In my subsequent analysis, my focus has been on exploring data-driven time series forecasting models for the “Temp_Avg” variable. These models are crafted to discern and leverage patterns from the historical temperature data, aiding in a more profound understanding of temperature variations over time. The models under consideration encompass diverse methodologies, including linear, exponential, quadratic, and those integrating additive or multiplicative seasonality. To enhance the models’ flexibility and adaptability, I augmented the dataset with terms such as t, t_squared, and log(t), where ‘t’ represents the time index. These additions are crucial for capturing and incorporating different temporal characteristics, ensuring the models are well-equipped to comprehend and predict the nuanced patterns embedded in the temperature dataset.
Data-Driven Time Series Forecasting Models Analysis:
- Linear Model: This model assumes a linear relationship between time and temperature. It yielded a Root Mean Square Error (RMSE) of approximately 14.56, indicating its performance in capturing linear trends.
- Exponential Model: The exponential model aims to capture exponential growth or decay in temperature over time. However, the extremely high RMSE value of approximately 4.37 suggests that this model may not be suitable for this dataset.
- Quadratic Model: The quadratic model introduces a squared term to account for curvature in the temperature trend. It resulted in an RMSE of around 14.66, indicating its ability to capture more complex patterns than the linear model.
- Additive Seasonality: This model considers seasonal variations in temperature and resulted in an RMSE of approximately 2.59, showcasing its effectiveness in capturing repeating patterns over the months.
- Additive Seasonality with Linear Trend: Combining linear trend and seasonal variations, this model produced an RMSE of about 2.63, indicating a slightly higher but still reasonable accuracy in capturing temperature fluctuations.
- Additive Seasonality with Quadratic Trend: Introducing a quadratic trend along with seasonality, this model achieved an RMSE of approximately 2.72, indicating its ability to capture more complex temperature patterns.
- Multiplicative Seasonality: This model considers both seasonal and overall multiplicative variations. However, the extremely high RMSE value suggests that it may not be the most suitable model for this dataset.
- Multiplicative Seasonality with Linear Trend: Similar to the multiplicative model, this includes a linear trend and seasonality. However, the extremely high RMSE value indicates potential limitations in accurately predicting temperature variations.
- Multiplicative Seasonality with Quadratic Trend: Combining a quadratic trend with multiplicative seasonality, this model yielded an extremely high RMSE value, suggesting challenges in accurately forecasting temperature patterns.
Conclusion: Among the models tested, the ones incorporating additive seasonality (both linear and quadratic trends) demonstrated the best performance, with lower RMSE values. These models effectively capture the seasonal variations in temperature, providing more accurate forecasts compared to other methods. The linear and quadratic models without seasonality demonstrated reasonable accuracy but were outperformed by the seasonal models. The exponential and multiplicative models, however, exhibited extremely high RMSE values, indicating potential limitations in their applicability to this temperature dataset.
