Time Series Forecasting Method to use both Predicted and Predictor variables

Question

I am learning Predictive modeling and building a Forecasting model to predict Insurance sales in US as a part of my academic project. I want to do Time Series forecasting.

I have Y(t) as my response variable and x(t),X(t-1),.....X(0) as my exploratory input varaibles that are correlated to the the response predicted variable. I have Y(t-1),Y(t-2),..... for close to 100 observations.

I want to build a Forecasting model that uses both the Y(t),Y(t-1)..so on and their corresponding X(t),X(t-1) to build the forecasting model to predict the Y(t=1).....so on.

When I went through some of the documentation available online, I saw that usually we generate a Timeseries ID and give the resposne variable and the time series ID( which is a continuous variable starting from 1 to count of response variables) and this will not use any of the X(t) values.

Is there any way where I can use both X(t),Y(t) to predict Y(t+1).

Thanks in Advance, Sai

Answer 1

I would start with analyzing trend. For example, you may try to estimate the regression equation

$Y_t = b_0 + b_1 t + b_2 X_t + e_t$

After estimating the residuals $e_t$ try to see if they are autocorrelated and if yes, you can build something like an ARMA model for the residuals. It would help if you post the time series plots of X, Y, and the scatterplot of Y against X.

Answer 2

Look at ARIMAX. These have both exogenous series and autocorrelation terms