I have daily data from last 2 years.
I want to do ARIMAX and the regressor component being autoregressive distributed lag of the same variable. Since it has impact, along with dummy variables to account for seasonality in the
xreg paratemer in
The challenge i am facing is predicting my predictor for future. For example, i used daily data for 2 year for model building. For forecasting into future, i also need values of lag variable, which i do not know. If i use 2 lags of daily data in the model, then in order to predict for future i will also need value of those lag variables as well. So to predict $Value$ at time $t$ i will need $Value$ at $t-1$ and $t-2$ which i have from past records. However, if i want to find value at $t+5$ then i will need to find $t+3$ and $t+4$. Not sure how to proceed in this direction. As stated earlier, i am using
auto.arima function from
forecast package in
My ultimate goal is to predict for next 365 days. What i assume to be a solution is that i predict for $t+1$ as it will require $t$ and $t-1$ as lag component which i already have. once done i can use this predicted $t+1$ component to predict for $t+2$ as i will know value of $t+1$ from previous iteration and $t$ from original values. Is it the right approach?