102.24551
## 2019.2548 68.98052 53.44455 86.03791 47.11622 97.59395
## 2019.2575 66.88283 51.80919 83.43373 45.67036 94.64857
## 2019.2603 64.78190 50.17196 80.82476 44.22313 91.69719
## 2019.2630 63.59440 49.24266 79.35479 43.40009 90.03762
## 2019.2658 64.00120 49.54799 79.87409 43.66525 90.63502
## 2019.2685 68.72669 53.19597 85.78407 46.87587 97.35001
## 2019.2712 72.11255 55.80583 90.02343 49.17123 102.17015
## 2019.2740 69.03956 53.41733 86.19976 47.06245 97.83938
## 2019.2767 67.08012 51.89117 83.76549 45.71374 95.08498
## 2019.2795 64.60797 49.96908 80.69018 44.01650 91.60234
## 2019.2822 63.38077 49.01042 79.16903 43.16815 89.88355
## 2019.2849 63.70063 49.24819 79.58014 43.37369 90.35842
## 2019.2877 68.46258 52.91948 85.54160 46.60287 97.13602
## 2019.2904 72.17859 55.78103 90.19771 49.11844 102.43243
## 2019.2932 68.95638 53.28051 86.18359 46.91238 97.88259
## 2019.2959 66.91876 51.69609 83.64904 45.51326 95.01251
## 2019.2986 64.59246 49.88932 80.75283 43.91864 91.73107
## 2019.3014 63.47496 49.01671 79.36723 43.14660 90.16517
## 2019.3041 64.13827 49.51936 80.20822 43.58516 91.12872
## 2019.3068 68.40008 52.79959 85.55019 46.46814 97.20670
## 2019.3096 72.01467 55.57904 90.08407 48.90993 102.36749
## 2019.3123 68.54355 52.88991 85.75437 46.53932 97.45611
## 2019.3151 66.89362 51.60683 83.70222 45.40625 95.13241
## 2019.3178 64.58025 49.81251 80.81919 43.82362 91.86386
## 2019.3205 63.37773 48.87556 79.32570 42.99549 90.17431
## 2019.3233 64.04211 49.37842 80.16879 43.43398 91.14081
## 2019.3260 68.48993 52.79767 85.74896 46.43747 97.49336
## 2019.3288 74.94947 57.76610 93.84972 50.80287 106.71311
## 2019.3315 73.49902 56.63730 92.04671 49.80572 104.67226
## 2019.3342 71.53654 55.11447 89.60184 48.46226 101.90109
## 2019.3370 69.13208 53.25176 86.60257 46.82023 98.49886
## 2019.3397 68.06958 52.42327 85.28376 46.08771 97.00749
## 2019.3425 68.76421 52.94808 86.16637 46.54498 98.02011
## 2019.3452 73.06103 56.24583 91.56367 49.43955 104.16912
## 2019.3479 76.92803 59.21150 96.42375 52.04174 109.70799
## 2019.3507 73.46295 56.53361 92.09366 49.68372 104.79060
## 2019.3534 71.61225 55.09886 89.78639 48.41853 102.17426
## 2019.3562 68.89538 52.99835 86.39232 46.56859 98.32059
## 2019.3589 67.93258 52.24773 85.19713 45.90498 96.96893
## 2019.3616 68.42314 52.61499 85.82456 46.22358 97.69167
## 2019.3644 73.20823 56.28382 91.83965 49.44238 104.54768
## 2019.3671 76.78777 59.02457 96.34385 51.84543 109.68478
## 2019.3699 73.09825 56.17784 91.72770 49.34060 104.43862
## 2019.3726 71.81731 55.18290 90.13308 48.46249 102.63205
## 2019.3753 68.79712 52.85219 86.35487 46.41155 98.33855
## 2019.3781 67.85205 52.11624 85.18066 45.76127 97.00990
## 2019.3808 68.58069 52.66589 86.10755 46.23983 98.07412
## 2019.3836 73.24290 56.23551 91.97426 49.36957 104.76532
## 2019.3863 76.78901 58.94700 96.44088 51.74548 109.86275
## 2019.3890 73.03749 56.05651 91.74220 49.20381 104.51930
## 2019.3918 71.31381 54.72320 89.58972 48.02929 102.07597
## 2019.3945 68.76850 52.76004 86.40429 46.30222 98.45518
## 2019.3973 67.96404 52.13297 85.40553 45.74791 97.32564
## 2019.4000 68.35526 52.42314 85.90923 45.99852 97.90818
## 2019.4027 72.84329 55.85454 91.56267 49.00511 104.36035
## 2019.4055 76.99633 59.02783 96.79655 51.78475 110.33539
## 2019.4082 73.18875 56.09822 92.02273 49.21033 104.90300
## 2019.4110 70.73750 54.20912 88.95315 47.54904 101.41261
## 2019.4137 70.94920 54.36110 89.23187 47.67820 101.73922
## 2019.4164 72.15981 55.27824 90.76715 48.47837 103.49869
## 2019.4192 72.37477 55.43246 91.05026 48.60939 103.83055
## 2019.4219 77.57888 59.40714 97.61088 52.09031 111.32171
## 2019.4247 81.73847 62.58062 102.85890 54.86817 117.31707
## 2019.4274 77.78251 59.54064 97.89441 52.19832 111.66444
## 2019.4301 76.13670 58.26986 95.83641 51.07981 109.32644
## 2019.4329 73.40435 56.16814 92.40996 49.23317 105.42682
## 2019.4356 72.16311 55.20799 90.85999 48.38737 103.66749
## 2019.4384 72.64886 55.56918 91.48433 48.69972 104.38886
## 2019.4411 77.64358 59.37849 97.78759 52.03363 111.59089
## 2019.4438 81.61801 62.40627 102.80744 54.68216 117.32947
## 2019.4466 77.78678 59.46570 97.99515 52.10106 111.84708
## 2019.4493 76.09049 58.15804 95.87148 50.95095 109.43265
## 2019.4521 73.50687 56.17279 92.62904 49.20747 105.74068
## 2019.4548 72.02907 55.03318 90.77937 48.20502 103.63812
## 2019.4575 72.36917 55.28269 91.22062 48.41940 104.15084
## 2019.4603 77.59295 59.26205 97.81867 51.90026 111.69376
## 2019.4630 81.38579 62.14724 102.61433 54.42236 117.17974
## 2019.4658 77.84536 59.43263 98.16398 52.04070 112.10733
## 2019.4685 75.88872 57.92799 95.70984 50.71884 109.31398
## 2019.4712 72.89474 55.63222 91.94653 48.70459 105.02478
## 2019.4740 72.17272 55.07092 91.04835 48.20906 104.00777
## 2019.4767 72.36410 55.20666 91.30234 48.32374 104.30685
## 2019.4795 77.02519 58.75167 97.19664 51.42237 111.05021
## 2019.4822 81.82999 62.40497 103.27392 54.61524 118.00379
## 2019.4849 78.00459 59.47659 98.45957 52.04794 112.51241
## 2019.4877 75.55126 57.59528 95.37600 50.39730 108.99805
## 2019.4904 73.08804 55.70713 92.27908 48.74096 105.46782
## 2019.4932 71.92584 54.81114 90.82416 47.95292 103.81383
## 2019.4959 74.37860 56.66975 93.93424 49.57474 107.37788
## 2019.4986 82.25556 62.65966 103.89641 54.81003 118.77594
## 2019.5014 86.62016 65.97225 109.42427 57.70273 125.10614
## 2019.5041 82.49685 62.82018 104.22967 54.94109 119.17724
## 2019.5068 80.20127 61.06082 101.34318 53.39785 115.88666
## 2019.5096 77.33367 58.86670 97.73297 51.47470 111.76787
## 2019.5123 75.97931 57.82506 96.03445 50.55956 109.83477
## 2019.5151 77.28473 58.80770 97.69775 51.41437 111.74658
## 2019.5178 81.26260 61.82313 102.74026 54.04610 117.52418
## 2019.5205 86.39875 65.71848 109.24875 57.44657 124.97982
## 2019.5233 82.49757 62.73950 104.32999 54.83790 119.36292
## 2019.5260 80.43341 61.15843 101.73338 53.45142 116.40203
## 2019.5288 77.42270 58.85835 97.93868 51.43683 112.06967
## 2019.5315 76.05509 57.80801 96.22171 50.51466 110.11429
## 2019.5342 76.87597 58.42119 97.27344 51.04616 111.32729
## 2019.5370 81.71903 62.09020 103.41551 54.24741 118.36675
## 2019.5397 86.25058 65.52123 109.16495 57.24022 124.95798
## 2019.5425 82.48995 62.65291 104.41935 54.72979 119.53592
## 2019.5452 79.93044 60.69775 101.19308 53.01741 115.85236
## 2019.5479 77.75043 59.03145 98.44644 51.55760 112.71734
## 2019.5507 76.12928 57.78999 96.40676 50.46907 110.39129
## 2019.5534 76.69675 58.21008 97.13848 50.83167 111.23851
## 2019.5562 81.68441 61.98418 103.46942 54.12282 118.49839
## 2019.5589 86.05746 65.29059 109.02342 57.00509 124.86962
## 2019.5616 82.30254 62.43035 104.28046 54.50324 119.44733
## 2019.5644 80.08388 60.73628 101.48298 53.01982 116.25274
## 2019.5671 77.39728 58.68800 98.09167 51.22747 112.37729
## 2019.5699 75.78730 57.45670 96.06410 50.14848 110.06367
## 2019.5726 76.19624 57.75618 96.59541 50.40564 110.68170
## 2019.5753 81.69385 61.91202 103.57872 54.02804 118.69331
## 2019.5781 86.12801 65.26054 109.21535 56.94539 125.16295
## 2019.5808 76.89465 58.25365 97.51996 50.82703 111.76916
## 2019.5836 70.72650 53.57104 89.70935 46.73748 102.82589
## 2019.5863 68.31428 51.73449 86.66126 45.13143 99.34044
## 2019.5890 66.68427 50.49089 84.60479 44.04288 96.99120
## 2019.5918 67.38379 51.01126 85.50370 44.49307 98.02990
## 2019.5945 72.09978 54.57145 91.50004 47.59437 104.91345
## 2019.5973 75.92979 57.45989 96.37346 50.10934 110.51050
## 2019.6000 72.49079 54.84746 92.02078 47.82712 105.52813
## 2019.6027 70.53097 53.35494 89.54488 46.52176 102.69734
## 2019.6055 67.98525 51.41983 86.32435 44.83075 99.01203
## 2019.6082 66.82563 50.53359 84.86320 44.05441 97.34422
## 2019.6110 67.14401 50.76514 85.27884 44.25259 97.82912
## 2019.6137 71.74033 54.23042 91.12866 47.26939 104.54853
## 2019.6164 75.92751 57.38522 96.46024 50.01509 110.67445
## 2019.6192 72.04383 54.44012 91.53844 47.44429 105.03610
## 2019.6219 70.35632 53.15533 89.40614 46.32076 102.59789
## 2019.6247 68.14363 51.47429 86.60579 44.85215 99.39259
## 2019.6274 66.81802 50.46383 84.93226 43.96804 97.48006
## 2019.6301 67.23666 50.77083 85.47569 44.23186 98.11189
## 2019.6329 71.98027 54.34294 91.51816 47.33999 105.05634
## 2019.6356 76.17339 57.49824 96.86222 50.08454 111.20013
## 2019.6384 71.95088 54.30115 91.50492 47.29576 105.05851
## 2019.6411 70.31358 53.05591 89.43443 46.20736 102.68983
## 2019.6438 67.78428 51.13818 86.22868 44.53350 99.01711
## 2019.6466 66.50555 50.16444 84.61314 43.68191 97.16999
## 2019.6493 67.20524 50.68308 85.51457 44.12989 98.21329
## 2019.6521 71.99127 54.28272 91.61654 47.26021 105.23006
## 2019.6548 75.81860 57.15831 96.49988 49.75969 110.84816
## 2019.6575 72.12364 54.36297 91.80909 47.32229 105.46858
## 2019.6603 70.43489 53.08054 89.67116 46.20215 103.02104
## 2019.6630 67.77420 51.06624 86.29512 44.44522 99.15055
## 2019.6658 64.35380 48.48035 81.95074 42.19114 94.16672
## 2019.6685 62.91130 47.38516 80.12429 41.23463 92.07557
## 2019.6712 67.01211 50.46486 85.35827 43.91099 98.09829
## 2019.6740 70.44245 53.03864 89.73946 46.14673 103.14185
## 2019.6767 67.27737 50.64647 85.71854 44.06179 98.52849
## 2019.6795 65.25989 49.11892 83.15890 42.72933 95.59416
## 2019.6822 63.21945 47.57463 80.56932 41.38255 92.62493
## 2019.6849 62.00328 46.65108 79.02969 40.57588 90.86236
## 2019.6877 62.75799 47.21048 80.00206 41.05908 91.98784
## 2019.6904 66.94913 50.35432 85.35590 43.78970 98.15180
## 2019.6932 70.49246 53.00989 89.88512 46.09531 103.36845
## 2019.6959 66.74863 50.18560 85.12240 43.63585 97.89929
## 2019.6986 65.35706 49.13057 83.35860 42.71503 95.87856
## 2019.7014 63.25825 47.54436 80.69217 41.33258 92.81922
## 2019.7041 62.25423 46.78141 79.42174 40.66599 91.36530
## 2019.7068 62.66850 47.08433 79.96062 40.92598 91.99271
## 2019.7096 66.73608 50.13147 85.16158 43.57103 97.98426
## 2019.7123 70.48328 52.93691 89.95500 46.00559 103.50784
## 2019.7151 67.38504 50.60096 86.01197 43.97193 98.97879
## 2019.7178 65.50084 49.17732 83.61773 42.73133 96.23142
## 2019.7205 63.41778 47.60492 80.96897 41.36167 93.19066
## 2019.7233 62.05836 46.57620 79.24355 40.46458 91.21221
## 2019.7260 62.52253 46.91624 79.84656 40.75669 91.91374
## 2019.7288 66.54910 49.92888 84.99978 43.37029 97.85370
## 2019.7315 70.34648 52.76853 89.86155 45.83322 103.45906
## 2019.7342 66.92896 50.19607 85.50697 43.59533 98.45354
## 2019.7370 65.15745 48.85880 83.25443 42.43047 95.86770
## 2019.7397 63.04390 47.26557 80.56421 41.04354 92.77741
## 2019.7425 62.11806 46.56320 79.39127 40.43037 91.43404
## 2019.7452 62.34021 46.72146 79.68541 40.56450 91.78022
## 2019.7479 63.91737 47.89501 81.71188 41.58004 94.12187
## 2019.7507 65.20207 48.84904 83.36491 42.40486 96.03371
## 2019.7534 62.22724 46.61208 79.57161 40.45974 91.67133
## 2019.7562 60.80143 45.53602 77.75834 39.52252 89.58956
## 2019.7589 58.54028 43.83484 74.87614 38.04293 86.27577
## 2019.7616 57.39216 42.96755 73.41703 37.28724 84.60132
## 2019.7644 57.69178 43.18426 73.80973 37.47228 85.06070
## 2019.7671 61.70443 46.17972 78.95351 40.06832 90.99587
## 2019.7699 65.05816 48.68109 83.25538 42.23526 95.96159
## 2019.7726 62.13946 46.48893 79.53043 40.33012 91.67551
## 2019.7753 60.24631 45.06467 77.11728 39.09140 88.90099
## 2019.7781 58.69196 43.89428 75.13722 38.07309 86.62532
## 2019.7808 57.46234 42.96713 73.57243 37.26591 84.82808
## 2019.7836 57.71643 43.14954 73.90715 37.42112 85.22084
## 2019.7863 61.68469 46.10816 78.99862 39.98376 91.09901
## 2019.7890 64.98881 48.56940 83.24072 42.11471 95.99857
## 2019.7918 62.21830 46.49071 79.70224 40.30904 91.92512
## 2019.7945 60.56638 45.24843 77.59595 39.22881 89.50297
## 2019.7973 58.37661 43.60484 74.79996 37.80085 86.28484
## 2019.8000 57.60033 43.01745 73.81463 37.28867 85.15502
## 2019.8027 58.03948 43.33784 74.38682 37.56339 85.82196
## 2019.8055 61.99373 46.28236 79.46486 40.11237 91.68795
## 2019.8082 65.20183 48.66890 83.58763 42.17740 96.45256
## 2019.8110 62.13320 46.37026 79.66376 40.18215 91.93210
## 2019.8137 60.47978 45.12842 77.55362 39.10292 89.50413
## 2019.8164 58.47296 43.62337 74.98972 37.79581 86.55203
## 2019.8192 57.05381 42.55719 73.17893 36.86912 84.46876
## 2019.8219 57.84252 43.13797 74.19991 37.36931 85.65407
## 2019.8247 61.57076 45.91043 78.99241 39.76786 91.19363
## 2019.8274 65.09336 48.52860 83.52224 42.03239 96.43080
## 2019.8301 61.82199 46.08169 79.33468 39.90987 91.60331
## 2019.8329 62.78964 46.79482 80.58656 40.52427 93.05617
## 2019.8356 62.57549 46.62711 80.32180 40.37583 92.75780
## 2019.8384 62.13796 46.29303 79.77018 40.08336 92.12808
## 2019.8411 62.07611 46.23892 79.70079 40.03334 92.05523
## 2019.8438 66.43659 49.47833 85.30998 42.83461 98.54171
## 2019.8466 70.08503 52.18642 90.00615 45.17549 103.97448
## 2019.8493 66.63077 49.60570 85.58075 42.93809 98.87011
## 2019.8521 64.90276 48.31084 83.37171 41.81396 96.32566
## 2019.8548 62.45644 46.48184 80.23929 40.22775 92.71386
## 2019.8575 61.53104 45.78519 79.06028 39.62171 91.35877
## 2019.8603 62.30655 46.35421 80.06672 40.11096 92.52906
## 2019.8630 66.25261 49.28142 85.14819 42.64055 98.40923
## 2019.8658 69.99827 52.05859 89.97335 45.03993 103.99406
## 2019.8685 66.80793 49.67729 85.88329 42.97630 99.27446
## 2019.8712 64.99765 48.32284 83.56654 41.80126 96.60407
## 2019.8740 62.69851 46.60547 80.62060 40.31250 93.20586
## 2019.8767 61.67773 45.83878 79.31790 39.64621 91.70702
## 2019.8795 62.04800 46.10599 79.80398 39.87419 92.27627
## 2019.8822 66.22558 49.20173 85.18762 42.54816 98.50905
## 2019.8849 69.74870 51.81026 89.73064 44.80042 103.77064
## 2019.8877 66.50221 49.39021 85.56468 42.70444 98.96061
## 2019.8904 65.00721 48.27157 83.65152 41.73395 96.75551
## 2019.8932 62.24959 46.21591 80.11293 39.95357 92.66987
## 2019.8959 61.82196 45.89052 79.57243 39.66916 92.05187
## 2019.8986 61.98553 46.00402 79.79283 39.76416 92.31406
## 2019.9014 66.44583 49.30584 85.54507 42.61480 98.97669
## 2019.9041 69.91726 51.87288 90.02545 44.82997 104.16870
## 2019.9068 66.34066 49.21088 85.43077 42.52606 98.85991
## 2019.9096 64.83368 48.08475 83.50044 41.54966 96.63370
## 2019.9123 62.49875 46.34506 80.50318 40.04328 93.17230
## 2019.9151 51.28629 38.02408 66.06880 32.85119 76.47229
## 2019.9178 44.42551 32.93180 57.23756 28.44945 66.25561
## 2019.9205 46.90827 34.76625 60.44377 30.03188 69.97244
## 2019.9233 49.76046 36.87384 64.12686 31.84998 74.24193
## 2019.9260 47.39015 35.11136 61.07972 30.32526 70.71965
## 2019.9288 46.24281 34.25543 59.60827 29.58370 69.02135
## 2019.9315 44.24624 32.77081 57.04164 28.29935 66.05454
## 2019.9342 43.78031 32.42017 56.44789 27.99438 65.37206
## 2019.9370 44.42016 32.88837 57.27990 28.39645 66.34077
## 2019.9397 47.08607 34.85622 60.72503 30.09320 70.33634
## 2019.9425 49.87665 36.91569 64.33181 31.86877 74.51977
## 2019.9452 47.38578 35.06611 61.12653 30.26970 70.81237
## 2019.9479 46.07300 34.08881 59.44034 29.42380 68.86434
## 2019.9507 44.74751 33.10244 57.73734 28.57020 66.89652
## 2019.9534 43.97960 32.52883 56.75345 28.07295 65.76165
## 2019.9562 44.47497 32.88961 57.39970 28.38211 66.51563
## 2019.9589 47.13572 34.85132 60.84111 30.07264 70.50904
## 2019.9616 49.72917 36.76260 64.19646 31.71940 74.40333
## 2019.9644 47.21152 34.89547 60.95380 30.10608 70.65057
## 2019.9671 46.02212 34.01056 59.42543 29.34036 68.88438
## 2019.9699 44.69659 33.02537 57.72088 28.48825 66.91369
## 2019.9726 43.74948 32.32007 56.50465 27.87769 65.50881
## 2019.9753 44.28189 32.70783 57.19925 28.20998 66.31921
## 2019.9781 46.94248 34.66713 60.64331 29.89753 70.31783
## 2019.9808 49.76760 36.74724 64.30079 31.68902 74.56453
## 2019.9836 47.26083 34.89038 61.06940 30.08543 70.82280
## 2019.9863 46.06553 34.00218 59.53208 29.31729 69.04527
## 2019.9890 44.26444 32.66720 57.21140 28.16409 66.35885
## 2019.9918 43.58305 32.15889 56.33754 27.72371 65.35030
## 2019.9945 44.08956 32.52711 56.99916 28.03899 66.12285
## 2019.9973 46.71031 34.45474 60.39458 29.69836 70.06715
## 2020.0000 48.20342 35.55008 62.33265 30.64014 72.32117model5 %>% forecast(h=90) %>% autoplot()+ xlab("Year") + ylab("Average Sales across all stores")
checkresiduals(model5)## Warning in checkresiduals(model5): The fitted degrees of freedom is based on the
## model used for the seasonally adjusted data.
##
## Ljung-Box test
##
## data: Residuals from STL + ETS(A,Ad,N)
## Q* = 98352, df = 360, p-value < 2.2e-16
##
## Model df: 5. Total lags used: 365model5_forecast = forecast(model5, h=90)