Time series forecasting plays a central role in economics and environmental sciences, where reliable predictions can inform policy and planning decisions. This study analyzes two monthly time series with contrasting characteristics: a non-seasonal series, the Consumer Price Index (CPI) for all urban consumers in the United States, and a strongly seasonal series, the monthly average temperature in the city of Chicago. For the CPI series, exploratory analysis reveals a pronounced upward trend and non-constant variance. After applying a logarithmic transformation and first differencing, the series is rendered approximately stationary. Model identification using autocorrelation, partial autocorrelation, extended autocorrelation functions, and information criteria suggests that an Autoregressive Moving Average (ARMA) (2,1) model for the differenced log series, equivalent to an Autoregressive Integrated Moving Average (ARIMA) (2,0,1) model for the original data, provides the best fit. Residual diagnostics, including Ljung-Box tests, support the adequacy of this specification. For the Chicago temperature series, strong annual seasonality is evident, while the mean and variance remain relatively stable over time. A seasonal ARIMA (SARIMA) model is fitted using automated selection based on Akaike’s Information Criterion (AIC), corrected AIC (AICc), and Bayesian Information Criterion (BIC), leading to ARIMA (0, 1, 1) (2, 1, 1)12 as the preferred model. Diagnostic checks confirm that this model captures the seasonal dependence structure satisfactorily. Both models are used to generate multi-step forecasts of CPI and temperature, respectively, demonstrating that appropriately chosen ARIMA and seasonal ARIMA models can produce reasonable and interpretable forecasts for non-seasonal and seasonal monthly data.