Lecture 5

Lecture will focus on on other time series models: higher order autoregressive models, moving average models, ARMA models, and ARIMA models.

Some viscosity data that fit an AR(2) model: http://www.stat.psu.edu/~rathbun/stat510/data/models/viscous.txt

The following data sets are the number of lynx and rabbits from the Hudson Bay Company records for 1849-1890, the number of Canadian lynx from 1821 to 1934, and the Beveridge wheat price annual index from 1500 to 1867. The last two datasets are availiable at: http://www.york.ac.uk/depts/maths/data/ts/

year	lynx	hare
1849	43253	24301
1850	20604	15621
1851	9303	26781
1852	6722	54827
1853	4850	82430
1854	4907	82814
1855	10764	91316
1856	21511	70685
1857	32264	84489
1858	33038	95534
1859	27460	62543
1860	15968	29590
1861	7927	15409
1862	4616	18516
1863	4570	39258
1864	4760	5052
1865	17044	155461
1866	34732	144519
1867	68097	106279
1868	70372	45909
1869	39119	22668
1870	19992	631
1871	8086	3070
1872	5679	9932
1873	4839	6434
1874	10045	60520
1875	17849	49053
1876	18868	50934
1877	43575	104123
1878	37490	87722
1879	21291	65585
1880	14767	17593
1881	10053	10950
1882	7591	17830
1883	8016	13595
1884	27119	13072
1885	51414	45118
1886	73878	53522
1887	78555	136726
1888	33720	137685
1889	18726	94150
1890	11455	36286

lynx	year
269	1821
321	1822
585	1823
871	1824
1475	1825
2821	1826
3928	1827
5943	1828
4950	1829
2577	1830
523	1831
98	1832
184	1833
279	1834
409	1835
2285	1836
2685	1837
3409	1838
1824	1839
409	1840
151	1841
45	1842
68	1843
213	1844
546	1845
1033	1846
2129	1847
2536	1848
957	1849
361	1850
377	1851
225	1852
360	1853
731	1854
1638	1855
2725	1856
2871	1857
2119	1858
684	1859
299	1860
236	1861
245	1862
552	1863
1623	1864
3311	1865
6721	1866
4245	1867
687	1868
255	1869
473	1870
358	1871
784	1872
1594	1873
1676	1874
2251	1875
1426	1876
756	1877
299	1878
201	1879
229	1880
469	1881
736	1882
2042	1883
2811	1884
4431	1885
2511	1886
389	1887
73	1888
39	1889
49	1890
59	1891
188	1892
377	1893
1292	1894
4031	1895
3495	1896
587	1897
105	1898
153	1899
387	1900
758	1901
1307	1902
3465	1903
6991	1904
6313	1905
3794	1906
1836	1907
345	1908
382	1909
808	1910
1388	1911
2713	1912
3800	1913
3091	1914
2985	1915
3790	1916
674	1917
81	1918
80	1919
108	1920
229	1921
399	1922
1132	1923
2432	1924
3574	1925
2935	1926
1537	1927
529	1928
485	1929
662	1930
1000	1931
1590	1932
2657	1933
3396	1934
year	index
1500	17.0
1501	19.0
1502	20.0
1503	15.0
1504	13.0
1505	14.0
1506	14.0
1507	14.0
1508	14.0
1509	11.0
1510	16.0
1511	19.0
1512	23.0
1513	18.0
1514	17.0
1515	20.0
1516	20.0
1517	18.0
1518	14.0
1519	16.0
1520	21.0
1521	24.0
1522	15.0
1523	16.0
1524	20.0
1525	14.0
1526	16.0
1527	25.5
1528	25.8
1529	26.0
1530	26.0
1531	29.0
1532	20.0
1533	18.0
1534	16.0
1535	22.0
1536	22.0
1537	16.0
1538	19.0
1539	17.0
1540	17.0
1541	19.0
1542	20.0
1543	24.0
1544	28.0
1545	36.0
1546	20.0
1547	14.0
1548	18.0
1549	27.0
1550	29.0
1551	36.0
1552	29.0
1553	27.0
1554	30.0
1555	38.0
1556	50.0
1557	24.0
1558	25.0
1559	30.0
1560	31.0
1561	37.0
1562	41.0
1563	36.0
1564	32.0
1565	47.0
1566	42.0
1567	37.0
1568	34.0
1569	36.0
1570	43.0
1571	55.0
1572	64.0
1573	79.0
1574	59.0
1575	47.0
1576	48.0
1577	49.0
1578	45.0
1579	53.0
1580	55.0
1581	55.0
1582	54.0
1583	56.0
1584	52.0
1585	76.0
1586	113.0
1587	68.0
1588	59.0
1589	74.0
1590	78.0
1591	69.0
1592	78.0
1593	73.0
1594	88.0
1595	98.0
1596	109.0
1597	106.0
1598	87.0
1599	77.0
1600	77.0
1601	63.0
1602	70.0
1603	70.0
1604	63.0
1605	61.0
1606	66.0
1607	78.0
1608	93.0
1609	97.0
1610	77.0
1611	83.0
1612	81.0
1613	82.0
1614	78.0
1615	75.0
1616	80.0
1617	87.0
1618	72.0
1619	65.0
1620	74.0
1621	91.0
1622	115.0
1623	99.0
1624	99.0
1625	115.0
1626	101.0
1627	90.0
1628	95.0
1629	108.0
1630	147.0
1631	112.0
1632	108.0
1633	99.0
1634	96.0
1635	102.0
1636	105.0
1637	114.0
1638	103.0
1639	98.0
1640	103.0
1641	101.0
1642	110.0
1643	109.0
1644	98.0
1645	84.0
1646	90.0
1647	120.0
1648	124.0
1649	136.0
1650	120.0
1651	135.0
1652	100.0
1653	70.0
1654	60.0
1655	72.0
1656	70.0
1657	71.0
1658	94.0
1659	95.0
1660	110.0
1661	154.0
1662	116.0
1663	99.0
1664	82.0
1665	76.0
1666	64.0
1667	63.0
1668	68.0
1669	64.0
1670	67.0
1671	71.0
1672	72.0
1673	89.0
1674	114.0
1675	102.0
1676	85.0
1677	88.0
1678	97.0
1679	94.0
1680	88.0
1681	79.0
1682	74.0
1683	79.0
1684	95.0
1685	70.0
1686	72.0
1687	63.0
1688	60.0
1689	74.0
1690	75.0
1691	91.0
1692	126.0
1693	161.0
1694	109.0
1695	108.0
1696	110.0
1697	130.0
1698	166.0
1699	143.0
1700	103.0
1701	89.0
1702	76.0
1703	93.0
1704	82.0
1705	71.0
1706	69.0
1707	75.0
1708	134.0
1709	183.0
1710	113.0
1711	108.0
1712	121.0
1713	139.0
1714	109.0
1715	90.0
1716	88.0
1717	88.0
1718	93.0
1719	106.0
1720	89.0
1721	79.0
1722	91.0
1723	96.0
1724	111.0
1725	112.0
1726	104.0
1727	94.0
1728	98.0
1729	88.0
1730	94.0
1731	81.0
1732	77.0
1733	84.0
1734	92.0
1735	96.0
1736	102.0
1737	95.0
1738	98.0
1739	125.0
1740	162.0
1741	113.0
1742	94.0
1743	85.0
1744	89.0
1745	109.0
1746	110.0
1747	109.0
1748	120.0
1749	116.0
1750	101.0
1751	113.0
1752	109.0
1753	105.0
1754	94.0
1755	102.0
1756	141.0
1757	135.0
1758	118.0
1759	115.0
1760	111.0
1761	127.0
1762	124.0
1763	113.0
1764	122.0
1765	130.0
1766	137.0
1767	148.0
1768	142.0
1769	143.0
1770	176.0
1771	184.0
1772	164.0
1773	146.0
1774	147.0
1775	124.0
1776	119.0
1777	135.0
1778	125.0
1779	116.0
1780	132.0
1781	133.0
1782	144.0
1783	145.0
1784	146.0
1785	138.0
1786	139.0
1787	154.0
1788	181.0
1789	185.0
1790	151.0
1791	139.0
1792	157.0
1793	155.0
1794	191.0
1795	248.0
1796	185.0
1797	168.0
1798	176.0
1799	243.0
1800	289.0
1801	251.0
1802	232.0
1803	207.0
1804	276.0
1805	250.0
1806	216.0
1807	205.0
1808	206.0
1809	208.0
1810	226.0
1811	302.0
1812	261.0
1813	207.0
1814	209.0
1815	280.0
1816	381.0
1817	266.0
1818	197.0
1819	177.0
1820	170.0
1821	152.0
1822	156.0
1823	141.0
1824	142.0
1825	137.0
1826	161.0
1827	189.0
1828	226.0
1829	194.0
1830	217.0
1831	199.0
1832	151.0
1833	144.0
1834	138.0
1835	145.0
1836	156.0
1837	184.0
1838	216.0
1839	204.0
1840	186.0
1841	197.0
1842	183.0
1843	175.0
1844	183.0
1845	230.0
1846	278.0
1847	179.0
1848	161.0
1849	150.0
1850	159.0
1851	180.0
1852	223.0
1853	294.0
1854	300.0
1855	297.0
1856	232.0
1857	179.0
1858	180.0
1859	215.0
1860	258.0
1861	236.0
1862	202.0
1863	174.0
1864	179.0
1865	210.0
1866	268.0
1867	267.0
1868	208.0
1869	224.0