What exactly is a "persistent/persistence model"?

Question

I'm new to time series forecasting and only got previous experience with image processing in therms of neural networks. My goal is to do create an ML forecasting model for time series data. Currently I'm reading up on papers and most of them talk about a "persistent/persistence model" which they use as a benchmark or compare their results to. But no one seems to properly explain, what it is and how it works? I'm native german, english is only my seconds language and "persistent/persistence model" has no meaningful translation. I would be so glad if someone could explain this to me or show me some reading material on the topic. Thanks in advance :)

Edit: For my fellow german friends: Ich denke "persistence model" im Deutschen läuft unter dem Begriff der naiven Prognose. Siehe Wikipedia

Answer 1

Persistence models assume the condition of the current situation are the same as the one in the target future, i.e. the conditions, and therefore the values of the time series, persist between the current and future time instants:

$$\hat x_{t+h}=x_t$$

where $h$ is your prediction horizon. This can be as simple as

• amount of sales tomorrow will be the same as today, i.e. $\hat x_t=x_{t-1}$
• amount of sales will be the same as the same day of the last week, i.e. $\hat x_t = x_{t-7}$
• amount of sales will be the same as the same day of last month, i.e. $\hat x_{t} = x_{t-f(t)}$, where $f(t)$ finds the correct offset depending on your month

I hope it helps.