# ARIMA for measuring effect size of mood stabilizing therapy?

Hi Im doing a research project regarding self-reported mood fluctuations. during a one year psychotherapy for 80 different subjects (they are in psychiatric treatment. The patients has trouble controlling their temper). I'll be measuring mood outbursts. I have daily measurements 0-5 of loss of temper, along with daily scorings of 8 different basic emotions. I'll also a monthly symptom severity index(0-100). So It's a rich time series with lots of info. I plan on doing ARIMA analysis, and wish to demonstrate significant differences in emotion regulation which I hope to find. I expect the tendency to be broad frequent waves changing over time to slimmer less frequent waves. I also expect to find the monthly symptom level to slightly taper off. 2 very basic questions: 1) Is arima a good path to follow here ? 2) Is arima-modelling especially sensitive to missing values ?

• ARIMA is suited for modelling a univariate time series, while you seem to have a multivariate dataset. If you want to investigate how one variable affects another one, it is already too much for ARIMA as it only considers one variable in total. May 10, 2017 at 14:00
• Thx Richard ! That is helpfull. (I'm very new to statistics- in the process of learning - hope my questions does not come across as to dumb). Still that "one variable" data I get from the timeseries I ought to be able to compare that with changes in the outcome questionnaires ? Open for good suggestions of ways to analyse that, thx :-) May 10, 2017 at 14:23

So, assuming temper is your "target" times series, $y(t)$, what you're essentially trying to do is get a sense of other indicators $\vec{x}(t)$ and how the effect/predict the target.

ARIMA is probably not the way to go.

A good, multivariate way to do this is to use python statsmodels, which has VAR implemented -- called Vector Auto Regression -- that allows for multiple time series $\vec{x}(t)$ to predict a target time series $y(t)$. It's essentially ARIMA -- when the target time series regresses on its own history -- applied to multiple variables.

ARIMA is very sensitive to missing values/variables, so you'll probably want to fill them in using mean/last-value or exlude that variable/time period from the study.

If you want to do something SUPER simple, in order to get a sense of what indicators "matter" in predicting mood outbursts, you might want to just correlate/regress $y(t)$ with a lagged set of predictors $\vec{x}(t-\tau)$ -- $\tau$ being 1,2,3,4 days, etc. -- and see which are significant. You can do this at mulitple lags to get a sense of effect; or, construct a cross correlation function in python statsmodels to get a full, univariate picture.

• Wow- This is exactly what I needed to know, so helpfull. Thank you !! Thats very exiting, and paves the way for me to use this in electronic diaries so clinicians can track patient progress "live". It will be possible to do this type of VAR-calculations in R also, right ? May 11, 2017 at 6:56
• And regressing y(t) for every single time series on different lagged set of variables is simple and a really good idea, thx ! May 20, 2017 at 16:03

The suggestion of @Rspeare is inadequate because it will inflate alpha type-I error rate, similar to experimentwise error rate while doing multiple t-tests (a t-test is after all the equivalent of case 1 regression). If you must conduct multiple case 1 regressions for $\hat{y_t}$, make sure to be more conservative in your alpha level of statistical significance and explicitly report your inflated error rate. Correcting for experimentwise error rate is plausible as well, but I'm nto sure how to do that with time series data.

For what it's worth, it seems like you are describing an interrupted time series, where the focus is not the behavior, but rather the effect of the intervention is the focus. Glass (1975) is the standard for this type of analysis with ARIMA models. Also, since you mentioned R, I suggest looking at Hyndaman & Khandakar's forecast package.

Also, you may be interested in ARIMAX models, which allow analysis of additional exogenous aggressors in an ARIMA model.

• Thx Jay - This is also extremely helpfull ! Yes I am definitely looking towards interrupted timeseries - this is precisely where I'm going. I'll have a look at Glass too. and be mindfull of of alpha type 1 error. Thanks a LOT May 25, 2017 at 8:08