The dynamic structure of climate is governed by changes in precipitation and temperature and can be studied by time series analysis of these factors. This paper describes investigation of time series and seasonal analysis of the monthly mean minimum and maximum temperatures and the precipitation for the Bhagirathi river basin situated in the state of Uttarakhand, India. The data used is from the year 1901–2000 (100 years). The seasonal ARIMA (SARIMA) model was used and forecasting was done for next 20 years (2001–2020). The auto-regressive (p) integrated (d) moving average (q) (ARIMA) model is based on Box Jenkins approach which forecasts the future trends by making the data stationary and removing the seasonality. It was found that the most appropriate model for time series analysis of precipitation data was SARIMA(0,1,1) (0,1,1)$_{12}$ (with constant) and of temperature data was SARIMA(0,1,0) (0,1,1)$_{12}$ (with constant). The model prediction results show that the forecast data fits well with the trend in the data. However, over-predictions are found in extreme rainfall events and temperature results. The information of pattern and trends can assist as a prediction tool for development of better water management practices in the area.