# Time Series with no Autocorrelation

I have a time series. I plotted it and saw that it is not stationary. Thus, I have calculated the difference. Then I plotted the autocorrelation and partial autocorrelation on the differences, along with the confidence bands. Non of the lags were out of the confidence bands, and the correlations for all lags are very low. I wanted to ask, does this mean that I cannot make good forecasts, or is there something else I could do. What should be the next stage? I would add and say that my series has no trend or seasonality (there is a trend down which at some point becomes a trend up, like a stock graph).

• Could you narrow down the topic? What are you trying to achieve, what sort of data is it? What you are describing can happen - plot brownian motion -clearly non-stationary and if you difference it, you get white noise - that is impossible to predict. Aug 25, 2016 at 10:19
• The data is a rate of a stock, which I know - hard to predict. After differentiating I got very small autocorrelations and partial autocorrelations. I just wanted to know if I am right that this is the end here, and the conclusion is that prediction is not possible. The data is very large, thus the confidence band is narrow. Yet, no correlations exceeded it, I think it says it all. Aug 25, 2016 at 16:26

The procedure that you had following is recommended for specify an ARMA model. Your results show that the series in difference is like a white noise process. Actually this mean that no ARMA model can make prediction better than a long run mean.

For example, results like yours was historically used to achieve conclusion of unpredictability for stock returns. However this conclusion is exaggerated because the results above can lead us to exclude linear auto-predictability but not predictability at all.

Firstly is possible to have better result using others predictor, not only lag values; think about Granger causality (predictability).

Secondly you can try to predict your variable with ARMA tool after some transformation of original data.

Otherwise you can to use model that involve non linear relations among predicted variable and predictors; an example is Artificial Neural Networks.

If your objective is prediction your work is not ending, its starting.

This indeed looks like the end of your tether. I would recommend forecasting either the overall mean, or the last observation, or using Single Exponential Smoothing.

(See here for a motivation for short answers. Longer answers are always welcome.)

• Could you resort to more traditional ML models in this case ?
– guy
May 14, 2020 at 22:32
• @guy: I don't quite see what "more traditional" ML models there would be. It sounds like there is pretty much zero structure in the OP's data, so the best one might do would run extremely simple models, like the ones I am recommending. (Of course, if one can think of any drivers, these should be incorporated - but it doesn't sound like it here.) May 15, 2020 at 6:54
• I suppose what I meant was let's say you have a multivariate time series and none of the input variables have a significant autocorrelation, you can just use a normal regression and train in it in a sliding window way to replicate the fact that it's a time series. What do you think?
– guy
May 15, 2020 at 19:48
• @guy: Sure, you can do that. But what would you regress the series on? It sounds like lags of the series itself are not useful (no autocorrelation), nor are trend or seasonal dummies. May 16, 2020 at 8:25
• Oh I am assuming you have some output/response variable time series that you would regress on in this situation (outside of the independent variables).
– guy
May 16, 2020 at 15:20