Transfer Function Confidence interval estimation

Question

I've obtained a Transfer Function model to predict the value of $y_t$ which is:

$$ y_t - \mu = \frac{0.0034 + 0.0024B^9}{1- 0.9B}x_{t-9} + \frac{1}{1+0.6B} a_t $$

I obtained this model with SAS, and each parameter is estimated as a T-Student distribution and the standard deviation for each parameter also is available. The $x_t$ is the input parameter and $a_t$ is the white noise.

I obtained predictions of $y_t$ with assigned values for different scenarios. Also, I need the confidence interval for the predicted values, but I do not know how I can calculated them. Please guide me how I can calculate them according to the obtained formula or with SAS commands.

Thanks, Afshin

score 2 · Accepted Answer · answered Sep 16 '15 at 16:52

If I am reading this correctly, you have created a time-series model to predict using transfer functions on external inputs, but would like to get confidence intervals of your predictions.

You can get all of this information by placing your model in PROC ARIMA and requesting output:

proc arima data=have;
    identify var=y crosscorr=(x1 x2 x3);
    estimate input=( (1)x1 /(2)x2 3$x3);
    forecast lead=12 out=Output_Dataset;
run;

Where,

(1)x1 has a numerator factor of 1

/(2)x2 has a denominator factor of 2

3$x3 is backshifted 3 lags

If you had both numerator and denominator factors and also want to backshift 3 lags, you would write, for example, 3$(1)/(2)x3.

PROC ARIMA automatically assumes you are using conditional least squares estimation. If you want to use maximum likelihood estimation, specify method=ML in the estimate statement.

You can specify the alpha of your confidence interval using the alpha= option in the forecast step. Otherwise, it will assume alpha=0.05.

The data set Output_Dataset will give you confidence intervals, predictions, and more.

Transfer Function Confidence interval estimation

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