tbats strange behaviour

[denadai2]

I write this issue because tbats is behaving strangely and I think it's a bug.

File: https://dl.dropboxusercontent.com/u/1118905/bug.RData
Source:

library(forecast)
load("bug.RData")
y <- msts(dat.ts, seasonal.periods=c(24, (7*24)))
fit <- tbats(y)
plot(fit)

It doesn't show the slope and season. Maybe it doesn't find the seasonality, but so why doesn't it show a warning message?

It behaves normally with

y <- msts(dat.ts, seasonal.periods=c(24))

Thanks

[robjhyndman]

The fitted model is clearly unstable which is a problem. I'll look into why that happens.

The seasonality is not being picked up because it is not correctly specified. The graph indicates the length of a day is less than 24 observations. This is also evident in the fitted model using seasonal.periods=24, where the level has tried to pick up some of the seasonality because of the mis-specification.

[slavarazbash]

Hi Marco,

In the first case, it seems that the algobfinds that the best model has no
seasonal components and no trend. It tries different nested models and
picks the one with the lowest AIC. I think that it is too early to call it
a bug.

Is this hourly data? Are you trying to model weekly seasonality in the
first example? If so, then you need at least four weeks to model weekly
seasonality. How many weeks of data do you have?

Best Regards,

Slava Razbash
On 19/09/2014 1:58 am, "Marco De Nadai" notifications@github.com wrote:

I write this issue because tbats is behaving strangely and I think it's a
bug.

File: https://dl.dropboxusercontent.com/u/1118905/bug.RData
Source:

library(forecast)
load("bug.RData")
y <- msts(dat.ts, seasonal.periods=c(24, (7*24))
fit <- tbats(y)
plot(fit)

It doesn't show the slope and season. Maybe it doesn't find the
seasonality, but so why doesn't it show a warning message?
[image: screen shot 2014-09-18 at 17 46 13]
https://cloud.githubusercontent.com/assets/190799/4322742/fc62ef1e-3f4a-11e4-843f-f447ff026128.png
It behaves normally with

y <- msts(dat.ts, seasonal.periods=c(24))

Thanks

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#87.

[robjhyndman]

Here is the fitted model:

fit
BATS(0.369, {2,3}, -, -)

Call: tbats(y = y)

Parameters
Lambda: 0.36928
Alpha: 0.60449
AR coefficients: 1.7239 -0.83751
MA coefficients: -0.98829 0.13707 -0.14475

Seed States:
[,1]
[1,] 11.111
[2,] 0.000
[3,] 0.000
[4,] 0.000
[5,] 0.000
[6,] 0.000

Sigma: 3.4771e+52
AIC: 9188.2

Slava: What are the four zero seed states? With no seasonality, and no trend, I was expecting only one seed state here.

[slavarazbash]

They are the arma states.
On 19/09/2014 8:55 am, "Rob J Hyndman" notifications@github.com wrote:

Here is the fitted model:

fit
BATS(0.369, {2,3}, -, -)

Call: tbats(y = y)

Parameters
Lambda: 0.36928
Alpha: 0.60449
AR coefficients: 1.7239 -0.83751
MA coefficients: -0.98829 0.13707 -0.14475

Seed States:
[,1]
[1,] 11.111
[2,] 0.000
[3,] 0.000
[4,] 0.000
[5,] 0.000
[6,] 0.000

Sigma: 3.4771e+52
AIC: 9188.2

Slava: What are the four zero seed states? With no seasonality, and no
trend, I was expecting only one seed state here.

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#87 (comment).

[robjhyndman]

OK. I wonder why the level heads out of control near the end. It looks like a "divide by something close to zero" problem.

Can you see why these give different models:

fit <- tbats(y)
by <- BoxCox(y, lambda=fit$lambda)
fit2 <- tbats(by, use.box.cox=FALSE)

The latter looks well behaved but the first approach isn't finding it for some reason.

[denadai2]

@robjhyndman @slavarazbash sorry I did not specified: hourly data, so that is a timeseries with frequency=24. I know that there is a daily and weekly seasonality (more or less of course). In the case posted I have one month of data.
I'm not an expert, as you see, but I'm trying a lot these algorithms :)

[slavarazbash]

Marco, how manys days of data do you have?
On 19/09/2014 11:09 am, "Marco De Nadai" notifications@github.com wrote:

@robjhyndman https://github.com/robjhyndman @slavarazbash
https://github.com/slavarazbash sorry I did not specified: hourly data,
so that is a timeseries with frequency=24. I know that there is a daily and
weekly seasonality (more or less of course).
I'm not an expert, as you see, but I'm trying a lot these algorithms :)

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#87 (comment).

[denadai2]

29 days and some hours :)

(you can load the data from dropbox if you want)

[denadai2]

so is it a bug?

[slavarazbash]

I have not had time to look at it non-superficially. I'll get back to you.
I have been working at my day job....
On 23/09/2014 10:25 pm, "Marco De Nadai" notifications@github.com wrote:

so is it a bug?

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#87 (comment).

[denadai2]

@slavarazbash ok

[harmbuisman]

Dear all, not sure if it is the same issue, but I also found some cases where tbats gives unstable output. There is no seasonality in this signal.

Reproduction:

library(forecast)
train = structure(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3255, 1570, 7960, 8270,
5520, 3930, 5450, 4130, 890, 6119, 5240, 0, 80, 360, 280, 480,
1440, 1000, 1352, 1200, 584, 704, 800, 480, 720, 656, 696, 560,
376, 520, 760, 1360, 1448, 1048, 1520, 1240, 360, 360, 120, 1000,
360, 560, 776, 576, 560, 720, 536, 280, 1632, 2984, 520, 360,
360, 700, 319.958334, 440, 904, 1000, 1224, 888, 1248, 1080,
1136, 1191, 1240, 800, 999.5, 1199, 2423, 2584, 1959.958333,
1479, 200, 696, 760, 400, 440, 464, 368, 344, 352, 368, 2960,
3320, 64, 464, 734, 460, 80, 120), .Tsp = c(1, 162, 1), class = "ts")
plot(forecast(tbats(train)))

[robjhyndman]

These problems have now been fixed by modifying the admissibility check to be stricter. i.e., the roots of the ARMA component and the eigenvalues of the matrix must now be further away from 1.