Error while fitting data in auto.arima - R - r

I am running auto.arima for forecasting time series data and getting the following error:
1: The time series frequency has been rounded to support seasonal
differencing.
2: In value[3L] : The chosen test encountered
an error, so no seasonal differencing is selected. Check the time
series data.
This is what I am executing:
fit <- auto.arima(data,seasonal = TRUE, approximation = FALSE)
I have weekly time series data.
This is how dput(data) looks like:
structure(c(12911647L, 12618317L, 12827388L, 12967840L, 13264925L,
13557838L, 13701131L, 13812463L, 13971928L, 13837658L, 13550635L,
13022371L, 13507596L, 13456736L, 12992393L, 12831883L, 13262301L,
12831691L, 12808893L, 12726330L, 11893457L, 12434051L, 12363464L,
12077055L, 12107221L, 11986124L, 11997087L, 12264971L, 12164412L,
12438279L, 12733842L, 12543251L, 12627134L, 12480153L, 12276238L,
12443655L, 12497753L, 12279060L, 12549138L, 12308591L, 12416680L,
12516725L, 12326545L, 12772578L, 12524848L, 13429830L, 14188044L,
16611840L, 16476565L, 15659941L, 10785585L, 12150894L, 13436366L,
12985213L, 13097555L, 13204872L, 13786040L, 13760281L, 13295389L,
14734578L, 15043941L, 14821169L, 14361765L, 14300180L, 14357964L,
14271892L, 13248168L, 13813784L, 14092489L, 14100024L, 13378374L,
13225650L, 12582444L, 13267163L, 13026181L, 12747286L, 12707074L,
12534595L, 12546094L, 13030406L, 12950360L, 12814398L, 13405187L,
13277755L, 13142375L, 12742153L, 12610817L, 12267747L, 12570075L,
12704157L, 12835948L, 12851893L, 12978880L, 13104906L, 12754018L,
13213958L, 13584642L, 13963433L, 14471672L, 16312595L, 16630000L,
16443882L, 11555299L, 12018373L, 13031876L, 13013945L, 13164137L,
13313246L, 13652605L, 13803606L, 13308310L, 14466211L, 15092736L,
15346015L, 14467260L, 14767785L, 13914271L, 14185070L, 13851028L,
13605858L, 13597999L, 13876994L, 13026270L, 13113250L, 12288727L,
12925846L, 13525010L, 12594472L, 12654512L, 12888260L), .Tsp = c(2016.00819672131,
2018.48047598209, 52.1785714285714), class = "ts")
This is how I am reading data from the csv
read_data <- read.csv(file="data.csv", header=TRUE)
data_ts <- ts(read_data, freq=365.25/7, start=decimal_date(ymd("2016-1-4")))
data <- data_ts[, 2:2]
This is the data in the csv:
Year si_act
1/4/16 12911647
1/11/16 12618317
1/18/16 12827388
1/25/16 12967840
2/1/16 13264925
2/8/16 13557838
2/15/16 13701131
2/22/16 13812463
2/29/16 13971928
3/7/16 13837658
3/14/16 13550635
3/21/16 13022371
3/28/16 13507596
4/4/16 13456736
4/11/16 12992393
4/18/16 12831883
4/25/16 13262301
5/2/16 12831691
5/9/16 12808893
5/16/16 12726330
5/23/16 11893457
5/30/16 12434051
6/6/16 12363464
6/13/16 12077055
6/20/16 12107221
6/27/16 11986124
7/4/16 11997087
7/11/16 12264971
7/18/16 12164412
7/25/16 12438279
8/1/16 12733842
8/8/16 12543251
8/15/16 12627134
8/22/16 12480153
8/29/16 12276238
9/5/16 12443655
9/12/16 12497753
9/19/16 12279060
9/26/16 12549138
10/3/16 12308591
10/10/16 12416680
10/17/16 12516725
10/24/16 12326545
10/31/16 12772578
11/7/16 12524848
11/14/16 13429830
11/21/16 14188044
11/28/16 16611840
12/5/16 16476565
12/12/16 15659941
12/19/16 10785585
12/26/16 12150894
1/2/17 13436366
1/9/17 12985213
1/16/17 13097555
1/23/17 13204872
1/30/17 13786040
2/6/17 13760281
2/13/17 13295389
2/20/17 14734578
2/27/17 15043941
3/6/17 14821169
3/13/17 14361765
3/20/17 14300180
3/27/17 14357964
4/3/17 14271892
4/10/17 13248168
4/17/17 13813784
4/24/17 14092489
5/1/17 14100024
5/8/17 13378374
5/15/17 13225650
5/22/17 12582444
5/29/17 13267163
6/5/17 13026181
6/12/17 12747286
6/19/17 12707074
6/26/17 12534595
7/3/17 12546094
7/10/17 13030406
7/17/17 12950360
7/24/17 12814398
7/31/17 13405187
8/7/17 13277755
8/14/17 13142375
8/21/17 12742153
8/28/17 12610817
9/4/17 12267747
9/11/17 12570075
9/18/17 12704157
9/25/17 12835948
10/2/17 12851893
10/9/17 12978880
10/16/17 13104906
10/23/17 12754018
10/30/17 13213958
11/6/17 13584642
11/13/17 13963433
11/20/17 14471672
11/27/17 16312595
12/4/17 16630000
12/11/17 16443882
12/18/17 11555299
12/25/17 12018373
1/1/18 13031876
1/8/18 13013945
1/15/18 13164137
1/22/18 13313246
1/29/18 13652605
2/5/18 13803606
2/12/18 13308310
2/19/18 14466211
2/26/18 15092736
3/5/18 15346015
3/12/18 14467260
3/19/18 14767785
3/26/18 13914271
4/2/18 14185070
4/9/18 13851028
4/16/18 13605858
4/23/18 13597999
4/30/18 13876994
5/7/18 13026270
5/14/18 13113250
5/21/18 12288727
5/28/18 12925846
6/4/18 13525010
6/11/18 12594472
6/18/18 12654512
6/25/18 12888260
I was able to read the data without any errors before, initially, I had 160 records & the model does not throw any error but, then for 80-20 test I removed the last 30 records and this error cropped up. Now also, if I run with all the data I don't get any error but is I run it with first 130 as 80% I get this error.


when using auto.arima with seasonal = TRUE the parameter S is not calibrated but taken from the frequency of the ts object you are providing. So in your case S = 52.17.
In case the frequency of the time series is not and integer, S is rounded to next integer so auto.arima takes S = 52.
With S=52 and a data of length 150 it becomes difficult to calibrate a seasonal arima model: e.g if P = 2 and and all other variables are zero the first 104 observations cannot be used. I guess that is what the warning is about. You are being told that the seasonal component cannot be calibrated due to the large coefficient S (or due to your short data).
So either you get a longer data history, or you aggregate your data to monthly data (such that S = 12).

Related

Fitting distributions with R

Good afternoon. I have a vector 'a' containing 16000 values. I get the descriptive statistics with the help of the following:
library(pastecs)
library(timeDate)
stat.desc(a)
skewness(a)
kurtosis(a)
Especially skewness=-0.5012, kurtosis=420.8073 (1)
Then I build a histogram of my empirical data:
hist(a, col="lightblue", breaks = 140, border="white", main="",
xlab="Value",xlim=c(-0.001,0.001))
After this I try to fit a theoretical distribution to my empirical data. I choose Variance-Gamma distribution and try to get its parameter estimates on my data:
library(VarianceGammma)
a_VG<-vgFit(a)
The parameter estimates are the following:
vgC=-11.7485, sigma=0.4446, theta=11.7193, nu=0.1186 (2)
Further, I create a sample from the Variance-Gamma distribution with the parameters from (2)
and build a histogram of created theoretical values:
VG<-rvg(length(a),vgC=-11.7485,sigma=0.4446,theta=11.7193,nu=0.1186)
hist(VG,breaks=140,col="orange",main="",xlab="Value")
Bu the second histogram differs absolutely from the first (empirical) histogram. Moreover, it is built on the basis of the parameters (2), which I got on the empirical data.
What's wrong with my code? How can I fix it?
P.S. When I type dput(a[abs(a) > 5e-4]) I get:
c(0.000801110480004752, 0.000588162271316861, 0.000555169128569233,
0.000502563410256229, 0.000854633994686438, 0.00593622112246628,
-0.000506168123513007, -0.000502909585836875, 0.000720924373137422,
0.00119141739181039, 0.000548159382141478, -0.000516511318695123,
-0.000744590777740584, 0.000595213912401249, 0.000514055190913965,
-0.000589061375421807, -0.00175392114572581, 0.000745548313668465,
-0.00075910234096277, -0.00059987613053103, 0.000583568488865538,
0.00426484136013094, 0.000610760059768012, 0.000575522836335551,
0.000823785810599276, 0.00181936036509178, -0.00073316272551871,
-0.00184238143420679, -0.000519146793923397, -0.00120324664043103,
-0.000882469414168696, -0.00148118339830283, 0.000929612782487155,
0.000565364610238817, 0.000578158613453894, 0.00060479145432879,
-0.00520576206828594, 0.000708404040882016, 0.00105224485893451,
0.000636486872540587, -0.00359655507585543, 0.000769164650506582,
0.000635701125126786, 0.000570489501935612, -0.000641260260277221,
0.000735092947873994, 0.000757195823062773, 0.000556002742616357,
-0.00207489740356159, -0.000553386431560554, 0.000511326871983186,
0.000504591469525195, -0.000749886905655472, -0.0013939718643865,
-0.000513742626250036, -0.00105021597423516, -0.00156667292147716,
0.000864563166150134, 0.00433724128055069, 0.00053855648931922,
-0.00150732363190365, 0.00052621785349416, 0.000987781100809215,
0.000560725818171903, 0.00176012436713435, -0.000594895431092368,
-0.000686229580335151, 0.00138682284509528, -0.000531964338888358,
-0.00179959148771403, 0.000574543871314503, -0.000686996216439084,
-0.000559043343629995, 0.00055881173674166, -0.000636332688477736,
-0.000623778186703561, -0.00173834148094443, -0.000567224129968125,
-0.00122578683434504, 0.00130960156515414, -0.000548203197176633,
-0.000522749285863711, -0.000820371086264871, 0.000756014225812507,
-0.000714081490558627, -0.000617600335221624, 0.000523639760748651,
-0.000578502663833191, 0.00107478825239227, 0.000612725356974764,
-0.00065509337422931, 0.000505887803587513, -0.000566716376848575,
0.000511727090058756, 0.000572807738912218, -0.000756026937699161,
0.000547948751494332, 0.000628323894238392, -0.000541350489317693,
-0.00133529454372372, -0.000590618859845904, -0.000700581963648972,
0.000735987224462775, 0.000528958898682319, 0.000838250041022448,
-0.000519084424130511, -0.00052258402856431, -0.000538130765869838,
-0.000631819887885854, 0.00054800880764283, 0.00266115500510899,
-0.000839092093771754, 0.000559253571783103, -0.000801028189803432,
-0.000608879021022801, -0.000538018076854385, -0.000689859734395171,
0.00329650346269972, 0.000765494493951024, -0.000689450477848297,
-0.000560199139975737, 0.00159082699266122, -0.00208548663121455,
-0.000598493596793759, 0.000563544422691464, 0.000626996183768824,
-0.000653166846808162, -0.000851350174739807, -0.00140687473245116,
-0.000887003220306326, -0.000765614651347946, -0.00100676206277761,
0.000724714394852555, 0.00108872127644233, -0.000678558537305918,
-0.000705087556212902, 0.000544828152248655, -0.000791700964308362,
0.000606125736727137, -0.00119335967326073, 0.00075413211796338,
0.000526038939010931, 0.00086543737231537, -0.000817788712950573,
-0.000584070926663571, 0.000619657281937691, 0.000680783312420274,
-0.000513831718574664, -0.00050972403875349, -0.00114542220685365,
-0.00070564389723593, -0.01057964950882, -0.000610357922434801,
0.000818264221596365, 0.000940825400308043, -0.000726555639413817,
-0.000591089505560305, 0.000564738888193972, -0.00068515060569041,
0.000668920238348747, -0.00110103375121717, -0.0015480433031172,
0.000663030855223568, 0.000500097431997304, -0.000600730311271391,
-0.000672397772962796, -0.000607852365856587, 0.000536711920570809,
0.000595055206488837, 0.000523123873687581, 0.000977280737528119,
0.000616410821629998, 0.000788593666889881, -0.000671642905915704,
0.000717328711735021, -0.000551853104219902, -0.000565153434708421,
-0.000802585212152707, 0.000536342062561701, 0.000682048510343591,
-0.000541902545439399, 0.000779676683974273, 0.000698841439971787,
0.000559313965908359, -0.00064986819016255, 0.000795421518319017,
0.00364973919549527, 0.000669658692276087, 0.00109045476974678,
0.000514411572742901, 0.000503832507211754, -0.000507376233564116,
0.001232871590787, 0.000561820312542594, -0.000501190337518054,
-0.000769036505996468, -0.000695537959007453, -0.000572065848166048,
-0.00167929926328192, 0.000597078186826749, 0.00710238430870014,
0.000745192112519888, -0.00116091022028009, -0.000791139281769659,
-0.00148898466632552, 0.000565144038962018, -0.000514019821833855,
-0.00148427996685285, -0.000822717245339888, -0.00062922111212238,
-0.000636011367371125, 0.00119640327632808, 0.000548455410294579,
0.000652678152560426, 0.000509244387833618, 0.000961872348987924,
0.000662064072514568, -0.00068116858054168, -0.000569930302445343,
0.00188358126928101, 0.00130560555273895, 0.000593470885775105,
0.00160093110088155, 0.000785262438315115, -0.000912313442922752,
0.000609996052359563, 0.000720137994393966, 0.000568163899000496,
0.00128685533068307, -0.000756787473447318, 0.000765932134255465,
0.00064884753100003, 0.000687571386270847, -0.000582094290400903,
-0.000693177295971736, -0.000601776208094762, 0.000503616387996786,
-0.000615095866544735, -0.000799593899689199, 0.000773750859128342,
-0.000522576090260074, 0.000503578107212022, -0.00104492224837571,
0.000547928732299141, 0.00310304337507183, 0.000893382870797765,
-0.000577792878910799, -0.000647710366578735, -0.00061992948706191,
0.000825702487162516, 0.000606579510524341, 0.000552792484727505,
0.000688600840895504, 0.000505093563534231, -0.000728420573667066,
-0.00157924525963438, -0.000603846616019865, -0.000521941317177976,
0.00150498158245682, -0.000584572670337735, 0.000713757870583365,
0.000524287801789924, 0.00107217649464886, 0.00213147531822244,
0.000566012832157625, -0.00069828890607937, 0.000641567963736378,
-0.000509531713644762, -0.000547564140049417, -0.00115275240244728,
0.000560465768010943, -0.000651807371497171, -0.00096487058986483,
0.000753687665266511, -0.000665599418910645, -0.000691278087025182,
-0.000578010050725553, -0.000685833148198256, 0.000698470819832764,
0.00102943368139208, -0.000725840586788706, 0.00125882415960632,
-0.000630791474954151, -0.000764813558678412, -0.000638539347184164,
0.000654486496518558, 0.000547453642294471, 0.000572020020495501,
-0.000605791001705214, 0.00660211658324172, 0.00114928683282756,
0.000985676480677711, -0.000694668292547718, -0.000528955637964401,
0.000647975568638159, 0.00116454536417443, 0.000506748841724303,
-0.000500925156604382, -0.000567015088082101, 0.00128711230206946,
0.000533633762033858, 0.00505991432758357, 0.000518058378462527,
-0.000592822519784875, 0.00177414999018666, 0.00059845426944527,
-0.000511614433724716, 0.0016614697907098, 0.000852196464322219,
0.00241689725305427, -0.000614317948913978, -0.000729717143318709,
-0.000612900648802039, -0.000727983564232204, -0.000694965869158182,
-0.000527752006066251, -0.000584233784708843, 0.000522097476268968,
0.000543092880677776, 0.000947121210698398, -0.00241810275096377,
0.00181893137435019, 0.000931873879297385, 0.000512116215015013,
0.000724985702444059, -0.000566713495050664, 0.000603953591362227
)
After fitting the data look like the following (empirical histogram-blue, theoretical histogram-orange):
The same when include freq=FALSE in hist

This will all be due to anomalous values in a not represented by the histogram you've shown. This could be the cause of both the very high kurtotsis, and the vgFit() algorithm failing to find a good fit.
Type dput(a[abs(a) > 5e-4]) in the console and copy the output into your question. People then may be able to recreate aomething like the vector a without having to get all 16000 values and debug the vgFit issue.
Thanks for the extra data. There are some extreme values in there, but I don;t think those are what is causing the problem in vgFit. Fitting 4 parameters which can be almost any value is difficult, but you can help it along by rescaling your data to something typical. Try this:
b <- (a-mean(a))/sd(a)
vgf <- vgFit(b)
vgf$param
VG <- rvg(16000, param = vgf$param)
VG_rescaled <- VG*sd(a)+mean(a)
hist(VG_rescaled, breaks=140, col="orange", main="", xlab="Value")
and see if the two histograms are close enough now.

Multiple Changepoint Analysis: penalty and significance

I am analyzing changes in unique users' ratings for different movies in time. In order to find significant changepoints in time, I am using the 'changepoint' package and the PELT method.
I understand that there are different types of penalties, however, I
am still unsure which one to use.
I tried to make an elbow plot to see the optimal number of changes,
but somehow it does not work. Here is what I have so far, based on,
for example, the movie "Inception".
Also, are all changepoints significant? Is there a way to prove
significance?
My data: timestamp_date = date; cummean = all ratings for the day:
timestamp_date cummean
18-07-2010 4.15384615
19-07-2010 4.23809524
20-07-2010 4.23880597
21-07-2010 4.24390244
22-07-2010 4.19387755
23-07-2010 4.21186441
24-07-2010 4.23758865
25-07-2010 4.28804348
26-07-2010 4.32126697
27-07-2010 4.34063745
28-07-2010 4.36330935
29-07-2010 4.35521886
30-07-2010 4.35448916
31-07-2010 4.34005764
1-08-2010 4.34741144
2-08-2010 4.35604113
3-08-2010 4.34725537
4-08-2010 4.33073497
5-08-2010 4.34051724
6-08-2010 4.34114053
7-08-2010 4.3467433
8-08-2010 4.32909091
9-08-2010 4.32901554
10-08-2010 4.32171799
11-08-2010 4.32316119
12-08-2010 4.32375189
13-08-2010 4.32532751
14-08-2010 4.32932011
15-08-2010 4.32855191
16-08-2010 4.33266932
17-08-2010 4.33246415
18-08-2010 4.33312102
19-08-2010 4.32982673
20-08-2010 4.33212121
21-08-2010 4.33195755
22-08-2010 4.33198614
23-08-2010 4.33370913
24-08-2010 4.3342511
25-08-2010 4.33441208
26-08-2010 4.33439153
27-08-2010 4.33541018
28-08-2010 4.331643
29-08-2010 4.32954545
30-08-2010 4.32992203
31-08-2010 4.330468
1-09-2010 4.33002833
2-09-2010 4.32679739
3-09-2010 4.32763401
4-09-2010 4.33091568
5-09-2010 4.33081033
6-09-2010 4.3289358
7-09-2010 4.33072917
8-09-2010 4.33104631
9-09-2010 4.33347422
10-09-2010 4.33430962
11-09-2010 4.33251029
12-09-2010 4.33292782
13-09-2010 4.33360129
14-09-2010 4.33359936
15-09-2010 4.33307024
16-09-2010 4.33268025
17-09-2010 4.33256528
18-09-2010 4.33358548
19-09-2010 4.33247232
20-09-2010 4.33734088
21-09-2010 4.33758621
22-09-2010 4.34044715
23-09-2010 4.34026846
24-09-2010 4.33878505
25-09-2010 4.33542631
26-09-2010 4.33409836
27-09-2010 4.33268482
28-09-2010 4.3332256
29-09-2010 4.33451157
30-09-2010 4.33545108
1-10-2010 4.33470032
2-10-2010 4.33550995
3-10-2010 4.33374384
4-10-2010 4.33455882
5-10-2010 4.33638026
6-10-2010 4.33704819
7-10-2010 4.33871933
8-10-2010 4.33881579
9-10-2010 4.33718861
10-10-2010 4.33931725
11-10-2010 4.34020918
12-10-2010 4.33927545
13-10-2010 4.33714286
14-10-2010 4.33730835
My code:
inds <- seq(as.Date("2010-07-18"), as.Date("2010-10-14"), by = "day")
myts <- ts(inception$cummean, start = c(2010, as.numeric(format(inds[1], "%j"))), frequency = 365)
#single changepoint: method AMOC
cpt <- changepoint::cpt.meanvar(myts)
cpts(cpt)
cpts.ts(cpt)
param.est(cpt)
plot(cpt)
summary(cpt)
#multiple changepoints: method PELT
mcpt <- changepoint::cpt.meanvar(myts, method = "PELT")
cpts(mcpt)
cpts.ts(mcpt)
param.est(mcpt)
ncpts(mcpt)
plot(mcpt)
summary(mcpt)
Also, as I use a ts.object, I cannot convert the date to appear right when I plot cpt, what am I doing wrong?
Thank you!!

How to decompose this time series data correctly in R?

We are trying to decompose a time series in R and we are able to do it but the results do not look right.
Here's the data with time stamps:
"_time","dummy_data"
"2017-02-05T00:00:00.000-0500","205.472222"
"2017-02-05T01:00:00.000-0500","169.443611"
"2017-02-05T02:00:00.000-0500","156.011944"
"2017-02-05T03:00:00.000-0500","177.169722"
"2017-02-05T04:00:00.000-0500","219.049167"
"2017-02-05T05:00:00.000-0500","215.821667"
"2017-02-05T06:00:00.000-0500","214.983333"
"2017-02-05T07:00:00.000-0500","246.723889"
"2017-02-05T08:00:00.000-0500","343.308889"
"2017-02-05T09:00:00.000-0500","473.200278"
"2017-02-05T10:00:00.000-0500","390.223333"
"2017-02-05T11:00:00.000-0500","373.974444"
"2017-02-05T12:00:00.000-0500","639.402500"
"2017-02-05T13:00:00.000-0500","512.378611"
"2017-02-05T14:00:00.000-0500","428.824444"
"2017-02-05T15:00:00.000-0500","477.611944"
"2017-02-05T16:00:00.000-0500","534.378611"
"2017-02-05T17:00:00.000-0500","716.046944"
"2017-02-05T18:00:00.000-0500","470.218056"
"2017-02-05T19:00:00.000-0500","411.426389"
"2017-02-05T20:00:00.000-0500","393.147222"
"2017-02-05T21:00:00.000-0500","368.726389"
"2017-02-05T22:00:00.000-0500","357.958056"
"2017-02-05T23:00:00.000-0500","379.284722"
"2017-02-06T00:00:00.000-0500","273.403056"
"2017-02-06T01:00:00.000-0500","269.764167"
"2017-02-06T02:00:00.000-0500","233.650000"
"2017-02-06T03:00:00.000-0500","227.802222"
"2017-02-06T04:00:00.000-0500","313.731389"
"2017-02-06T05:00:00.000-0500","327.502778"
"2017-02-06T06:00:00.000-0500","333.327500"
"2017-02-06T07:00:00.000-0500","393.542778"
"2017-02-06T08:00:00.000-0500","659.569167"
"2017-02-06T09:00:00.000-0500","770.509444"
"2017-02-06T10:00:00.000-0500","1037.536667"
"2017-02-06T11:00:00.000-0500","935.926667"
"2017-02-06T12:00:00.000-0500","791.124722"
"2017-02-06T13:00:00.000-0500","903.093889"
"2017-02-06T14:00:00.000-0500","802.309167"
"2017-02-06T15:00:00.000-0500","792.085000"
"2017-02-06T16:00:00.000-0500","728.378056"
"2017-02-06T17:00:00.000-0500","740.647222"
"2017-02-06T18:00:00.000-0500","737.986111"
"2017-02-06T19:00:00.000-0500","502.763056"
"2017-02-06T20:00:00.000-0500","475.400556"
"2017-02-06T21:00:00.000-0500","522.482500"
"2017-02-06T22:00:00.000-0500","410.664722"
"2017-02-06T23:00:00.000-0500","370.423611"
"2017-02-07T00:00:00.000-0500","278.871667"
"2017-02-07T01:00:00.000-0500","290.182500"
"2017-02-07T02:00:00.000-0500","220.329167"
"2017-02-07T03:00:00.000-0500","252.641944"
"2017-02-07T04:00:00.000-0500","355.666667"
"2017-02-07T05:00:00.000-0500","273.100833"
"2017-02-07T06:00:00.000-0500","315.117778"
"2017-02-07T07:00:00.000-0500","359.764167"
"2017-02-07T08:00:00.000-0500","691.946944"
"2017-02-07T09:00:00.000-0500","941.796667"
"2017-02-07T10:00:00.000-0500","859.472222"
"2017-02-07T11:00:00.000-0500","949.285278"
"2017-02-07T12:00:00.000-0500","790.790833"
"2017-02-07T13:00:00.000-0500","952.915000"
"2017-02-07T14:00:00.000-0500","1136.490278"
"2017-02-07T15:00:00.000-0500","1175.359444"
"2017-02-07T16:00:00.000-0500","859.848889"
"2017-02-07T17:00:00.000-0500","718.357778"
"2017-02-07T18:00:00.000-0500","698.445278"
"2017-02-07T19:00:00.000-0500","630.867778"
"2017-02-07T20:00:00.000-0500","485.426389"
"2017-02-07T21:00:00.000-0500","571.723056"
"2017-02-07T22:00:00.000-0500","458.161944"
"2017-02-07T23:00:00.000-0500","336.733333"
"2017-02-08T00:00:00.000-0500","344.001111"
"2017-02-08T01:00:00.000-0500","315.671111"
"2017-02-08T02:00:00.000-0500","285.107778"
"2017-02-08T03:00:00.000-0500","281.013611"
"2017-02-08T04:00:00.000-0500","260.244722"
"2017-02-08T05:00:00.000-0500","233.998056"
"2017-02-08T06:00:00.000-0500","260.235833"
"2017-02-08T07:00:00.000-0500","362.811944"
"2017-02-08T08:00:00.000-0500","633.142500"
"2017-02-08T09:00:00.000-0500","872.285278"
"2017-02-08T10:00:00.000-0500","938.051389"
"2017-02-08T11:00:00.000-0500","951.735278"
"2017-02-08T12:00:00.000-0500","967.694444"
"2017-02-08T13:00:00.000-0500","960.494167"
"2017-02-08T14:00:00.000-0500","1039.334444"
"2017-02-08T15:00:00.000-0500","808.363889"
"2017-02-08T16:00:00.000-0500","661.919722"
"2017-02-08T17:00:00.000-0500","604.166944"
"2017-02-08T18:00:00.000-0500","464.267500"
"2017-02-08T19:00:00.000-0500","425.867500"
"2017-02-08T20:00:00.000-0500","537.951111"
"2017-02-08T21:00:00.000-0500","528.523611"
"2017-02-08T22:00:00.000-0500","401.029444"
"2017-02-08T23:00:00.000-0500","396.677778"
"2017-02-09T00:00:00.000-0500","263.640833"
"2017-02-09T01:00:00.000-0500","233.905278"
"2017-02-09T02:00:00.000-0500","202.222778"
"2017-02-09T03:00:00.000-0500","194.326944"
"2017-02-09T04:00:00.000-0500","208.162222"
"2017-02-09T05:00:00.000-0500","257.111667"
"2017-02-09T06:00:00.000-0500","277.464444"
"2017-02-09T07:00:00.000-0500","403.655000"
"2017-02-09T08:00:00.000-0500","700.535278"
"2017-02-09T09:00:00.000-0500","888.195278"
"2017-02-09T10:00:00.000-0500","690.172778"
"2017-02-09T11:00:00.000-0500","822.210556"
"2017-02-09T12:00:00.000-0500","801.144167"
"2017-02-09T13:00:00.000-0500","983.958056"
"2017-02-09T14:00:00.000-0500","1003.791111"
"2017-02-09T15:00:00.000-0500","1085.289722"
"2017-02-09T16:00:00.000-0500","740.004167"
"2017-02-09T17:00:00.000-0500","616.664444"
"2017-02-09T18:00:00.000-0500","473.841389"
"2017-02-09T19:00:00.000-0500","570.906944"
"2017-02-09T20:00:00.000-0500","568.685000"
"2017-02-09T21:00:00.000-0500","547.024722"
"2017-02-09T22:00:00.000-0500","369.073889"
"2017-02-09T23:00:00.000-0500","431.275833"
"2017-02-10T00:00:00.000-0500","211.516667"
"2017-02-10T01:00:00.000-0500","169.348611"
"2017-02-10T02:00:00.000-0500","185.133611"
"2017-02-10T03:00:00.000-0500","173.875278"
"2017-02-10T04:00:00.000-0500","250.226667"
"2017-02-10T05:00:00.000-0500","237.783056"
"2017-02-10T06:00:00.000-0500","247.450000"
"2017-02-10T07:00:00.000-0500","375.930278"
"2017-02-10T08:00:00.000-0500","605.365000"
"2017-02-10T09:00:00.000-0500","647.407500"
"2017-02-10T10:00:00.000-0500","714.873889"
"2017-02-10T11:00:00.000-0500","767.262778"
"2017-02-10T12:00:00.000-0500","643.721389"
"2017-02-10T13:00:00.000-0500","653.969722"
"2017-02-10T14:00:00.000-0500","656.156111"
"2017-02-10T15:00:00.000-0500","763.260833"
"2017-02-10T16:00:00.000-0500","579.947778"
"2017-02-10T17:00:00.000-0500","734.142500"
"2017-02-10T18:00:00.000-0500","636.389722"
"2017-02-10T19:00:00.000-0500","360.105833"
"2017-02-10T20:00:00.000-0500","438.675278"
"2017-02-10T21:00:00.000-0500","420.990833"
"2017-02-10T22:00:00.000-0500","343.326111"
"2017-02-10T23:00:00.000-0500","293.787778"
"2017-02-11T00:00:00.000-0500","282.809444"
"2017-02-11T01:00:00.000-0500","249.653889"
"2017-02-11T02:00:00.000-0500","163.781111"
"2017-02-11T03:00:00.000-0500","245.236111"
"2017-02-11T04:00:00.000-0500","284.649444"
"2017-02-11T05:00:00.000-0500","337.534167"
"2017-02-11T06:00:00.000-0500","258.772222"
"2017-02-11T07:00:00.000-0500","322.805833"
"2017-02-11T08:00:00.000-0500","380.436667"
"2017-02-11T09:00:00.000-0500","523.488056"
"2017-02-11T10:00:00.000-0500","478.361111"
"2017-02-11T11:00:00.000-0500","422.119722"
"2017-02-11T12:00:00.000-0500","425.315000"
"2017-02-11T13:00:00.000-0500","465.892222"
"2017-02-11T14:00:00.000-0500","412.729167"
"2017-02-11T15:00:00.000-0500","493.920000"
"2017-02-11T16:00:00.000-0500","381.506667"
"2017-02-11T17:00:00.000-0500","458.291667"
"2017-02-11T18:00:00.000-0500","433.393611"
"2017-02-11T19:00:00.000-0500","415.926389"
"2017-02-11T20:00:00.000-0500","349.008056"
"2017-02-11T21:00:00.000-0500","353.280000"
"2017-02-11T22:00:00.000-0500","399.022778"
"2017-02-11T23:00:00.000-0500","316.480556"
"2017-02-12T00:00:00.000-0500","252.727222"
"2017-02-12T01:00:00.000-0500","274.278333"
"2017-02-12T02:00:00.000-0500","269.609444"
"2017-02-12T03:00:00.000-0500","221.645278"
"2017-02-12T04:00:00.000-0500","294.641389"
"2017-02-12T05:00:00.000-0500","347.502222"
"2017-02-12T06:00:00.000-0500","313.468333"
"2017-02-12T07:00:00.000-0500","330.429722"
"2017-02-12T08:00:00.000-0500","369.703333"
"2017-02-12T09:00:00.000-0500","518.679167"
"2017-02-12T10:00:00.000-0500","542.199167"
"2017-02-12T11:00:00.000-0500","475.780833"
"2017-02-12T12:00:00.000-0500","419.468056"
"2017-02-12T13:00:00.000-0500","447.899444"
"2017-02-12T14:00:00.000-0500","526.429722"
"2017-02-12T15:00:00.000-0500","517.046111"
"2017-02-12T16:00:00.000-0500","515.500833"
"2017-02-12T17:00:00.000-0500","631.053056"
"2017-02-12T18:00:00.000-0500","708.575000"
"2017-02-12T19:00:00.000-0500","453.120000"
"2017-02-12T20:00:00.000-0500","554.589444"
"2017-02-12T21:00:00.000-0500","453.551389"
"2017-02-12T22:00:00.000-0500","419.450556"
"2017-02-12T23:00:00.000-0500","328.177778"
"2017-02-13T00:00:00.000-0500","293.752500"
"2017-02-13T01:00:00.000-0500","246.943889"
"2017-02-13T02:00:00.000-0500","213.986944"
"2017-02-13T03:00:00.000-0500","219.086111"
"2017-02-13T04:00:00.000-0500","303.708611"
"2017-02-13T05:00:00.000-0500","353.969167"
"2017-02-13T06:00:00.000-0500","346.050833"
"2017-02-13T07:00:00.000-0500","470.292222"
"2017-02-13T08:00:00.000-0500","844.538056"
"2017-02-13T09:00:00.000-0500","1100.996667"
"2017-02-13T10:00:00.000-0500","1271.799167"
"2017-02-13T11:00:00.000-0500","1447.440000"
"2017-02-13T12:00:00.000-0500","1034.428611"
"2017-02-13T13:00:00.000-0500","1076.172222"
"2017-02-13T14:00:00.000-0500","1087.887222"
"2017-02-13T15:00:00.000-0500","1259.043333"
"2017-02-13T16:00:00.000-0500","1140.602778"
"2017-02-13T17:00:00.000-0500","1148.073889"
"2017-02-13T18:00:00.000-0500","761.544722"
"2017-02-13T19:00:00.000-0500","568.453056"
"2017-02-13T20:00:00.000-0500","574.121667"
"2017-02-13T21:00:00.000-0500","458.542500"
"2017-02-13T22:00:00.000-0500","495.431389"
"2017-02-13T23:00:00.000-0500","404.716111"
"2017-02-14T00:00:00.000-0500","412.116667"
"2017-02-14T01:00:00.000-0500","310.014444"
"2017-02-14T02:00:00.000-0500","236.658333"
"2017-02-14T03:00:00.000-0500","222.509167"
"2017-02-14T04:00:00.000-0500","315.510556"
"2017-02-14T05:00:00.000-0500","369.872778"
"2017-02-14T06:00:00.000-0500","334.670000"
"2017-02-14T07:00:00.000-0500","461.795000"
"2017-02-14T08:00:00.000-0500","753.752222"
"2017-02-14T09:00:00.000-0500","923.558333"
"2017-02-14T10:00:00.000-0500","1107.344722"
"2017-02-14T11:00:00.000-0500","1194.949722"
"2017-02-14T12:00:00.000-0500","937.735833"
"2017-02-14T13:00:00.000-0500","1068.374722"
"2017-02-14T14:00:00.000-0500","1145.634167"
"2017-02-14T15:00:00.000-0500","988.993889"
"2017-02-14T16:00:00.000-0500","1067.995278"
"2017-02-14T17:00:00.000-0500","927.699722"
"2017-02-14T18:00:00.000-0500","739.886389"
"2017-02-14T19:00:00.000-0500","667.679722"
"2017-02-14T20:00:00.000-0500","604.938333"
"2017-02-14T21:00:00.000-0500","543.166667"
"2017-02-14T22:00:00.000-0500","442.916944"
"2017-02-14T23:00:00.000-0500","373.767778"
"2017-02-15T00:00:00.000-0500","337.545833"
"2017-02-15T01:00:00.000-0500","259.629167"
"2017-02-15T02:00:00.000-0500","186.775556"
"2017-02-15T03:00:00.000-0500","212.818611"
"2017-02-15T04:00:00.000-0500","274.319722"
"2017-02-15T05:00:00.000-0500","308.578056"
"2017-02-15T06:00:00.000-0500","316.756389"
"2017-02-15T07:00:00.000-0500","417.723611"
"2017-02-15T08:00:00.000-0500","841.546944"
"2017-02-15T09:00:00.000-0500","1067.051111"
"2017-02-15T10:00:00.000-0500","1109.526389"
"2017-02-15T11:00:00.000-0500","1087.352222"
"2017-02-15T12:00:00.000-0500","1045.260000"
"2017-02-15T13:00:00.000-0500","1285.351389"
"2017-02-15T14:00:00.000-0500","1064.570833"
"2017-02-15T15:00:00.000-0500","1067.725556"
"2017-02-15T16:00:00.000-0500","1055.146111"
"2017-02-15T17:00:00.000-0500","1014.010833"
"2017-02-15T18:00:00.000-0500","720.152500"
"2017-02-15T19:00:00.000-0500","732.987778"
"2017-02-15T20:00:00.000-0500","758.056111"
"2017-02-15T21:00:00.000-0500","799.688611"
"2017-02-15T22:00:00.000-0500","766.204722"
"2017-02-15T23:00:00.000-0500","722.300000"
"2017-02-16T00:00:00.000-0500","507.248333"
"2017-02-16T01:00:00.000-0500","424.247778"
"2017-02-16T02:00:00.000-0500","390.718056"
"2017-02-16T03:00:00.000-0500","364.996944"
"2017-02-16T04:00:00.000-0500","383.408889"
"2017-02-16T05:00:00.000-0500","414.637778"
"2017-02-16T06:00:00.000-0500","349.056667"
"2017-02-16T07:00:00.000-0500","542.903889"
"2017-02-16T08:00:00.000-0500","878.198056"
"2017-02-16T09:00:00.000-0500","1137.686389"
"2017-02-16T10:00:00.000-0500","1277.625278"
"2017-02-16T11:00:00.000-0500","1184.350278"
"2017-02-16T12:00:00.000-0500","923.879444"
"2017-02-16T13:00:00.000-0500","1066.437500"
"2017-02-16T14:00:00.000-0500","1290.296667"
"2017-02-16T15:00:00.000-0500","1026.999722"
"2017-02-16T16:00:00.000-0500","949.582500"
"2017-02-16T17:00:00.000-0500","857.506111"
"2017-02-16T18:00:00.000-0500","831.030278"
"2017-02-16T19:00:00.000-0500","720.440556"
"2017-02-16T20:00:00.000-0500","492.239167"
"2017-02-16T21:00:00.000-0500","508.844722"
"2017-02-16T22:00:00.000-0500","559.846667"
"2017-02-16T23:00:00.000-0500","332.631389"
"2017-02-17T00:00:00.000-0500","349.220833"
"2017-02-17T01:00:00.000-0500","237.833333"
"2017-02-17T02:00:00.000-0500","202.662778"
"2017-02-17T03:00:00.000-0500","232.843889"
"2017-02-17T04:00:00.000-0500","316.059167"
"2017-02-17T05:00:00.000-0500","338.066667"
"2017-02-17T06:00:00.000-0500","363.631389"
"2017-02-17T07:00:00.000-0500","460.921944"
"2017-02-17T08:00:00.000-0500","764.931111"
"2017-02-17T09:00:00.000-0500","931.416944"
"2017-02-17T10:00:00.000-0500","1032.328611"
"2017-02-17T11:00:00.000-0500","1247.801111"
"2017-02-17T12:00:00.000-0500","1159.197500"
"2017-02-17T13:00:00.000-0500","1282.267222"
"2017-02-17T14:00:00.000-0500","1183.746667"
"2017-02-17T15:00:00.000-0500","992.880278"
"2017-02-17T16:00:00.000-0500","791.148611"
"2017-02-17T17:00:00.000-0500","599.060278"
"2017-02-17T18:00:00.000-0500","487.915556"
"2017-02-17T19:00:00.000-0500","492.801111"
"2017-02-17T20:00:00.000-0500","413.024167"
"2017-02-17T21:00:00.000-0500","632.193056"
"2017-02-17T22:00:00.000-0500","493.108611"
"2017-02-17T23:00:00.000-0500","424.018889"
"2017-02-18T00:00:00.000-0500","384.328056"
"2017-02-18T01:00:00.000-0500","310.441944"
"2017-02-18T02:00:00.000-0500","205.145556"
"2017-02-18T03:00:00.000-0500","205.454167"
"2017-02-18T04:00:00.000-0500","253.227500"
"2017-02-18T05:00:00.000-0500","312.188889"
"2017-02-18T06:00:00.000-0500","321.928889"
"2017-02-18T07:00:00.000-0500","406.977778"
"2017-02-18T08:00:00.000-0500","452.448889"
"2017-02-18T09:00:00.000-0500","502.578333"
"2017-02-18T10:00:00.000-0500","489.765278"
"2017-02-18T11:00:00.000-0500","540.568333"
"2017-02-18T12:00:00.000-0500","510.270000"
"2017-02-18T13:00:00.000-0500","456.691944"
"2017-02-18T14:00:00.000-0500","494.579722"
"2017-02-18T15:00:00.000-0500","502.795556"
"2017-02-18T16:00:00.000-0500","429.950556"
"2017-02-18T17:00:00.000-0500","428.196667"
"2017-02-18T18:00:00.000-0500","478.975833"
"2017-02-18T19:00:00.000-0500","362.479167"
"2017-02-18T20:00:00.000-0500","366.515000"
"2017-02-18T21:00:00.000-0500","400.625833"
"2017-02-18T22:00:00.000-0500","374.313056"
"2017-02-18T23:00:00.000-0500","310.666667"
We use the following code to load and decompose this time series:
library("forecast")
data <- read.csv("data.csv")
x <- msts(data, seasonal.periods=c(24,168))
decom <- decompose(x[,2], "multiplicative")
plot(decom)
The decomposition looks like this:
The 'observed' and 'seasonal' components looks almost identical, the 'trend' doesn't seem right since it is rising up too sharply, and the 'random' component looks constant.
So we are not sure if we made a mistake in decomposing or loading this time series in R. Is there another way of decomposing this time series so that it makes more sense or is correct? Should we be loading the data another way so that the time stamps get properly assigned to the data values?

How to fit a loess curve over this decomposed time series data in R?

We have time series data with some seasonality from the past 4 years. We want to predict the general rise in trend next year. For this, we decomposed the time series and observed the trend line:
However, this trend line is placed in the middle of the values rather than the values themselves. We are not satisfied with simply extrapolating this trend line since it falls very short of expected traffic.
Since we are interested in only the general rise in trend and not the seasonality, we remove the seasonality from the components:
mydata <- read.csv("values.csv")
mydataseries <- ts(mydata, start=c(2012,1,1),frequency = 365.25
mydataseriescomponents <- decompose(mydataseries)
mydataseriesminusseasons <- mydataseries - mydataseriescomponents$seasonal
We are now trying to fit a loess() curve in R around this time series data minus the seasonal component, that is mydataseriesminusseasons:
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921907140.7
957529712.9
934518615.5
1183156116
1151402673
893513180.3
829956342
839183085.7
904103129.6
972880817.6
1227505644
1192421196
904138184.4
944757497
1375038689
1328415139
1193189782
1253504218
1251929547
1185272494
1244859781
1231641700
1171271060
1343450107
1393786279
1416773258
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1582950274
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3184736742
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3196099484
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3645589701
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5072864386
5232041565
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3245094491
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4331144672
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3622317542
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4483667233
5577532419
5303025177
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5385575901
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5021515141
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5703914224
5678717816
5600943246
5110447244
4590128626
4877035122
5442054864
5540200590
5229513831
4574668437
3734155348
2825747731
2665659550
3218611753
3177069031
3225833078
2857378098
2605242926
2290489544
2556941031
3052363819
3023655743
3139325913
3183875762
3084641745
2584707861
2573111682
2596449197
3119292036
3103807890
3003440326
3050225234
2639037382
2719271674
3174072606
2288642761
2407051251
2769659370
2792708736
2422258872
2550055714
3094896689
3167462954
3145311598
2982505987
2846929030
2410677820
2528516371
3317404595
3405548963
3264859256
3217887704
3076794348
2682319143
2752574869
3546644862
3387139453
3465822066
3527697761
3304648740
2671176465
2775904656
3369489444
3186975051
3265608930
3125970955
2336383605
2101672532
2227649209
3046717349
3161392531
3174174168
3069526988
3140929673
2396972936
2491933483
3274873818
3471396399
3449881421
3260944652
3059846681
2300326480
2410144424
3280639160
3165080129
1880734112
2026731745
1851573264
1593311358
1623039610
1888090770
1983714225
1990135314
1884610261
1966858510
1881518298
1817889199
2209334095
2213195958
3180360773
3506589476
3266458246
2314386847
2203488644
2979775043
2887785856
3029641480
2854946175
2971200632
2338656676
2508827357
3221768984
3271647981
1494100499
2557318665
2566743784
2024262236
2326858931
2898711691
2629767554
2418419575
2529673112
2517326919
2394071701
2882872031
3958018274
4398615549
4850186215
4769908627
3875047506
3686152334
3944845885
4407300286
5483421647
5150638137
5610203814
4608824221
3183456836
4173041229
5250468129
5281994707
5707036828
5352424541
5755606494
4561838923
5206514812
6017273753
5965257129
6031374315
6079040231
4379684817
2770833772
3855818791
4754914912
4592227424
4426284753
4410453960
4025381538
3174239722
3637497533
4441638488
4174099821
3906145103
3894032411
3032325960
2296152859
3634154800
5013642209
4862468183
4819578542
4516969809
3607317085
2438327317
3732908830
5107431888
4696140901
1856348267
1237864483
406427050.9
166776835.3
1498808575
1828048545
1624152578
1349901570
1420774156
998226407.7
1012022910
1532830520
1859891754
1422784584
1300680502
1969725485
1936125754
1730921235
2284540775
2480696530
2271292433
2177291835
2174315253
1943550394
1789789173
2208387982
2445973421
2180115879
2053590351
2057128187
1868753587
1794479025
2093710971
2310482091
1882157273
1506021669
1535469156
2038211764
2132884419
2539631965
2937476532
2237006540
1897259543
801631140.7
589473184.2
116334380.3
674275361.3
1282712559
1119202007
1004676722
781599593.7
1184057471
1405174402
2414122535
3215047803
3117104932
2843730513
2338714670
1830982498
1282357057
1398445510
1709185553
1343346425
1299455992
1382754660
1451688601
1355952002
1395566041
1646971917
1518132724
1378268909
1383505613
1477733701
1396182586
1340692285
1513095775
952400088.2
654084246.7
626929432.3
700786606
523798987.3
1212948425
1567710490
1072360130
1057312922
876650104.6
1532682661
1439342205
1801524855
2099113224
1992935512
2063753470
1849349346
1589462235
1341435771
1147947080
2071354378
2006092710
2105408195
1234206054
656144711.4
1208902786
1232216105
2213555415
2017146411
1991371378
994748835.5
1523018258
551904050.2
4489317425
7011882149
7509029269
7405531928
6627086822
5118361296
2929515389
4386298474
6193577031
6201888044
5600929516
5249637157
4071570693
3812427933
4814958529
6581889904
6706593436
6538328968
5770674289
5146640592
3869631764
5168489883
7218970135
7319257013
6818980598
6581026441
4463128268
2549197744
2751600290
3586655201
3073231312
2610229695
2664878334
2445857027
3333286739
5342397336
8218514365
7400486992
7351969323
6170498161
6166815740
4938259613
5123232548
6952344511
7484834076
7975757356
6042108897
3954139391
2561409558
3636287452
6659637045
6610145475
6303751643
5790815423
5286756045
532871596.2
2403662106
2933984545
2177296758
1954486433
1713519574
1459802901
4020142932
5383799348
6858179971
7112822894
6327294007
5759923625
5042533123
3796835736
5750880779
7453820307
7335397513
6962686301
7790660114
6724956363
5003169135
6701050938
7992041249
7756326177
7913301179
7741411043
6785177818
6284270117
6963921883
7785974652
7574222100
7588499293
5788919572
4105788142
2859825648
2924210471
4069907537
3895077405
3979654780
2075329893
1979403277
1632081713
1877890303
2412917344
3763581680
3726439732
3673898152
3345262416
2191053212
2548906553
3841133834
3846853011
3492242728
3479185981
3290714847
2514060721
2645599322
2791855040
3791586130
However, we are not familiar with the form of the loess() function and it seems to expect a formula which we do not know. We tried the following:
y <- c(mydata)
x <- 1:1614
lo <- loess(y~x)
We get the error: Error in model.frame.default(formula = y ~ x) :
invalid type (list) for variable 'y'
How do we fit a loess curve around the values to get the general trend line? Also, after removing the seasonal component we have some negative values for some reason. Would this affect the loess() curve?

Resampling multivariate time series in R

I have a set of bivariate time series and want to resample them to the same length. I thought that it might be a good idea to use the mean length of all time series, since I wanted to avoid that some series will be shortened or extended too much. My first naive idea was using the resample method of the signal package, and resample each dimension of a series separately. I don't like this idea very much, since I have the fear that the alignment between the dimensions might suffer from the independent resampling, but I hoped this effect might be negligible.
My current problem is that the resampling of the data creates artifacts at the end and beginning of a series. It seems that the resample method assumes that the series starts from zero. Now I'm wondering if there is a more suitable resampling method which in the best case is readily available (in R) and maybe also supports bivariate time series.
Plot:
http://i.stack.imgur.com/3OwAt.png
Code example:
example <- c(-2014.1, -2014.1, -2014.1, -2014, -2014, -2013.9, -2013.9,
-2013.7, -2013.5, -2013.4, -2013.1, -2012.9, -2012.6, -2012.4,
-2012, -2011.7, -2011.4, -2011, -2010.5, -2010.1, -2009.5, -2009.1,
-2008.6, -2008, -2007.5, -2006.9, -2006.4, -2005.7, -2005.1,
-2004.4, -2003.7, -2003, -2002.4, -2001.5, -2000.7, -1999.9,
-1999.1, -1998.2, -1997.4, -1996.5, -1995.6, -1994.6, -1993.6,
-1992.6, -1991.7, -1990.7, -1989.7, -1988.9, -1987.9, -1986.9,
-1985.9, -1984.9, -1984, -1983, -1982.1, -1981.1, -1980.1, -1979.2,
-1978.2, -1977.2, -1976.4, -1975.4, -1974.4, -1973.4, -1972.4,
-1971.5, -1970.5, -1969.6, -1968.6, -1967.6, -1966.6, -1965.7,
-1964.7, -1963.9, -1962.9, -1961.9, -1960.9, -1959.9, -1958.9,
-1957.9, -1956.9, -1955.9, -1955, -1954, -1953, -1952.1, -1951.5,
-1951.1, -1950.6, -1950.1, -1949.6, -1949.2, -1948.7, -1948.2,
-1947.9, -1947.4, -1946.9, -1946.4, -1945.9, -1945.4, -1944.9,
-1944.4, -1943.9, -1943.4, -1943, -1942.5, -1942, -1941.5, -1941,
-1940.6, -1940.1, -1939.6, -1939.1, -1938.7, -1938.2, -1937.7,
-1937.2, -1936.7, -1936.2, -1935.7, -1935.4, -1934.9, -1934.4,
-1933.9, -1933.4, -1932.9, -1932.4, -1931.9, -1931.4, -1931,
-1930.5, -1930, -1929.5, -1929, -1928.6, -1928.1, -1927.6, -1927.1,
-1926.6, -1926.2, -1925.7, -1925.2, -1924.7, -1924.4, -1923.9,
-1923.4, -1922.9, -1922.4, -1921.9, -1921.4, -1920.9, -1920.4,
-1919.9, -1919.4, -1919, -1918.5, -1918, -1917.5, -1917, -1916.6,
-1916.1, -1915.6, -1915.1, -1914.6, -1914.2, -1913.7, -1913.2,
-1912.7, -1912.2, -1911.7, -1911.4, -1910.9, -1910.4, -1909.9,
-1909.4, -1908.9, -1908.4, -1907.9, -1907.5, -1906.9, -1906.5,
-1906, -1905.5, -1905, -1904.6, -1904, -1903.6, -1903.1, -1902.7,
-1902.2, -1901.7, -1901.2, -1900.7, -1900.4, -1899.9, -1899.4,
-1898.9, -1898.4, -1897.9, -1897.4, -1896.9, -1896.4, -1895.9,
-1895.2, -1895, -1894.5, -1894, -1893.6, -1893.1, -1892.6, -1892.1,
-1891.6, -1891.2, -1890.7, -1890.2, -1889.7, -1889.2, -1888.9,
-1888.4, -1887.9, -1887.4, -1886.9, -1886.4, -1885.6, -1885.4,
-1884.9, -1884.5, -1884, -1883.5, -1883, -1882.5, -1882.1, -1881.6,
-1881.1, -1880.6, -1880.2, -1879.7, -1879.2, -1878.7, -1878.4,
-1877.9, -1877.4, -1876.9, -1876.1, -1875.6, -1875.1, -1874.6,
-1874.1, -1873.6, -1873.2, -1872.7, -1872.2, -1871.7, -1871.4,
-1870.7, -1870.4, -1869.9, -1869.4, -1868.9, -1868.4, -1867.9,
-1867.4, -1867.2, -1866.4, -1866, -1865.5, -1865, -1864.5, -1864.1,
-1863.6, -1863.1, -1862.6, -1862.1, -1861.7, -1861.2, -1860.7,
-1860.2, -1859.7, -1859.4, -1858.9, -1858.4, -1857.9, -1857.4,
-1856.9, -1856.4, -1855.9, -1855.4, -1854.9, -1854.5, -1854,
-1853.5, -1853.1, -1852.6, -1852.1, -1851.6, -1851.1, -1850.7,
-1850.2, -1849.7, -1849.2)
plot(example, t="l", main="Original")
plot(resample(example,250,length(example)), t="l", main="Resampled")

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