Given below are Excel outputs for various estimated autoregressive models for the number of people employed on a full-time basis (in thousands) from January 2019 through June 2022. You are also given that the number of people employed on a full-time basis for April, May and June for 2020 are 8012, 8061 and 8018 in thousands respectively.

First-Order Autoregressive (AR1) Model:

	Coefficients	Standard Error	t Stat	P-value
Intercept	6539.477	1261.347	5.185	0.000
LAG_1	0.181	0.158	1.145	0.260

Second-Order Autoregressive (AR2) Model:

	Coefficients	Standard Error	t Stat	P-value
Intercept	3265.098	1392.402	2.345	0.025
LAG_1	0.072	0.139	0.520	0.606
LAG_2	0.519	0.139	3.735	0.001

Third-Order Autoregressive (AR3) Model:

	Coefficients	Standard Error	t Stat	P-value
Intercept	1848.437	1308.410	1.413	0.167
LAG_1	-0.175	0.056	-3.113	0.002
LAG_2	0.473	0.124	3.815	0.001
LAG_3	0.472	0.145	3.252	0.003

Fourth-Order Autoregressive (AR4) Model:

	Coefficients	Standard Error	t Stat	P-value
Intercept	2013.032	1323.469	1.521	0.138
LAG_1	-0.095	0.169	-0.558	0.580
LAG_2	0.551	0.150	3.667	0.001
LAG_3	0.445	0.148	3.009	0.005
LAG_4	-0.153	0.166	-0.921	0.364

a. Using a 5% level of significance, what is the appropriate autoregressive model for number of people employed on a full-time basis? Fully explain your answer. (3 marks)

b. If one decides to use the Third-Order Autoregressive model, what willbethe predicted number of people employed on a full-time basis for July 2022?