Is it possible to predict data with 11 months cycle?

[nai-kon]

I have a monthly data with 11months cycle like below.
The peak appears every 11 months and shifts by one month each year.

(the data is very simplified for explanation)

I tried to predict it with Prophet but the result was incorrect.

I also tried with 12 months cycle data and the result was correct.

Prophet analyzes seasonality on a weekly or yearly basis. So it seems that data with cycles that are not divisors of 12 (11 months, 24 months, etc.) cannot be predicted correctly.

It seems that manually set cycle to add_seasonality() will solve the problem, but the cycle depends on the dataset so it need to automatically analyze the cycle from the data.

Sample data and code

11month_span.csv

import pandas as pd
import matplotlib.pyplot as plt
from prophet import Prophet

df = pd.read_csv("11month_span.csv")
df["date"] = pd.to_datetime(df["date"])
df.columns = ["ds", "y"]

train_data = df[df.ds < "2024-1"]

model = Prophet()
model.fit(train_data)

future = model.make_future_dataframe(periods=12, freq="MS")
pred = model.predict(future)

model.plot(pred, include_legend=True)
plt.savefig("test.png")