You obtain the following sample autocorrelations and partial autocorrelations for a sample of 100 observations from actual data.

1. Every sample autocorrelation and partial autocorrelation for a given lag follows the same normal distribution, with mean zero and variance 1. Calculate the 95% confidence interval and determine which acf and pacf lags are significant.

2. What is the most likely ARMA(p,q) process that has generated this data ? Explain why.

3. Test whether the first 3 lags for the acf are jointly different from zero. Explain which test you use, and show what the null and alternative hypotheses are in this case.

L Lag acf | pacf 1 1 2 3 4 5 6 0.420 | 0.104 | 0.032 -0.186 -0.138 0.042 0.632 | 0.381 / 0.268 | 0.199 | 0.205 | 0.101 | L Lag acf | pacf 1 1 2 3 4 5 6 0.420 | 0.104 | 0.032 -0.186 -0.138 0.042 0.632 | 0.381 / 0.268 | 0.199 | 0.205 | 0.101 |