My auto correlation coefficients plot of human walk looks like this. This walk data is recorded with accelerometer sensor inside the pocket. Human walk is periodic, and I need to determine that period i.e when walk cycle repeats it self. This plot starts at Lag 1 as we can see value is little bit below 1. The first dominant period after lag 1 occurs at lag 116 which is also the period of this walk signal. But at lag 58 I also see a small peak that peak also occurs at equal lag intervals of approximately around 116. I would like to know best way of determining periodicity from this ACF plot.

Lag vs ACF Plot

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Data plot

  • $\begingroup$ I have seen similar acf's where two distinct frequencies are present. The best way for me to specifically answer your question is to actually have access to your data. Please post the data in excel format or scale the data before you post. $\endgroup$
    – IrishStat
    Commented Feb 2, 2015 at 16:33

1 Answer 1


Before Box and Jenkins and their army of zealots (of which I was a leader!) focused/limited their approach to ARIMA (memory based) solutions while a rich history of deterministic models (i.e. seasonal dummies ) was in vogue.

The acf and pacf are descriptive statistics. In order for these to be useful in identifying an ARIMA model a few things are necessary ( a.k.a. the small print). The data set under analysis needs to be free of Pulses/Level Shifts, ,Seasonal pulses, Local Time Trends and the ARIMA model needs constant parameters and constant error variance for all time intervals.

It appears to me that your data is driven by systematic/deterministic factors that can be characterized as seasonal dummies. The fact that your series is auto-correlated does not necessarily imply the need for an auto-projective model (ARIMA). I took your data and used a commercially available piece of software which automatically suggested a potentially useful model after rejecting the ARIMA approach.

Here is the Actual and Forecast enter image description here . The forecasts for the next 580 periods are enter image description here The equation is here enter image description here and here enter image description here . Note that all models are wrong but some are useful ( ascribed to G.E.P. Box)


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