Statistical Signal Processing basically refers to the analysis of random signals using appropriate statistical techniques. Statistical approaches are crucial in signal processing when signals are stochastic. The development of acceptable methodologies for estimating model parameters, the evaluation of model performances, and the design of suitable models to explain the behavior of the system all make use of statistics. Machine learning and statistical approaches have been receiving extensive attention from both the academia and industry, and its foundation lies in statistics. We found unutilized meteorological data recorded for 36 years in Bahir Dar Meteorological Agency which has not been used for any kind of analysis or prediction which is important to minimize the difficulty of weather prediction and Risks of extreme weather conditions like floods and droughts. The need for accurate time-series analysis for this data is very necessary and demanding to show the temperature, rainfall, drought, flooding and other weather patterns in the region. This thesis presents a unique statistical, classical machine learning (ML) and deep learning (DL) modeling approach for analyzing temperature and rainfall time series prediction retrievals using meteorological variable observations from automatic weather stations. The study uses models based on statistical time series (ARIMA), machine learning (SVM), KNN, random forest (RF), and deep learning (MLP, GRU, LSTM) algorithms. The goodness-of-fit and performance of these models were validated using metrics such as Mean Square Error, Mean Absolute Error, Root Mean Square Error, Coefficient of Determination, learning curves, and computational complexity. The results show that ML models outperform statistical models in temperature prediction, while SVR outperforms ARIMA, KNN, and RF in loss metrics. KNN outperforms ARIMA, SVR, and RF in rainfall prediction, while ARIMA outperforms SVR by 12.2%. Overall, MLP and KNN are the best signal processing models for temperature and rainfall time series prediction. Keywords: DL, ML, Statistical signal Processing,Time series, Weather