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mitchelloharawild/sunspot_cycle_forecasting.R

Created November 14, 2025 10:03
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Comparing ETS and ARIMA forecasts of cyclical patterns in annual sunspots
Raw
sunspot_cycle_forecasting.R
library(tsibble)
library(fable)
library(ggplot2)
# Sunspot data from https://www.sidc.be/SILSO/datafiles
sunspots <- tsibble(
Year = seq(1700, 2024, by = 1),
Sunspots = c(
8.3, 18.3, 26.7, 38.3, 60, 96.7, 48.3, 33.3, 16.7, 13.3, 5, 0, 0, 3.3, 18.3,
45, 78.3, 105, 100, 65, 46.7, 43.3, 36.7, 18.3, 35, 66.7, 130, 203.3, 171.7,
121.7, 78.3, 58.3, 18.3, 8.3, 26.7, 56.7, 116.7, 135, 185, 168.3, 121.7, 66.7,
33.3, 26.7, 8.3, 18.3, 36.7, 66.7, 100, 134.8, 139, 79.5, 79.7, 51.2, 20.3,
16, 17, 54, 79.3, 90, 104.8, 143.2, 102, 75.2, 60.7, 34.8, 19, 63, 116.3,
176.8, 168, 136, 110.8, 58, 51, 11.7, 33, 154.2, 257.3, 209.8, 141.3, 113.5,
64.2, 38, 17, 40.2, 138.2, 220, 218.2, 196.8, 149.8, 111, 100, 78.2, 68.3,
35.5, 26.7, 10.7, 6.8, 11.3, 24.2, 56.7, 75, 71.8, 79.2, 70.3, 46.8, 16.8,
13.5, 4.2, 0, 2.3, 8.3, 20.3, 23.2, 59, 76.3, 68.3, 52.9, 38.5, 24.2, 9.2,
6.3, 2.2, 11.4, 28.2, 59.9, 83, 108.5, 115.2, 117.4, 80.8, 44.3, 13.4, 19.5,
85.8, 192.7, 227.3, 168.7, 143, 105.5, 63.3, 40.3, 18.1, 25.1, 65.8, 102.7,
166.3, 208.3, 182.5, 126.3, 122, 102.7, 74.1, 39, 12.7, 8.2, 43.4, 104.4,
178.3, 182.2, 146.6, 112.1, 83.5, 89.2, 57.8, 30.7, 13.9, 62.8, 123.6, 232,
185.3, 169.2, 110.1, 74.5, 28.3, 18.9, 20.7, 5.7, 10, 53.7, 90.5, 99, 106.1,
105.8, 86.3, 42.4, 21.8, 11.2, 10.4, 11.8, 59.5, 121.7, 142, 130, 106.6, 69.4,
43.8, 44.4, 20.2, 15.7, 4.6, 8.5, 40.8, 70.1, 105.5, 90.1, 102.8, 80.9, 73.2,
30.9, 9.5, 6, 2.4, 16.1, 79, 95, 173.6, 134.6, 105.7, 62.7, 43.5, 23.7, 9.7,
27.9, 74, 106.5, 114.7, 129.7, 108.2, 59.4, 35.1, 18.6, 9.2, 14.6, 60.2,
132.8, 190.6, 182.6, 148, 113, 79.2, 50.8, 27.1, 16.1, 55.3, 154.3, 214.7,
193, 190.7, 118.9, 98.3, 45, 20.1, 6.6, 54.2, 200.7, 269.3, 261.7, 225.1, 159,
76.4, 53.4, 39.9, 15, 22, 66.8, 132.9, 150, 149.4, 148, 94.4, 97.6, 54.1,
49.2, 22.5, 18.4, 39.3, 131, 220.1, 218.9, 198.9, 162.4, 91, 60.5, 20.6, 14.8,
33.9, 123, 211.1, 191.8, 203.3, 133, 76.1, 44.9, 25.1, 11.6, 28.9, 88.3,
136.3, 173.9, 170.4, 163.6, 99.3, 65.3, 45.8, 24.7, 12.6, 4.2, 4.8, 24.9,
80.8, 84.5, 94, 113.3, 69.8, 39.8, 21.7, 7, 3.6, 8.8, 29.6, 83.2, 125.5,
154.7
),
index = Year
)
cols <- c(ETS = "#2b8cbe", ARIMA = "#f16913")
sunspots |>
model(
ETS = ETS(Sunspots),
ARIMA = ARIMA(Sunspots)
) |>
forecast(h = 30) |>
autoplot(tail(sunspots, 80), level = 50) +
coord_cartesian(ylim = c(0, 300)) +
guides(fill_ramp = "none") +
scale_fill_manual(values = cols, name = "Model") +
scale_colour_manual(values = cols, name = "Model") +
labs(
title = "Forecasting cyclical data with <span style='color:#2b8cbe'>**ETS**</span> and <span style='color:#f16913'>**ARIMA**</span>",
fill = "Model", colour = "Model",
y = "Number of Sunspots", x = "Year"
) +
theme_minimal() +
theme(
legend.position = "none",
plot.title.position = "panel",
plot.title = ggtext::element_markdown(size = 14, hjust = 0)
)
ggsave(
filename = "sunspots-ets-arima-forecast.png",
width = 6, height = 4
)
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