# Daily data, R forecasts only yield straight line?

I've tried ets, tbats, and arima - I can't seem to get anything but a straight line out of this.

Example I tried:

hbf_ts2 <- msts(hbf$TheValue, seasonal.periods = c(7, 365.25)) fit2 <- tbats(hbf_ts2) fc2 <- forecast(fit2, h=60) plot(fc2)  Putting this into the PowerBI forecaster though yielded a meaningful forecast with no problem (2 mins, 2 maxes at the appropriate times of the forecasted year). Edit: Added PowerBI pic showing what I believe are correct mins around mar/apr & sep/oct and maxes around jul/aug & dec. My question can be interpreted as: how to reverse engineer what PowerBI sees? Can somebody show me how to get a forecast to pick out the pattern(s) in this data?  TheDate TheValue 2016-01-01 492905 2016-01-02 1601949 2016-01-03 1151405 2016-01-04 2186586 2016-01-05 1113354 2016-01-06 309563 2016-01-07 2055883 2016-01-08 999319 2016-01-09 2354847 2016-01-10 971635 2016-01-11 711481 2016-01-12 1187269 2016-01-13 1493296 2016-01-14 1656428 2016-01-15 1372378 2016-01-16 1649070 2016-01-17 1372722 2016-01-18 1066177 2016-01-19 2289296 2016-01-20 463604 2016-01-21 1783337 2016-01-22 591826 2016-01-23 1921277 2016-01-24 1002645 2016-01-25 1288591 2016-01-26 1801679 2016-01-27 2463919 2016-01-28 1145362 2016-01-29 963447 2016-01-30 1722081 2016-01-31 1112340 2016-02-01 1389396 2016-02-02 1018990 2016-02-03 1290466 2016-02-04 1274589 2016-02-05 1027891 2016-02-06 2120179 2016-02-07 1766689 2016-02-08 1159126 2016-02-09 2731442 2016-02-10 1380733 2016-02-11 957275 2016-02-12 692530 2016-02-13 926444 2016-02-14 500533 2016-02-15 783966 2016-02-16 1045921 2016-02-17 1807967 2016-02-18 2594422 2016-02-19 434663 2016-02-20 2057508 2016-02-21 1991184 2016-02-22 1134781 2016-02-23 1169244 2016-02-24 1315783 2016-02-25 505407 2016-02-26 697467 2016-02-27 930899 2016-02-28 836639 2016-02-29 1175764 2016-03-01 1729977 2016-03-02 1214509 2016-03-03 1313172 2016-03-04 1898133 2016-03-05 567347 2016-03-06 570458 2016-03-07 797164 2016-03-08 262597 2016-03-09 1133707 2016-03-10 1474149 2016-03-11 993599 2016-03-12 1140452 2016-03-13 470952 2016-03-14 2144962 2016-03-15 1010312 2016-03-16 816210 2016-03-17 778302 2016-03-18 1410789 2016-03-19 2098186 2016-03-20 617023 2016-03-21 783786 2016-03-22 984688 2016-03-23 896679 2016-03-24 802999 2016-03-25 992319 2016-03-26 803603 2016-03-27 412898 2016-03-28 1041051 2016-03-29 1203917 2016-03-30 609461 2016-03-31 1277114 2016-04-01 1513692 2016-04-04 1615950 2016-04-05 2399861 2016-04-06 1568040 2016-04-07 1785726 2016-04-08 993752 2016-04-09 1183265 2016-04-10 1186096 2016-04-11 842837 2016-04-12 1673087 2016-04-13 1476926 2016-04-14 1958557 2016-04-15 418363 2016-04-16 592586 2016-04-18 418754 2016-04-19 1733697 2016-04-20 1304147 2016-04-21 1045310 2016-04-22 860830 2016-04-23 1840458 2016-04-24 744558 2016-04-25 1046460 2016-04-26 1246456 2016-04-27 714769 2016-04-28 1595069 2016-04-29 764510 2016-04-30 1943821 2016-05-01 1345685 2016-05-02 860365 2016-05-03 1582654 2016-05-04 1159752 2016-05-05 911923 2016-05-06 954731 2016-05-07 860921 2016-05-08 2082131 2016-05-09 2401106 2016-05-10 1586094 2016-05-11 1513561 2016-05-12 551191 2016-05-13 942977 2016-05-14 1514368 2016-05-15 834673 2016-05-16 1464914 2016-05-17 2825643 2016-05-18 1919046 2016-05-19 1106938 2016-05-20 1477300 2016-05-21 1389177 2016-05-22 1131176 2016-05-23 1013731 2016-05-24 1770357 2016-05-25 1346478 2016-05-26 1302532 2016-05-27 2240548 2016-05-28 1653050 2016-05-29 1969550 2016-05-30 797389 2016-05-31 1979795 2016-06-01 1020901 2016-06-02 1494291 2016-06-03 1976515 2016-06-04 1905873 2016-06-05 1303286 2016-06-06 942723 2016-06-07 2214164 2016-06-08 2321545 2016-06-09 1177346 2016-06-10 1240553 2016-06-11 1458808 2016-06-12 874046 2016-06-13 1423719 2016-06-14 1368339 2016-06-15 1472794 2016-06-16 1681757 2016-06-17 1191515 2016-06-18 1794076 2016-06-19 1338900 2016-06-20 2128570 2016-06-21 2709468 2016-06-22 1481802 2016-06-23 1820330 2016-06-24 1775269 2016-06-25 1350577 2016-06-26 1768682 2016-06-27 1489650 2016-06-28 2198414 2016-06-29 1106565 2016-06-30 2088400 2016-07-01 1983991 2016-07-02 1377339 2016-07-03 1817443 2016-07-04 1135847 2016-07-05 2552720 2016-07-06 1105784 2016-07-07 1807094 2016-07-08 1524917 2016-07-09 652983 2016-07-10 576085 2016-07-11 1568422 2016-07-12 2221462 2016-07-13 2717538 2016-07-14 1824117 2016-07-15 2261913 2016-07-16 1572669 2016-07-17 2366064 2016-07-18 2385405 2016-07-19 1931224 2016-07-20 1724003 2016-07-21 2035054 2016-07-22 1235362 2016-07-23 1308190 2016-07-24 1986094 2016-07-25 1958964 2016-07-26 1691101 2016-07-27 2205191 2016-07-28 1051101 2016-07-29 757187 2016-07-30 1751114 2016-07-31 1071575 2016-08-01 2059648 2016-08-02 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2017-01-23 629802 2017-01-24 1367775 2017-01-25 1111216 2017-01-26 1949142 2017-01-27 819318 2017-01-28 1839211 2017-01-29 175179 2017-01-30 800008 2017-01-31 1407335 2017-02-01 1038374 2017-02-02 669512 2017-02-03 778464 2017-02-04 1457364 2017-02-05 797369 2017-02-06 1118268 2017-02-07 1276264 2017-02-08 1578296 2017-02-09 2960152 2017-02-10 1143752 2017-02-11 1958829 2017-02-12 3245721 2017-02-13 1356475 2017-02-14 1062092 2017-02-15 881009 2017-02-16 1266027 2017-02-17 829273 2017-02-18 2103150 2017-02-19 1335047 2017-02-20 2437420 2017-02-22 974614 2017-02-23 1189815 2017-02-24 1012674 2017-02-25 1828608 2017-02-26 1655255 2017-02-27 1173650 2017-02-28 504155 2017-03-01 730735 2017-03-02 1596667 2017-03-03 458890 2017-03-04 2297390 2017-03-05 1655067 2017-03-06 2227014 2017-03-07 1950607 2017-03-08 1933252 2017-03-09 738067 2017-03-10 1119581 2017-03-11 1166814 2017-03-12 820901 2017-03-13 1526354 2017-03-14 1165152 2017-03-15 1736698 2017-03-16 2289070 2017-03-17 1407411 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1005578 2018-06-04 1857927 2018-06-05 2710759 2018-06-06 2151611 2018-06-07 590602 2018-06-09 994103 2018-06-10 1189664 2018-06-11 1804087 2018-06-12 3249893 2018-06-13 2140094 2018-06-14 4001751 2018-06-15 952523 2018-06-16 1004758 2018-06-17 765776 2018-06-18 1928883 2018-06-19 2353313 2018-06-20 781372 2018-06-21 1442026 2018-06-22 678432 2018-06-23 2885504 2018-06-24 819634 2018-06-25 1863066 2018-06-26 1328277 2018-06-27 2221043 2018-06-28 1522942 2018-06-29 1896754 2018-06-30 1196607 2018-07-01 546782 2018-07-02 2179502 2018-07-03 1570718 2018-07-04 3333997 2018-07-05 2702911 2018-07-06 1272268 2018-07-07 1855696 2018-07-08 1783158 2018-07-09 1444503 2018-07-10 2053629 2018-07-11 906335 2018-07-12 1864814 2018-07-13 717539 2018-07-14 2136551 2018-07-15 1273029 2018-07-16 1772809 2018-07-17 1661216 2018-07-18 2713665 2018-07-19 1363139 2018-07-20 1141465 2018-07-21 1253139 2018-07-22 1331203 2018-07-23 1491406 2018-07-24 1402238 2018-07-25 75357 2018-07-26 1525053 2018-07-27 2397020 2018-07-28 1971354 2018-07-29 1772911 2018-07-30 3052149 2018-07-31 2361227 2018-08-01 1360559 2018-08-02 2519580 2018-08-03 988896 2018-08-04 2677285 2018-08-05 1171423 2018-08-06 2155847 2018-08-07 1461634 2018-08-08 1452754 2018-08-09 1437879 2018-08-10 1132824 2018-08-11 982006 2018-08-12 1120162 2018-08-13 1671429 2018-08-14 3025344 2018-08-15 1069422 2018-08-16 1195537 2018-08-17 882980 2018-08-18 2760260 2018-08-19 1459098 2018-08-20 1574928 2018-08-21 1842542 2018-08-22 1857758 2018-08-23 1811214 2018-08-24 1177500 2018-08-25 2351327 2018-08-26 1253109 2018-08-27 1352088 2018-08-28 2468555 2018-08-29 1872385 2018-08-30 1391215 2018-08-31 1378033 2018-09-01 1153951 2018-09-02 901030 2018-09-03 1949716 2018-09-04 1754018 2018-09-05 2064959 2018-09-06 437698 2018-09-07 953701 2018-09-08 602979 2018-09-09 737062 2018-09-10 1466196 2018-09-11 1316563 2018-09-12 1419652 2018-09-13 1513515 2018-09-14 1100097 2018-09-15 2513661 2018-09-16 1338282 2018-09-17 1282230 2018-09-18 1621023 2018-09-19 712422 2018-09-20 1069738 2018-09-21 1093389 2018-09-22 1757139 2018-09-23 2229094 2018-09-24 1608801 2018-09-25 1776676 2018-09-26 715061 2018-09-27 2061564 2018-09-28 1775204 2018-09-29 596271 2018-09-30 1052694 2018-10-01 2005555 2018-10-02 1201587 2018-10-03 1506207 2018-10-04 1135962 2018-10-05 1425691 2018-10-06 1929594 2018-10-07 1558859 2018-10-08 2644698 2018-10-09 2168196 2018-10-10 601651 2018-10-11 704045 2018-10-12 1468953 2018-10-13 1144636 2018-10-14 621194 2018-10-15 1507004 2018-10-16 1328006 2018-10-17 905645 2018-10-18 946435 2018-10-19 1379612 2018-10-20 1165128 2018-10-21 1662357 2018-10-22 1934873 2018-10-23 2031270 2018-10-24 1404769 2018-10-25 1107453 2018-10-26 1065420 2018-10-27 1436357 2018-10-28 1283520 2018-10-29 687467 2018-10-30 1542343 2018-10-31 1857454 2018-11-01 1348635 2018-11-02 971220 2018-11-03 1579107 2018-11-05 1850613 2018-11-06 2203924 2018-11-07 1478081 2018-11-08 904263 2018-11-09 894744 2018-11-10 2138165 2018-11-11 2545984 2018-11-12 1273497 2018-11-13 1234634 2018-11-14 1319511 2018-11-15 750258 2018-11-16 1607310 2018-11-17 595905 2018-11-18 1045006 2018-11-19 3356163 2018-11-20 1962632 2018-11-21 854751 2018-11-22 295059 2018-11-23 906795 2018-11-24 713094 2018-11-25 1043280 2018-11-26 974499 2018-11-27 1200869 2018-11-28 1252872 2018-11-29 1189154 2018-11-30 1647594 2018-12-01 1743667 2018-12-03 339700 2018-12-04 1814194 2018-12-05 1140506 2018-12-06 2009347 2018-12-07 1304115 2018-12-08 1986904 2018-12-09 1392328 2018-12-10 1466535 2018-12-11 1634210 2018-12-12 1201033 2018-12-13 1518156 2018-12-14 911461 2018-12-15 2941987 2018-12-16 1313848 2018-12-17 1958368 2018-12-18 1606970 2018-12-19 2916651 2018-12-20 1509846 2018-12-21 938201 2018-12-22 1204572 2018-12-23 2729989 2018-12-24 2192122 2018-12-26 2516399 2018-12-27 1668535 2018-12-30 1600417 2018-12-31 2237816  • There is very little pattern I can discern in your data. Where are the "appropriate times" at which you believe there should be a maximum or a minimum? A flat line can be surprisingly often the optimal forecast, so have you compared the performance of PowerBI and say msts() on a holdout sample? I may write up an answer later on why I see very little pattern here. – Stephan Kolassa Jan 22 at 7:40 • Updated question with the PowerBI comparison. – sherifffruitfly Jan 22 at 9:56 • Thank you. This is actually a very good question. I will write up an answer later today or tomorrow, and I ask the close and down voters to hold back. – Stephan Kolassa Jan 22 at 10:02 • Yes, this question asks how to perform an action in R. However, it needs statistical expertise to understand or answer, which is a direct quote from the page detailing what is on topic here. Specifically, I intend to argue why a flat line forecast is probably the most appropriate here for statistical reasons, and why PowerBI is likely peddling snake oil. I have nominated the question for reopening and hope for the best. – Stephan Kolassa Jan 22 at 16:42 ## 1 Answer You have three years of daily data, which is a good amount. As you write, you may have (intra-weekly and intra-yearly), so it is a good idea to look at models that can model such patterns, like or . Let's start by looking at your series (I'm using R, and I created a data.frame similar to your hbf): with(hbf,plot(TheDate,TheValue,type="o",pch=19))  No patterns are readily apparent. Let us use appropriate seasonplots to examine any seasonalities. We will start with the intra-weekly seasonality: library(forecast) seasonplot(ts(hbf$TheValue,frequency=7),pch=19)


I do not see a seasonal pattern here. Let's look at an STL decomposition:

plot(stl(ts(hbf\$TheValue,frequency=7),s.window="periodic"))


Again, there is no visible seasonality here. (Yes, there is a seasonal component in the STL plot, but note the scales given by the gray boxes. The seasonal component is completely negligible. See here for more information.)

For good measure, here are beanplots of your series by weekday:

library(beanplot)
with(hbf,beanplot(TheValue~TheDateFactor,what=c(0,1,0,0),col="lightgray",border=NA))
with(hbf,points(as.numeric(TheDateFactor)+runif(nrow(hbf),-.3,.3),TheValue,pch=19,cex=0.6))


Again, there is no weekly pattern.

We can repeat the exercise with the yearly seasonality, though only the seasonplots and the STL plots make sense:

seasonplot(ts(hbf$$TheValue,frequency=365),pch=19) plot(stl(ts(hbf$$TheValue,frequency=365),s.window="periodic"))


Just as for weekly seasonality, no pattern is apparent.

While we are plotting, let's also look at ACF and PACF plots:

acf(hbf$$TheValue) pacf(hbf$$TheValue)


Yes, a few of the (partial) autocorrelations exceed the significance limits. However, they do so only very slightly, and in a series of more than 1,000 observations, such small exceedances do not really indicate anything relevant. Also, note that there are no obvious periodicities of period 7 in the (P)ACF plots, which we would expect if there were any kind of weekly seasonality.

Bottom line: your data are pretty much not seasonal.

Why do methods like tbats() give you a flat line forecast? Time series (like any other data with a random component) consist of signal and noise. Classical signals are trend, seasonality, autoregression and moving average effects, or the effects of causal drivers (which I assume you do not have). Signal, by definition, is patterns that are forecastable. Everything else is not signal, it is noise. You can call noise "randomness".

Forecasting algorithms try to separate the signal and the noise. They forecast the forecastable part, the signal. It does not make sense to forecast the unforecastable part - it will always make the forecast worse.

There is no seasonal signal in your data, nor is there trend. There is some very little ARMA signal, per the (P)ACF plots. Fitting an ARIMA model picks up on this:

plot(forecast(auto.arima(hbf_ts2),h=100))


Note that the forecast wiggles a tiny little bit at the beginning, but is again essentially a flat line. This is because the ARMA signal is very weak.

Given the pretty much complete lack of signal in your data, I am very sure that such a forecast will be near-optimal. Flat forecasts can beat more "wiggly" ones surprisingly often.

I suggest you try a holdout forecast comparison: hold out the last (say) three months of data, fit a PowerBI model, a TBATS one and an ARIMA one to the remaining data, forecast out into the holdout sample, and compare the Mean Squared Error. I'll bet you a beverage of your choice that PowerBI will not be optimal. (I'll be at a couple of forecasting conferences later this year where you can claim your prize.)

Final question: why does PowerBI give you a very wiggly forecast? I'll be cynical here. I believe that PowerBI does not attempt to give you a good forecast. It wants to give you a forecast that looks sophisticated, so you will believe that PowerBI is sophisticated. Complexity for its own sake will usually make forecasts worse. I very much recommend the special issue of simple vs. complex methods in forecasting in the Journal of Business Research (vol. 68, no. 8, 2015). I do believe that complex methods have their place, but only if there are clear drivers for your series, and there are none such here.

In the end, I'd trust the people behind the forecast package for R much more than the people behind PowerBI. Rob Hyndman, who maintains the package, is probably the world's foremost expert in forecasting. He just stepped down from a decade-long tenure as the editor in chief of the International Journal of Forecasting. He knows what he is doing, and the forecast package is the state of the art, proven over many years. In contrast, after 13 years in forecasting, I have never seen PowerBI in this field. And the screenshot you show does not impress me. It truly looks like snake oil.

• I'm not so sure about this blanket condemnation. I won't defend PowerBI, about which I know nothing, but wish only to point out that (1) the pacf peaks at 7 and 14, although small, support a weekly seasonal model; (2) a robust spread-vs-level plot (based on rolling MADs and medians) indicates a square root transformation could be helpful; and (3) applying the OP's R analysis to the square roots actually produces a varying forecast (from 1.13M to 2.04M). It looks qualitatively like a hybrid of yours and PowerBI's (which does appear to forecast a lot of noise) and shows four quarterly extrema. – whuber Jan 23 at 18:21
• Thank you kindly for the detailed analysis - gives me plenty to think about & test! – sherifffruitfly Jan 23 at 18:45
• @whuber: yes, the TBATS model fits a Box-Cox parameter of about 0.5, in line with your suggestion of a square root transform. One may be able to do better than a simple flat forecast. I'll admit that the PowerBI plot raised my hackles. I get this kind of question at my day job, and I'm honestly a bit tired of the entire "if it's more complex, it must be better" idea... – Stephan Kolassa Jan 23 at 20:47