In my recent analysis, I delved into various data-driven models to predict future temperatures using the historical data of “Temp_Avg.” These models are designed to pick up on patterns in the temperature changes over time, helping us better understand and foresee temperature fluctuations. I considered a range of methods, from simple linear and exponential models to more complex ones involving quadratic trends and seasonal variations. To make these models flexible, I added terms like ‘t,’ ‘t_squared,’ and ‘log(t)’ to the dataset, representing different time-related characteristics.
Let’s take a look at how these models performed:
- Linear Model: This assumes a straightforward, linear relationship between time and temperature. It did reasonably well, with a Root Mean Square Error (RMSE) of about 14.56, indicating its ability to capture linear trends.
- Exponential Model: This model, attempting to catch exponential growth or decay in temperature, didn’t perform as well, showing a high RMSE of about 4.37. This suggests it might not be the best fit for our dataset.
- Quadratic Model: Introducing a squared term to account for curvature in temperature trends, this model did fairly well with an RMSE of around 14.66, capturing more complex patterns than the linear model.
- Additive Seasonality: Considering seasonal variations, this model performed impressively with an RMSE of approximately 2.59, showing its effectiveness in capturing repeating patterns over months.
- Additive Seasonality with Linear Trend: Combining a linear trend with seasonal variations, this model achieved an RMSE of about 2.63, indicating reasonably accurate predictions of temperature fluctuations.
- Additive Seasonality with Quadratic Trend: Introducing a quadratic trend along with seasonality, this model did well with an RMSE of approximately 2.72, capturing more complex temperature patterns.
- Multiplicative Seasonality: Considering both seasonal and overall multiplicative variations, this model didn’t perform well, showing an extremely high RMSE.
- Multiplicative Seasonality with Linear Trend: Similar to the multiplicative model, including a linear trend and seasonality, this model also showed an extremely high RMSE, suggesting challenges in accurately predicting temperature variations.
- Multiplicative Seasonality with Quadratic Trend: Combining a quadratic trend with multiplicative seasonality, this model yielded an extremely high RMSE, indicating difficulties in accurately forecasting temperature patterns.
Conclusion: Among the tested models, those incorporating additive seasonality (both linear and quadratic trends) performed the best, with lower RMSE values. These models effectively captured seasonal variations in temperature, providing more accurate forecasts compared to other methods. The linear and quadratic models without seasonality did reasonably well but were outperformed by the seasonal models. On the other hand, the exponential and multiplicative models showed challenges and might not be the best choices for predicting temperatures in this dataset.