# time series help!!!

#### mathy1991

##### New Member
Hi, I've been asked to model some time series data, and decide on an ARIMA model that fits the data. The ACF function is here:

Lag ACF T LBQ
1 0.586150 4.69 23.04
2 0.408311 2.51 34.39
3 0.329731 1.86 41.92
4 0.273238 1.46 47.18
5 0.202848 1.05 50.12
6 0.177614 0.90 52.42
7 0.268110 1.35 57.75
8 0.308876 1.51 64.95
9 0.168360 0.80 67.12
10 0.058480 0.27 67.39
11 0.021731 0.10 67.43
12 -0.013771 -0.06 67.44
13 -0.087347 -0.41 68.07
14 -0.141421 -0.66 69.76
15 -0.093529 -0.43 70.52
16 0.005236 0.02 70.52

Can anyone tell me does this tie in with any form of ARIMA model? It has neither exponential decay nor dampened sine wave pattern so I'm not sure what sort of ARIMA model it is....can an ARIMA model be fit to any time series data?

EDIT: I have also included the Partial ACF

Lag PACF T
1 0.586150 4.69
2 0.098623 0.79
3 0.086449 0.69
4 0.045795 0.37
5 -0.011158 -0.09
6 0.036542 0.29
7 0.193089 1.54
8 0.108800 0.87
9 -0.164746 -1.32
10 -0.125295 -1.00
11 -0.039242 -0.31
12 -0.025928 -0.21
13 -0.076606 -0.61
14 -0.110575 -0.88
15 -0.012256 -0.10
16 0.137233 1.10

#### noetsi

##### No cake for spunky
It is pretty much impossible to see raw data this way and interpret it. You need to see the physical ACF and PACF lags to determine if the are deteriating and at what rate.

In theory an ARIMA model can fit any data. If you are saying that are no MA and or AR paramaters and no trends (so you don't have to distance anything) then you have a (0,0,0) Arima model essentially white noise. If you are saying that the spikes don't deteriate at all then likely you have a violation of an ARIMA assumption, notably a trend that needs to be distanced.

Have you run a Dickey Fuller test or an argumented Dickey Fuller test?

#### mathy1991

##### New Member
It is pretty much impossible to see raw data this way and interpret it. You need to see the physical ACF and PACF lags to determine if the are deteriating and at what rate.

In theory an ARIMA model can fit any data. If you are saying that are no MA and or AR paramaters and no trends (so you don't have to distance anything) then you have a (0,0,0) Arima model essentially white noise. If you are saying that the spikes don't deteriate at all then likely you have a violation of an ARIMA assumption, notably a trend that needs to be distanced.

Have you run a Dickey Fuller test or an argumented Dickey Fuller test?
If I PM you the images of ACF and PACF can you give me some help on determining which sort of ARIMA model it is?

Thanks.

#### noetsi

##### No cake for spunky
I can try. But I am no expert in time series. I am learning it myself, really just a beginner. I could look in my notebooks and see if I can find anything to approximate it but that would be it.

One other thing I should warn you of. ARIMA is truly an art form. The same ACF and PACF can represent different ARIMA paramaters. Only the expertise of the person looking at it and strong knowledge of the data can really decide. Thus a (1,0,1) might represent the data and you believe that a (2,1,2) does. And in practice you could both be right.

Have you looked at the raw time series data to see if there is any obvious trend over time in it (one that suggests you need to distance the data)?

#### mathy1991

##### New Member
I can try. But I am no expert in time series. I am learning it myself, really just a beginner. I could look in my notebooks and see if I can find anything to approximate it but that would be it.

One other thing I should warn you of. ARIMA is truly an art form. The same ACF and PACF can represent different ARIMA paramaters. Only the expertise of the person looking at it and strong knowledge of the data can really decide. Thus a (1,0,1) might represent the data and you believe that a (2,1,2) does. And in practice you could both be right.

Have you looked at the raw time series data to see if there is any obvious trend over time in it (one that suggests you need to distance the data)?
I have mailed you pictures of the time series, acf and pacf, still got no idea which ARIMA model is appropriate, does my time series have a constant mean and variance? And is that ACF exponentially decaying? It looks like it is but I'm not quite sure. Did you get my PM?

#### noetsi

##### No cake for spunky
Yes I answered it. The ACF does not suggest to me exponential decay. It, and the raw data itself suggests you have a trend (which means your means shifts over time). Unfortunately it is not a simple trend because it trends up for a time then down for a time, perhaps tied to a cyle (I dont know your data so you would have to access if a cycle is reasonable).

To me the PACF (which I would think indicative of a first order MA) does not seem consistant with either the raw data nor the ACF. I would specify a distancing of 1 (0,1,0) and see what the ACF and PACF looks then.