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Variance of white noise

Started by Tom Killwhang September 28, 2020
I was reading Box and Jenkins Time series analysis and noticed that when they calculated power spectrum they had a factor 2 in the numerator - see
http://www.ru.ac.bd/stat/wp-content/uploads/sites/25/2019/03/504_05_Box_Time-Series-Analysis-Forecasting-and-Control-2015.pdf

equation (3.1.12).

I couldn't figure out where the 2 is coming from but then I wondered if they define noise a different way in stats. Just like when we have sine waves and take an FFT the magnitude is divided by 2 when we show the two sided spectrum, is it fair to do the same with white-noise? I think them may have multiplied it by 2 so that for the full spectrum =pi to +pi it gets halved. We don't seem to do this in engineering do we?