I have a problem where I have to predict a variable X that is dependent on several other variables a,b,c,d... I have the data containing the values of these variables a,b,c,d.. and also X up to a certain point in time T. I do not have an explicit relationship between a,b,c,d... and X but I have managed to fit the dependencies using a linear regression model. My goal is to predict X into the future beyond time point T. How do I approach this?. I had considered auto regression but then I would have to disregard the variables a,b,c,d.. as it would be based solely upon the past values of X. Would this cause a problem in accuracy? I had also thought of using auto regression separately on the variables a,b,c,d... and then using those projections and the original linear regression model to predict X at various points in time. Which would be a better model? Also is there any other way to implement this? And what are some good python libraries that I can use for these models and any you may suggest? Any help would be appreciated. Thanks!
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2$\begingroup$ It sounds like you have a time series data. If the data are time series in nature then you may have to look for VAR (Vector Auto Regressive) or VARMA models. $\endgroup$– Blain WaanCommented Nov 25, 2012 at 7:52
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$\begingroup$ VAR sounds good. I will give it a try . Thanks. I had found a library named statsmodels that supports it $\endgroup$– user17151Commented Nov 25, 2012 at 8:03
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2 Answers
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Some examples of possible starting points:
regression model with ARMA errors
transfer function models (Box and Jenkins)
state space models with regression terms (e.g. see Harvey's Forecasting, Structural Time Series Models and the Kalman Filter)
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You could run VARs but that would be equivalent to running univariate predictive regressions rather that contemporaneous i.e. run $$y_{t}=\beta_1+\beta_2x^1_{t-1}+\beta_3x^2_{t-1}+...+\beta_kx^k_{t-1} +\epsilon_{t}$$ to predict you simple need to fit the model and project i.e. a conditional expectation $$ E(y_{t+1} | I_t) $$ which just means to fit the regression with data at time $t$.
