I use `cpgram`

function in R to produce a cumulative periodogram of a monthly time series. Its horizental axis is a number between 0 and 6 labeled as frequency: what does these numbers mean, since the frequency in cumulative periodogram should be between 0 and 0.5 like the ones shown below (upper ones)?

Also, do you know how can I create cumulative periodograms like these plots?

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#### Best Answer

The x-axis is labeled in "number of cycles per unit of time". It is a bit akward at first. For instance, assume you have a monthly time series starting February, 2000. You might define it as:

` series <- ts(datavalues, start=c(2000,2), frequency=12) `

This means that the time unit is 1 year and there are 12 data points per time unit. Then, functions like `spectrum`

and `cpgram`

label the x axis in frequencies giving their number of cycles per year. So 6 is the Nyquist frequency, 6 periods per year or a two month long cycle, the highest frequency observable with monthly data (higher frequencies are aliased).

HTH.