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If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

http://stats.stackexchange.com/questions/245056/ar1-forecasting/245089#245089AR(1) forecasting contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses/exceptional/extreme values these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used. If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

http://stats.stackexchange.com/questions/245056/ar1-forecasting/245089#245089 contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses/exceptional/extreme values these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used. If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

AR(1) forecasting contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses/exceptional/extreme values these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used. If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

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If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

http://stats.stackexchange.com/questions/245056/ar1-forecasting/245089#245089 contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses/exceptional/extreme values these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used. If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

http://stats.stackexchange.com/questions/245056/ar1-forecasting/245089#245089 contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses/exceptional values these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used. If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

http://stats.stackexchange.com/questions/245056/ar1-forecasting/245089#245089 contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses/exceptional/extreme values these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used. If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

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If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

http://stats.stackexchange.com/questions/245056/ar1-forecasting/245089#245089 contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses/exceptional values these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used.If If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

http://stats.stackexchange.com/questions/245056/ar1-forecasting/245089#245089 contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used.If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

http://stats.stackexchange.com/questions/245056/ar1-forecasting/245089#245089 contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses/exceptional values these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used. If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

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