Let {X
n
:n∈N}be a linear process with bounded probability density function f(x). We study the estimation of the quadratic functional ∫ R
f
2(x)dx. With a Fourier transform on the kernel function and the projection method, it is shown that, under certain mild conditions, the estimator
2
false/
false(
n
false(
n
−
1
false)
h
n
false)
∑
1
≤
i
<
j
≤
n
K
false(
false(
X
i
−
X
j
false)
false/
h
n
false)
has similar asymptotical properties as the i.i.d. case studied in Giné and Nickl if the linear process {X
n
:n∈N}has the defined short range dependence. We also provide an application to
L
2
2
divergence and the extension to multi‐variate linear processes. The simulation study for linear processes with Gaussian and α‐stable innovations confirms our theoretical results. As an illustration, we estimate the
L
2
2
divergences among the density functions of average annual river flows for four rivers and obtain promising results.