# Physical interpretation of an AR(n) series

#### rogojel

##### TS Contributor
Hi,
I am learning TS analysis but my angle is probably diffent from the usual. Being in six sigma I need to reduce the variability of a process that I can prove is basically AR(3) which with 3 runs on the average per day means one day's runs influence the next day in the mathematical model.

My question is: does it make sense to hunt for some physical process/property that could produce this effect or is an AR series such a mathematical abstraction that this is hopeless ? I know that in multiple regression the physical interpretation of the coefficients can be tricky - any ideas for time series?

thanks a lot!

rogojel,

#### rogojel

##### TS Contributor
It is a press-filter and the value we track is the time it takes to filter a charge . The filering times are a strongly correlated AR(3) . If I take the raw time aeries no other factor has any significant indluence on filtering times. Now I am thinking of either use skipping or a filter to generate a modified data set I could analyse for influencing factors. Does this make sense?

regards

#### Miner

##### TS Contributor
Is there any correspondence between the auto regressive period and filter changes or with new batches of material to be filtered? For example, the condition of a filter (if reused) would affect subsequent times until it is replaced. Or the purity of a batch to be filtered would affect the time of each charge until a new batch is filtered.

#### rogojel

##### TS Contributor
hi,
yes, these are exactly the physical causes we can look for. My question is whether this makes sense or are we just hunting a mathematical abstraction?

#### Miner

##### TS Contributor
No. The AR(3) should relate to a physical reality provided that reality is repetitive at a consistent frequency.

#### rogojel

##### TS Contributor
hi,
I am a bit further and would lke to know if this makes sense: my goal is to find factors that influence the filtering time and not to predict future times. So I analysed the time using the Yule- Walker algorithm and based on the order of the AR model and the coefficients found I built a recursive filter and transformed the DV and also the numeric IVs. Then I built a simple regression model using he transformed variables and though the model is not great (R-sq about 0.3) it did give me 3 parameters that have a significant influence.

Apparently I can translate the results back to the unfilteted variables - so this is what I am doing. I used this brilliant book to learn the technique BTW http://www.amazon.de/Analysis-Serie...erryberry&qid=1460382374&ref_=sr_1_15&sr=8-15

#### Miner

##### TS Contributor
Then I built a simple regression model using he transformed variables and though the model is not great (R-sq about 0.3) it did give me 3 parameters that have a significant influence.
This sounds like there is a lot of common cause variation compared to special cause. Did you try plotting the times on an IMR chart? You may have a basically in-control process, which is essentially a stationary time series.

#### rogojel

##### TS Contributor
Yes, so it is, though I am not a big fan of the terminology . The time series is quite variable, but most of it comes feom the natural behaviour of autocorrelated series - this also reduces my power a lot. By filtering I eliminate a part of the natural variation so my power increases and I can see some influencing factors.

As an aside - autocorrelation is counted as special or common cause ?

regards

#### Miner

##### TS Contributor
Common cause. I've run into it before with an extrusion process. Any measurements made on the extrusion (other than the cut length) were autocorrelated until 20 minutes had passed, which happened to coincide with a change in the batch of rubber.

I suppose you could call them background noise and signal (or assignable cause).

#### rogojel

##### TS Contributor
yepp,
this is why I dislike this terminology - it is subjective. If you could define a link between the rubber and the autocorrelation then it is a signal or assignable cause. If you don't it is just background noise and common cause.

#### Miner

##### TS Contributor
On the other hand, if the rubber changes are a normal part of the process, which cannot be adjusted back by an operator, it is background noise and therefore common cause. Definitely subject to interpretation.