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I am having trouble deciphering the equation from SPSS Output for a time series model. In particular this concerns two outpust.

  1. The expert model suggest for a time series of monthly sales a MA 1 process and a difference 1 and ln transformation. The MA 1 process has a beta of 0.687. I feel that I miss information from the output.

$$ \Delta ln{(sales_t)} = 0.687 \Delta \ln{(sales_{t-1})} $$

  1. For another sales series, the expert modeler suggests an ARIMA (1,0,0). For the sales series, it is a simple AR 1 process with beta 0.352 and a constant 15.524. An independent variable 'ad budget' is included as well. It suggests for the 'ad budget with Lag 0 as a numerator with 0.407 and with Lag 1 as a denominator with -0.811. I am particularly unsure if it is -0.811 or $\frac{1}{-0.811}$

This is what I came up with so far.

$$ ln{(sales_t)} = 15.524 + 0.352 \ln{(sales_{t-1})} + 0.407 \ln{(budget_{t})} - 0.811 \frac{1}{\ln{(budget_{t-1})}} $$

Thanks for any input regarding both outputs.

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