Statistical analysis is carried out for satellite-based global daily tropospheric and stratospheric temperature anomaly and solar irradiance data sets. Behavior of the series appears to be nonstationary with stationary daily increments. Estimating long-range dependence between the increments reveals a remarkable difference between the two temperature series. Global average tropospheric temperature anomaly behaves similarly to the solar irradiance anomaly. Their daily increments show antipersistency for scales longer than 2 months. The property points at a cumulative negative feedback in the Earth climate system governing the tropospheric variability during the last 22 years. The result emphasizes a dominating role of the solar irradiance variability in variations of the tropospheric temperature and gives no support to the theory of anthropogenic climate change. The global average stratospheric temperature anomaly proceeds like a 1-dim random walk at least up to 11 years, allowing good presentation by means of the autoregressive integrated moving average (ARIMA) models for monthly series.