# Predicting the Number of Sunspots Per Month and Per Quarter Using ARIMA Models

## DOI:

https://doi.org/10.58445/rars.187## Keywords:

Statistics, Astronomy, Data Modeling## Abstract

The number of sunspots in a given year changes as the sun goes through solar cycles, with peaks happening at regular intervals. When these peaks are plotted, a curve appears, similar to the oscillating sinusoidal wave. Because of its oscillatory nature, predictions of future sunspot values could be found since it is safe to assume that the number of sunspots would always follow a pattern. However, a simple, ordinary sine function, or any algebraic function for that matter, would not allow us to plot and predict future data points due to the complexity of the curve at hand. This led us to the hypothesis that in order to predict the future number of sunspots, models that involve autoregressive and moving average components (namely the ARIMA model) would be the most effective. In order to measure effectiveness, the mean-squared error (MSE) would be used, with a lower value (closer to 0) meaning better fit. The reason why we chose these sophisticated models was because these models took into account prior data points and their trends and seasonality to predict future data points. This essentially meant that this model would predict based on prior points, not on a fixed point or equation, like the sine curve. After plotting all of these models and finding the MSE for each, we drew the conclusion that the ARIMA model proved to produce the most accurate curve, with a MSE of only 460, as compared to the MSE that the best sine curve could produce: 21 million.

## References

Solar cycle progression. Solar Cycle Progression | NOAA / NWS Space Weather Prediction Center. (n.d.). Retrieved October 15, 2022, from https://www.swpc.noaa.gov/products/solar-cycle-progression

Shetty, C. (2020, September 22). Time Series models. Medium. Retrieved October 15, 2022, from https://towardsdatascience.com/time-series-models-d9266f8ac7b0

Mehandzhiyski, V. (2021, October 20). What is a moving average model? 365 Data Science. Retrieved October 15, 2022, from https://365datascience.com/tutorials/time-series-analysis-tutorials/moving-average-model

Peixeiro, M. (2021, December 6). Defining the moving average model for time series forecasting in Python. Medium. Retrieved October 15, 2022, from https://towardsdatascience.com/defining-the-moving-average-model-for-time-series-forecasting-in-python-626781db2502

Srujan, K. (2020, September 1). Predicting sunspots using Arima. Kaggle. Retrieved October 15, 2022, from https://www.kaggle.com/code/krishnasrujan/predicting-sunspots-using-arima/notebook

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Copyright (c) 2023 Suvrath Arvind, Clayton Greenberg

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