# Seasonally adjusted data used in time series forecasting

I am looking at two time series, from 01/01/2000 to the present:

I was hoping to construct a multivariate ts model, and use the New Orders Index to forecast the manufacturing industry unemployment rate. However, am I correct in assuming it is not 'ideal' to use seasonally adjusted data to predict another time series? Because doesn't SA cause (ideally) all the seasonal time series structure to be removed from the data?

### EDIT:

Sorry, it just now hit me to link to the data I was using by putting it on Google Drive. It's in .csv files, for easy viewing with any program.

Below is the New Orders Index time series, with the dashed line indicating the mean of 54.61. It looks fairly stationary to me; a decent spike in 2008, but definitely reverts to the mean.

> plot.ts(OrdersIndex[,2])
> mean(OrdersIndex[,2])
[1] 54.60829
> abline(h=c(54.61), lty=2)
>


The ACF and PACF of the series are below. ACF displays dampened sine-wave behavior, PACF has a sharp cut-off after lag 1. This suggests an AR(1) model, as the ACF's slow dying off (at lags > 1) is due to the auto correlation at lag 1.

> Acf(OrdersIndex[,2], plot=T)   #the Acf() function is part of 'forecast' package
> Acf(OrdersIndex[,2], plot=T, type=c('partial'))
>


After running an arima(1,0,0) model with a mean, the ACF and PACF of the residuals do not show significant spikes at any lags.

> OrdersIndex100 <- arima(OrdersIndex[,2], order=c(1,0,0))
> OrdersIndex100

Call:
arima(x = OrdersIndex[, 2], order = c(1, 0, 0))

Coefficients:
ar1  intercept
0.8738    54.6979
s.e.  0.0341     1.9399

sigma^2 estimated as 12.39:  log likelihood = -517.44,  aic = 1040.88
>


Running an Ljung-Box test on the residuals indicates there is not any time series structure left in the data.

> LBQPlot(OrdersIndex100\$residuals, k=1)   # LBQPlot() is part of 'FitAR' package
>


### Conclusion

The conclusion I arrive at is that the seasonally adjusting done to the data by the ISM (Institute of Supply Management) effectively removed all the seasonality from the data. So, this SA data would be less useful in modeling than non-SA data (this is assuming that I would be using this data series as the Input, and the unemployment data series as the Output). Is this a valid conclusion? You all see any glaring problems with my analysis?

• Seasonal adjustment does not guarantee that all seasonality is removed from the data . Take any seasonally adjusted series and examine it for both significant acf structure at lag 12 or significant deterministic structure and upon finding this you will concur. I you want me to test this out post your seasonally adjusted series in an excel file – IrishStat Feb 13 '16 at 22:10