Precession in an accretion-powered pulsar is expected to produce characteristic variations in the pulse properties .
Assuming surface intensity maps with one and two hotspots , we compute theoretically the periodic modulation of the mean flux , pulse-phase residuals and fractional amplitudes of the first and second harmonic of the pulse profiles .
These quantities are characterised in terms of their relative precession phase offsets .
We then search for these signatures in 37 days of X-ray timing data from the accreting millisecond pulsar XTE J1814 - 338 .
We analyse a 12.2-d modulation observed previously and show that it is consistent with a freely precessing neutron star only if the inclination angle is < 0.1 ^ { \circ } , an a priori unlikely orientation .
We conclude that if the observed flux variations are due to precession , our model incompletely describes the relative precession phase offsets ( e.g .
the surface intensity map is over-simplified ) .
We are still able to place an upper limit on \epsilon of 3.0 \times 10 ^ { -9 } independently of our model , and estimate the phase-independent tilt angle \theta to lie roughly between 5 ^ { \circ } and 10 ^ { \circ } .
On the other hand , if the observed flux variations are not due to precession , the detected signal serves as a firm upper limit for any underlying precession signal .
We then place an upper limit on the product \epsilon \cos \theta of \leq 9.9 \times 10 ^ { -10 } .
The first scenario translates into a maximum gravitational wave strain of 10 ^ { -27 } from XTE J1814 - 338 ( assuming a distance of 8 kpc ) , and a corresponding signal-to-noise ratio of \leq 10 ^ { -3 } ( for a 120 day integration time ) for the advanced LIGO ground-based gravitational wave detector .