Autocorrelation

Quarterly data = 36 quarters
Model: autoregressive model with a lag one independent variable (which is statistically different from zero)

Also include lag two and lag four terms, given the magnitude of the autocorrelations of the residuals shown below?

Significance level: 5%
df: 36-1=35
Critical t-value: 2.03 for a two tail test, 1.69 for a one-tail test

Autocorrelation

Lag	Autocorrelation	Standard error	t-statistic
1	0.0829	0.1690	0.49
2	0.1293	0.1690	0.76
3	0.0227	0.1690	0.13
4	0.1882	0.1690	1.11

n: number of observations = 36 - 1 = 35 → one quarter is lost because we have a lag one term, so there are 35 observations in the regression.
Standard error = 1/df^0.5 = 1/35^0.5 = 0.1690
t = autocorrelation/standard error

The critical t-value is 2.03 for a two-tail test, so none of the t-statistics indicate that the autocorrelations are significantly different from zero. Therefore, we do not need to include additional lag terms.