<p>Non-linear trends are very common in time series data, especially in multidimensional modeling such as panel data. Traditional panel autoregressive models are not well-suited to capturing non-linear trends. In this paper, we proposed a panel autoregressive model with a non-linear time trend, and this model is handled by a spline function. The spline function divides the time trend into piecewise segments, fitting a suitable polynomial to each segment. The inference of the proposed model is developed under a Bayesian setup. The model’s estimator is determined using a conditional posterior distribution with various loss functions. The Markov Chain Monte Carlo (MCMC) technique is used to obtain the estimated value of the Bayes estimators in both the simulated series and the real series. A comparison is made with the maximum likelihood estimator based on mean absolute error and mean squared error. We apply the proposed model to the foreign direct investment (FDI) series for India, Brazil, and South Africa to analyse its significance. The FDI trends in India (2005), Brazil (1997), and South Africa (1999) reflect significant economic reforms, liberalisation efforts, and improved regulatory frameworks that fostered a more favourable environment for foreign investment. These trends highlight the importance of continuous policy improvements, addressing structural challenges, and maintaining political and economic stability to sustain FDI inflows across these countries.</p>