I want to simulate cyclic behaviour, using cos or sin?

Hi,

I need som help regarding modelling of cyclic behaviour around a mean value. Can I do this using a sin or cos function somehow? The thought is that I am going create a vector x that contains a certain number of values (Nu) like this:

y=mean_value+something here=?? +error

The error I am going to create using randn, but how can I get this y-vector to have cyclic behaviour around the mean value?

I am thinking about using a loop somehow (see code sequence under). Can anyone help me? :)

if I write like this:
  x=[1:1:10]
  mean_value=74.3;
  Nu=10;
  simulation_values=zeros(Nu,1);
  q=length(simulation_values);

for i=1:q
  % code
end

Thanks!

[José-Luis]

Sounds like a job for a seasonal ARIMA model:

https://se.mathworks.com/help/econ/arima-class.html