You originally had 500,000 readings, 128 per second for 3,907 seconds. After taking the readings at 1 second interval (N=3907) the plot is here . AUTOBOX identified a break point in parameters at period 2343 +/- 300 time points. Taking the most recent 1565 values this is then the identified model (1,1,0) with an ACF of the residuals here suggesting model insufficiency . It appears that there is significant auto-projective structure at period 60 suggesting an hourly effect .There were a few (8) anomalous data points ( also visually obvious) which were identified and rectified/adjusted . Some sort of SARIMA might be necessary of the form (1,1,0)(1,0,0)60 . I will sharpen my pencil and try to resolve this.

You originally had 500,000 readings, 128 per second for 3,907 seconds. After taking the readings at 1 second interval (N=3907) the plot is here . AUTOBOX identified a break point in parameters at period 2343 +/- 300 time points. Taking the most recent 1565 values this is then the identified model (1,1,0) with an ACF of the residuals here suggesting model insufficiency . It appears that there is significant auto-projective structure at period 60 suggesting an hourly effect .There were a few (8) anomalous data points ( also visually obvious) which were identified and rectified/adjusted . Some sort of SARIMA might be necessary of the form (1,1,0)(1,0,0)60 . I will sharpen my pencil and try to resolve this as ARIMA modelling is an ITERATIVE PROCESS.

AFTER ADDING A 60 PERIOD COEFFICIENT :

this captures the short-term (second) and the long-term (hourly) structure

You originally had 500,000 readings, 128 per second for 3,907 seconds. After taking the readings at 1 second interval (N=3907) the plot is here . AUTOBOX identified a break point in parameters at period 2343 +/- 300 time points. Taking the most recent 1565 values this is then the identified model (1,1,0) with an ACF of the residuals here and a plot of the residuals here suggesting model sufficiency . There were a few (8) anomalous data points ( also visually obvious) which were identified and rectified/adjusted .

You originally had 500,000 readings, 128 per second for 3,907 seconds. After taking the readings at 1 second interval (N=3907) the plot is here . AUTOBOX identified a break point in parameters at period 2343 +/- 300 time points. Taking the most recent 1565 values this is then the identified model (1,1,0) with an ACF of the residuals here suggesting model insufficiency . It appears that there is significant auto-projective structure at period 60 suggesting an hourly effect .There were a few (8) anomalous data points ( also visually obvious) which were identified and rectified/adjusted . Some sort of SARIMA might be necessary of the form (1,1,0)(1,0,0)60 . I will sharpen my pencil and try to resolve this.