I am studying ARIMA models and find it hard to validate the model in terms of "it's a good, useful model" and "I shouldn't use that model for prediction".

So at first I started with the easiest model, a random walk, where the model uses the mean value of the series.

Let's say I have the series:

data1<-c(1,1,1,1,1,1,1,1,1,1,1,1,1) data2<-c(1,2,1,1,1,1,1,1,1,2,2,1,1) data2<-c(10,-5,33,1,96,45,-978,3,15,8,9,32,12)

All three are random walks, but obviously the values of the first series data1 are better to predict than for data2 or data3.

My question is, how can I quantify this kind of reliability in a metric? (Ideally in a single metric from 1.0 for data1 and ~0 for data3). Probably the variance is the metric, but how can I standardize it to tell if the predictions from the models will be "good" (1.0) or "bad" (0.0)?

I am studying ARIMA models and find it hard to validate the model in terms of "it's a good, useful model" and "I shouldn't use that model for prediction".

So at first I started with the easiest model, a random walk, where the model uses the mean value of the series.

Let's say I have the series:

data1<-c(1,1,1,1,1,1,1,1,1,1,1,1,1)
data2<-c(1,2,1,1,1,1,1,1,1,2,2,1,1)
data2<-c(10,-5,33,1,96,45,-978,3,15,8,9,32,12)

All three are random walks, but obviously the values of the first series data1 are better to predict than for data2 or data3.

My question is, how can I quantify this kind of reliability in a metric? (Ideally in a single metric from 1.0 for data1 and ~0 for data3). Probably the variance is the metric, but how can I standardize it to tell if the predictions from the models will be "good" (1.0) or "bad" (0.0)?