Hi Cdc,
Predicting future values based on past data is indeed a central aspect of time series analysis and system identification. Let me clarify some of your points and guide you through the process of making a prediction for a future time point.
Firstly, the "predict" function in MATLAB is used to predict the output of a system given past inputs and outputs. The "nshift" parameter specifies how many steps ahead you want to predict. The function does not require future data; it only uses past data to make the prediction.
When you create an "iddata" object with the same input and output, as in "dat = iddata(r,r);", you're essentially saying that the output of your system is the same as the input. This is not typical for system identification, where you usually have a distinct input and the system's response as the output. If you're trying to predict future values of a univariate time series (a single sequence of data), you would normally use past values of that sequence to predict future ones.
For a univariate time series, you can create an iddata object with no input (u) and the time series data as the output (y):
r = rand(100,1); % Your time series data
dat = iddata(r, []); % Create iddata object with no input
To predict the next value in the time series, you can use the predict function with nshift = 1:
nshift = 1;
prd = predict(dat, tf1, nshift);
The output of prd will be an iddata object with the predicted values. The first nshift values of prd.y will be NaN because the model cannot predict the first few values without past data. The rest of the values will be the model's one-step-ahead prediction based on the past data.
To extract the predicted values, you can use:
predicted_values = prd.y;
If you want to predict just the next single time point, you can look at the last value of predicted_values:
next_point_prediction = predicted_values(end);
Regarding the "forecast" function, it is used for multi-step prediction when you have a model and want to predict several steps into the future based on past data. The error you're seeing suggests that there's a mismatch between the model's expected inputs and outputs and the data provided. Since you're working with a univariate time series, you don't need to use "forecast" for a single step prediction.
Lastly, when using the System Identification app, you can test models for their predictive capabilities by withholding some data from the estimation process (the "Estimation Data") and then using the "Validation Data" to test the model's predictions. This validation data is used to simulate the scenario where the model must use past data to generate future predictions.
Hope this helps!
