Question: 1. Generate a simple random walk data. Apply first-order differencing. Did it remove non-stationarity? Apply second-order differencing. Did it remove non-stationarity? 2. Consider the immigration
1. Generate a simple random walk data. Apply first-order differencing. Did it remove non-stationarity? Apply second-order differencing. Did it remove non-stationarity?
2. Consider the immigration data from BB. Stationary? If not stationary then try to stationarize the data.
3. Consider the Monthly Australian Beer Consumption data from BB. Decompose the data and interpret. What are the seasonal effects for January and July? What is the de-seasonalized forecast if the production on September 1995 is 140?
immigration data
| yr | count |
| 1820 | 8385 |
| 1821 | 9127 |
| 1822 | 6911 |
| 1823 | 6354 |
| 1824 | 7912 |
| 1825 | 10199 |
| 1826 | 10837 |
| 1827 | 18875 |
| 1828 | 27382 |
| 1829 | 22520 |
| 1830 | 23322 |
| 1831 | 22633 |
| 1832 | 60482 |
| 1833 | 58640 |
| 1834 | 65365 |
| 1835 | 45374 |
| 1836 | 76242 |
| 1837 | 79340 |
| 1838 | 38914 |
| 1839 | 68069 |
| 1840 | 84066 |
| 1841 | 80289 |
| 1842 | 104565 |
| 1843 | 52496 |
| 1844 | 78615 |
| 1845 | 114371 |
| 1846 | 154416 |
| 1847 | 234968 |
| 1848 | 226527 |
| 1849 | 297024 |
| 1850 | 369980 |
| 1851 | 379466 |
| 1852 | 371603 |
| 1853 | 368645 |
| 1854 | 427833 |
| 1855 | 200877 |
| 1856 | 200436 |
| 1857 | 251306 |
| 1858 | 123126 |
| 1859 | 121282 |
| 1860 | 153640 |
| 1861 | 91918 |
| 1862 | 91985 |
| 1863 | 176282 |
| 1864 | 193418 |
| 1865 | 248120 |
| 1866 | 318568 |
| 1867 | 315722 |
| 1868 | 138840 |
| 1869 | 352768 |
| 1870 | 387203 |
| 1871 | 321350 |
| 1872 | 404806 |
| 1873 | 459803 |
| 1874 | 313339 |
| 1875 | 227498 |
| 1876 | 169986 |
| 1877 | 141857 |
| 1878 | 138469 |
| 1879 | 177826 |
| 1880 | 457257 |
| 1881 | 669431 |
| 1882 | 788992 |
| 1883 | 603322 |
| 1884 | 518592 |
| 1885 | 395346 |
| 1886 | 334203 |
| 1887 | 490109 |
| 1888 | 546889 |
| 1889 | 444427 |
| 1890 | 455302 |
| 1891 | 560319 |
| 1892 | 579663 |
| 1893 | 439730 |
| 1894 | 285631 |
| 1895 | 258536 |
| 1896 | 343267 |
| 1897 | 230832 |
| 1898 | 229299 |
| 1899 | 311715 |
| 1900 | 448572 |
| 1901 | 487918 |
| 1902 | 648743 |
| 1903 | 857046 |
| 1904 | 812870 |
| 1905 | 1026499 |
| 1906 | 1100735 |
| 1907 | 1285349 |
| 1908 | 782870 |
| 1909 | 751786 |
| 1910 | 1041570 |
| 1911 | 878587 |
| 1912 | 838172 |
| 1913 | 1197892 |
| 1914 | 1218480 |
| 1915 | 326700 |
| 1916 | 298826 |
| 1917 | 295403 |
| 1918 | 110618 |
| 1919 | 141132 |
| 1920 | 430001 |
| 1921 | 805228 |
| 1922 | 309556 |
| 1923 | 522919 |
| 1924 | 706896 |
| 1925 | 294314 |
| 1926 | 304488 |
| 1927 | 335175 |
| 1928 | 307255 |
| 1929 | 279678 |
| 1930 | 241700 |
| 1931 | 97139 |
| 1932 | 35576 |
| 1933 | 23068 |
| 1934 | 29470 |
| 1935 | 34956 |
| 1936 | 36329 |
| 1937 | 50244 |
| 1938 | 67895 |
| 1939 | 82998 |
| 1940 | 70756 |
| 1941 | 51776 |
| 1942 | 28781 |
| 1943 | 23725 |
| 1944 | 28551 |
| 1945 | 38119 |
| 1946 | 108721 |
| 1947 | 147292 |
| 1948 | 170570 |
| 1949 | 188317 |
| 1950 | 249187 |
| 1951 | 205717 |
| 1952 | 265520 |
| 1953 | 170434 |
| 1954 | 208177 |
| 1955 | 237790 |
| 1956 | 321625 |
| 1957 | 326867 |
| 1958 | 253265 |
| 1959 | 260686 |
| 1960 | 265398 |
| 1961 | 271344 |
| 1962 | 283763 |
| 1963 | 306260 |
| 1964 | 292248 |
| 1965 | 296697 |
| 1966 | 323040 |
| 1967 | 361972 |
| 1968 | 454448 |
| 1969 | 358579 |
| 1970 | 373326 |
| 1971 | 370478 |
| 1972 | 384685 |
| 1973 | 398515 |
| 1974 | 393919 |
| 1975 | 385378 |
| 1976 | 499093 |
| 1977 | 458755 |
| 1978 | 589810 |
| 1979 | 394244 |
| 1980 | 524295 |
| 1981 | 595014 |
| 1982 | 533624 |
| 1983 | 550052 |
| 1984 | 541811 |
| 1985 | 568149 |
| 1986 | 600027 |
| 1987 | 599889 |
| 1988 | 641346 |
| 1989 | 1090172 |
| 1990 | 1535872 |
| 1991 | 1826595 |
| 1992 | 973445 |
| 1993 | 903916 |
| 1994 | 803993 |
| 1995 | 720177 |
| 1996 | 915560 |
| 1997 | 797847 |
| 1998 | 653206 |
| 1999 | 644787 |
| 2000 | 841002 |
| 2001 | 1058902 |
| 2002 | 1059356 |
| 2003 | 703542 |
| 2004 | 957883 |
| 2005 | 1122257 |
| 2006 | 1266129 |
| 2007 | 1052415 |
| 2008 | 1107126 |
| 2009 | 1130818 |
| 2010 | 1042625 |
| 2011 | 1062040 |
| 2012 | 1031631 |
| 2013 | 990553 |
| 2014 | 1016518 |
| 2015 | 1051031 |
| 2016 | 1183505 |
Australian
| Month | Monthly beer production in Australia: megalitres. Includes ale and stout. Does not include beverages with alcohol percentage less than 1.15. Jan 1956 ? Aug 1995 |
| 1956-01 | 93.2 |
| 1956-02 | 96 |
| 1956-03 | 95.2 |
| 1956-04 | 77.1 |
| 1956-05 | 70.9 |
| 1956-06 | 64.8 |
| 1956-07 | 70.1 |
| 1956-08 | 77.3 |
| 1956-09 | 79.5 |
| 1956-10 | 100.6 |
| 1956-11 | 100.7 |
| 1956-12 | 107.1 |
| 1957-01 | 95.9 |
| 1957-02 | 82.8 |
| 1957-03 | 83.3 |
| 1957-04 | 80 |
| 1957-05 | 80.4 |
| 1957-06 | 67.5 |
| 1957-07 | 75.7 |
| 1957-08 | 71.1 |
| 1957-09 | 89.3 |
| 1957-10 | 101.1 |
| 1957-11 | 105.2 |
| 1957-12 | 114.1 |
| 1958-01 | 96.3 |
| 1958-02 | 84.4 |
| 1958-03 | 91.2 |
| 1958-04 | 81.9 |
| 1958-05 | 80.5 |
| 1958-06 | 70.4 |
| 1958-07 | 74.8 |
| 1958-08 | 75.9 |
| 1958-09 | 86.3 |
| 1958-10 | 98.7 |
| 1958-11 | 100.9 |
| 1958-12 | 113.8 |
| 1959-01 | 89.8 |
| 1959-02 | 84.4 |
| 1959-03 | 87.2 |
| 1959-04 | 85.6 |
| 1959-05 | 72 |
| 1959-06 | 69.2 |
| 1959-07 | 77.5 |
| 1959-08 | 78.1 |
| 1959-09 | 94.3 |
| 1959-10 | 97.7 |
| 1959-11 | 100.2 |
| 1959-12 | 116.4 |
| 1960-01 | 97.1 |
| 1960-02 | 93 |
| 1960-03 | 96 |
| 1960-04 | 80.5 |
| 1960-05 | 76.1 |
| 1960-06 | 69.9 |
| 1960-07 | 73.6 |
| 1960-08 | 92.6 |
| 1960-09 | 94.2 |
| 1960-10 | 93.5 |
| 1960-11 | 108.5 |
| 1960-12 | 109.4 |
| 1961-01 | 105.1 |
| 1961-02 | 92.5 |
| 1961-03 | 97.1 |
| 1961-04 | 81.4 |
| 1961-05 | 79.1 |
| 1961-06 | 72.1 |
| 1961-07 | 78.7 |
| 1961-08 | 87.1 |
| 1961-09 | 91.4 |
| 1961-10 | 109.9 |
| 1961-11 | 116.3 |
| 1961-12 | 113 |
| 1962-01 | 100 |
| 1962-02 | 84.8 |
| 1962-03 | 94.3 |
| 1962-04 | 87.1 |
| 1962-05 | 90.3 |
| 1962-06 | 72.4 |
| 1962-07 | 84.9 |
| 1962-08 | 92.7 |
| 1962-09 | 92.2 |
| 1962-10 | 114.9 |
| 1962-11 | 112.5 |
| 1962-12 | 118.3 |
| 1963-01 | 106 |
| 1963-02 | 91.2 |
| 1963-03 | 96.6 |
| 1963-04 | 96.3 |
| 1963-05 | 88.2 |
| 1963-06 | 70.2 |
| 1963-07 | 86.5 |
| 1963-08 | 88.2 |
| 1963-09 | 102.8 |
| 1963-10 | 119.1 |
| 1963-11 | 119.2 |
| 1963-12 | 125.1 |
| 1964-01 | 106.1 |
| 1964-02 | 102.1 |
| 1964-03 | 105.2 |
| 1964-04 | 101 |
| 1964-05 | 84.3 |
| 1964-06 | 87.5 |
| 1964-07 | 92.7 |
| 1964-08 | 94.4 |
| 1964-09 | 113 |
| 1964-10 | 113.9 |
| 1964-11 | 122.9 |
| 1964-12 | 132.7 |
| 1965-01 | 106.9 |
| 1965-02 | 96.6 |
| 1965-03 | 127.3 |
| 1965-04 | 98.2 |
| 1965-05 | 100.2 |
| 1965-06 | 89.4 |
| 1965-07 | 95.3 |
| 1965-08 | 104.2 |
| 1965-09 | 106.4 |
| 1965-10 | 116.2 |
| 1965-11 | 135.9 |
| 1965-12 | 134 |
| 1966-01 | 104.6 |
| 1966-02 | 107.1 |
| 1966-03 | 123.5 |
| 1966-04 | 98.8 |
| 1966-05 | 98.6 |
| 1966-06 | 90.6 |
| 1966-07 | 89.1 |
| 1966-08 | 105.2 |
| 1966-09 | 114 |
| 1966-10 | 122.1 |
| 1966-11 | 138 |
| 1966-12 | 142.2 |
| 1967-01 | 116.4 |
| 1967-02 | 112.6 |
| 1967-03 | 123.8 |
| 1967-04 | 103.6 |
| 1967-05 | 113.9 |
| 1967-06 | 98.6 |
| 1967-07 | 95 |
| 1967-08 | 116 |
| 1967-09 | 113.9 |
| 1967-10 | 127.5 |
| 1967-11 | 131.4 |
| 1967-12 | 145.9 |
| 1968-01 | 131.5 |
| 1968-02 | 131 |
| 1968-03 | 130.5 |
| 1968-04 | 118.9 |
| 1968-05 | 114.3 |
| 1968-06 | 85.7 |
| 1968-07 | 104.6 |
| 1968-08 | 105.1 |
| 1968-09 | 117.3 |
| 1968-10 | 142.5 |
| 1968-11 | 140 |
| 1968-12 | 159.8 |
| 1969-01 | 131.2 |
| 1969-02 | 125.4 |
| 1969-03 | 126.5 |
| 1969-04 | 119.4 |
| 1969-05 | 113.5 |
| 1969-06 | 98.7 |
| 1969-07 | 114.5 |
| 1969-08 | 113.8 |
| 1969-09 | 133.1 |
| 1969-10 | 143.4 |
| 1969-11 | 137.3 |
| 1969-12 | 165.2 |
| 1970-01 | 126.9 |
| 1970-02 | 124 |
| 1970-03 | 135.7 |
| 1970-04 | 130 |
| 1970-05 | 109.4 |
| 1970-06 | 117.8 |
| 1970-07 | 120.3 |
| 1970-08 | 121 |
| 1970-09 | 132.3 |
| 1970-10 | 142.9 |
| 1970-11 | 147.4 |
| 1970-12 | 175.9 |
| 1971-01 | 132.6 |
| 1971-02 | 123.7 |
| 1971-03 | 153.3 |
| 1971-04 | 134 |
| 1971-05 | 119.6 |
| 1971-06 | 116.2 |
| 1971-07 | 118.6 |
| 1971-08 | 130.7 |
| 1971-09 | 129.3 |
| 1971-10 | 144.4 |
| 1971-11 | 163.2 |
| 1971-12 | 179.4 |
| 1972-01 | 128.1 |
| 1972-02 | 138.4 |
| 1972-03 | 152.7 |
| 1972-04 | 120 |
| 1972-05 | 140.5 |
| 1972-06 | 116.2 |
| 1972-07 | 121.4 |
| 1972-08 | 127.8 |
| 1972-09 | 143.6 |
| 1972-10 | 157.6 |
| 1972-11 | 166.2 |
| 1972-12 | 182.3 |
| 1973-01 | 153.1 |
| 1973-02 | 147.6 |
| 1973-03 | 157.7 |
| 1973-04 | 137.2 |
| 1973-05 | 151.5 |
| 1973-06 | 98.7 |
| 1973-07 | 145.8 |
| 1973-08 | 151.7 |
| 1973-09 | 129.4 |
| 1973-10 | 174.1 |
| 1973-11 | 197 |
| 1973-12 | 193.9 |
| 1974-01 | 164.1 |
| 1974-02 | 142.8 |
| 1974-03 | 157.9 |
| 1974-04 | 159.2 |
| 1974-05 | 162.2 |
| 1974-06 | 123.1 |
| 1974-07 | 130 |
| 1974-08 | 150.1 |
| 1974-09 | 169.4 |
| 1974-10 | 179.7 |
| 1974-11 | 182.1 |
| 1974-12 | 194.3 |
| 1975-01 | 161.4 |
| 1975-02 | 169.4 |
| 1975-03 | 168.8 |
| 1975-04 | 158.1 |
| 1975-05 | 158.5 |
| 1975-06 | 135.3 |
| 1975-07 | 149.3 |
| 1975-08 | 143.4 |
| 1975-09 | 142.2 |
| 1975-10 | 188.4 |
| 1975-11 | 166.2 |
| 1975-12 | 199.2 |
| 1976-01 | 182.7 |
| 1976-02 | 145.2 |
| 1976-03 | 182.1 |
| 1976-04 | 158.7 |
| 1976-05 | 141.6 |
| 1976-06 | 132.6 |
| 1976-07 | 139.6 |
| 1976-08 | 147 |
| 1976-09 | 166.6 |
| 1976-10 | 157 |
| 1976-11 | 180.4 |
| 1976-12 | 210.2 |
| 1977-01 | 159.8 |
| 1977-02 | 157.8 |
| 1977-03 | 168.2 |
| 1977-04 | 158.4 |
| 1977-05 | 152 |
| 1977-06 | 142.2 |
| 1977-07 | 137.2 |
| 1977-08 | 152.6 |
| 1977-09 | 166.8 |
| 1977-10 | 165.6 |
| 1977-11 | 198.6 |
| 1977-12 | 201.5 |
| 1978-01 | 170.7 |
| 1978-02 | 164.4 |
| 1978-03 | 179.7 |
| 1978-04 | 157 |
| 1978-05 | 168 |
| 1978-06 | 139.3 |
| 1978-07 | 138.6 |
| 1978-08 | 153.4 |
| 1978-09 | 138.9 |
| 1978-10 | 172.1 |
| 1978-11 | 198.4 |
| 1978-12 | 217.8 |
| 1979-01 | 173.7 |
| 1979-02 | 153.8 |
| 1979-03 | 175.6 |
| 1979-04 | 147.1 |
| 1979-05 | 160.3 |
| 1979-06 | 135.2 |
| 1979-07 | 148.8 |
| 1979-08 | 151 |
| 1979-09 | 148.2 |
| 1979-10 | 182.2 |
| 1979-11 | 189.2 |
| 1979-12 | 183.1 |
| 1980-01 | 170 |
| 1980-02 | 158.4 |
| 1980-03 | 176.1 |
| 1980-04 | 156.2 |
| 1980-05 | 153.2 |
| 1980-06 | 117.9 |
| 1980-07 | 149.8 |
| 1980-08 | 156.6 |
| 1980-09 | 166.7 |
| 1980-10 | 156.8 |
| 1980-11 | 158.6 |
| 1980-12 | 210.8 |
| 1981-01 | 203.6 |
| 1981-02 | 175.2 |
| 1981-03 | 168.7 |
| 1981-04 | 155.9 |
| 1981-05 | 147.3 |
| 1981-06 | 137 |
| 1981-07 | 141.1 |
| 1981-08 | 167.4 |
| 1981-09 | 160.2 |
| 1981-10 | 191.9 |
| 1981-11 | 174.4 |
| 1981-12 | 208.2 |
| 1982-01 | 159.4 |
| 1982-02 | 161.1 |
| 1982-03 | 172.1 |
| 1982-04 | 158.4 |
| 1982-05 | 114.6 |
| 1982-06 | 159.6 |
| 1982-07 | 159.7 |
| 1982-08 | 159.4 |
| 1982-09 | 160.7 |
| 1982-10 | 165.5 |
| 1982-11 | 205 |
| 1982-12 | 205.2 |
| 1983-01 | 141.6 |
| 1983-02 | 148.1 |
| 1983-03 | 184.9 |
| 1983-04 | 132.5 |
| 1983-05 | 137.3 |
| 1983-06 | 135.5 |
| 1983-07 | 121.7 |
| 1983-08 | 166.1 |
| 1983-09 | 146.8 |
| 1983-10 | 162.8 |
| 1983-11 | 186.8 |
| 1983-12 | 185.5 |
| 1984-01 | 151.5 |
| 1984-02 | 158.1 |
| 1984-03 | 143 |
| 1984-04 | 151.2 |
| 1984-05 | 147.6 |
| 1984-06 | 130.7 |
| 1984-07 | 137.5 |
| 1984-08 | 146.1 |
| 1984-09 | 133.6 |
| 1984-10 | 167.9 |
| 1984-11 | 181.9 |
| 1984-12 | 202 |
| 1985-01 | 166.5 |
| 1985-02 | 151.3 |
| 1985-03 | 146.2 |
| 1985-04 | 148.3 |
| 1985-05 | 144.7 |
| 1985-06 | 123.6 |
| 1985-07 | 151.6 |
| 1985-08 | 133.9 |
| 1985-09 | 137.4 |
| 1985-10 | 181.6 |
| 1985-11 | 182 |
| 1985-12 | 190 |
| 1986-01 | 161.2 |
| 1986-02 | 155.5 |
| 1986-03 | 141.9 |
| 1986-04 | 164.6 |
| 1986-05 | 136.2 |
| 1986-06 | 126.8 |
| 1986-07 | 152.5 |
| 1986-08 | 126.6 |
| 1986-09 | 150.1 |
| 1986-10 | 186.3 |
| 1986-11 | 147.5 |
| 1986-12 | 200.4 |
| 1987-01 | 177.2 |
| 1987-02 | 127.4 |
| 1987-03 | 177.1 |
| 1987-04 | 154.4 |
| 1987-05 | 135.2 |
| 1987-06 | 126.4 |
| 1987-07 | 147.3 |
| 1987-08 | 140.6 |
| 1987-09 | 152.3 |
| 1987-10 | 151.2 |
| 1987-11 | 172.2 |
| 1987-12 | 215.3 |
| 1988-01 | 154.1 |
| 1988-02 | 159.3 |
| 1988-03 | 160.4 |
| 1988-04 | 151.9 |
| 1988-05 | 148.4 |
| 1988-06 | 139.6 |
| 1988-07 | 148.2 |
| 1988-08 | 153.5 |
| 1988-09 | 145.1 |
| 1988-10 | 183.7 |
| 1988-11 | 210.5 |
| 1988-12 | 203.3 |
| 1989-01 | 153.3 |
| 1989-02 | 144.3 |
| 1989-03 | 169.6 |
| 1989-04 | 143.7 |
| 1989-05 | 160.1 |
| 1989-06 | 135.6 |
| 1989-07 | 141.8 |
| 1989-08 | 159.9 |
| 1989-09 | 145.7 |
| 1989-10 | 183.5 |
| 1989-11 | 198.2 |
| 1989-12 | 186.8 |
| 1990-01 | 172 |
| 1990-02 | 150.6 |
| 1990-03 | 163.3 |
| 1990-04 | 153.7 |
| 1990-05 | 152.9 |
| 1990-06 | 135.5 |
| 1990-07 | 148.5 |
| 1990-08 | 148.4 |
| 1990-09 | 133.6 |
| 1990-10 | 194.1 |
| 1990-11 | 208.6 |
| 1990-12 | 197.3 |
| 1991-01 | 164.4 |
| 1991-02 | 148.1 |
| 1991-03 | 152 |
| 1991-04 | 144.1 |
| 1991-05 | 155 |
| 1991-06 | 124.5 |
| 1991-07 | 153 |
| 1991-08 | 146 |
| 1991-09 | 138 |
| 1991-10 | 190 |
| 1991-11 | 192 |
| 1991-12 | 192 |
| 1992-01 | 147 |
| 1992-02 | 133 |
| 1992-03 | 163 |
| 1992-04 | 150 |
| 1992-05 | 129 |
| 1992-06 | 131 |
| 1992-07 | 145 |
| 1992-08 | 137 |
| 1992-09 | 138 |
| 1992-10 | 168 |
| 1992-11 | 176 |
| 1992-12 | 188 |
| 1993-01 | 139 |
| 1993-02 | 143 |
| 1993-03 | 150 |
| 1993-04 | 154 |
| 1993-05 | 137 |
| 1993-06 | 129 |
| 1993-07 | 128 |
| 1993-08 | 140 |
| 1993-09 | 143 |
| 1993-10 | 151 |
| 1993-11 | 177 |
| 1993-12 | 184 |
| 1994-01 | 151 |
| 1994-02 | 134 |
| 1994-03 | 164 |
| 1994-04 | 126 |
| 1994-05 | 131 |
| 1994-06 | 125 |
| 1994-07 | 127 |
| 1994-08 | 143 |
| 1994-09 | 143 |
| 1994-10 | 160 |
| 1994-11 | 190 |
| 1994-12 | 182 |
| 1995-01 | 138 |
| 1995-02 | 136 |
| 1995-03 | 152 |
| 1995-04 | 127 |
| 1995-05 | 151 |
| 1995-06 | 130 |
| 1995-07 | 119 |
| 1995-08 | 153 |
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