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I got some clue here Large coefficients and std. errors

Without scaling the dependent variable (online_unit_sale) my output is as below. Flag1 and Flag2 are the covariates and their coefficients are in thousands. However scaling DV lowers the coefficients.

auto.arima(ts_data,xreg = regressor)
Series: ts_data 
Regression with ARIMA(4,1,2) errors 

Coefficients:
      ar1     ar2     ar3      ar4      ma1      ma2    Flag1       Flag2  
     0.1464  0.1650  0.0041  -0.0594  -0.2069  -0.7684  5891.982   10600.219
s.e.  0.1228  0.1172  0.0916   0.0791   0.1073   0.1065  3479.626   3436.101

sigma^2 estimated as 63660026:  log likelihood=-2421.42
AIC=4860.85   AICc=4861.66   BIC=4891.91

My query is even for flag variable which are just 0 and 1 is it ok to get large coefficients?

Thanks

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Large coefficients does not mean anything themselves.

Suppose that your store announces a one-day discount and you want to discover the effect of that on sales.

If your variables and ARIMA (lags, etc) explains the time series behaviour very well (low AIC/BIC), a large coefficient could tell how much of sells were caused by the discount.

But with high AIC/BIC, large coefficients could mean just lack of covariates, and bad choice of ARIMA parameters. If the theorical model does not translate reality to math, the hipothesis will lead to wrong coefficients.

Remember that Flag1 and Flag2 just moves the time series level/mean, case 1, and does nothing case 0.

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