Clear (cnoisy);

noisydat = 
      NDSolve[{x''[t] + 0.15  x'[t] - x[t] + x[t]^3 == 
            0.3  Cos[t], x[0] == -1, x'[0] == 1}, 
        x, {t, 0, 200}, MaxSteps -> 3000]

Plot[x[t] /. noisydat, {t, 0, 200}]

Plot[(x[t] /. noisydat)*(x[t + 0.0] /. noisydat),  {t, 0, 
        150}]

cnoisy = 
        Table[(∫_0^40)(x[t] /. noisydat)*(x[t + i] /. 
                  noisydat) \[DifferentialD]t, {i, 0, 40}];