**Abstract**

The Vostok ice core data cover 420,000 years indicating the natural regularity of Earth's surface temperature and climate. Here, we consider four major cycles of similar duration, ranging from 86,000 to 128,000 years, comprising 15% of periods for the warming interglacials compared to some 85% of cooling periods. Globally, we are near the peak of a rapid warming period. We perform a detailed frequency analysis of temperature and CO2 cycles, as a primary stage in building a logical Climate Prediction Engine (CPE), illustrated with specific harmonics. This analysis can be repeated for all harmonics and various cycle combinations. Our time correlation estimates the CO2 time lag for temperature at 400–2300 years, depending on the cycle, longer on average than previously concluded. We also perform Fast-Fourier transform analysis, identifying a full harmonic spectrum for each cycle, plus an energy analysis to identify each harmonic amplitude to achieve further prediction analysis using a Kalman filter harmonic bank. For Vostok data we can use combinations of different cycles compared to the most recent for learning and then the current ongoing cycle for testing. Assuming causal time regularity, more cycles can be employed in training, hence reducing the prediction error for the next cycle. This results in prediction of climate data with both naturally occurring as well as human forced CO2 values. We perform this detailed time and frequency analysis as a basis for improving the quality of our climate prediction methodologies, with particular attention to testing alternative hypotheses of the possible causes of climate change. These include the effect on albedo of suspended dust and increasing water vapor with temperature in initiating interglacial warming, the effect of temperature and pH values of surface water on ambient level of CO2 in the atmosphere and finding a larger latent heat capacity in the atmosphere required to sustain its circulatory motions, leading to friction and turbulent release of heat in boundary layer. All these potentials can be examined in an effective CPE.

**Keywords:** Vostok data, time and frequency analysis, Kalman filter harmonic bank, climate prediction engine, machine learning
