My data which has no significance in ACF and PACF plot fits very poorly to my observed data. There are similar cases like my case too which when there's no significance in PACF and ACF their prediction performs very poorly (e.g predicting stock prices). I have not found any article that mentions that having significance in ACF PACF plot would also be assumption if we want to do time series forecasting so i thought if our data is stationary then we're good to go on building a time series model.

My question is, is it a must or do we need to have significance in ACF PACF in order to do time series forecasting? if yes, why is it so important to have significance ACF PACF in order to have a good fitting time series model?


1 Answer 1


The main issue that can arise when conducting time series analysis is that correlations between series - or indeed between the lags of a series - can be evident even though the correlation is simply a function of time and not theoretically relevant.

Moreover, forecasting a time series assumes that the mean, variance, and autocorrelation of the series is constant. Otherwise, the model has no basis upon which to forecast future values.

As a result, ACF and PACF is testing to see if correlations between the lags of a time series actually have theoretical value or are simply a function of time.

Here is a visual of AAPL's stock price from April 2014 - April 2018:


Here are the autocorrelation and partial autocorrelation plots:


partial autocorrelation

Now, let's get the first-difference of the series and convert it to a stationary one.

first difference

Here are the autocorrelation and partial autocorrelation plots:

autocorrelation 2

partial autocorrelation 2

We now observe that the autocorrelation after lag 0 has dropped off quite dramatically, and falls within the confidence interval - the series is now stationary and therefore future values of this stationary series can be predicted with much more confidence, with the correlations falling within the confidence band accordingly.

When attempting to predict the stock price of a non-stationary series, the following was obtained in this instance:


While this is predicting the general direction of the future price in this case, it does not account for a sudden shift in trend (e.g. due to a market crash) that the model would not pick up. This is why stock price forecasting is inherently difficult - the mean, variance, and autocorrelation are constantly changing from that of past data and therefore the model's predictions frequently become redundant over time.

Disclaimer: The above is simply meant to provide insight on the use of ACF and PACF in forecasting time series. None of the above is intended as any investment advice.

  • $\begingroup$ What you said was useful and clear but to summarize it: Don't try to predict prices. try to predict returns. The latter is also difficult but there is a greater chance of success. $\endgroup$
    – mlofton
    May 1, 2020 at 18:57
  • $\begingroup$ Predicting returns (by taking the log of price) at least helps to smooth out volatility. So yes, predicting returns is a more useful endeavour - although such a series is also likely to be nonstationary. $\endgroup$ May 1, 2020 at 18:59
  • $\begingroup$ okay thank you for explaining but why in my case even when the autocorrelation and partial autocorrelation after lag 0 has dropped off quite dramatically, and falls within the confidence interval, it fits very poorly to the observed model (i assume if my model predicts well then it will fit the observed data goodly, please correct me if i'm wrong) , this is my case it's not predicting stock but it's predicting income of company $\endgroup$ May 2, 2020 at 16:01
  • $\begingroup$ @Michael Grogan: It's not the smoothing out of volatility so much as the differencing since the differenced series is almost ( or some would say completely ) a white noise/ i.i.d process. $\endgroup$
    – mlofton
    May 2, 2020 at 20:50
  • $\begingroup$ Well yes, taking a first difference will make a time series stationary in most cases - though there are some exceptions. $\endgroup$ May 3, 2020 at 11:35

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