Since the late 70’s, successive satellite missions have been monitoring the sun’s activity, recording total solar irradiance observations. These measurements provide estimates of the Earth’s energy imbalance, i.e. the difference of energy absorbed and emitted by our planet. With this amount of TSI data, solar irradiance reconstruction models can be better validated which can also improve studies looking at past climate reconstructions (e.g., Maunder minimum). Various algorithms have been proposed to merge the various TSI measurements recorded over the last 4 decades. We develop a 3-step algorithm based on data fusion, including a stochastic noise model to take into account the short and long-term correlations. We develop a wavelet filter in order to eliminate specific correlations introduced by the data fusion. Comparing with previous products,the mean value difference is below 0.1 W/m2and the discrepancy with the solar minima is mostly below 0.05 W/m2. Next, we model the frequency spectrum of this 40-year TSI composite time series with a Generalized Gauss-Markov model(with white noise) due to an observe flattening at high frequencies. It allows us to fit a linear trend in these TSI time series by joint inversion with the stochastic noise model via a maximum-likelihood estimator. Our results show that the amplitude of such trend is ∼ -0.009+/-0.01 W/(m2.yr). We conclude that the trend in these composite time series is mostly an artifact due to the solar noise.