AR(p) Autoregressive time series approach.

The following data is British exports in the early 1800s. Figures are in millions of British pounds. (A historic note: During this time there was no inflation, so there is no need to deflate the numbers to a constant price level. There always were price adjustments, but long-run inflation did not become common until the 20^th century when Keynesian economics was introduced.)

Export growth should be expected from 1820 to 1850. During this era, the industrial revolution created more productive industries. David Ricardo was a member of the Parliament at this time, and his theory of comparative advantage transformed public policy, increasing the openness of British trade.

Year	Exports
1820	36.4
1821	36.7
1822	37
1823	35.4
1824	38.4
1825	38.9
1826	31.5
1827	37.2
1828	36.8
1829	35.8
1830	38.3
1831	37.2
1832	36.5
1833	39.7
1834	41.6
1835	47.4
1836	53.3
1837	42.1
1838	50.1
1839	53.3
1840	51.4
1841	51.6
1842	47.4
1843	52.3
1844	58.6
1845	60.1
1846	57.8
1847	58.8
1848	52.8
1849	63.6
1850	71.4

Use a few time-series, autoregressive lag models.

Check if the AR(p) model is improved with the data transformations with first differencing, squaring, and/or logging of data (or not). Use the results to identify which model would be the best for use in forecasting.

Once you have the best model, use it to forecast exports up to 1854. Explain your results.

Can you please explain in detail how you found the answer, explain the methods used, and explain the report the findings.