The above is in regards to ARIMA modeling. Thanks The figure shows the ACFs for

Question

The above is in regards to ARIMA modeling. Thanks

The figure shows the ACFs for 36 random numbers, 360 random numbers and for 1,000 random numbers 3113 Lag 5 10 5 20 0 5 10 15 20 25 30 Lag Lag 1. Explain the differences among these figures. Do they all indicate the data are white noise? 2. Why are the critical values at different distances from the mean of zero? Why are the autocorrelations different in each figure when they each refer to white noise? 3. What is the purpose of taking a first difference of time series data? 4. To what does the order of a p, d, and q refer in an arima model?

Explanation / Answer

1)

These figures show the correlation between different lags of the series (shown on the x axis). The y axis (the correlation) has the same scale for each plot, but the x axis shows an increasing number of lags as the series gets longer.

If the data are white noise (random) then we expect the correlations to be below the blue line, which indicates a significant lag.

For all the plots, the correlations of the lags shown are all below the significance level so they are all indicitive of white noise.

2)

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